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The photorefractive effect in Lithium Niobate Cornish, William D 1976

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THE  PHOTOREFRACTIVE EFFECT IN LITHIUM NIOBATE  by  WILLIAM D. CORNISH B.Sc-  (Hon), Queen's U n i v e r s i t y a t K i t g s t o n ,  M.A.Sc., U n i v e r s i t y o f B r i t i s h  1969  Columbia, 1972  A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE  REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY  i n t h e Department of Electrical  We a c c e p t t h i s required  THE  Engineering  t h e s i s as conforming  to the  standard  UNIVERSITY OF BRITISH COLUMBIA NOVEMBER, 1975  In  presenting  this  an a d v a n c e d d e g r e e the I  Library  further  for  agree  in  at  University  the  make  it  partial  freely  that permission  representatives.  this  thesis  for  It  financial  fulfilment  of  of  Columbia,  British  available for  for  extensive  s c h o l a r l y p u r p o s e s may be g r a n t e d  by h i s of  shall  thesis  by  the  shall  of  The U n i v e r s i t y  £  of  ^  c  ^ r ! ^  British  2075 Wesbrook Place Vancouver, Canada V6T 1W5  Date  >  f<  CXc/**  ,  j ^<&  Columbia  '^j  v>  I  agree  and  copying or  for  that  study.  this  thesis  my D e p a r t m e n t  be a l l o w e d  written permission.  Department  reference  Head o f  not  requirements  copying of  i s understood that gain  the  or  publication  without  my  ABSTRACT  Exposure of the i n s u l a t i n g f e r r o e l e c t r i c c r y s t a l ,  lithium  niobate, to l i g h t of the appropriate wavelength causes small changes i n the r e f r a c t i v e i n d i c e s .  This phenomenon which has recently been named  the photorefractive effect allows phase holograms to be stored i n the crystal.  The work described i n t h i s thesis was undertaken to obtain an  understanding of the mechanisms of the photorefractive effect tion with possible engineering a p p l i c a t i o n s .  i n connec-  The process i s thought to  involve the s p a t i a l r e d i s t r i b u t i o n of photo-excited electrons among traps.  Space charge f i e l d s develop which modulate the r e f r a c t i v e indices  through the e l e c t r o - o p t i c  effect.  I n i t i a l l y , the mechanisms proposed for charge transport were d i f f u s i o n and d r i f t i n an i n t e r n a l f i e l d of p y r o e l e c t r i c o r i g i n .  Using  these mechanisms, Amodei had treated the i n i t i a l development of phase holograms on the assumption that the electron transport length was short. A t h e o r e t i c a l treatment without the r e s t r i c t i o n of short transport  length  i s presented which shows that the e f f i c i e n c y of hologram writing increases for increased transport length up to a c e r t a i n l i m i t .  In a d d i t i o n ,  it  i s shown that the resolution of the recording medium i s not limited by increased transport length.  More r e c e n t l y , Glass, von der Linde and Negran  have proposed a new phenomenon, the bulk photovoltaic e f f e c t , as being responsible for charge transport.  Photocurrent measurements are presented  which provide further evidence for the existence of this  effect.  The r e l a t i v e contributions of d r i f t , d i f f u s i o n and the bulk photovoltaic effect to the photorefractive process are investigated by applying a f i e l d during hologram formation.  i  It  i s found that the e f f e c t s  of p o s i t i v e and  negative  o f asymmetry depends It i s  a r e not  voltages  degree  illuminated. ex-  exposure i n f l u e n c e  exposure  development of these space charge f i e l d s i s d i s c u s s e d .  sion, d r i f t  i n a p p l i e d and  space charge f i e l d s , and  by  to  I s concluded t h a t the holograms were w r i t t e n by a c o m b i n a t i o n o f  voltaic  the  I t i s thought t h a t t h e s e e f f e c t s a r e caused  space charge f i e l d s which are produced by  The  The  applied during previous  a p p l i e d during the c u r r e n t  diffraction efficiency. large scale  symmetric.  on what f r a c t i o n of the c r y s t a l i s  a l s o found t h a t b o t h the v o l t a g e s  posures and  light.  applied f i e l d s  It  diffu-  the b u l k p h o t o -  effect. The  importance of m u l t i p l e i n t e r n a l r e f l e c t i o n s between  f a c e s o f the c r y s t a l had  not p r e v i o u s l y been c o n s i d e r e d .  the  I t i s shown  t h a t i n measuring the p h o t o r e f r a c t i v e s e n s i t i v i t y by h o l o g r a p h i c , ,  ellips  metric  refle-  and  c t i o n s may  adjustable-compensator techniques, cause s e r i o u s e r r o r s . Two  methods of p r o b i n g  i n d i c e s are o u t l i n e d . was  modified  niobate  neglecting multiple  and  l a r g e s c a l e changes i n the r e f r a c t i v e  In the f i r s t method an automated  programmed to measure the b i r e f r i n g e n c e o f the l i t h i u m  c r y s t a l s and  the change i n b i r e f r i n g e n c e due the e x t e n t  to i l l u m i n a t i o n .  T h i s method har- y i e l d e d i n f o r m a t i o n  on  space charge f i e l d s , the u n i f o r m i t y  of the c r y s t a l and  heating  ellipsometer  c r y s t a l s under d i f f e r e n t c o n d i t i o n s .  of o p t i c a l l y - i n d u c e d the e f f e c t s of  A second and more r a p i d  method of i n s p e c t i n g l a r g e s c a l e changes i n the r e f r a c t i v e i n d i c e s i s based on making the The  c r y s t a l a c t as a F a b r y - P e r o t  interferometer.  s e n s i t i v i t y of p h o t o r e f r a c t i v e c r y s t a l s to l i g h t has  a s s o c i a t e d w i t h i m p u r i t i e s and  defects  i n the c r y s t a l l a t t i c e .  of m o d i f y i n g the v a l e n c e s t a t e o f i r o n i m p u r i t i e s are  ii  important  been  Methods since  the p h o t o r e f r a c t i v e s e n s i t i v i t y i s dependent on the amount o f  2+ present  i n the c r y s t a l and  on the r a t i o o f Fe  3+ methods used to c o n v e r t carbonate.  Fe  .  One  of  the  2+ t o Fe  i s heating  the c r y s t a l i n l i t h i u m reducing  i r o n i m p u r i t i e s , changes the b i r e f r i n g e n c e o f the c r y s t a l and r a t e a t which space charge f i e l d s decay. i s caused by  2+  3+ to Fe  I t i s shown t h a t t h i s t r e a t m e n t , i n a d d i t i o n t o  last effect  Fe  I t i s suggested t h a t  the d e s t r u c t i o n of s h a l l o w  reduces  the  the  traps.  A f u r t h e r charge t r a n s p o r t mechanism has. been s u g g e s t e d ' i n which  2+ i n t e r v a l e n c e t r a n s f e r of e l e c t r o n s between Fe occurs.  3+ and  Fe  I t i s argued t h a t i f , i n s t e a d , e l e c t r o n s e n t e r  band, luminescence should  be  observable.  impurity the  states  conduction  I t i s shown t h a t a p h o t o i  luminescence band which i s a s s o c i a t e d t-;ith i r o n may  be  observed i n the r e g i o n of 770  iii  nm.  i m p u r i t i e s i n the  crystal  TABLE OF CONTENTS Page ABSTRACT  i  TABLE OF CONTENTS  iv  LIST OF ILLUSTRATIONS  ;  LIST OF TABLES  viii x i i  ACKNOWLEDGEMENT  xiii  1.  INRODUCTION  1  2.  PHYSICAL MODELS FOR THE PHOTOREFRACTIVE EFFECT  7  2.1  Introduction  7  2.2  The E l e c t r o - o p t i c Nature o f the P h o t o r e f r a c t i v e Effect  2.3  The I n t e r n a l F i e l d  2.4  Johnston's P o l a r i z a t i o n Model  10  2.5  The Formation o f Holograms By D r i f t o r D i f f u s i o n . . 2.5.1 I n t r o d u c t i o n 2.5.2 A n a l y s i s f o r Short D r i f t o r D i f f u s i o n Length . 2.5.3 The E f f e c t s o f Beam C o u p l i n g 2.5.3.1 C o u p l i n g d u r i n g W r i t i n g I 2.5.3.2 I n t e r a c t i o n s d u r i n g Readout 2.5.4 A n a l y s i s w i t h A r b i t r a r y D r i f t o r D i f f u s i o n Length 2.5.5 D i s c u s s i o n  12 12 14 16 16 19  2.6  The Bulk P h o t o v o l t a i c E f f e c t  26  2.7  Transient Photorefractive E f f e c t s  28  2.8  Defect  29  2.9  Discussion  31  2.9.1 2.9.2 2.9.3  Bulk P h o t o v o l t a i c E f f e c t B u i l t - i n F i e l d s of P y r o e l e c t r i c O r i g i n . . . . Diffusion  31 33 33  ELLIPSOMETRIC PROBE OF THE PHOTOREFRACTIVE EFFECT IN LiNbOg.  37  l  3.  7  3.1 >. 3.2  Theory  Sites  Introduction  . . . . . .  Theory and O p e r a t i o n  o f the E l l i p s o m e t e r iv  8  22 24  37 39  Page 3.3  S e n s i t i v i t y of the Ellipsometer  44  3.4  The Automated E l l i p s o m e t e r  44  3.5  Sample Alignment  47  3.6  Temperature C o n t r o l f o r E l l i p s o m e t e r Measurements  . .  .47  3.7  The E f f e c t s o f M u l t i p l e I n t e r n a l R e f l e c t i o n s 3.7.1 The E f f e c t on the Measurement o f t h e B i r e fringence 3.7.2 The E f f e c t o f M u l t i p l e I n t e r n a l R e f l e c t i o n s on the P h o t o r e f r a c t i v e P r o c e s s  49  53  B i r e f r i n g e n c e Measurements Along t h e c - a x i s o f t h e Crystal  54  O p t i c a l l y - i n d u c e d B i r e f r i n g e n c e Change Due t o a OneD i m e n s i o n a l Gaussian Beam 3.9.1 I n t r o d u c t i o n 3.9.2 T h e o r e t i c a l C o n s i d e r a t i o n s 3.9.3 E x p e r i m e n t a l R e s u l t s 3.9.4 D i s c u s s i o n  59 59 62 65 68  3.8  3.9  3.10 Measurements on C r y s t a l s Heated i n IJ^COg 3.10.1 I n t r o d u c t i o n 3.10.2 E x p e r i m e n t a l Procedures and R e s u l t s 3.10.3 D i s c u s s i o n 4.  5.  49  68 68 . . . . . . 6 9 71  THE USE OF FABRY PEROT FRINGES TO OBSERVE THE PHOTOREFRACTIVE EFFECT  77  4.1  Introduction  77  4.2  E x p e r i m e n t a l Procedures  4.3  Experimental Results  79  4.4  Discussion  81  . .  77  . . . . .  EXPERIMENTAL CONSIDERATIONS FOR HOLOGRAM FORMATION  . . . . . .  83  5.1  Elementary E q u a t i o n s  83  5.2  The O p t i c a l System  85  5.3  Hologram Storage  90  v  Page 6.  INFLUENCE OF MULTIPLE INTERNAL REFLECTIONS AND THERMAL EXPANSION ON THE EFFECTIVE DIFFRACTION EFFICIENCY OF HOLOGRAMS IN L i N b 0  93  3  7.  8.  6.1  Introduction  93  6.2  Theory  93  6.3  Experimental Results  100  PHOTOCURRENTS IN LITHIUM NIOBATE 7.1  Introduction  7.2  E x p e r i m e n t a l Procedure . . . . .  7.3  Results  10.  103  7.4  Discussion  . . . .  103 104 108  . .  THE EFFECTS OF INTERNAL AND APPLIED FIELDS ON HOLOGRAMS STORED IN L i N b 0  9.  103  ......  112  3  8.1  Introduction  112  8.2  E x p e r i m e n t a l Procedures  .  114  8.2.1  Sample P r e p a r a t i o n  8.2.2  Multiple Internal Reflections  . 114  and Hologram Measurements  .  115  8.3  Results  121  8.4  Discussion  122  LUMINESCENCE DUE TO IRON CENTRES  . . . . . . . . . . . . . .  129  9.1  Introduction  129  9.2  Experimental Procedures  129  9.3  R e s u l t s and D i s c u s s i o n  .  131 137  CONCLUSIONS 1 0 . 1 S u g g e s t i o n s f o r F u r t h e r Research  . . . . . . .  REFERENCES  vi  139 141  Page APPENDIX A  FURTHER PROPERTIES OF L i N b 0  147  3  A.l  Miscellaneous Physical Properties  147  A.2  C r y s t a l Growth  148  A.3  Thermal B l e a c h i n g and F i x i n g o f Holograms i n LiNb0  148  3  APPENDIX B  THE ELECTRO-OPTIC BEHAVIOUR OF L i N b 0  APPENDIX C  COUPLED WAVE THEORY FOR THICK HOLOGRAM GRATINGS  APPENDIX D  SOURCES OF L i N b 0  APPENDIX E  THE APPLICATION OF LITHIUM NIOBATE IN A HOLOGRAPHIC MEMORY SYSTEM . . . . .  160  APPENDIX F  ELLIPSOMETER ALIGNMENT  166  APPENDIX G  ELLIPSOMETRIC INVESTIGATION OF THE ELECTRO-OPTIC  APPENDIX H  3  151  3  . .  CRYSTALS  154 159  AND ELECTROSTRICTIVE EFFECTS IN T a ^  172  G.l  Introduction  172  G.2  Experimental Procedures  174  G. 3  Results  175  PROGRAMS USED TO CONTROL THE ELLIPSOMETER SYSTEM H. l  . .  Intoduction  180 180  H.2  Main Programs  184  H.3  S u b r o u t i n e s C a l l e d by t h e Main Programs . . . .  190  vii  LIST OF ILLUSTRATIONS Page Fig.  2.1  O p t i c a l l y i n d u c e d b i r e f r i n g e n c e change caused by a c i r c u l a r beam  9 13  Fig.  2.2  C o n f i g u r a t i o n f o r r e c o r d i n g holograms  Fig.  2.3  Fig.  2.4  E x p e r i m e n t a l arrangement f o r r e c o r d i n g s i m p l e phase g r a t i n g s S p a t i a l r e l a t i o n s o f t h e i n t e n s i t y , space c h a r g e , space charge f i e l d , and i n d e x m o d u l a t i o n i n a sinusoidal grating  21  R e l a t i o n s o f t h e c r y s t a l axes and t h e two w r i t i n g beams f o r d i f f e r e n t c o n f i g u r a t i o n s o f f o r m i n g holograms  35  Schematic o f c o m p u t e r - c o n t r o l l e d system  38  Fig.  Fig. Fig. Fig.  Fig. Fig.  2.5  3.1 3.2 3.3  3.4 3.5  ellipsometer  V e c t o r r e l a t i o n s o f t h e e l l i p s o m e t e r elements and t h e p r i n c i p a l axes o f t h e c r y s t a l  41  Schematic o f t h e a p p a r a t u s used t o t h e r m o s t a t the l i t h i u m n i o b a t e c r y s t a l s d u r i n g e l l i p someter measurement  48  T y p i c a l measurement o f t h e temperature s t a b i l i t y i n s i d e t h e i n s u l a t e d box  48  E f f e c t o f temperature on t h e p o l a r i z e r r e a d i n g when measuring t h e b i r e f r i n g e n c e i n a 3 mm t h i c k c r y s t a l of LiNb0  50  The d i f f e r e n c e i n t h e p o l a r i z e r r e a d i n g s o f two scans a l o n g t h e c - a x i s showing t h e s c a t t e r i n the readings  50  3  Fig.  Fig.  3.6  3.7  18  C a l c u l a t e d change i n A as a f u n c t i o n o f a change i n t h e b i r e f r i n g e n c e and t h e t h i c k n e s s  52  Fig.  3.8  M u l t i p l e r e f l e c t i o n s i n a d i e l e c t r i c slab .  Fig.  3.9  V a r i a t i o n w i t h t h i c k n e s s i n t h e mean i n t e n s i t y due t o m u l t i p l e r e f l e c t i o n s The v a r i a t i o n i n t h e p o l a r i z e r r e a d i n g a l o n g the c - a x i s o f an undoped c r y s t a l  56  V a r i a t i o n i n t h e p o l a r i z e r and a n a l y s e r a l o n g t h e c - a x i s o f an undoped c r y s t a l  57  Fig.  Fig.  3.10  3.11  viii  . .  54  55  readings  Page Fig.  Fig.  Fig.  Fig.  Fig.  Fig.  Fig.  3.12  3.13  3.14  3.15  3.16  3.17  3.18  V a r i a t i o n i n the p o l a r i z e r r e a d i n g c - a x i s of a Fe-doped c r y s t a l  3.19  Fig.  3.20  3.21  58  60  Method used to i l l u m i n a t e c r y s t a l s w i t h a narrow beam of l i g h t  61  P r o f i l e of the l i g h t i n t e n s i t y a l o n g the c - a x i s of the c r y s t a l f o r the method of i l l u m i n a t i o n shown i n F i g . 3.14 . . .  61  The space charge f i e l d s (E ) developed f o r the cases of d r i f t and d i f f u s i o n caused by the i n t e n s i t y d i s t r i b u t i o n g(x)  .  E l l i p s o m e t r i c scan of the o p t i c a l l y - i n d u c e d b i r e f r i n g e n c e change caused by a s i n g l e l a s e r beam f o c u s s e d by a c y l i n d r i c a l l e n s E l l i p s o m e t r i c scan of the  64  66  optically-induced  change i n a Fe-doped c r y s t a l .  The change i n the p o l a r i z e r r e a d i n g h e a t i n g i n Li CC> . . • 2  Fig.  the  T h e o r e t i c a l f i t of the p o l a r i z e r r e a d i n g s a l o n g the c - a x i s of an . undoped c r y s t a l  birefringence Fig.  along  caused  ...  67  by 70  3  T h e o r e t i c a l f i t of the p o l a r i z e r r e a d i n g s a l o n g the c - a x i s of an undoped c r y s t a l a f t e r treatment i n I ^ C O ^  -70  Change i n the p o l a r i z e r r e a d i n g due to i r r a d i a t i o n of t h r e e p l a c e s a l o n g the c - a x i s w i t h a one-dimensional Gaussian beam  72  Fig.  3.22  Thermal decay of o p t i c a l damage i n an undoped l i t h i u m n i o b a t e c r y s t a l b e f o r e h e a t i n g i n L i C O ^ . . 73  Fig.  3.23  L o g a r i t h m of the change i n AP of time  Fig.  Fig.  Fig.  4.1  4.2  5.1  as a  function 74  O p t i c a l arrangement f o r t a k i n g photographs of the F a b r y - P e r o t i n t e r f e r e n c e f r i n g e s  78  F a b r y - P e r o t f r i n g e s i n an Fe-doped c r y s t a l showing o p t i c a l l y - i n d u c e d changes i n the refractive indices  80  Interference  84  pattern  ix  of two  p l a n e waves  '  Page Fig.  5.2  Fig.  5.3  Fig.  5.4  Fig.  5.5  D i f f r a c t i o n o f t h e r e f e r e n c e wave b y hologram g r a t i n g  5.6  85  E x p e r i m e n t a l arrangement f o r measuring the d i f f r a c t i o n e f f i c i e n c y o f p l a n e wave h o l o g r a m s Alternative diffraction  arrangement efficiency  for  measuring  of  .  87 the  the o p t i c a l bench .  89  B u i l d - u p of the e f f e c t i v e d i f f r a c t i o n w i t h time i n a Fe-doped c r y s t a l  efficiency 90  6.1  Multiple  Fig.  6.2  E f f e c t i v e d i f f r a c t i o n e f f i c i e n c y of a hologram in a lithium niobate crystal plotted against temperature change ..  96  E x p e r i m e n t a l l y o b t a i n e d r e f l e c t e d i n t e n s i t y of a n a r g o n i o n l a s e r beam i n c i d e n t o n a 3 mm t h i c k c r y s t a l of undoped L i N b O ^ p l o t t e d a g a i n s t t i m e of exposure  97  E f f e c t i v e d i f f r a c t i o n e f f i c i e n c y of a hologram i n a Fe-doped LiNbO^ c r y s t a l p l o t t e d a g a i n s t temperature  98  Time development o f t h e p y r o e l e c t r i c and p h o t o c u r r e n t s d u r i n g i l l u m i n a t i o n and of t h e p y r o e l e c t r i c current a f t e r the l i g h t i s turned off .  .105  P h o t o c u r r e n t i n an undoped LiNbO^ c r y s t a l different intensities  105  6.3  Fig.  6.4  Fig.  7.1  Fig.  7.2  Fig.  7.3  Fig.  7.4 c  I n i t i a l stage of hologram formation u n d o p e d c r y s t a l a t two w a v e l e n g t h s Initial  8.1  Measurement o f  Fig.  8.2  Effect  of  two w a v e l e n g t h s  one w r i t e ,  .  . . .  for  an 106  i n an F e .  .  .  .106  read-erase cycle .  .  .  H6  the a p p l i e d f i e l d  t a n c e o f LiNb0 8.3  in  stage of hologram formation  doped c r y s t a l a t  Fig.  Fig.  i n a hologram g r a t i n g  95  Fig.  Fig.  reflections  37  the  The a p p a r a t u s u s e d and a measurement o f stability  Fig.  the  on the  .  .  .•.  transmit-  117  3  E f f e c t of p r i o r exposure at d i f f e r e n t v o l t a g e s on hologram w r i t i n g f o r p a r t i a l illumination o f the sample  x  119  Fig.  Fig. Fig.  Fig..  8.4  Normalized values of a r c s i n n vs. applied f i e l d for a hologram w r i t t e n w i t h the c r y s t a l only partly illuminated  8.5  Time development o f writing for p a r t i a l  8.6  9.1  1/2 arcsin n during illumination  126  Schematic of t h a apparatus used to measure photoluminescence i n LiNbO^  130  Fig.  9.3  A b s o r p t i o n s p e c t r u m f o r undoped and f o r a F e doped LiNbOo c r y s t a l b e f o r e and a f t e r h e a t i n g in Li C0 2  at  the  Photoluminescence s p e c t r a of L i N b 0  Fig.  120  I d e a l i z e d i l l u s t r a t i o n of the development of the " d c " space charge f i e l d i n a p a r t i a l l y illuminated crystal  3  e  123  9.2  9.4  a  hologram  Fig.  Fig.  -. ?.  300°K .  .  132  133-  3  Photoluminescence s p e c t r a of Fe-doped L i N b 0 a t 300 K f o r two d i f f e r e n t w a v e l e n g t h s o f excitation - . .  3  A.l  Apparatus f o r the C z o c h r a l s k i growth of i n an e l e c t r i c f i e l d  LiNb0  .  .  135  3  149 i  Fig.  C.l  Model of  Fig.  E.l  Schematic of  Fig.  F.l  Zero c o r r e c t i o n f o r  Fig.  F.2  C o r r e c t i o n s to  Fig.  F.3  Zero c o r r e c t i o n f o r  Fig.  G.l  L o w e r p a r t o f if),A d o m a i n f o r i n c r e a s i n g n e s s o f t a n t a l u m up t o t h r e e c y c l e s  Fig.  G.2  Fig.  G.3  "  a thick  Upper p a r t  of  hologram g r a t i n g  . . . . . . .  154  a h o l o g r a p h i c memory s y s t e m . . . . the angle of  incidence scale .  t h e a n a l y s e r and p o l a r i z e r  scales  t h e q u a r t e r wave p l a t e  C o n t o u r s o f c o n s t a n t i n d e x and c o n s t a n t t h i c k n e s s on a t a n t a l u m s u b s t r a t e  167  .  167  scale .  167  thick177  i{i,A d o m a i n  xi  161  177 film 179  LIST OF TABLES Page Table  5.1  S e n s i t i v i t y o f LiNbO^ t o hologram s t o r a g e  91  Table  7.1  E f f e c t s o f s h o r t - c i r c u i t and o p e n - c i r c u i t c o o l i n g on the p h o t o c u r r e n t  107  P h o t o c u r r e n t s measured d u r i n g hologram f o r m a t i o n i n an Fe-doped and undoped c r y s t a l a t two d i f f e r e n t wavelengths  107  A comparison o f g L c a l c u l a t e d from the photoc u r r e n t t o g L c a l c u l a t e d from t h e d i f f r a c t i o n efficiency  110  . . . .  159  . . .  165  Table  Table  7.2  7.3  Table  D.l  L i t h i u m n i o b a t e c r y s t a l s used  Table  E.l  A comparison o f some computer memory systems  Table  H.l  Main programs used t o c o l l e c t d a t a and c o n t r o l the automated e l l i p s o m e t e r ,  181  S u b r o u t i n e s used by t h e main programs i n Table H . l  182  Table  H.2  xii  i n t h i s study  listed  ACKNOWLEDGEMENT  I would l i k e to thank my supervisor, Dr. L. Young f o r h i s encouragement and guidance during the course of t h i s research.  I am  grateful for the assistance received from Dr. R. Parsons i n the luminescence studies.  I wish to express my appreciation to Mr. D.  Daines and Mr. J . Stuber for their assistance i n the machine shop, to Mr. A. MacKenzie for drawing many of the graphs and to Mrs. A. Semmens for typing a portion of the thesis.  The National Research Council of  Canada (Grant No. A3392), the Defence Research Board of Canada(Grant No. 5501-67) and the H.R. MacMillan family (fellowship) are g r a t e f u l l y acknowledged  for t h e i r f i n a n c i a l support.  xiii  xiv  1  CHAPTER 1 INTRODUCTION  In c e r t a i n i n s u l a t i n g c r y s t a l s , exposure to l i g h t of appropriate  wavelength induces s m a l l changes i n the r e f r a c t i v e i n d i c e s .  T h i s phenomenon has  r e c e n t l y been named the p h o t o r e f r a c t i v e  Phase holograms may  be  to two  s t o r e d i n p h o t o r e f r a c t i v e c r y s t a l s by  i n t e r f e r i n g coherent l i g h t beams.  The  1966), s t r o n t i u m  barium n i o b a t e  t i t a n a t e , l i t h i u m t a n t a l a t e (Ashkin (Ostrowsky et a l . 1970).  (SBN)  (Thaxter  et a l . 1966)  and  et  niobate  In a d d i t i o n , the p a r a e l e c t r i c c r y s t a l ,  e f f e c t i f an e l e c t r i c f i e l d  i s a p p l i e d to the c r y s t a l  The work d e s c r i b e d  was  (Ashkin  potassium  (KTN)  above i t s C u r i e p o i n t , e x h i b i t s  here was  of the mechanisms i n v o l v e d  connection  exposure  1969), barium  potassium t a n t a l a t e n i o b a t e  standing  effect.  p h o t o r e f r a c t i v e e f f e c t has  been found i n f e r r o e l e c t r i c c r y s t a l s such as l i t h i u m n i o b a t e al.  the  with p o s s i b l e engineering  the  (Chen 1967).  undertaken to o b t a i n an under-  i n the p h o t o r e f r a c t i v e e f f e c t i n applications.  Lithium  niobate  chosen as the m a t e r i a l f o r the study because i t seemed the most  p r o m i s i n g m a t e r i a l f o r a p p l i c a t i o n s and are r e a d i l y a v a i l a b l e .  because h i g h q u a l i t y c r y s t a l s  A l t h o u g h more was  e f f e c t i n l i t h i u m niobate  than i n other  known about the  photorefractive  c r y s t a l s , the b a s i c mechanisms  were not understood, the s p e c i f i c a t i o n of the m a t e r i a l f o r a p p l i c a t i o n s was p r o p e r t i e s of the  incomplete and  i t was  not  c l e a r how  engineering  to o p t i m i z e  the  crystal.  * More p r e c i s e l y , the l i g h t induces a change i n the o p t i c a l  indicatrix.  2  When l i t h i u m n i o b a t e  f i r s t became a v a i l a b l e i n s i n g l e c r y - .  s t a l s o f o p t i c a l q u a l i t y , i t s h i g h e l e c t r o - o p t i c a l c o e f f i c i e n t s and o t h e r p r o p e r t i e s made i t a t t r a c t i v e f o r use i n e l e c t r o - o p t i c m o d u l a t o r s . I t was found, however, t h a t i l l u m i n a t i o n caused o p t i c a l  inhomogeneities  to form i n t h e c r y s t a l and these degraded the performance o f t h e modulator.  The c r y s t a l s were most s e n s i t i v e t o t h e b l u e and green wave-  lengths of l i g h t .  The o b j e c t i v e o f the f i r s t  i n v e s t i g a t i o n s was t o  f i n d ways o f e l i m i n a t i n g t h e p h o t o r e f r a c t i v e e f f e c t .  C o n t r o l o f impur-  i t i e s i n the c r y s t a l , e s p e c i a l l y i r o n , was found t o be important i n this  regard. , Chen, LaMacchia and F r a s e r  out  (1968) were t h e f i r s t  to point  t h a t t h e p h o t o r e f r a c t i v e e f f e c t can be used t o s t o r e t h i c k phase  holograms i n l i t h i u m n i o b a t e .  I n c o n t r a s t t o p h o t o g r a p h i c methods,  no development o r b l e a c h i n g p r o c e s s e s be o p t i c a l l y o r t h e r m a l l y  erased  are required.  The holograms c a n  and new holograms w r i t t e n .  e f f i c i e n c i e s approaching 100% a r e t h e o r e t i c a l l y p o s s i b l e . d i f f r a c t i o n e f f i c i e n c i e s o f up t o 60% have been r e p o r t e d  Diffraction Experimentally,  (Amodei e t a l .  1972). Chen e t a l . ' s d i s c o v e r y c r e a t e d  i n t e r e s t i n the p o t e n t i a l  a p p l i c a t i o n o f l i t h i u m n i o b a t e as a h o l o g r a p h i c o p t i c a l computer memories. s e v e r a l companies.  s t o r a g e medium.in  This a p p l i c a t i o n i s being  i n v e s t i g a t e d by  I t was shown by van Heerden (1963) t h a t t h e o r e t - .  3  i c a l l y the u l t i m a t e storage V  c a p a c i t y o f a volume hologram i s V / A ;Vbits where  i s the volume and A i s the wavelength o f l i g h t .  T h i s means t h a t  12 3 t h e o r e t i c a l l y more than 10 b i t s can be s t o r e d i n a 1 cm crystal. One basis.  .' •  method o f o p t i c a l l y s t o r i n g d a t a i s on a page by page  Each page c o n t a i n i n g N b i t s would be w r i t t e n o r read  as a  3  hologram. x-y  A l a r g e number of holograms would be s t o r e d e i t h e r i n an  a r r a y or i n s u p e r p o s i t i o n .  For a w r i t i n g time of  w r i t i n g r a t e would beN/x: b i t s / s e c .  x sec,  the  For i n s t a n c e , i f hologram  storage  4 of a page c o n t a i n i n g 10  b i t s r e q u i r e d 1 ms,  the w r i t i n g r a t e would  be  10^ b i t s / s e c . Another method was not r e q u i r e the page of data only prototype  suggested by C a r l s e n to be assembled b e f o r e  page composers have been b u i l t .  w r i t t e n one b i t at a time i n an x-y b i t on a page. time.  C a r l s e n has  The  storage.  Presently,  data could  a r r a y w i t h random access  Data would be read out  Experimentally,  (1974) which would  i n p a r a l l e l , one  be  to  any  page at a  s t o r e d pages of 16,000 b i t s i n i r o n -  doped l i t h i u m n i o b a t e . A number of review a r t i c l e s a r e a v a i l a b l e which d i s c u s s advantages and 1972,  l i m i t a t i o n s of o p t i c a l memories (Rajchman 1970,  Anderson 1972,  (See Appendix E  H i l l 1972,  Kiemle 1974,  Chen and  the  King  Zook 1975).  ).  I t i s b e l i e v e d t h a t the mechanism of the p h o t o r e f r a c t i v e e f f e c t may  be b r o a d l y  d e s c r i b e d as f o l l o w s .  Exposure of a  t i v e c r y s t a l to l i g h t of the a p p r o p r i a t e wavelength causes t a t i o n of e l e c t r o n s from t r a p s . e l e c t r o n s among t r a p s s e t s up  the  space charge f i e l d s which a f f e c t  be a l t e r e d by f u r t h e r exposure to l i g h t .  g e n e i t i e s may  photo-exci-  A s p a t i a l r e d i s t r i b u t i o n of  r e f r a c t i v e i n d i c e s v i a the e l e c t r o - o p t i c e f f e c t . may  photorefrac-  be removed by h e a t i n g  The The  the  space charge  fields  o p t i c a l inhomo-  the c r y s t a l to a p p r o x i m a t e l y  o  200  C.  E l e c t r o n s are t h e r m a l l y  e x c i t e d and  uniformly  d i s t r i b u t e d so  t h a t on c o o l i n g , the f l u c t u a t i o n s i n the r e f r a c t i v e i n d i c e s are removed.  The mechanisms which r e d i s t r i b u t e the e l e c t r o n s a r e  of  primary i n t e r e s t  i n current  research.  Rapid development of the s u b j e c t o c c u r r e d of t h i s study.  At i t s b e g i n n i n g ,  i t was  during  recognized  the  course  that both d r i f t  and  d i f f u s i o n were p o s s i b l e t r a n s p o r t mechanisms (Amodei 1971a, 1971b) but t h e i r r e l a t i v e importance was  not  of the development of r e f r a c t i v e d i f f u s i o n was  established.  A theoretical  index g r a t i n g s through d r i f t  treatment or  made w i t h o u t the r e s t r i c t i o n of a s h o r t m i g r a t i o n  as assumed by Amodei (1971a),  This i s discussed  length  i n Chapter 2.  It  was  shown t h a t the e f f i c i e n c y of hologram w r i t i n g i n c r e a s e s f o r i n c r e a s e d migration  l e n g t h up  l e n g t h would not  to a c e r t a i n  limit  G l a s s , von  limit.  Also, increased  the r e s o l u t i o n of the r e c o r d i n g medium.  der L i n d e  t h a t the p h o t o r e f r a c t i v e e f f e c t anism which they have l a b e l l e d  and  Negran (1974b, 1975a) have proposed  i n v o l v e s an e n t i r e l y new  to i n t e r n a l  f i e l d s of p y r o e l e c t r i c  p h o t o v o l t a i c e f f e c t i s o u t l i n e d i n Chapter 2 and experimental  t r a n s p o r t mech-  the " b u l k p h o t o v o l t a i c e f f e c t " ,  mechanism i s thought to be r e s p o n s i b l e f o r p h o t o c u r r e n t s viously attributed  migration  This  which were p r e -  origin.  The  i n l a t e r chapters  r e s u l t s which bear upon the e f f e c t a r e  bulk (7,8,9)  discussed.  I n measuring the d i f f r a c t i o n e f f i c i e n c y of phase holograms stored i n i n s u l a t i n g  crystals,  the e f f e c t of m u l t i p l e  r e f l e c t i o n s between the c r y s t a l f a c e s had of the b u i l d - u p  internal  been n e g l e c t e d .  of the d i f f r a c t i o n e f f i c i e n c y w i t h  Measurements  time have been used  t o t e s t v a r i o u s p h y s i c a l models f o r the p h o t o r e f r a c t i v e e f f e c t .  Usually  a prototype  plane  waves.  hologram has been w r i t t e n by  I t i s then n e c e s s a r y to r e l a t e  the i n t e r f e r e n c e o f two  the o b s e r v a b l e  diffraction  e f f i c i e n c y t o the p r e d i c t e d r e f r a c t i v e i n d e x m o d u l a t i o n . of m u l t i p l e r e f l e c t i o n s a r e d i s c u s s e d neglecting multiple reflections  i n Chapter 5.  The  effects  I t i s shown t h a t  can cause s e r i o u s e r r o r s .  Small  o  changes i n temperature  (approximately  1 C) such as those t h a t  are  5  e a s i l y produced by exposure to medium i n t e n s i t y l a s e r beams produce s u f f i c i e n t change i n c r y s t a l t h i c k n e s s  to produce s i g n i f i c a n t e f f e c t s .  In Chapter 7, the e f f e c t s of a p p l y i n g the c r y s t a l  are i n v e s t i g a t e d .  t r a n s p o r t mechanism and may hologram f o r m a t i o n .  The  an e x t e r n a l f i e l d  to  T h i s i s a u s e f u l method of p r o b i n g  the  a l s o be a u s e f u l means of c o n t r o l l i n g  published  data obtained  from u s i n g  this  tech-  n i q u e were i n apparent c o n t r a d i c t i o n .  I t i s shown t h a t the r e s u l t s of  such an experiment depend on the f i e l d  applied during previous  to l i g h t as w e l l as on the f i e l d It  applied during  the c u r r e n t  exposure  experiment.  i s a l s o shown t h a t the p o r t i o n of the c r y s t a l i l l u m i n a t e d w i l l  determine the magnitude of the space charge f i e l d  t h a t may  develop i n  the c r y s t a l . D i f f e r e n t i l l u m i n a t i o n geometries g i v e d i f f e r e n t r e s u l t s . Since  the a p p l i e d f i e l d  changes the o p t i c a l t h i c k n e s s  the e f f e c t of m u l t i p l e r e f l e c t i o n s may  of the  a l s o a f f e c t the r e s u l t s .  O b s e r v a t i o n s of o p t i c a l l y induced changes i n the gence due  to s i n g l e beams can produce u s e f u l i n f o r m a t i o n .  s a t o r method of Chen (1969) i s slow and It  does not a l l o w f o r  i s shown (Chapter 3) t h a t e l l i p s o m e t r y has  i t s usefulness  has  computer c o n t r o l .  been c o n s i d e r a b l y I t i s shown t h a t  increased  adjustable  birefrinThe  compen-  absorption.  c e r t a i n advantages  and  through automatic  , as i n hologram s t u d i e s , the e f f e c t s  of i n t e r n a l m u l t i p l e r e f l e c t i o n s must be e l l i p s o m e t r i c and  crystal,  taken i n t o account i n the  compensator methods.  In a d d i t i o n to  using  the e l l i p s o m e t e r , i t i s shown t h a t l a r g e s c a l e changes i n the r e f r a c t i v e index can be r a p i d l y i n s p e c t e d Perot  interferometer The  (Chapter  i f the c r y s t a l i s made to a c t as a F a b r y 4)  s e n s i t i v i t y of p h o t o r e f r a c t i v e c r y s t a l s to l i g h t has  a s s o c i a t e d w i t h i m p u r i t i e s i n the c r y s t a l s and  d e f e c t s r e l a t e d to  been  the  6  n o n - s t o i c h i o m e t r y of the c r y s t a l  (Peterson  et a l . 1972).  primary importance to determine the n a t u r e and s i t e s from which e l e c t r o n s may  be p h o t o - e x c i t e d  I t I s of  p r o p e r t i e s of the and  trapped.  defect  The  most  e f f i c i e n t method found to i n c r e a s e the p h o t o r e f r a c t i v e s e n s i t i v i t y been the a d d i t i o n of i r o n i m p u r i t i e s al.  ( P h i l l i p s et a l . 1972,  has  P e t e r s o n et  1973). P h i l l i p s and  niobate  Staebler  (1974) have shown t h a t h e a t i n g  c r y s t a l s w h i l e packed i n L ^ C O ^  lithium  reduced i r o n i m p u r i t i e s from  3 + 2 + Fe  to Fe  .  sensitivity  They have used t h i s method to c o n t r o l p h o t o r e f r a c t i v e  ( S t a e b l e r and  P h i l l i p s 1974a).  C r y s t a l s t r e a t e d by  method have been s t u d i e d w i t h the e l l i p s o m e t e r g r a p h i c methods (Chapter 7 ) .  this  (Chapter 3) and  I t i s shown t h a t i n a d d i t i o n to  by  reducing  the i r o n i m p u r i t i e s , the treatment changes the b i r e f r i n g e n c e of c r y s t a l and  holo-  the  d e c r e a s e s the r a t e at which the o p t i c a l l y - i n d u c e d space  charge f i e l d s decay. treatment d e s t r o y s  To  e x p l a i n these r e s u l t s i t i s proposed t h a t  the  shallow traps.  To determine whether e l e c t r o n s enter  the c o n d u c t i o n band or  whether charge t r a n s p o r t i s the r e s u l t of i n t e r v a l e n c e t r a n s f e r , a search  f o r luminescence was  observed  made.  (Chapter 8) which was  the c r y s t a l .  The  ment i n L i C 0 „ . o  A luminescence band a t 770  nm  was  a s s o c i a t e d w i t h the i r o n i m p u r i t i e s i n  luminescence was  stronger  i n c r y s t a l s a f t e r heat t r e a t -  7  CHAPTER 2 PHYSICAL MODELS FOR  2.1  THE  PHOTOREFRACTIVE EFFECT  Introduction As was  mentioned i n the p r e v i o u s  chapter,  a number of models  have been proposed to e x p l a i n the p h o t o r e f r a c t i v e e f f e c t . ment of these models i s now understanding  2.2  The  of the  o u t l i n e d to show how  develop-  they a f f e c t the  present  process.  E l e c t r o - o p t i c Nature of the P h o t o r e f r a c t i v e E f f e c t Chen, LaMacchia and  Fraser  (1968) found t h a t the  s t r u c t i o n o f holograms s t o r e d i n l i t h i u m n i o b a t e was efficient ation.  The  recon-  o n l y 1/10  as  f o r o r d i n a r y r a y i l l u m i n a t i o n as f o r e x t r a o r d i n a r y r a y  To e x p l a i n t h i s o b s e r v a t i o n ,  r e f r a c t i v e process  illumin-  they suggested t h a t t h e p h o t o -  r e s p o n s i b l e f o r hologram s t o r a g e  i n v o l v e d the  electro-  * o p t i c e f f e c t i n the c r y s t a l .  The  diffraction efficiency  n  is  propor-  2 t i o n a l to s i n (aAn), where a i s a c o n s t a n t the r e f r a c t i v e i n d e x m o d u l a t i o n f o r Chen e t a l . ' s o b s e r v a t i o n  and  An  ( K o g e l n i k 1969).  (An )/(An ) - 0.3. e o  i s the a m p l i t u d e of This implies that T h i s ic  consistent with  the e l e c t r o - o p t i c c o e f f i c i e n t r ^ which a f f e c t s the o r d i n a r y i n d e x 1/3  t h a t which a f f e c t s the e x t r a o r d i n a r y i n d e x In c o n t r a s t w i t h t h i s , G a y l o r d  being  ^^2'  e t a l . (1972) observed  no  dependence of the d i f f r a c t e d power on the p o l a r i z a t i o n of the  readout  beam. They have s i n c e found  obser-  ( p r i v a t e communication) t h a t t h i s  v a t i o n was p e c u l i a r to one p a r t i c u l a r c r y s t a l and a l l o t h e r measurements Appendix 2 c o n t a i n s an o u t l i n e of the e l e c t r o - o p t i c e f f e c t i n l i t h i u m niobate.  8  they have made a r e c o n s i s t e n t w i t h Chen e t a l . ' s o b s e r v a t i o n s . speculated  t h a t the holograms they saw  were not caused by  They  the mechan-  isms u s u a l l y a s s o c i a t e d w i t h the p h o t o r e f r a c t i v e e f f e c t . To j u s t i f y u s i n g the r e l a t i v e magnitudes of r ^ ^ and  r ^  to  account f o r the p o l a r i z a t i o n dependence of r e a d i n g holograms, Chen e t a l . proposed t h a t the r e f r a c t i v e I n d i c e s were modulated by a space charge field  d i r e c t e d along  the x^ or c - a x i s of the c r y s t a l .  The next s e c t i o n  d e t a i l s f u r t h e r experiments conducted by Chen to v e r i f y  2.3  The  Internal Field Using  Theory  an a d j u s t a b l e compensator method (Sec. 3.1),  observed changes i n b i r e f r i n g e n c e induced Fig.  this.  2.1(a) shows the o p t i c a l l y induced  l i n e s p a r a l l e l and p e r p e n d i c u l a r reverses s i g n along  Chen (1969)  w i t h a s i n g l e l a s e r beam.  change i n b i r e f r i n g e n c e a l o n g  to the c - a x i s .  the c - a x i s but not a l o n g  The b i r e f r i n g e n c e  the b - a x i s .  To  explain  t h i s o b s e r v a t i o n , Chen proposed a model i n which an e l e c t r o n c o u l d e x c i t e d from one t h e r e was  t r a p and  then captured  i n another.  an i n t e r n a l e l e c t r i c f i e l d E  He  be  assumed t h a t  d i r e c t e d from the p o s i t i v e end o  of spontaneous p o l a r i z a t i o n of the c r y s t a l to the n e g a t i v e a n t i p a r a l l e l to the spontaneous p o l a r i z a t i o n v e c t o r P . g  of the f i e l d was crystal.  One  gence w h i l e  determined by a p p l y i n g an e x t e r n a l f i e l d  and  The to  the o t h e r d i r e c t i o n enhanced the change. e l e c t r o n s to d r i f t  along  Chen appears to have e n v i s i o n e d  r e e x c i t e d many times,  the birefrin-  T h i s f i e l d would  the c - a x i s toward the beam that a f t e r being  these e l e c t r o n s would d r i f t  i l l u m i n a t e d a r e a and would remain trapped  that i s ,  direction  d i r e c t i o n of the f i e l d r e t a r d e d the change i n t h e  cause p h o t o - e x c i t e d periphery.  end,  out o f  retrapped the  a t l e v e l s too deep to  be  beam - diameter  DISTANCE  F i g . 2.1 (a) The s o l i d l i n e ( ) shows the change i n birefringence along the c-axis and the dashed l i n e ( ) the change along the b-axis due to a beam of c i r c u l a r symmetry (X= 488 nm). (b) Chen's postulated space charge f i e l d d i s t r i b u t i o n which causes the observed change i n A(n - n ) . e  o  10  reexcited by  the  by  thermal p r o c e s s e s .  trapped e l e c t r o n s  the  electrons  via  the  and  originated  electro-optic  The  space ,charge f i e l d ,  p o s i t i v e l y ionized  E  , created  SO  c e n t e r s from which  caused the observed r e f r a c t i v e index v a r i a t i o n  effect  ( F i g . 2.1(b)).  Since l i t h i u m  niobate  exhibits a linear electro-optic linearly related  to the  space charge f i e l d  e f f e c t , the v a r i a t i o n A(n -n ) i s e o s p a t i a l v a r i a t i o n of the e l e c t r i c f i e l d .  required  f o r the magnitude of the observed  The  effect  4 was  6.7: x 10  V/cm.  To v e r i f y t h a t  t h e r e was  c r y s t a l , Chen looked f o r and  .  I t was  suggested t h a t  since a portion  of the  the  t h e r e f o r e the  his observations. existed,  2.4  consistent  with a f i e l d  f i e l d might be  in  the The  opposite  of p y r o e l e c t r i c  However, Chen p o i n t e d out  f i e l d would be  to  origin  that  i n the wrong d i r e c t i o n  A l t h o u g h i t seemed e v i d e n t t h a t  Chen d i d not  residing  l i g h t used to form the hologram would cause non-  u n i f o r m h e a t i n g of the c r y s t a l . (dP/dT< 0) and  internal field  found a s h o r t c i r c u i t p h o t o c u r r e n t .  d i r e c t i o n of the p h o t o c u r r e n t was P  an  an  internal  for  field  account f o r i t s o r i g i n s .  Johnston's P o l a r i z a t i o n Model To  remove the need to assume a b u i l t - i n f i e l d  of unknown  o r i g i n , Johnston (1970) proposed an a l t e r n a t i v e model i n which photoinduced v a r i a t i o n s refractive effect. i n the  i n the macroscopic p o l a r i z a t i o n caused the Illumination  of the  c r y s t a l would e x c i t e  c o n d u c t i o n band r e s u l t i n g i n a change i n the d e n s i t y  t r a p s i n the  r e g i o n of i l l u m i n a t i o n .  change i n the p o l a r i z a t i o n .  The  photoelectrons  of  filled  T h i s i n t u r n would cause a l o c a l  d i v e r g e n c e of the  polarization  produces a f i e l d which skews the d i f f u s i o n a l p r o c e s s of e l e c t r o n s  in  11  the c o n d u c t i o n band.  A f t e r the l i g h t i s t u r n e d o f f , t h e r e remains  change i n the macroscopic p o l a r i z a t i o n which  a  i n d u c e s a change i n the  r e f r a c t i v e i n d i c e s o f the c r y s t a l . U s i n g t h i s model, J o h n s t o n was f o r the s p a t i a l l y dependent  a b l e t o account  qualitatively  f e a t u r e s o f Chen's o b s e r v a t i o n s ( F i g . 2 . 1 ) .  However, Amodei(1971 a), and Amodei and S t a e b l e r (1972b) have shown t h a t t h e r e a r e a number o f d i f f i c u l t i e s w i t h t h i s mechanism.  They c o n c l u d e d  that  a v e r y l a r g e number o f e l e c t r o n s would be r e q u i r e d  t o e n t e r the c o n d u c t i o n  band to account f o r the g e n e r a t i o n o f the f i e l d s n e c e s s a r y t o skew t h e e l e c t r o n i c motion.  The same magnitude of i n d u c e d i n d e x change c o u l d  r e s u l t from space charge f i e l d s c r e a t e d t h r o u g h s i m p l e d i f f u s i o n  and  retrapping processes.  less  The number o f e l e c t r o n s i n v o l v e d would be  3 by a f a c t o r o f 10  than would be r e q u i r e d i n Johnston's model.  In 13  a d d i t i o n , they o b s e r v e d t h a t J o h n s t o n ' s r e s i s t i v i t y measurement ohms) which l e d him t o c o n c l u d e t h a t any i n t e r n a l f i e l d s would i n a s h o r t time, was  a b n o r m a l l y low.  (10 relax  T y p i c a l v a l u e s would a l l o w f i e l d s  to remain f o r many weeks. Amodei and S t a e b l e r ( 1 9 7 2 b ) suggested t h a t the b u i l t - i n which Chen used t o e x p l a i n h i s r e s u l t s was developed when the c r y s t a l was development  o f such a f i e l d may  of pyroelectri?. o r i g i n  c o o l e d from a h i g h temperature. be e x p l a i n e d i n the f o l l o w i n g  A r e c t a n g u l a r 3m f e r r o e l e c t r i c c r y s t a l w i t h no f r e e and no n e t space charges would have a f i e l d i z a t i o n charge  P  and  The way. charges  corresponding to a p o l a r -  p e r u n i t a r e a on f a c e s normal t o the c - a x i s . rem  field  This  '  would, i n f a c t , be above normal d i e l e c t r i c breakdown v a l u e s .  In p r a c t i c e ,  the c r y s t a l would have been c o o l e d from some h i g h temperature a t which a p p r e c i a b l e c o n d u c t i v i t y e x i s t e d , s u f f i c i e n t to c a n c e l the f i e l d .  Excess  12  charges would accumulate c l o s e to each c - f a c e .  As c o o l i n g p r o g r e s s e s ,  the c o n d u c t i v i t y w i l l f r e e z e out w h i l e the remanent p o l a r i z a t i o n P c o n t i n u e s to change.  F i n a l l y , an uncompensated component of P  r e m  rem will  e x i s t g i v i n g a b u i l t - i n f i e l d of magnitude  1 r T  l  T  r  S  3P • ( - ^ ) d  and T Q a r e the temperature - a t which the c o n d u c t i v i t y d i s a p p e a r s  where and  T  a1  O  the temperature of the experiment r e s p e c t i v e l y , and e  i s the  permittivity.  2.5  The Formation 2.5.1  of Holograms by D r i f t or D i f f u s i o n  Introduction To probe the mechanism of hologram s t o r a g e i n l i t h i u m n i o b a t e ,  it  i s convenient  by c a u s i n g two crystal.  The  to a n a l y z e the f o r m a t i o n of a p r o t o t y p e hologram formed  coherent p l a n e waves to i n t e r f e r e i n the volume of r e s u l t i n g i n t e r f e r e n c e p a t t e r n i s s i n u s o i d a l and  the  the  \ .  i n t e n s i t y i s of the form I =  IQ(1  where k i s the s p a t i a l frequency ratio  + m cos kx)  of the p a t t e r n , arid m"is  ^2 ]_) :the modulation _  and x i s i n the p l a n e of the two beams and p e r p e n d i c u l a r to t h e i r  bisector. k = 2n/%  For two beams i n t e r s e c t i n g a t an a n g l e 20 as shown i n Fig.2.2 where % = A/(2 s i n 6 ) and  A i s the wavelength of the  light.  Amodei (1971a) has used t h i s c o n f i g u r a t i o n to a n a l y z e f o r m a t i o n of holograms.  He assumed t h a t t h e d r i f t o r d i f f u s i o n l e n g t h  of p h o t o - e x c i t e d e l e c t r o n s was  v e r y much s m a l l e r than the g r a t i n g p e r i o d  i.  *  the  A d e f i n i t i o n of the modulation  r a t i o i s g i v e n i n Chapter  5.  13  c+  -X  F i g . 2.2 C o n f i g u r a t i o n f o r r e c o r d i n g holograms. The two p l a n e waves R and S i n t e r f e r e t o produce a s i n u s i o d a l l i g h t i n t e n s i t y p a t t e r n w i t h a p e r i o d I. The c+ end o f t h e c r y s t a l ( o f t h i c k n e s s d) i s shown i n the p o s i t i v e x d i r e c t i o n .  14  Staebler  and Amodei(1972b) have shown t h a t depending on  mechanism of charge t r a n s p o r t , the p e r i o d i c index m o d u l a t i o n may s h i f t e d i n phase w i t h r e s p e c t it.  to the i n t e n s i t y m o d u l a t i o n t h a t  O b s e r v a t i o n s on the t r a n s f e r of energy between the two  beams, and  the assumption t h a t f r e e e l e c t r o n s moved a v e r y  ance b e f o r e b e i n g d i f f u s i o n and  retrapped  the be  created  writing short  dist-  (Amodei 1971b)led them to conclude t h a t b o t h  d r i f t were r e s p o n s i b l e  f o r the g r a t i n g f o r m a t i o n .  In  Sec.2.5.4 i t i s shown t h a t the i n t e r p r e t a t i o n of t h e i r r e s u l t s depends on how  f a r e l e c t r o n s move.  2.5.2  A n a l y s i s f o r Short D r i f t or D i f f u s i o n Length Chen et a l . (1968) found t h a t they c o u l d s t o r e holograms  w i t h a r e s o l u t i o n of g r e a t e r  than 1600  lines/mm.  assume t h a t the d i s p l a c e m e n t o f e l e c t r o n s due be  t o the i l l u m i n a t i o n must  a f r a c t i o n of a m i c r o n to be a b l e to r e c o r d  sity.  T h i s l e d them to  the v a r i a t i o n i n i n t e n -  Because of t h i s , Amodei assumed t h a t i n d e v e l o p i n g  i t would be r e a s o n a b l e to r e s t r i c t  the d r i f t  a  theory,  or d i f f u s i o n l e n g t h to a  f r a c t i o n of the g r a t i n g wavelength. Amodei assumed t h a t the r a t e of promotion of e l e c t r o n s the c o n d u c t i o n band g(x) at  l e a s t i n the i n i t i a l  be  taken as u n i f o r m l y  to be p r o p o r t i o n a l to the i n t e n s i t y of stages of hologram f o r m a t i o n  filled.  The  n(x)  =  The  of the d r i f t  i s given  g  Q  and  by  d i f f u s i o n components,  (2.2)  i s p r o p o r t i o n a l to I  s p a t i a l d i s t r i b u t i o n of the c u r r e n t was  may  or d i f f u s i o n  g T ( 1 + m cos kx) O i  where x i s the l i f e t i m e of c a r r i e r s and Eq. 2.1).  light,  when the t r a p s  assumption of s h o r t d r i f t  l e n g t h i m p l i e s t h a t the f r e e - c a r r i e r c o n c e n t r a t i o n  into  q  ( in  taken as the  sum  15  J(x)  =uneE(x) + eD dn(x) dx  ,  2  3  *  where e i s the e l e c t r o n i c charge, u i s the m o b i l i t y f o r e l e c t r o n s , E ( x ) i s the t o t a l e l e c t r o n i c f i e l d electrons.  and D i s the d i f f u s i o n c o n s t a n t f o r  The r a t e a t which space charge d e n s i t y , p  accumulates a t  any p o i n t i s g i v e n by t h e c o n t i n u i t y e q u a t i o n ^ Combining  t h i s w i t h Eq. 2.3  =  "  V  -  J  -  (2.4)  the b u i l d - u p of the space charge d e n s i t y  can be expressed as •t p(t)  ='o  The space charge f i e l d  d(uneE +eD dn/dx) d t dx  (2.5)  supported by the space charge d e n s i t y i s E  sc  (x) =  _P dx  (2.6)  e  where e i s the d i e l e c t r i c c o n s t a n t of the m a t e r i a l . In to  Eq. 2.'4, the space charge d e n s i t y p which Amodei has used  c a l c u l a t e the space charge f i e l d ,  i n c l u d e s n o t o n l y the trapped  charge d e n s i t y , but a l s o the f r e e charge d e n s i t y i n the c o n d u c t i o n band. These e q u a t i o n s , then, d e s c r i b e t h e s i t u a t i o n d u r i n g i l l u m i n a t i o n .  After  i l l u m i n a t i o n ceases the f r e e e l e c t r o n d e n s i t y decays. Amodei c o n s i d e r e d ( i ) t r a n s p o r t due to d r i f t J = nepE, where E = - E  q  (the space charge f i e l d  t r a n s p o r t e q u a t i o n , and the b u i l t - i n f i e l d e l e c t r o n s to d r i f t  E  g c  only,  i s n e g l e c t e d i n the  i s taken n e g a t i v e  to cause  i n the p o s i t i v e x d i r e c t i o n ) ; and ( i i ) t r a n s p o r t  due t o d i f f u s i o n o n l y J = eD dn. dx for d r i f t only  S o l u t i o n of <Eqs. 2.4 to 2.6 y i e l d  ( e y T E t g m ) cos kx — Q  E  =  sc  e  o  (2.7)  16  and f o r d i f f u s i o n o n l y , E  sc  = (eDt/rg mk) o  s i n kx  &  (2.8)  e  Thus, w i t h the above assumption of s h o r t d r i f t o r d i f f u s i o n l e n g t h , a response i s o b t a i n e d w i t h a d i f f e r e n c e of IT/2 i n phase s h i f t  according  to whether d r i f t o r d i f f u s i o n i s o p e r a t i v e . I t i s i n t e r e s t i n g t o n o t e (Young et a l . (1974)) t h a t t h e s h o r t e r the d i f f u s i o n o r d r i f t l e n g t h s a r e assumed t o be, t h e s l o w e r  the  p r o d u c t i o n of the i n d e x g r a t i n g s i n c e the e l e c t r o n s a r e assumed t o r e t u r n more n e a r l y t o t h e i r o r i g i n a l p o s i t i o n s .  2.5.3  The E f f e c t s o f Beam C o u p l i n g S t a e b l e r and Amodei (1972b) have c o n s i d e r e d the i m p l i c a t i o n s  o f beam c o u p l i n g d u r i n g r e a d i n g and w r i t i n g holograms.  They have shown  t h a t c o u p l e d wave a n a l y s i s a l l o w s the d e t e r m i n a t i o n o f whether the p e r i o d i c i n d e x g r a t i n g s a r e s h i f t e d w i t h r e s p e c t t o the p e r i o d i c i n t e n s i t y p a t t e r n s w h i c h produce them. I n the case they c o n s i d e r e d ,  two  coherent beams R and S a r e s y m m e t r i c a l l y i n c i d e n t a t an a n g l e 6 r e l a t i v e to  the z a x i s as shown i n F i g . 2.2.  Both waves a r e p o l a r i z e d p e r p e n -  d i c u l a r to the p l a n e o f i n c i d e n c e and a r e i n c i d e n t on a r e g i o n w i t h p e r i o d i c v a r i a t i o n s of r e f r a c t i v e in  =  t h a t extends from z = 0 t o z = d.  index, cos kx The  (2.9)  two waves R and  i n the form R = r ( z ) e x p ( - i ( 2 Tr cos 6 z + A  kx))  S can be w r i t t e n  17  S = s(z) exp(-i(2 TT cos 6 - kx))  (2.10)  z  X Kogelnik (1969) (see Appendix C) using coupled wave theory has shown that f o r a nonabsorbing phase grating and perfect Bragg conditions, dr(z) = -i'ks(z) dz  (2.11)  ds(z) = -iKr(z) dz where K = frn^/(X cos 9 ) . The coupled wave equations have the general solution r(z) = a exp (iio'z) + b exp  ( - I K Z )  (2.12(a))  s(z) = -a exp ( I K Z ) + b exp (-i^z)  If we l e t the boundary conditions be r(0) = 1 and s(0) = A exp (-i<f>) then the c o e f f i c i e n t s a and b can be determined and the beam amplitudes become r(z) = cos ( K Z ) - i A exp (-i<}>) s i n (<z) s(z) = - i  s i n ( K Z ) + A exp (-i<f>) cos ( K Z )  (2.12(b))  The i n t e n s i t i e s of the two beams are given by .  12  2  1^  = |'r | = cos  (KZ)  I  2 2 = |s | = s i n  (KZ)  2 2 + A sin 2 + A  2 cos  (KZ)  - A sin  (KZ)  ( 2 K Z ) sin  < j >  + A s i n (2kz) s i n <f>  (2.13)  If the beams have equal incident amplitudes, then A = 1 and Eq. 2.13 gives I J J = 1 - s i n ( 2 K Z ) sincf) Ig = 1 + s i n ( 2 K Z ) sin<j>  (2.14)  Staebler and Amodei(l972b) have shown that these equations also describe the s i t u a t i o n where the two waves have a fixed phase r e l a t i o n s h i p , but the phase grating i s moveable along the x axis with An = n^ cos (kx +<j>). Eq. 2.14 now indicates that the energy transfer  18  b e t w e e n beams d e p e n d s o n t h e p o s i t i o n o f interference phase s h i f t it  pattern.  the g r a t i n g w i t h respect to  The p h a s e f a c t o r  between the l i g h t  intensity  <> f InEq. pattern  2.14 r e p r e s e n t s and t h e i n d e x  the  the  modulation  produces. 2.5.3.1  Coupling During  Writing  U s i n g the experimental arrangement  shown i n F i g .  2.3,  S t a e b l e r and Amodei (1972b) f o u n d t h a t d u r i n g h o l o g r a m f o r m a t i o n  there  was e n e r g y t r a n s f e r r e d  analysis  of  the t r a n s p o r t  process during recording  formed by d i f f u s i o n by d r i f t  produce a phase s h i f t  produce a phase s h i f t  the values of beams.  between the beams.  <>j o t h e r  4> = 0 ,  than zero or  .  From A m o d e i ' s (1971) (sec. 2.5.2), <> f = Eq.  holograms  TT / 2 a n d h o l o g r a m s 2.14 i n d i c a t e s t h a t  IT c a u s e e n e r g y t r a n s f e r  T h i s was t a k e n a s e v i d e n c e f o r  holograms s t o r e d by  F i g . 2.3 E x p e r i m e n t a l arrangement phase g r a t i n g s .  for  recording  formed only  between  the  diffusion.  simple  19  2.5.3.2  I n t e r a c t i o n s D u r i n g Readout  When a p r e v i o u s l y r e c o r d e d hologram p o s s i b l e f o r a new hologram  i s read o u t , i t i s  t o be w r i t t e n by t h e i n t e r f e r e n c e o f t h e  r e a d i n g beam and the d i f f r a c t e d  beam.  D u r i n g r e a d o u t , t h e S beam i s  b l o c k e d so t h a t the boundary c o n d i t i o n s a r e s (0) = 0, and r ( 0 ) = 1. From Eq. 2.12, the amplitude o f t h e two beams w i t h i n the d i f f r a c t i o n grating  n = n^ cos(kx) a r e g i v e n by r (z) = cos (kz) (2.15) s(z) = - i s i n  The i n t e r f e r e n c e p a t t e r n produced  ( K Z )  by these two beams i s found by sub-  s t i t u t i n g Eq. 2.15 i n t o Eq. 2.10 w i t h the r e s u l t X  total  l  =  s I  r +  = 1 + s i n ( 2 K ) s i n (kx)  (2.16)  z  I f the mechanism o f hologram modulation p r o p o r t i o n a l t o the i n t e n s i t y  f o r m a t i o n produces  an index  then t h e new g r a t i n g A n  will  2  be An  2  = n^ s i n (kx)  (2.17)  The t o t a l phase m o d u l a t i o n w i l l be An  t  = n^ cos (kx) + n  S t a e b l e r and Amodei.(1972b) argued phase g r a t i n g . pursued  This effect  2  s i n (kx)  that the e f f e c t  of  (2.18) was t o bend t h e  on the t o t a l d i f f r a c t i o n e f f i c i e n c y  except t o p o i n t out t h a t the e f f e c t  was n o t  s h o u l d be the same f o r  readout w i t h the R beam o r t h e S beam. In t h e case where hologram lation shifted  by  f o r m a t i o n produces an index modu-  TT/2, the new g r a t i n g An^ w i l l be An  3  = n  3  The t o t a l phase m o d u l a t i o n w i l l be  cos (kx)  ^  ^  20  A  The e f f e c t o f grating.  n  t  =  +  n  3^  C  O  (2.20)  S  i s t o i n c r e a s e o r d e c r e a s e the e f f e c t i v e n e s s o f t h e  A l t h o u g h t h e v a l u e o f n^ w i l l be l a r g e r toward t h e back o f  the g r a t i n g , t h e d i f f r a c t i o n e f f i c i e n c y depends o n l y on t h e amplitude of the g r a t i n g  (Kermish 1969).  An example o f t h i s i s shown i n F i g . 2.4.  Curve 3 i l l u s t r a t e s a phase g r a t i n g t h a t r e s u l t e d from d i f f u s i o n o f electrons.  The space charge and t h e space charge f i e l d p r o d u c i n g t h i s  g r a t i n g a r e shown i n c u r v e s 1 and 2 r e s p e c t i v e l y . a positive field shown.  I t i s assumed t h a t  d e c r e a s e s the index when - t h e c - a x i s i s o r i e n t e d as  When t h e R beam i s used f o r r e a d o u t , i t i n t e r f e r e s w i t h t h e  d i f f r a c t e d beam t o form a l i g h t - i n t e n s i t y p a t t e r n shown by t h e f o u r t h curve.  The i n t e n s i t y maximum i s on t h e +x s i d e o f t h e peaks i n c u r v e  3 because  the R beam i s p r o p a g a t i n g i n the +x d i r e c t i o n .  The f i f t h  and s i x t h c u r v e s show t h e space charge and t h e space charge f i e l d r e s u l t i n g from d i f f u s i o n o f e l e c t r o n s due t o the i n t e n s i t y p a t t e r n o f c u r v e 4.  The induced index change A n ^ w i l l e i t h e r enhance o r degrade  the o r i g i n a l index p a t t e r n fta^ depending on the d i r e c t i o n o f t h e +caxis.  I f t h e c r y s t a l i s o r i e n t e d i n the same way as i t was f o r the  p r o d u c t i o n o f A n ^ , then enhancement o c c u r s .  I f the c r y s t a l i s r e v e r s e d  so t h a t t h e +c end o f t h e c r y s t a l i s f a c i n g i n the -x d i r e c t i o n , t h e total d i f f r a c t i o n e f f i c i e n c y w i l l be degraded.  The same r e s u l t i s ob-  t a i n e d i f t h e c r y s t a l i s not r e v e r s e d but t h e S beam i s used f o r r e a d o u t . T h i s r e v e r s e s t h e phase o f the l i g h t m o d u l a t i o n , and t h e space charge t h a t accumulates opposes i  t h e space charge a l r e a d y p r e s e n t .  S t a e b l e r and Amodei's coupled-wave  a n a l y s i s has shown t h a t  i n t e r a c t i o n between t h e two beams used i n holography depends on t h e s i n e of the phase a n g l e $ between t h e i n t e n s i t y m o d u l a t i o n and t h e index  21  F i g . 2.4 (1): sinusoidal space charge created by a s i n u s o i d a l l i g h t pattern. (2): the space charge f i e l d created by (1). (3): v a r i a t i o n i n the r e f r a c t i v e index caused by (2) through the e l e c t r o - o p t i c e f f e c t . (4): a second l i g h t i n t e n s i t y pattern which creates (5), a space charge and (6), a space charge f i e l d . The space charge f i e l d either enhances of degrades the grating An^ depending oh the d i r e c t i o n of the +c end of the c r y s t a l .  22  modulation.  U s i n g Amodei's treatment of the f o r m a t i o n  grams, they r e s t r i c t for  the v a l u e of <|> to  charge t r a n s p o r t and  charge t r a n s p o r t . uous f u n c t i o n . smoothly. short d r i f t  TT/2 when d i f f u s i o n i s r e s p o n s i b l e  to zero or TT when d r i f t  I t i s not obvious why  i s responsible for  <j> should be  such a d i s c o n t i n -  P h y s i c a l l y i t would be more r e a s o n a b l e  f o r <$> to v a r y  In the next s e c t i o n i t i s shown t h a t i f the r e s t r i c t i o n of or d i f f u s i o n l e n g t h i s removed, then d r i f t w i l l  v a l u e of cj> depending on the d r i f t  allow  any  l e n g t h where as the v a l u e of <j> f o r  d i f f u s i o n w i l l be ±T/2 independent of the d i f f u s i o n 2.5.4  of phase h o l o -  length.  A n a l y s i s w i t h A r b i t r a r y D r i f t or D i f f u s i o n Length The need f o r the assumption t h a t the d r i f t  l e n g t h be s h o r t may Wong, Thewalt and  or  diffusion  be removed by u s i n g the c o n t i n u i t y e q u a t i o n  Cornish  1974) 3n = g - n + _! 3t e 3x  (2.21)  T  In the i n i t i a l  (Young,  stages of hologram f o r m a t i o n ,  the r a t e of change of  c o n c e n t r a t i o n of f r e e e l e c t r o n s i n the c o n d u c t i o n  the  band i s zero at con-  s t a n t l i g h t i n t e n s i t y so t h a t 0 =  g - n _ x  +  l | J e 9x  Amodei's (1971a) assumption t h a t n = gt corresponds to dropping (1/e)  9J/8x i n Eq.  2.22.  g i v e s the r a t e of trapped interest.  T h i s term i s the n e g a t i v e  of g - n / x , which  space-charge b u i l d - u p c a u s i n g  the e f f e c t s of  For the d r i f t o n l y case, J ( x ) = neyE where E=••-E .  g = g p ( l + m cos  ( k x ) ) , Eq.  dx  2.22  becomes  — = —=—(1 L yE Q  + m cos  kx)  the term  Writing  23  where L = u E ^ and g solved  i s p r o p o r t i o n a l to I  Q  (Eq. 2.1). T h i s may be  to y i e l d n(x)  =  x g u(x) + 'n(O) - x g  -  -: o •'•2 2 1 + L V g  m  exp(-x/L)  xg m o  H  (cos kx - k L s i n kx)  (2.24)  2 2 1 + L k where u ( x ) i s a u n i t step f u n c t i o n and n(0) i s the i n i t i a l v a l u e  o f the  Then w i t h 3p /t.3vt = ->9j/c3x and c3E /$X = p/e , sc the space charge f i e l d may be w r i t t e n free electron concentration.  E  = _ t _ f(g T - n ) d x e^ex .  g c  S u b s t i t u t i n g i n Eq. 2.25, and e x c l u d i n g  (2.25)  terms due t o the t e r m i n a t i o n o f  the p e r i o d i c l i g h t p a t t e r n , the form o f the space charge f i e l d i s  E  = S  This equation pattern with  e  g  F  k e  o  m  I  k L 2  Ia  s i n kx +  2  2 2 + k L  kL cos k x 2 2 'J 1 + k L  the impulse response which, f o r t h i s case,  (2.26)  o f the l i g h t  i s proportional  ( I n the d i f f u s i o n case, we have two e x p o n e n t i a l s  back-to-  P h y s i c a l l y we have a p o s i t i v e space charge wave due t o the  removal o f e l e c t r o n s from t r a p s p l u s a n e g a t i v e their  V l  can a l s o be d e r i v e d by t a k i n g t h e c o n v o l u t i o n  to e x p ( - x / L ) . back.)  t  C  space charge wave due t o  retrapping. For  the d i f f u s i o n - o n l y case,  the s o l u t i o n f o r the space charge f i e l d  E  s p S  C  J = eDdn/dx.  due t o d i f f u s i o n i s  2 eg mtkL' = ° s i n kx (l+k L )e 0  9  2  , 2  W r i t i n g L' = (Dx) ,  (2.27)  24  2.5.5  Discussion For t h e case o f space charge f i e l d s developed by d r i f t , t h e  phase s h i f t between the p e r i o d i c l i g h t  i n t e n s i t y p a t t e r n and t h e p e r i o -  d i c space charge f i e l d depends on the d r i f t  length.  Lk<<l, Amodei's e x p r e s s i o n i s o b t a i n e d ( w i t h E a much l a r g e r space charge f i e l d E  sc  = ( t e g m/ek) s i n kx. o  I n Eq. 2.26, f o r  "« c o s kx) .  c  F o r Lk>> 1  i s o b t a i n e d g i v e n by .  The response f o r t h i s case i s due t o the  p o s i t i v e space charge wave o n l y , t h e n e g a t i v e charge due t o r e t r a p p e d electrons being uniform.  I t i s a l s o independent o f E  phase s h i f t between t h e l i g h t  (for Lk«l)  and x.  The  i n t e n s i t y p a t t e r n and the index g r a t i n g  produced depends on t h e magnitude o f t h e d r i f t zero  q  to T / 2 ( f o r L k  > : >  l e n g t h L and v a r i e s  from  l).  In t h e case o f d i f f u s i o n - f o r m e d space charge f i e l d s , f o r l a r g e enough L'k, t h e same l i m i t i n g c a s e i s o b t a i n e d as f o r d r i f t o n l y w i t h Lk^>l.  However, whatever  the magnitude of L'k the phase s h i f t  remains  the same because the f r e e e l e c t r o n s have e q u a l p r o b a b i l i t y o f moving i n either  direction. The magnitudes  o f L ( f o r the d r i f t  case) t o which  Staebler  and Amodei's r e s u l t s on coupled wave a n a l y s i s a p p l y a r e c r u c i a l . .  A phase  s h i f t halfway between t h e two l i m i t i n g c a s e s i s a c h i e v e d when L k = 1. The d r i f t 9= 15°  l e n g t h i s then g i v e n by L = E U X = 1/2 T = X / 4 T T r n 9 . F o r Q  and X = 500nm a d r i f t  9= 45°, L = 56.3 nm).  S  l e n g t h o f 153.7 nm i s c a l c u l a t e d .  (For  The a c t u a l v a l u e o f L w i l l depend on t h e d i s t a n c e 4  between empty t r a p s , and t h e i r c r o s s s e c t i o n .  Taking E  q  = 10  V/cm  (which i s s m a l l e r than Chen's (1969) e s t i m a t e o f the p y r o e l e c t r i c field  i n h i s c r y s t a l s ) and u = 15 cm /Vsec 2  ( e x t r a p o l a t e d from  (Jorgensen e t a l . 1969)), a v a l u e o f x = 10 ^  1000°K  sec i s o b t a i n e d .  The  N  p y r o e l e c t r l c f i e l d would be expected t o be r a t h e r an u n c o n t r o l l e d  25  quantity  which depends on the h i s t o r y , i n p a r t i c u l a r the t h e r m a l h i s t o r y , of  the  c r y s t a l so t h a t the v a l u e of L would depend on the p a r t i c u l a r specimen used. I t has  been suggested by  p h y s i c a l processes l i g h t beam may formation. volved  Amodei(1972b) t h a t  i n v o l v e d i n the p h o t o r e f r a c t i v e e f f e c t due  not n e c e s s a r i l y be  More s p e c i f i c a l l y ,  i n the l i g h t  become i m p o r t a n t .  The  the h i g h e r  q u e s t i o n may  two  p l a n e waves.  length L  and  drift  be  Taking,  l e n g t h L to be  to s i n g l e  the s p a t i a l f r e q u e n c i e s  tend  s h o r t compared to the r e c i p r o c a l of  to d i f f u s i o n i f  E <<Dk. Q  due  to d r i f t would be  Using  T = 300°K and  6 = 6.75° ( c a l c u l a t e d from an a n g l e of i n c i d e n c e of  (D = K'Tu/e) f o r a wavelength X = 500nm, temperature  V/cm,  where K'  t o dominate, the t o t a l f i e l d 10 V/cm.  I f the d r i f t  i s the Boltzmann c o n s t a n t .  Thus a r a t h e r compl.->.te  an i n c r e a s e i n w r i t i n g e f f i c i e n c y up  to a c e r t a i n l i m i t .  or d i f f u s i o n i s o p e r a t i v e  the s i n u s o i d a l l i g h t  suppression  Also, i n  in a particular experi-  be  refractive  i n t e n s i t y which produced i t must  i n mind the f o l l o w i n g c o n s i d e r a t i o n s .  produced by d i f f u s i o n w i l l  the  or d i f f u s i o n would cause  ment, e v i d e n c e based on d e t e c t i n g a s p a t i a l s h i f t between the  interpreted bearing  few  required.  I n c o n c l u s i o n , an i n c r e a s e i n d r i f t  be  diffusion  l e n g t h were»not n e g l i g i b l e compared to 1/k,  o f the t o t a l f i e l d would be  d e c i d i n g whether d r i f t  For  15°),  i n the c r y s t a l would have to be o n l y a  f i e l d would have to be even s m a l l e r .  i n d e x g r a t i n g and  small  the E i n s t e i n r e l a t i o n  D  o  to  f o r s i m p l i c i t y , both d i f f u s i o n  between u and  E « K ' T k / e = 765  in-  t e s t e d by c o n s i d e r i n g a hologram  the s p a t i a l frequency, the space charge f i e l d compared to t h a t due  the  the same as o p e r a t e i n hologram  i n t e n s i t y p a t t e r n , the more d i f f u s i o n w i l l  formed by 1  S t a e b l e r and  s h i f t e d by ±TT/2 i n the r e f e r e n c e  A grating frame  26  d e f i n e d by the l i g h t beams, the s i g n depending on the d i r e c t i o n o f t h e c(+)  a x i s with respect  drift,  t o the l i g h t beams.  the s h i f t depends on the d r i f t  i s the same as f o r d i f f u s i o n .  F o r a g r a t i n g produced by  l e n g t h L.  F o r L>>l/k, the s h i f t  F o r L<<l/k, t h e r e w i l l be e i t h e r 0 o r it  s h i f t depending on t h e d i r e c t i o n o f t h e f i e l d c a u s i n g d r i f t , respect  with  t o the c(+) d i r e c t i o n and the s i g n o f the a p p r o p r i a t e e l e c t r o -  optic coefficient.  I f the f i e l d  i s a b u i l t - i n f i e l d of p y r o e l e c t r i c  o r i g i n , then changing t h e d i r e c t i o n o f the c(+) a x i s a l s o r e v e r s e s the f i e l d and so has no e f f e c t on the d i r e c t i o n o f e l e c t r o n motion w i t h r e s p e c t to  t h e c r y s t a l axes.  mediate s h i f t s . decide  Intermediate values  of L g i v e  inter-  I n g e n e r a l , o t h e r e v i d e n c e w i l l be r e q u i r e d t o  the p o i n t , f o r example,tests o f the e f f e c t o f an a p p l i e d  field  such as t h a t r e p o r t e d by S t a e b l e r and Amodei (1972b). Recently, wave theory  Vahey (1975) has presented  o f hologram s t o r a g e  i n LiNbO^.  a nonlinear  coupled-  C l o s e d - form s o l u t i o n s a r e  found t o d e s c r i b e the energy exchange between beams d u r i n g  recording.:.:  The"time development o f the d i f f r a c t i o n e f f i c i e n c y i s a l s o  described.  Using  the concept o f Sec. 2.5.4  (Young e t a l . 1974) which i n v o l v e s the  dependency o f the phase s h i f t between the phase g r a t i n g and the l i g h t i n t e r f e r e n c e p a t t e r n on the d r i f t equations provide  l e n g t h o f e l e c t r o n s , Vahey's  a good d e s c r i p t i o n o f S t a e b l e r et a l . ' ( 1 9 7 2 b )  coupled-  wave experiments.  2.6 The Bulk P h o t o v o l t a i c  Effect  G l a s s , von der L i n d e and Negran(l974b, 1975a) have proposed t h a t the p h o t o r e f r a c t i v e e f f e c t i s caused by an e n t i r e l y new t r a n s p o r t mechanism which they have l a b e l l e d  the "bulk p h o t o v o l t a i c  effect".  27  Chynoweth (1956) and Chen (1969) observed  that photocurrents  would f l o w i n BaTiO^ and LiNbO^ r e s p e c t i v e l y , : . i n the absence o f a p p l i e d fields. due  In both cases the e f f e c t was  to space charge e f f e c t s .  accounted  f o r by i n t e r n a l  G l a s s e t al.(1974b)  fields  stated that a f t e r  20  hours of c o n t i n u o u s i l l u m i n a t i o n , the ;photocutrents which they measured remained  constant.  The p h o t o c o n d u c t i v i t y would r e l a x any  internal  f i e l d s and a decay o f the p h o t o c u r r e n t would be n o t i c e a b l e . _ o b s e r v a t i o n s of the p h o t o c u r r e n t a r e p r e s e n t e d i n Chapter have used account  Experimental  7.  Glass et a l .  the b u l k p h o t o v o l t a i c e f f e c t r a t h e r than i n t e r n a l f i e l d s to  f o r the p h o t o c u r r e n t .  phenomenon  perhaps'  A l t h o u g h the p h y s i c s of t h i s  have not been f u l l y  G l a s s et a l . a r e j u s t i f i e d  new  e s t a b l i s h e d , i t appears  that  i n proposing that i t e x i s t s .  G l a s s , von der L i n d e and Negran have p o s t u l a t e d t h a t e l e c t r o n s c o n t r i b u t i n g to the p h o t o c u r r e n t and i n asymmetric p o t e n t i a l w e l l s  (Fe  the p h o t o r e f r a c t i v e p r o c e s s  2+  ions)  reside  Upon e x c i t a t i o n , t h e r e i s  a g r e a t e r p r o b a b i l i t y t h a t they w i l l move i n one d i r e c t i o n than  another.  2+ They account  f o r t h i s phenomenon by assuming t h a t the Nb-Fe  i n the ±c-direction a r e d i f f e r e n t .  distances  The asymmetry a t a l l the d e f e c t s has  the same e f f e c t and t h e r e i s a net e l e c t r o n i c c u r r e n t  F o l l o w i n g the  e x c i t a t i o n of the e l e c t r o n , the i o n i z e d i m p u r i t y i s d i s p l a c e d a l o n g the p o l a r a x i s of  the c r y s t a l due  to Franck-Condon r e l a x a t i o n .  g i v e s r i s e to a displacement c u r r e n t  This  A f t e r a c e r t a i n time  the  e l e c t r o n i c momentum w i l l become random and no l o n g e r c o n t r i b u t e to the current u n t i l recombination. b i n a t i o n p r o c e s s may  G l a s s e t a l . a l s o suggest  be asymmetric.  t h a t the recom-  The p r o b a b i l i t i e s of  recombination  from e l e c t r o n s approaching a t r a p from the ±c-direction a r e d i f f e r e n t a net recombination current J  arises.  and  A f t e r r e c o m b i n a t i o n the i m p u r i t y  28  moves back t o i t s o r i g i n a l p o s i t i o n but t h i s p r o c e s s current  s i n c e the i m p u r i t y and captured  t o t a l steady-state  c o n t r i b u t e s no  e l e c t r o n move t o g e t h e r .  The  c u r r e n t J i s g i v e n by J = J  el 1  + J  - J = Kal e2 r  (2.28)  0  The term K i s  where a i s t h e a b s o r p t i o n and I t h e i n t e n s i t y o f l i g h t . dependent on t h e n a t u r e o f t h e a b s o r p t i o n  centre  (the d i r e c t i o n a l  pro-  b a b i l i t i e s and mean f r e e paths o f e l e c t r o n i c motion on e x c i t a t i o n and r e c o m b i n a t i o n ) and the photon energy.  Even i f t h e n e t e l e c t r o n i c  c u r r e n t c r e a t e d by e x c i t a t i o n and r e c o m b i n a t i o n i s z e r o , t h e r e w i l l be a n e t c u r r e n t due t o t h e i o n i c d i s p l a c e m e n t  ^  n  °P  e n  still  circuit,  the c u r r e n t J w i l l charge the c r y s t a l J = K a l + eyE so t h a t a f i e l d E w i l l be c r e a t e d which w i l l  (2.29) saturate at E  = KcxI/ue. sat  2.7 T r a n s i e n t P h o t o r e f r a c t i v e E f f e c t s In a d d i t i o n t o the p r e v i o u s models which attempt t o e x p l a i n o p t i c a l i n h o m o g e n e i t i e s which p e r s i s t l o n g a f t e r t h e i l l u m i n a t i o n i s removed, G l a s s process  e t a l . (1975a, 1975b) have s t u d i e d a p h o t o r e f r a c t i v e  that p e r s i s t s f o r only a very  t h a t the p r o c e s s  s h o r t time ('vlOysec).  They suggest  i s caused by a v a r i a t i o n i n the p o l a r i z a t i o n .  Thermal  e x c i t a t i o n o f the c r y s t a l r e s u l t s i n a p y r o e l e c t r i c p o l a r i z a t i o n due t o thermal expansion.  O p t i c a l e x c i t a t i o n produces a p o l a r i z a t i o n change due  to a change o f the d i p o l e moment o f the e x c i t e d d e f e c t . produce a displacement c u r r e n t J = d D / d t , where D e  displacement.  processes  i s the e l e c t r o n i c  The l i f e t i m e o f the e f f e c t i s determined by the r e l a x -  a t i o n time o f the e x c i t e d s t a t e . ved  £  These  3+ i n LiNbO, doped w i t h Cr ions  These t r a n s i e n t e f f e c t s have been o b s e r ( G l a s s e t a l . 1975a, 1975b) but n o t  29  i n "undoped" or iron-doped l i t h i u m n i o b a t e .  2.8  Defect  Sites The  p h o t o r e f r a c t i v e e f f e c t i s most e f f i c i e n t when l i g h t of  wavelengths 400  to 5 00nm i s used  i s thought to occur 1973).  As was  ( S e r r e z e and  Goldner 1973).  from t r a p s w i t h i n the 3.72  ev band gap  mentioned i n Chapter 1, b o t h i m p u r i t i e s and  r e l a t e d to the n o n - s t o i c h i o m e t r y  the  Excitation  (Clark et a l . defects  of the c r y s t a l a c t as d e f e c t  P h i l l i p s et a l . (1972) have shown t h a t the gamma i r r a d i a t i o n  sites. (of  un-  s t a t e d energy) of undoped LiNbO^ i n c r e a s e s the p h o t o r e f r a c t i v e sensi-r.. t i v i t y by  i n c r e a s i n g the c o n c e n t r a t i o n  electron traps.  In a d d i t i o n , i m p u r i t y doping w i t h  manganese, copper, rhodium and et a l . 1971,  of l a t t i c e d e f e c t s which a c t  1973;  As was the b e s t dopant.  chromium ( P h i l l i p s et a l . 1972,  Mikami et a l . 1973,  s e n s i t i v i t y of the  (Peterson  iron,  Peterson  G l a s s et al.(l'9 74a) improve ;  the  crystal. pointed  out i n Chapter 1, i r o n has  S t u d i e s of n o m i n a l l y  et a l . 1971,  1973;  so f a r proven to  be  pure l i t h i u m n i o b a t e have r e v e a l e d  the presence of i r o n c o n t a m i n a t i o n of 10 ppm tested  elements such as  as  to 100  Nash 1973).  ppm  i n a l l samples  These i m p u r i t i e s are  thought to be c h i e f l y r e s p o n s i b l e f o r the p h o t o r e f r a c t i v e e f f e c t i n "undoped" l i t h i u m n i o b a t e . have suggested  Peterson  et a l . (1971) and  C l a r k et a l . (1973)  , though not c o n c l u s i v e l y shown, t h a t the i r o n r e p l a c e s a  l i t h i u m i o n i n the c r y s t a l l a t t i c e .  Recently,  suggested t h a t the most l i k e l y s i t e of the Fe  3+  Keune et a l . (1975) have i o n i s the Nb  site,  based on the M o s s b a u e r - e f f e c t study o f i r o n i m p u r i t i e s i n LiNbO^. They were not a b l e to i d e n t i f y the most l i k e l y s i t e f o r the Fe C o n v e r s i o n of i r o n i m p u r i t i e s to the d i v a l e n t s t a t e  2+  ions.  increases  30  the o p t i c a l a b s o r p t i o n in  i n the r e g i o n o f 470 nm w i t h a subsequent  the p h t o t r e f r a c t i v e s e n s i t i v i t y .  1973)  that o p t i c a l absorption  I t has been suggested  increase  (Clark et a l .  causes the i n t e r v a l e n c e t r a n s f e r  of an  2+ 5+ 2+ 3+ e l e c t r o n from a Fe i o n t o a Nb i o n . The Fe i s c o n v e r t e d t o Fe when i t l o s e s an e l e c t r o n .  2+ 5+ A f t e r the Fe -»• Nb  t r a n s f e r , the e l e c t r o n  i s f r e e t o move i n the c o n d u c t i o n band which i s made up o f Nb d o r b i t a l s . 3+ R e t r a p p i n g o c c u r s a t Fe  ions.  As might be expected, t h e p h o t o r e f r a c t i v e s e n s i t i v i t y may be c o n t r o l l e d by t h e o x i d a t i o n s t a t e o f t h e i r o n i m p u r i t i e s . (1968) found t h a t f i e l d  annealing  l i t h i u m niobate  Smith e t a l .  a t 600°C w i t h a c u r r e n t  2 d e n s i t y o f 5 ma/cm crystal.  decreased the p h o t o r e f r a c t i v e s e n s i t i v i t y o f t h e  L a t e r P e t e r s o n e t a l . (1971) showed t h a t simply  a n n e a l i n g the  c r y s t a l i n a i r o r oxygen a t 600°C f o r about 75 hours decreased the induced change about 22 times. undetectable.  The.applied  F i e l d annealing  field  made any induced change;  caused the i r o n i o n s t o m i a g r a t e towards the  negative  electrode.  A yellow-brown d e p o s i t  e v e n t u a l l y appeared on t h e  negative  e l e c t r o d e as i r o n came r i g h t out o f the c r y s t a l .  U s i n g EPR  techniques,  i t was shown t h a t a n n e a l i n g t h e c r y s t a l s i n a i r o r oxygen 3+ c o n v e r t e d about 96% of the i r o n t o Fe ( C l a r k e t a l . 1973). 3+ Methods which c o n v e r t  Fe  2+ t o Fe  c r y s t a l s i n an argon atmosphere and h e a t i n g packed i n a l i t h i u m s a l t The  Li2C0  3  such as L i 2 C 0  treatment i s d i s c u s s e d  3  i n c l u d e h e a t i n g the the c r y s t a l s i n a i r w h i l e  ( P h i l l i p s and S t a e b l e r  i n Chapter 3.  * A d e f i n i t i o n o f i n t e r v a l e n c e t r a n s f e r i s given^iin Sec.  1967).  1974a).  9.3  (Hush  «  31  2.9  Discussion At the p r e s e n t  involved  time, i t i s thought t h a t the charge t r a n s p o r t  i n the p h o t o r e f r a c t i v e e f f e c t may  J = ne E + e D ^ y  The  r e l a t i v e c o n t r i b u t i o n s of the d r i f t ,  terms are u n s e t t l e d .  +  be d e s c r i b e d  Kctl  .  (2.30)  d i f f u s i o n and  These w i l l be d i s c u s s e d  by  bulk  photovoltaic  i n the f o l l o w i n g  three  sections. The  space charge f i e l d  (E  ) . may  be c a l c u l a t e d u s i n g Eqs.  2.4,  sc j 2.6,2.21 and  2.30  and  the change i n the i n d i c e s of r e f r a c t i o n found from 3 n. An.  where r „  i s the a p p r o p r i a t e  appropriate 2.9.1  index of  new  ).  (2.31)  e l e c t r o - o p t i c c o e f f i c i e n t and  n^ i s the  refraction.  Bulk P h o t o v o l t a i c The  = - - j j - r . .(E  term i n Eq.  Effect 2.30  dcoO  i s formally equivalent  c u r r e n t d e n s i t y which would be produced by d r i f t (either b u i l t - i n or applied) provided  i n a constant  t h a t the l i g h t  to  field  i n t e n s i t y d i d not  change a p p r e c i a b l y over d i s t a n c e s comparable to t h a t t r a v e l l e d by e l e c t r o n before  trapping.  t i o n produced by l i g h t  I n t h i s case,  the e x t r a e l e c t r o n  i s gx where g i s the l o c a l r a t e of  generation  ol) and x i s t h e i r l i f e t i m e .  a f i e l d E , the d r i f t  x u  do not process  E . v  I f we  i n f a c t t r a v e l f a r i n the above sense, we by c o n s i d e r i n g a " v i r t u a i ' *  f i e l d s are p r e s e n t , magnitude of E  due  field  With  assume t h a t the may  electrons  a l l o w f o r the  new  to be added on to whatever  to space charge or e x t e r n a l a p p l i c a t i o n .  i s u n c e r t a i n and  an  concentra-  of f r e e e l e c t r o n s ( p r o p o r t i o n a l to current i s e g  the  i s probably  dependent on  various  The  32  p r o p e r t i e s o f the c r y s t a l .  I n one c a s e G l a s s  e t a l . (1974b)  claim  t h a t t h e p h o t o c u r r e n t c o u l d be reduced t o zero w i t h an a p p l i e d 4 o f 6 x 10 V/cm f o r a r a d i a n t /  2 i n t e n s i t y o f 0.32 W/cm d e c r e a s i n g t o  o  3.8 x 10 V/cm f o r 0.08 W/cm .  I n another case ( G l a s s e t a l . 1975a) they  3 1.8 x 10 V/cm was r e q u i r e d  show t h a t 0.32 W/cm  2  field  to cancel the photocurrent f o r  and 1.2 x 1 0 V/cm f o r 0.08 W/cm . 3  2  The e x p e r i m e n t a l d a t a i n 3  Chapter 8 suggests t h a t the " v i r t u a l " f i e l d , i n the c r y s t a l i n v e s t i g a t e d . using only d r i f t  The a n a l y s e s  E , i s a p p r o x i m a t e l y 10 V/cm o f hologram development  and d i f f u s i o n p r e s e n t e d e a r l i e r i n t h i s  chapter  a r e n o t i n v a l i d a t e d by t h e p r e s e n c e o f t h e b u l k p h o t o v o l t a i c The  extent  t o which the p h o t o v o l t a i c  effect i s responsible  p r o c e s s depends on t h e magnitudes o f o t h e r  f i e l d s present.  mental d a t a i n Chapter 8 demonstrates t h i s  point.  It describe  should,  however, be noted t h a t t h e term  Kctl  effect.  f o r the The e x p e r i -  does n o t e x a c t l y  the r e s u l t o f t h e proposed new mechanism when the l i g h t  i n t e n s i t y changes r a p i d l y w i t h d i s t a n c e . a d e l t a function of l i g h t  Thus, t h e impulse r e s p o n s e t o  6(x - a) i n v o l v e s a n e x p o n e n t i a l  tail  associ-  ated w i t h t h e l o s s o f t h e i n i t i a l momentum, i n a d d i t i o n t o t h e e f f e c t s o f d i f f u s i o n and d r i f t which have been d i s c u s s e d the mean d i s t a n c e according  to Glass  involved  i n the i n i t i a l  e t al.(1974b),  previously.  flight  this distance  Although  i s o n l y 0.08 nm, i s too s h o r t  t o be  d i r e c t l y m e a n i n g f u l and must imply t h a t most e x c i t e d e l e c t r o n s do n o t escape from t h e i r t r a p s . able distances  Those t h a t do escape may t r a v e l q u i t e  on t h e s c a l e d e f i n e d by t h e hologram g r a t i n g .  appreci-  33  2.9.2  B u i l t - i n F i e l d of P y r o e l e c t r i c O r i g i n A l t h o u g h a new  t r a n s p o r t mechanism i s b e l i e v e d to be  involved,  the p r e s e n c e of b u i l t - i n f i e l d s of p y r o e l e c t r i c o r i g i n may  also  important i n some c i r c u m s t a n c e s .  2.4  the c r y s t a l s from a h i g h e r f i e l d s on  As was  discussed  i n Sec.  be cooling  temperature w i l l c r e a t e l a r g e f i e l d s .  The  the s u r f a c e s of the c r y s t a l w i l l n o r m a l l y d i s a p p e a r w i t h  passage of time due  to s t r a y charges or l e a k a g e p a t h s .  However,  the  the  f i e l d s a r e so l a r g e t h a t i t seems q u i t e p o s s i b l e t h a t i n j e c t i o n or e x t r a c t i o n of e l e c t r o n s should  s e t up  space charges w i t h i n the  w i t h the r e s u l t t h a t l a r g e f i e l d s a r e s t i l l after applying 2.9.3  an e x t e r n a l  even  short.  discussed  i n Sec.  would r e q u i r e t h a t the t o t a l f i e l d  2.5.5, a d i f f u s i o n - d o m i n a t e d i n the c r y s t a l be  T h i s would i n c l u d e the v i r t u a l f i e l d  due  t o the b u l k  i n Sec.  2.5.5  V/cm.  photovoltaic that  to c l a i m t h a t d i f f u s i o n c u r r e n t s a r e n e g l i g i b l e  compared to p h o t o c u r r e n t s . V/cm  process  l e s s than 100  G l a s s e t ' a l . ( 1 9 7 4 b ) have used an argument s i m i l a r to  discussed  o f 10"*  i n the c r y s t a l  Diffusion As was  effect.  present  crystal  can be produced.  T h e i r e v i d e n c e i s t h a t space charge However, as was  discussed  i n Sec.  fields 2.9.1,  3  the development of space charge f i e l d s l i m i t e d to V/cm  appear p o s s i b l e .  10  3  V/cm  In t h i s c a s e d i f f u s i o n would p l a y a  to 2 x  10  significant  role. Staebler by has  diffusion.  et a l . (1972b,1974a) c l a i m to have s t o r e d  Some of the c o n f u s i o n  a r i s e n because holograms a r e not  o f the c r y s t a l i s p e r p e n d i c u l a r form the hologram.  o v e r the p r e c i s e r o l e o f d i f f u s i o n r e a d i l y s t o r e d when the  t o the p l a n e of the two  E x a m i n a t i o n of  holograms  c-axis  beams used  the e l e c t r o - o p t i c t e n s o r  to  o f LiNbO-  34  i l l u s t r a t e s why The  equation  <~1 n e  holograms may  f o r the o p t i c a l i n d i c a t r i x i s  " 22 2 r  E  +  13 3  r  E  <r 2 n e  +  ±  + where  not be s t o r e d i n t h i s c o n f i g u r a t i o n .  +  2  l  2  33 3  r  (  ) x  E  r  E 5 1  ) x  3  2  +  n  +  ) 2 3 x  2  ^2  +  x  r  22 2 E  +  r  13 3 E  ) x  2 2  o  - 22 l  2 (  +  r  2  (  r  E  51 l E  l 2  ) x  )  X  x  3 l x  =  (2.32)  1  a r e t h e e l e c t r i c f i e l d components i n t h e X j ,  and  x^ d i r e c t i o n s r e s p e c t i v e l y ; n  Q  and n  &  a r e t h e o r d i n a r y and  and  extraordinary  i n d i c e s of r e f r a c t i o n . In the u s u a l c o n f i g u r a t i o n f o r s t o r i n g holograms, the  c-axis  (x^) i s i n the p l a n e of i n c i d e n c e and n o r m a l t o t h e b i s e c t o r o f t h e beams as shown i n F i g . 2 . 5 ( a ) . From Eq. (30.8  3.32  the major e f f e c t s a r e a change i n n  x 10 ^  cm/V).  The  x^ o r x  2  T h i s c r e a t e s an e l e c t r i c f i e l d  cm/V)and a change i n n change i n n  Q  g  Eg.  p r o p o r t i o n a l to  p r o p o r t i o n a l to r ^  Q  two  r ^  (8.6 x 10  o c c u r s whether t h e l i g h t i s p r o p a g a t i n g  ^  i n the  directions. I f the c r y s t a l i s turned  t h r o u g h 90°  so t h a t the c - a x i s i s  n o r m a l t o t h e p l a n e o f i n c i d e n c e , t h e f i e l d component t h a t i s c r e a t e d depends i n w h i c h c r y s t a l d i r e c t i o n t h e l i g h t i s p r o p a g a t i n g . shows t h e case where t h e g r a t i n g v e c t o r p l a n e s of c o n s t a n t creates a f i e l d E 2  cm/V)  w i l l result.  term 2 r ^ j E x x 2  2  3  (the d i r e c t i o n normal to  r e f r a c t i v e index) i s i n the x A change i n n The  Q  2  direction.  p r o p o r t i o n a l to r  o n l y change i n n  g  2  2  £  the  This  (3.4 x  10  w i l l be caused by t h e  which produces a r o t a t i o n of the i n d i c a t r i x .  however has a v e r y s m a l l e f f e c t on n .  F i g . 2.5(b)  cross  This  To r e a d holograms i n t h i s  con-  35  36  f i g u r a t i o n the e l e c t r i c v e c t o r i n the X 2 d i r e c t i o n . for  holograms s t o r e d Fig.  The  of the l i g h t would have to be  e f f i c i e n c y would be about  100  polarized  times l e s s t h a n  i n the c o n f i g u r a t i o n o f F i g . 2 . 5 ( a ) .  2.5(c) shows the c a s e where the g r a t i n g v e c t o r  x^ d i r e c t i o n .  This creates'a  d i r e c t e f f e c t on  either n  a small r o t a t i o n . charge f i e l d has  f i e l d E^.  or n ,  g  Q  I t i s evident the g r e a t e s t  f a c t t h a t holograms a r e not  In t h i s case there  is in i s no  the o n l y change i n i n d i c a t r i x t h a t the E^ component of the  e f f e c t on  being  space  the i n d i c e s o f r e f r a c t i o n .  e a s i l y s t o r e d when the c - a x i s o f the  i s normal to the p l a n e s o f i n c i d e n c e  i s not  d i f f u s i o n as a t r a n s p o r t mechanism.  Amodei (1971b,1972b) has  space charge f i e l d s of  be developed by d i f f u s i o n .  (1969) r e p o r t e d  1500  V/cm  may  a v a l i d argument  (Chen d i d not  t a t i o n except to say t h a t the c - a x i s was  shown t h a t  normal to the p l a n e of  u n a b l e to e x p l a i n why  he c o u l d not  w i t h the c - a x i s normal to the p l a n e of i n c i d e n c e . evidence i s presented by  crystal  against  s p e c i f i c a l l y s t a t e the  A l t h o u g h Amodei b e l i e v e d d i f f u s i o n t o be a v a l i d  mechanism, he was  and  The  Chen  s t o r i n g holograms i n the c o n f i g u r a t i o n o f F i g . 2.5(b) a t  much reduced e f f i c i e n c y .  dence.)  the  effect.  inci-  transport  s t o r e holograms  In Chapter 8 more  to support hologram f o r m a t i o n  the b u l k p h o t o v o l t a i c  orien-  b o t h by d i f f u s i o n  37  CHAPTER 3 ELLIPSOMETRIC PROBE OF THE  3.1  PHOTOREFRACTIVE EFFECT IN LiNbOg  Introduction A u s e f u l method f o r p r o b i n g  the p h o t o r e f r a c t i v e e f f e c t i n  LiNbO^ i n v o l v e s the measurement of the b i r e f r i n g e n c e of a sample a t a r r a y of p o s i t i o n s b e f o r e the i n d i c e s .  and  a f t e r the o p t i c a l l y - i n d u c e d change i n  In t h i s study an e l l i p s o m e t e r was  changepin'-biref riagencen-  used;to measure  ( F i g . 3.1)  the s i g n a l to the d e t e c t o r  n u l l e d by r o t a t i n g the a n a l y s e r  and  p l a t e set a t ±45° azimuth.  changes i n r e l a t i v e phase and  The  p o l a r i z e r with a quarter  o r t h o g o n a l l i n e a r p o l a r i z a t i o n s are o b t a i n e d  detail later in this  the  • -  In e l l i p s o m e t r y  of two  an  as  is  wave amplitude  discussed  in  chapter.  In the adjustable-compensator method used by Chen (1969) and others  (Glass  1972,  Serreze  Babinet compensator and i z e r are c r o s s e d  1973)  ttie f a s t and  the c r y s t a l c o i n c i d e .  at ±45° azimuth and  compensator phase r e t a r d a t i o n .  slow axes of a The  analyser  a n u l l i s obtained  T h i s method does not  Soleil-  and  polar-  by a d j u s t i n g  allow  for  the  dichroism,  w h i l e e l l i p s o m e t r y does. E l l i p s o m e t r y has been used e x t e n s i v e l y f o r the study of f i l m s on s u r f a c e s by r e f l e c t e d l i g h t  (see Appendix G) but  have been a p p l i e d to the present laboratory  (Wong 1973,  Cornish,  problem a p a r t Moharam and  i t does not  from work i n t h i s  Young 1975a).  Automation  i s n e c e s s a r y to r e a l i z e the p o t e n t i a l of the method which would wise be e x c e s s i v e l y l a b o r i o u s .  In our  seem to  other-  system, the instrument i s b a l a n c e d  under computer c o n t r o l on a l i n e or g r i d of p o i n t s b e f o r e  and  after  38  POLARIZER  QWP  CRYSTAL  ANALYSER Pl-DTODETECTOR  -<]  LASER  MOTOR DRIVE CIRCUITS  ENCODER OUTPUT UNIT  INTERFACE  i  I PDP8E  i  VARIABLE GAIN  AMPLIFIER  COMPUTER  I N C R E M E N T A L  i  P L O T T E R  I  TELETYPE  F i g . 3.1 system.  Schematic o f c o m p u t e r - c o n t r o l l e d  ellipsometer  39  exposure t o the l a s e r beam which causes t h e index changes.  The  o p t i c a l p r o p e r t i e s which a r e probed u s i n g e l l i p s o m e t r i c o r a d j u s t a b l e compensator techniques  d i f f e r from those probed u s i n g  holographic  techniques.  From e l l i p s o m e t r i c measurements, the b i r e f r i n g e n c e may be  calculated.  I n holography, changes i n the index f o r a p a r t i c u l a r  p o l a r i z a t i o n a r e observed r a t h e r than the b i r e f r i n g e n c e .  3.2  Theory and O p e r a t i o n The  of the E l l i p s o m e t e r  e l l i p s o m e t e r measures the r a t i o  m i t t i v i t i e s f o r l i g h t with the E-vector r i g h t angles  t o the c - a x i s  (T ) .  along  (p) o f the complex t r a n s the c - a x i s  (T ) and a t  When no m u l t i p l e r e f l e c t i o n s o f l i g h t  occur w i t h i n the sample, p = tanip; exp A = T^/T^  where t .  and t„„ a r e the F r e s n e l t r a n s m i s s i o n c o e f f i c i e n t s f o r the  ITT  2TT  a i r / c r y s t a l and c r y s t a l / a i r i n t e r f a c e s i r - l i g h t , s i m i l a r l y t_  2q  for t ^  and  : . 6 = 2iTdn / A , where d = sample t h i c k n e s s , n = e x t r a o r d i n a r y ' • _TT e o' ^ ' e J  index (as m o d i f i e d and ^ - i s a  similarly  by the e l e c t r o - o p t i c e f f e c t ) , ^ d e f i n e d u s i n g n , the o r d i n a r y Q  L i g h t from a monochromatic, u n p o l a r i z e d  q  = vacuum wavelength; index. source (He-Ne l a s e r  i n t h i s case) i s passed through t h e p o l a r i z e r which produces p o l a r i z e d l i g h t o f azimuth P. plate, e l l i p t i c a l l y two  Q  linearly  A f t e r passage through the q u a r t e r wave  polarized light  i s i n c i d e n t on the sample.  o r t h o g o n a l l y p o l a r i z e d waves, a f t e r p a s s i n g  The  through t h e sample,  s u f f e r a r e l a t i v e phase r e t a r d a t i o n ( A ) and a r e l a t i v e amplitude r e duction  ( t a n ij) ) . For a measurement, the e l l i p s o m e t e r i s b a l a n c e d by v a r y i n g  40  the parameters o f the e l l i p t i c  p o l a r i z a t i o n o f the l i g h t  i n c i d e n t upon :  the -sample u n t i l the t r a n s m i t t e d p o l a r i z a t i o n i s l i n e a r and can be e x t i n guished when t h e a n a l y s e r i s s e t t o azimuth A.  The parameter v a r i a t i o n  i s a c h i e v e d by r o t a t i n g t h e p o l a r i z e r w i t h the q u a r t e r wave p l a t e f i x e d at  ±45° azimuth.  (For a l l measurements i n t h i s t h e s i s , the QWP = -45°.)  T h i s method o f v a r y i n g the e l l i p t i c i t y  o f the l i g h t i s chosen because  the c a l c u l a t i o n o f A and tan\pfrom the e x t i n c t i o n azimuths o f P and A is greatly simplified. The  convention  f o r measuring a n g l e s  i s as f o l l o w s .  F o r the  normal mode o f o p e r a t i o n , t h a t i s f o r measurements made by r e f l e c t i n g light  from t h e sample, the p o l a r i z e r , a n a l y s e r and q u a r t e r wave p l a t e  angles a r e measured from the p l a n e o f i n c i d e n c e . measured c o u n t e r - c l o c k w i s e  when l o o k i n g towards the l i g h t  the:experiments to be d e s c r i b e d i n t h i s c h a p t e r , p o l a r i z e r arm o f the e l l i p s o m e t e r was n o r m a l l y The  P o s i t i v e angles are  the l i g h t  source.  In  from the  i n c i d e n t on the c r y s t a l .  o p t i c a l p r o p e r t i e s o f the c r y s t a l were probed by t r a n s m i t t i n g l i g h t  through the c r y s t a l r a t h e r than r e f l e c t i n g l i g h t from i t s s u r f a c e . The  c - a x i s o f the c r y s t a l was a l i g n e d t o be p e r p e n d i c u l a r t o t h e n o r m a l l y  i n c i d e n t beam and a t zero In d e t e r m i n i n g and A i t i s convenient  azimuth. the r e l a t i o n s h i p s between A and P, and t a n ^  to f o l l o w the path o f the l i g h t which i s i n c i d e n t  on the p o l a r i z e r through t o the a n a l y s e r u s i n g t h e Jones v e c t o r s and matrices(Shurcliff  1962).  The p o l a r i z e r i n i t i a l l y i s a t azimuth P and  the f a s t a x i s o f the q u a r t e r wave plate(QWP) i s a t Q. R e f e r r i n g to Fig.  3.2, the l i g h t  from the p o l a r i z e r , r e s o l v e d i n the d i r e c t i o n s o f  the f a s t and slow axes o f t h e QWP Jones v e c t o r  can be r e p r e s e n t e d  by t h e n o r m a l i z e d  41  cos(P -  Q)  sin(P -  Q)  (3.2)  X-  F i g . 3.2 F a s t a x i s of the QWP ( F ) ; slow a x i s of the QWP ( S ) ; o p t i c a x i s of the c r y s t a l (X); azimuth of the p o l a r i z e r ( P ) .  The  r a t i o of the complex t r a n s m i t t i v i t i e s of the QWP  may  be  written  as p  c  = T  c  exp(-iA  c  )  = T (cosA -isinA ) c c c where T  c  (3.3)  i s the r a t i o of the t r a n s m i t t a n c e a l o n g the f a s t a x i s to t h a t  a l o n g the slow a x i s and Jones m a t r i x i s  i s the r e l a t i v e phase r e t a r d a t i o n .  The  42  1  0 (3.4)  0  P,  To r o t a t e the c o o r d i n a t e a x i s of the l i g h t axes of the QWP  from the f a s t and  slow  to axes p a r a l l e l to the c r y s t a l ' s o p t i c a x i s and  p e r p e n d i c u l a r to t h i s a x i s , the c o u n t e r - r o t a t o r m a t r i x cos Q  -sin Q  sin Q  cos Q  (3.5)  i s used.  The  represented  sample i s simply another  i n a manner s i m i l a r to the QWP, p  and  b i r e f r i n g e n t p l a t e and  = T  s  s  e x p ( i A )= T (cosA s s s r  can  be  so t h a t + i.sinA ) s  (3.6)  the Jones m a t r i x i s g i v e n by  1 (3.7)  0 The  s t a t e of p o l a r i z a t i o n of the l i g h t a f t e r p a s s i n g through  the sample  i s g i v e n by r  1  0  0  a  1  0  cos(P-Q) sin(P-Q)  cosQcos(P-Q) - s i n Q g  sin(P-Q)  (3.8) p {sinQ s  cos(P-Q) +p  c  cos Q  sin(P-Q)}  For t h i s l i g h t to be e x t i n g u i s h e d by the a n a l y z e r i t must be p o l a r i z e d w i t h an azimuth e, g i v e n by  tan e =  p { s i n Q c o s ( P - Q ) + p cos Q _s c cosQcos(P-Q) - p s i n Q c  sin(P-Q)} sin(P-Q)  linearly  43  p {tan Q  = —  1 - p  c  + p  °-  tanQ  tan(P-Q)}  .  (3.9)  tan(P-Q)  The a n a l y s e r must be 90° from e to e x t i n q u i s h the l i g h t , so t h a t  tan A = N  — - — tan e p t a n Q tan(P-Q) - 1 -£ p {tan Q + p  .  (3.10)  tan(P-Q)} = 1), with Q = 45°, p  Assuming a p e r f e c t q u a r t e r wave p l a t e ( T c and  Eq. 3.10 can be s o l v e d f o r p  t a n Q = -1.  n p  =  g  to g i v e  1 - i tan(P+45°) p t a n A [ l + i tan(P+45  S u b s t i t u t i n g Eq. 3.6 and e q u a t i n g • and  A T  g  s  = + 1/tan A  —=. .  (3.11)  )J  r e a l and imaginary  = -2P - 90° ± nn,  =- i c  parts  n = 0,1,2,...  .  yields (3.12) (3.13)  Thus the p o l a r i z e r r e a d i n g i s p r o p o r t i o n a l to the phase change and the tangent of the a n a l y s e r r e a d i n g i s p r o p o r t i o n a l to the i n v e r s e o f the t r a n s m i t t a n c e  ratio.  The r e l a t i o n between the phase change^ and the  b i r e f r i n g e n c e of the c r y s t a l i s A s T  s  =  2jrd (n -n ) . 7 — e o  (3.14)  —  A  i s r e l a t e d to the r a t i o of the a b s o r p t i o n c o e f f i c i e n t s a l o n g the  f a s t and slow axes of the c r y s t a l . For c o n s t a n t  t h i c k n e s s , a change i n  P i n d i c a t e s a change i n b i r e f r i n g e n c e and a change i n A i n d i c a t e s a change i n the r a t i o of the two a b s o r p t i o n c o e f i c i e n t s a l o n g principal directions.  the two  44  3.3  S e n s i t i v i t y of the U s i n g Eqs.  Ellipsometer  3.12  and  3.14  the s e n s i t i v i t y of the  to changes i n b i r e f r i n g e n c e can e a s i l y be computed. tial  p o l a r i z e r reading  and  P^  the r e a d i n g  I f P^  ellipsometer i s the  ini-  a f t e r a change i n b i r e f r i n g e n c e  A(n -n ) , then e o  A (  The  v o>  =  n  s e n s i t i v i t y of the p o l a r i z e r (and  (  -  3  analyser)  reading  1  is  5  )  0.01°  _g c o r r e s p o n d i n g to a change of 3.5 thick  x 10  i n b i r e f r i n g e n c e f o r a 1.0  mm  crystal. However, the r e s o l u t i o n of the measurements i s l i m i t e d by  temperature dependence of the r e f r a c t i v e i n d i c e s . temperature, the change i n the b i r e f r i n g e n c e  the  For a 1°C change i n  (at X = .650  nm)  is  -4 ^0.5  x 10  (Boyd et a l . 1967).  For a 1.0  mm  thick crystal this  corre-  sponds to 13° change i n the p o l a r i z e r . E r r o r s may and  a r i s e i n e l l i p s o m e t r y due  imperfect^alignment  of the i n s t r u m e n t .  n e g l i g i b l e compared to the u n c e r t a i n t y in 3.4  Automated The  introduced  e l l i p s o m e t e r was  voltage pin  source).  small f l u c t u a t i o n s  F.)  8/E)  a Rudolph type 43603-200E, m o d i f i e d  as i n d i c a t e d i n F i g . 3.1.  1 raw He-Ne l a s e r (model 133,unpolarized) was d e t e c t o r was  by  Ellipsometer  computer c o n t r o l (PDP  The  components  These e r r o r s however, are  the temperature of the c r y s t a l . ( S e e Appendix The  to i m p e r f e c t  a photomultiplier I t was  (RCA  used as a l i g h t  of the a n a l y s e r  a 632.8 nm  Physics  source.  8645 tube w i t h a Kepco  mounted on the end  h o l e , a ground g l a s s d i f f u s e r and  A Spectra  for  arm  interference  regulated with a filter  45  (10 nm band pass) used a t i n g the d e t e c t o r . room l i g h t i n g .  to r e s t r i c t  T h i s allowed  The Rudolph 546.1  s p u r i o u s l i g h t s i g n a l s from the instrument nm  on the Rudolph graduated 632.8  c i r c l e and  to be used w i t h normal  q u a r t e r wave p l a t e was  w i t h a q u a r t z S o l e i l - B a b i n e t compensator  illumin-  replaced  (Gaertner model L-135) mounted  s e t f o r q u a r t e r wave r e t a r d a t i o n a t  nm. The p o l a r i z e r and a n a l y s e r were d r i v e n through a n t i - b a c k l a s h  gears by s t e p p i n g motors (IMC Magnetics a b s o l u t e s h a f t encoders  ( D e c i t r a k TR 511-CW/D) to read the a n g l e s .  s e n s i t i v i t y of the s h a f t encoders was Balances reproduced  Corp. #PIN 008-008) w i t h  0.01  which was  w i t h l i t t l e more s c a t t e r .  The  The  one motor s t e p .  encoder output  unit  c o n v e r t e d the a n g l e s t o b i n a r y - c o d e d d e c i m a l f o r i n p u t t o the computer v i a the i n t e r f a c e .  The  i n t e r f a c e was  D i g i t a l Equipment Corp. components. through  the i n t e r f a c e .  The  The motor d r i v e s were c o n t r o l l e d  e r r o r s i g n a l from the d e t e c t o r was  by a v a r i a b l e g a i n a m p l i f i e r and an  c o n s t r u c t e d mostly of standard  i n t e r f a c e d w i t h the computer  a n a l o g - t o - d i g i t a l c o n v e r t e r (DEC A811,  analog e r r o r s i g n a l was  a c c u r a c y of 0.1%  amplified through  F.S.).  The  d i s p l a y e d on a meter to a l l o w manual n u l l i n g of  the e l l i p s o m e t e r . A second  s e t of s t e p p i n g motors was  used  about i n a p l a n e p e r p e n d i c u l a r to the p o l a r i z e r arm A n t i - b a c k l a s h gears between the motor and be moved i n 0.8  um  to move the  crystal  of the e l l i p s o m e t e r .  stage allowed the sample to  steps, i f desired.  Programs and d a t a were s t o r e d on a d u a l Dectape u n i t . incremental p l o t e r  (Houston model DP-10) allowed g r a p h i c a l o u t p u t .  programs to c o n t r o l the system were w r i t t e n i n a combination and  assembly language and are l i s t e d  i n Appendix H.  An The  of F o r t r a n  46  The b a l a n c e procedure used was based on the p r i n c i p l e t h a t the l i g h t a t the d e t e c t o r v a r i e s s y m m e t r i c a l l y f o r s m a l l e x c u r s i o n s o f the p o l a r i z e r and a n a l y s e r from t h e i r b a l a n c e p o s i t i o n s p o l a r i z e r was b a l a n c e d f i r s t  and then the a n a l y s e r .  at  scatter.  each b a l a n c e  to  reduce-  The  (Archer 1962) .  The  T h i s was r e p e a t e d  computer  determines  which way i t must d r i v e the p o l a r i z e r t o reduce t h e e r r o r s i g n a l and i t d r i v e s the motor u n t i l the e r r o r s i g n a l goes through t h e minimum. It  then sums a number o f r e a d i n g s ( u s u a l l y 12) a f t e r each s t e p and then  r e v e r s e s , d r i v i n g t h e motor through the p o s i t i o n o f minimum s i g n a l .  It  then takes a r u n n i n g sum o f r e a d i n g s on the p r e s e n t s i d e o f t h e minimum, adding one and d r o p p i n g the t w e l f t h p r e v i o u s r e a d i n g , u n t i l t h i s sum e q u a l s the sum taken on the o t h e r s i d e o f the minimum. point  The b a l a n c e  (the mid p o i n t between the sums) i s c a l c u l a t e d and t h e p o l a r i z e r  driven to that p o i n t .  T h e . a n a l y s e r i s then b a l a n c e d i n t h e same manner.  T h i s e n t i r e procedure i s completed  a second  time and then t h e a n a l y s e r  and p o l a r i z e r r e a d i n g s , as g i v e n by t h e s h a f t encoders, a r e s t o r e d . To measure the b i r e f r i n g e n c e a l o n g , f o r i n s t a n c e , t h e c - a x i s of  t h e c r y s t a l , t h e e l l i p s o m e t e r i s b a l a n c e d and then t h e c r y s t a l i s  moved a s m a l l d i s t a n c e p e r p e n d i c u l a r t o t h e p r o b i n g beam.  T h i s proced-  ure i s f o l l o w e d r e p e a t e d l y and a f t e r each e l l i p s o m e t e r b a l a n c e , the a n a l y s e r reading,, p o l a r i z e r r e a d i n g and c r y s t a l p o s i t i o n a r e s t o r e d i n the computer memory.  When the memory b u f f e r i s f i l l e d  t r a n s f e r e d t o t h e magnetic pletion.  tape u n i t and the p r o c e s s c o n t i n u e s to com-  D u r i n g the scan the p o l a r i z e r r e a d i n g may be p l o t t e d .  the scan, the d a t a s t o r e d on t h e magnetic plotted.  the data i s  After  tape may be p r o c e s s e d and  47  3.5  Sample Alignment The c r y s t a l s were a l i g n e d u s i n g the He-Ne l a s e r of the  ometer.  The c r y s t a l s were s u p p l i e d  (see Appendix D) w i t h the edges of  the r e c t a n g u l a r c r y s t a l s p a r a l l e l to the c r y s t a l axes. the c r y s t a l was  ellips-  The c - a x i s o f  a l i g n e d to zero azimuth by a d j u s t i n g the c r y s t a l  to make the a p p r o p r i a t e edge p a r a l l e l to the l a s e r beam.  tilt  To a d j u s t the  a n g l e of i n c i d e n c e of the l a s e r beam to 90°, the c r y s t a l was a d j u s t e d to cause the beam to be r e f l e c t e d back on i t s e l f .  The c r y s t a l was  then  s l i g h t l y m i s a l i g n e d so t h a t the r e f l e c t e d beam would not e n t e r the p i n h o l e of the q u a r t e r wave p l a t e .  T h i s prevented the p o s s i b i l i t y of  problems due to m u l t i p l e r e f l e c t i o n s between the sample and the q u a r t e r wave p l a t e  3.6  (Oldham  Temperature  1967).  C o n t r o l f o r E l l i p s o m e t e r Measurements  As was mentioned  p r e v i o u s l y , t h e r m o s t a t i n g the c r y s t a l i s  n e c e s s a r y f o r measurements made on the e l l i p s o m e t e r . ' F i g . 3.3 schematic of the apparatus used. ated p l a s t i c box.  The c r y s t a l was  shows a  e n c l o s e d i n an  insul-  A f a n and a p r o p o r t i o n a l temperature c o n t r o l l e r  (YSI  model 72) w i t h a t h e r m i s t e r d e t e c t o r and a f i n e w i r e h e a t e r were used to m a i n t a i n the temperature to w i t h i n ±0.02°C.  No windows were used, the  e l l i p s o m e t e r arms p r o j e c t i n g through h o l e s i n the box. A thermometer (HP model 2802A) was  digital  used to measure the a b s o l u t e temp-  e r a t u r e to a p p r o x i m a t e l y ±0.05°C, and another t h e r m i s t e r  i n a bridge  c i r c u i t was  used t o measure v a r i a t i o n s i n temperature w i t h a  of 0.01°C.  The temperature was m a i n t a i n e d a few degrees above room  temperature  (approximately 29°C).  temperature s t a b i l i t y a c h i e v e d .  F i g . 3.4  sensitivity  g i v e s an i n d i c a t i o n o f the  S i n c e most of the s c a t t e r i n e l l i p s o -  48  iPOLARIZER \ ARM  - SAMPLE THERMISTER  HEATER  INSULATED BOX  FAN PROPORTIONAL TEMPERATURE CONTROLLER  F i g . 3.3 Schematic o f t h e a p p a r a t u s used t o t h e r m o s t a t t h e l i t h i u m n i o b a t e c r y s t a l s d u r i n g e l l i p s o m e t e r measurements.  0.06 0.04 <  0.02 0  0  16 TIME  24  32  40  48  / minutes  F i g . 3.4 T y p i c a l measurement o f t h e temperature s t a b i l i t y i n s i d e t h e i n s u l a t e d box. The temperature was m o n i t o r e d w i t h t h e t h e r m i s t e r b r i d g e circuit.  49  meter r e a d i n g s  was  due  to temperature f l u c t u a t i o n s , b e t t e r c o n t r o l would  extend the s e n s i t i v i t y of the i n s t r u m e n t . adequate f o r the p r e s e n t control increases  purpose.  The  However the setup  e f f e c t i v e n e s s of  i f the o p t i c a l p a t h l e n g t h . i s  was  temperature  reduced so t h a t t h i n  c r y s t a l s are more s u i t a b l e f o r t h i s type of experiment. F i g . 3.5  shows the e f f e c t of r e p e a t e d l y  someter w i t h the LiNbO^ c r y s t a l the temperature s l o w l y F i g . 3.6 The  t h i c k ) f i x e d a t one  changed from 28.0  C to 24.0  The  the  p o s i t i o n , while  i s t y p i c a l of the s c a t t e r i n the p o l a r i z e r  the c - a x i s of a c r y s t a l  (3 mm  f o r two  readings. repeated  thick).  E f f e c t s of M u l t i p l e I n t e r n a l R e f l e c t i o n s  3.7.1  The  E f f e c t on the Measurement of the  Birefringence  When m u l t i p l e r e f l e c t i o n s of the l i g h t occur between surfaces  ellip-  C.  p o i n t s are the d i f f e r e n c e i n the p o l a r i z e r r e a d i n g s  scans a l o n g  3.7  (3mm  balancing  of the c r y s t a l ,  the r e l a t i o n s of the e l l i p s o m e t r y  to the o p t i c a l p r o p e r t i e s of the c r y s t a l are not as p r e v i o u s l y shown.  readings  straightforward  I f the l i g h t source employed i s a ' l a s e r ,  coherence l e n g t h w i l l g e n e r a l l y be t h e r e f o r e always l o n g e r (which are <_1 cm) .  as  longer  than the t h i c k n e s s  In c o n s i d e r i n g  the  than a few  the  centimeters  and  of the c r y s t a l s examined  the passage of an o p t i c a l wave  through a c r y s t a l , both the amplitude and  phase must be accounted f o r .  Because a p o r t i o n of the wave w i l l be r e f l e c t e d each time i t i s i n c i d e n t on a boundary, many waves w i l l be p r e s e n t travelling  i n a d i r e c t i o n other  Constructive  and  w i t h i n the sample, h a l f  than t h a t of the' i n c i d e n t l i g h t wave.  d e s t r u c t i v e interference w i l l occur.  i s analogous to the t r a n s m i s s i o n  of l i g h t  The  situation  through t h i n s o l i d  films  50  260 r  215 (•  170 ^ 28  26  24  TEMPERATURE / °C  F i g . 3.5 The e f f e c t o f temperature on t h e p o l a r i z e r r e a d i n g when measu r i n g the b i r e f r i n g e n c e i n a 3 mm t h i c k c r y s t a l o f LiNbO^.  +lr  60 01  •a  ••• . *  o  •  • • •• •.• *  • • • • »  <  -1  1 0.5  I  DISTANCE ALONG C  1  2.0  2.5  AXIS / mm  F i g . 3.6 The d i f f e r e n c e i n t h e p o l a r i z e r r e a d i n g s o f two scans a l o n g t h e c - a x i s showing t h e s c a t t e r i n the r e a d i n g s .  51  (Heavens 1955). For holds.  t h e case where t h e r e a r e no m u l t i p l e r e f l e c t i o n s , Eq. 3.1  However, when m u l t i p l e r e f l e c t i o n s a r e c o n s i d e r e d t h e e x p r e s -  s i o n s f o r t h e t r a n s m i t t i v i t i e s , Trr and To, a r e o f t h e form V2  e  *P(-^>  T = 1 - r,  (  3  A  6  )  exp (-216)  S u b s t i t u t i n g t h e s e i n Eq. 3.1, t h e r e s u l t o b t a i n e d i s A (1 - r P  2  exp(-2i<5 )) a  (3.17)  =  (1 - r ^  2  exp(-2io^))  where A i s t h e v a l u e p would have i f m u l t i p l e r e f l e c t i o n s a r e absent. r  and r  a  are Fresnel r e f l e c t i o n c o e f f i c i e n t s .  Here  From t h i s f o r m u l a , i t  TT  f o l l o w s t h a t t h e observed A and t h e r e l a t i v e phase change (6^ -<5 ) a  are r e l a t e d t h r o u g h t a n A= B t a n ( 6 ;  7r  -S ),  (3.18)  a  where 1 - R R  + (R  -R ) s i n ( 6  + <5„)/sin(6 -- 6-i.)  1 + R R  - (R  + R ) cos(6  n  B = air  and  R  a  = r  2  a  were a b s e n t .  , R  IT  = r  TT  a  2  .  T  7  .  7  n  +<5 )/cos(6 r  ir  0  rT  -  &)  "  Here B would be u n i t y i f m u l t i p l e  v  reflections  The importance o f m u l t i p l e r e f l e c t i o n s does n o t seem t o  have been noted when u s i n g t h i s method method).  a  ( o r the a d j u s t a b l e - c o m p e n s a t o r  U s i n g these methods, d a t a t h a t has been p r e v i o u s l y p u b l i s h e d  may be i n e r r o r t o some e x t e n t (Chen 1969, S e r r e z e e t a l . 1973, G l a s s e t al.  1972, G l a s s e t a l . 1 9 7 4 b , Wong 1973).  F i g . 3.7 shows t h e change i n  A ( v e r t i c a l s c a l e ) as a f u n c t i o n o f change i n b i r e f r i n g e n c e and a l s o of t h i c k n e s s f o r assumed v a l u e s o f t h e v a r i o u s parameters. and  n  g  (Here n^  were assumed t o have changed due t o a space c h a r g e f i e l d ,  with  F i g . 3.7 C a l c u l a t e d change i n A ( v e r t i c a l ) as a f u n c t i o n o f (a) change i n b i r e f r i n g e n c e A(n -n ) ( c a l c u l a t e d a p p r o p r i a t e to e l e c t r o - o p t i c e f f e c t w i t h f i e l d as shown) and (b) t h i c k n e s s . Probe wavelength = 632.8nm. e  53  the n u m e r i c a l v a l u e s of the e l e c t r o - o p t i c c o e f f i c i e n t s from Turner ( 1 9 6 6 ) b e i n g used.) For the range shown, the change i n A i s n e a r l y  proportional  to the change i n the b i r e f r i n g e n c e , but the s e n s i t i v i t y depends on the o p t i c a l thickness  of the c r y s t a l .  3.7.2 The E f f e c t o f M u l t i p l e I n t e r n a l R e f l e c t i o n s on the Photorefractive  Process  The p h o t o r e f r a c t i v e p r o c e s s i n l i t h i u m n i o b a t e depends on the i n t e n s i t y o f the i l l u m i n a t i o n and, i n the i n i t i a l cess,  the r e l a t i o n s h i p i s b e l i e v e d  s t a g e o f the p r o -  to be l i n e a r . I n s i g h t  i n t o the  e f f e c t of m u l t i p l e r e f l e c t i o n s can be gained by c o n s i d e r i n g  the simple  case o f a p l a n e , u n i f o r m l i g h t wave n o r m a l l y i n c i d e n t on the c r y s t a l . In the absence o f m u l t i p l e r e f l e c t i o n s the i n t e n s i t y w i l l be u n i f o r m throughout  the c r y s t a l  the amplitude  (no a b s o r p t i o n ) . With m u l t i p l e  f ( z ) of the e l e c t r i c  field  reflections,  as a f u n c t i o n of d i s t a n c e  z  i n t o the c r y s t a l may be o b t a i n e d by summing beams. R e f e r r i n g to F i g . 3 . 8 the sum of the beams a t a d i s t a n c e  z i n t o the sample i s  f ( z ) = t ^ exp(-i27rnz/;y) + t j t ^ exp(-i2irn(2d - z)/X) + tjr T h i s i s a geometric  r  ' exp(-i2Trn(2d + z)/X) •+ . . .  s e r i e s w i t h a sum  t , e x p ( - i z 6 / d ) ( 1 + r e x p ( - 2 i ( l - z/d)6) f (z) = _2 1 - r where air  T  2  =  r  \  =  r  »  (3.19)  t  n  e  F  r  e  s  n  e  l  2  (3.20)  exp(-216)  r e f l e c t i o n c o e f f i c i e n t o f the c r y s t a l /  i n t e r f a c e and 6 = 2Trnd/A f o r normal  incidence.  54  F i g . 3.8  Multiple  reflections  i n a dielectric  slab.  E f f e c t i v e l y , a s t a n d i n g wave i s s e t up between t h e c r y s t a l and  the amplitude o f t h e wave v a r i e s  periodically  surfaces,  through the c r y s t a l .  I f the c r y s t a l t h i c k n e s s i s changed s l i g h t l y , t h e r e l a t i v e phase o f the waves launched a f t e r r e f l e c t i o n w i l l be d i f f e r e n t , of  the forward t r a v e l l i n g and backward t r a v e l l i n g waves w i l l be  I f the mean i n t e n s i t y it  and the i n t e r f e r e n c e  i s found t o v a r y  altered.  o f the l i g h t w i t h i n the sample i s c a l c u l a t e d , p e r i o d i c a l l y w i t h sample t h i c k n e s s as shown i n  F i g . 3.9. Because n  e  and n„ a r e not e q u a l , d i f f e r e n t mean 0  w i t h i n the c r y s t a l w i l l r e s u l t same i n c i d e n t  3.8  f o r TT and o p o l a r i z e d  intensities  l i g h t f o r the  intensity.  B i r e f r i n g e n c e Measurements A l o n g the c - a x i s of the C r y s t a l In i n i t i a l l y p r o b i n g t h e c r y s t a l s a l o n g t h e c - a x i s i t was  found t h a t the p o l a r i z e r  reading varied  considerably. Figs.  3.10 and  3.11 show scans a l o n g two undoped LiNbO^ c r y s t a l s and F i g . 3.12 shows a scan a l o n g an Fe-doped (0.015 mole%) c r y s t a l . C o n s i d e r i n g F i g . 3.11, i t would appear t h a t e i t h e r t h e  55  N  F i g . 3.9 V a r i a t i o n w i t h t h i c k n e s s i n t h e mean i n t e n s i t y o f l i g h t , due t o m u l t i p l e r e f l e c t i o n s . The i n c i d e n t beam i s o f u n i t i n t e n s i t y , d = t h i c k n e s s , d = 1 mm and X = 441.6 nm.  56  '210T  170  0  2  DISTANCE ALONG  C - AXIS  (mm)  F i g . 3.10 The v a r i a t i o n i n the p o l a r i z e r r e a d i n g a l o n g t h e c - a x i s o f the undoped c r y s t a l #5 (see Appendix D ) .  110  DISTANCE ALONG  C - AXIS  (mm)  F i g . 3.11 V a r i a t i o n i n the p o l a r i z e r (P) and a n a l y s e r (A) r e a d i n g s a l o n g the c - a x i s o f the undoped c r y s t a l #4 (see Appendix D ) .  58  n o  r  100  60 £90  80  70  6  0  0 DISTANCE ALONG  t 2 C - AXIS  L (mm)  F i g . 3.12 V a r i a t i o n i n t h e p o l a r i z e r r e a d i n g a l o n g the c - a x i s o f t h e Fe-doped c r y s t a l #2 (see Appendix D ) .  59  b i r e f r i n g e n c e or the t h i c k n e s s a r e v a r y i n g p e r i o d i c a l l y a l o n g ( v a r i a t i o n i n P) and (variation i n A). the data  a l s o t h a t the d i c h r o i s m . i s v a r y i n g  can be  g r a d i e n t i n t h i c k n e s s and constant.  c-axis  periodically  However, when m u l t i p l e r e f l e c t i o n s a r e allowed  i n F i g . 3.11  remaining  the  f i t t e d , u s i n g Eq.  3.17,  assuming a  for simple  e x t r a o r d i n a r y index, w i t h the o r d i n a r y  T h i s i s shown i n F i g . 3.13.  The  index  gradient i n t h i c k -  ness i s w i t h i n the t o l e r a n c e s of the o p t i c a l p o l i s h i n g ( s i d e s p a r a l l e l to 10 a r c seconds) and  the g r a d i e n t i n n^ c o u l d have been caused by  g r a d i e n t i n the n o n - s t o i c h i o m e t r y melt.  p u l l e d from  I t i s b e l i e v e d t h a t n^ i s dependant on the Li20:Nb20^ r a t i o  t h a t n^  3.9  of the sample as i t was  i s not  a the  but  (Bergman e t a l . 1968).  O p t i c a l l y - I n d u c e d B i r e f r i n g e n c e Change due  to a One-Dimensional  G a u s s i a n Beam 3.9.1  Introduction Wong (1973) has  shown t h a t c o n s i d e r a b l e s i m p l i f i c a t i o n  of  the a n a l y s i s of the o p t i c a l l y - i n d u c e d index change i s achieved when the problem i s made s p a t i a l l y one-dimensional, and  exposure i s m i n i -  mized to reduce s a t u r a t i o n e f f e c t s . To  i n v e s t i g a t e the p h o t o r e f r a c t i v e e f f e c t , c r y s t a l s were  i r r a d i a t e d w i t h a narrow s t r i p of l i g h t from a He-Cd l a s e r t h a t spanned the c r y s t a l as shown i n F i g . 3.14. l a s e r beam was  reduced w i t h two  The  curve  diameter of  microscope o b j e c t i v e s and  w i t h a c y l i n d r i c a l l e n s to g i v e a g a u s s i a n as shown i n F i g . 3.15.  The  p r o f i l e along  i n F i g . 3.15  Gamma S c i e n t i f i c Model 2900 scanning  was  (X = 441.6nm)  then expanded the c - a x i s ,  measured w i t h  auto-photometer.  the  a  60  1051  DISTANCE  ALONG  C - AXIS  (m m )  F i g . 3.13 The c i r c l e s a r e the p o l a r i z e r r e a d i n g s shown i n F i g . 3.11 The s o l i d curve was c a l c u l a t e d w i t h the f o l l o w i n g assumed parameter^: t h i c k n e s s = 1.00 mm + 1.92 wavelengths/cm,,n = 2.20657 + 3.75 x l O /cm, n  o  = 2.29058.  6  61  F i g . 3.15 P r o f i l e o f the l i g h t i n t e n s i t y a l o n g the c - a x i s o f t h e c r y s t a l f o r the method o f i l l u m i n a t i o n shown i n F i g . 3.14.  62  3.9.2  Theoretical The  Considerations  shape of the expected b i r e f r i n g e n c e can be  determined  m a t h e m a t i c a l l y f o r a s i m p l i f i e d model. As w i l l be shown, the e l l i p s o meter can be used to d i f f e r e n t i a t e between induced index changes to a d r i f t dominated p r o c e s s and migration  due  a d i f f u s i o n dominated p r o c e s s .  The  l e n g t h of the e x c i t e d e l e c t r o n s can be measured i f i t i s  long enough to be r e s o l v e d by  the  instrument.  For the l i n e a r i z e d model where the space charge f i e l d i s s m a l l compared to the t o t a l f i e l d pancy i s c o n s i d e r e d  i n the c r y s t a l and  to be only s l i g h t l y p e r t u r b e d ,  the t r a p occu-  the r a t e of genera-  t i o n of e l e c t r o n s i s p r o p o r t i o n a l to the l i g h t i n t e n s i t y ,  and  of c a p t u r e of e l e c t r o n s i s p r o p o r t i o n a l to the f r e e e l e c t r o n t i o n . T h i s i s analogous to the case d i s c u s s e d the s p a t i a l v a r i a t i o n sinusoidal.  The  of the l i g h t i n t e n s i t y  £  -  i f a  i s gaussian rather  c u r r e n t due  (3.21) (3.22)  (3.23)  9x  ~  _  ( 3  R  t o the p h o t o v o l t a i c e f f e c t i s f o r m a l l y i n an e l e c t r i c f i e l d ,  T h i s e f f e c t i s i n c l u d e d as p a r t of EQ.  the d r i f t - o n l y case, the space charge f i e l d E  sc (x)  2 4  )  e  v a l e n t to what would be produced by d r i f t i n Chapter 2.  are  £. = 11  sc 9x 9 E  than  g(light) - 0  +  "dt  discussed  i n Chapter.2 except t h a t  + eD9n/9x  0  rate  concentra-  e q u a t i o n s of Chapter 2 which govern the p r o c e s s J = -neyE  The  the  = n ( x ) e E ty / e  O n  i s given .  equi-  as For  by . . (3.25)  ^ 63  For the d i f f u s i o n - o n l y case, E  s c  the space charge f i e l d  ( x ) = -(eD't/e ) 3n(x)  i s given  by  .  (3.26)  3x Eq.  3.21  and  3.22  are used to c a l c u l a t e n(x)  and  dn/dx.  For  arbitrary  i n t e n s i t y v a r i a t i o n , the number of e l e c t r o n s i n the c o n d u c t i o n n(x),  i s g i v e n by the c o n v o l u t i o n of the i n t e n s i t y p a t t e r n , g ( x ) ,  w i t h the impulse considered  response,  (Wong 1973, For d r i f t ,  h(x), a t x = o, f o r the p r o c e s s  the impulse  exp(-x/L)  exponentials  (DT)  w i t h the impulse  2  sc  is two  (3.28) convolution of  g(light)  response i s  light  * h(x)  = fl  g(y)h(x-y)dy  i n t e n s i t y f u n c t i o n has  (3.29)  the form  ,2 2, exp(-ax). Fig.  E  response a t x = 0 i s  i s the d i f f u s i o n l e n g t h . The  where the g a u s s i a n Q  the impulse  l e n g t h and  exp(-|x|/L')  g(x)  g = g  o  back-to-back:  = h j-  h(x) where L' =  (3.27)  i s the u n i t s t e p f u n c t i o n , L i s the d r i f t  equal to uEQ-r.For d i f f u s i o n , decaying  response i s  = y E  where u(x)  being  Young e t a l . 1974).  h(x)  and  band,  3.16  shows the  (x) f o r the two  illustrated  s p a t i a l v a r i a t i o n of g ( x ) ,  cases of d r i f t  and  d i f f u s i o n . The  n(x) situation  i s f o r l o n g m i g r a t i o n l e n g t h . I f the m i g r a t i o n  were v e r y s h o r t , n(x) would be a r e p l i c a of g ( x ) .  length  64  DRIFT  DIFFUSION  Fig.3.16 The space charge f i e l d s (E ) developed f o r the c a s e s o f d r i f t and d i f f u s i o n , cansed by the i n t e n s i f y d i s t r i b u t i o n g ( x ) . n(x) i s t h e s p a t i a l d i s t r i b u t i o n o f e l e c t r o n s i n the c o n d u c t i o n band d u r i n g illumination.  65  3.9.3  Experimental  Results  The r e s u l t s o f measurements  on a number o f c r y s t a l s ,  both  undoped and Fe-doped (0.015 mole %) a l l showed the shape c h a r a c t e r i s t i c of a d r i f t - d o m i n a t e d p r o c e s s . ment on an undoped c r y s t a l . t a i l on the c u r v e s .  F i g . 3.17  i l l u s t r a t e s a t y p i c a l measure-  There was no apparent  one-sided  exponential  I n the doped c r y s t a l s , the magnitude o f the induced  index change was as much as t e n times as g r e a t as t h a t seen i n undoped crystals. F i g . 3.18 shows the r e s u l t s of a measurement crystal.  on an Fe-doped  I n s t e a d of a s i n g l e peak o c c u r r i n g as would be expected,  peaks developed.  P o s s i b l y , the l a r g e change i n the i n d i c e s was  to a p p r e c i a b l y change the o p t i c a l p a t h l e n g t h o f the c r y s t a l .  two  sufficient Due to  m u l t i p l e r e l e c t i o n s , the s e n s i t i v i t y o f the e l l i p s o m e t e r may have been decreased  (see F i g . 3.7) c a u s i n g AP  the two peaks even though A(n  to decrease  - n ) may have i n c r e a s e d .  In the narrow beam experiments, what would be expected involving diffusion.  i n the r e g i o n between  the shape of the curve i s  f o r a p r o c e s s i n v o l v i n g d r i f t r a t h e r than one The l a c k of an e x p o n e n t i a l t a i l on e i t h e r s i d e  of the i l l u m i n a t e d r e g i o n i n d i c a t e s t h a t the m i g r a t i o n l e n g t h i s s m a l l e r than the r e s o l u t i o n of the instrument i s l i m i t e d by the diameter  (<<100ym).  The s p a t i a l  resolution  of the p r o b i n g beam s i n c e , i n the setup  used, the sample c o u l d be d i s p l a c e d i n s t e p s of a p p r o x i m a t e l y The r e s o l u t i o n might be i n c r e a s e d by r e d u c i n g the p r o b i n g beam and u s i n g d e c o n v o l u t i o n techniques  lym. diameter  to e x t r a c t the i n f o r m a t i o n on the  s p a t i a l v a r i a t i o n i n the b i r e f r i n g e n c e .  T h i s would be u s e f u l f o r  examining m a t e r i a l s i n which the e l e c t r o n s were d i s p l a c e d more than  1'.ym.  R e c e n t l y von der L i n d e e t al.(1975a, 1975b) have claimed t h a t p h o t o r e f r a c t i v e  66  F i g . 3.17 E l l i p s o m e t r i c scan o f t h e o p t i c a l l y - i n d u c e d b i r e f r i n g e n c e change caused by a s i n g l e l a s e r beam f o c u s s e d by a c y l i n d r i c a l l e n s . Top: Change i n p o l a r i z e r r e a d i n g A P a l o n g c - a x i s . Bottom; Scan o f i n t e n s i t y a c r o s s l a s e r beam on same h o r i z o n t a l s c a l e as A P c u r v e .  67  0  1 DISTANCE ALONG C - AXIS  2  3 /mm  F i g . 3.18 E l l i p s o m e t r i c scan o f t h e o p t i c a l l y - i n d u c e d b i r e f r i n g e n c e change i n an Fe-doped (0.015 mole %) c r y s t a l . Top: Change i n t h e p o l a r i z e r r e a d i n g a l o n g the c - a x i s . Bottom: Scan o f t h e i n t e n s i t y of the l a s e r beam c a u s i n g t h e change.  68  p r o c e s s e s i n KTN  i n v o l v e the r e d i s t r i b u t i o n of e l e c t r o n s w i t h a  l e n g t h of about 12 3.9.4  drift  ym.  Discussion E l l i p s o m e t r y i s b e t t e r s u i t e d than adjustable-compensator  methods f o r s t u d y i n g dichroism it  p h o t o r e f r a c t i v e e f f e c t s because i n e l l i p s o m e t r y  i s accounted f o r w h i l e i n adjustable-compensator methods  i s not.  In the adjustable-compensator method,-in the absence of  m u l t i p l e r e f l e c t i o n s , f i x e d d i c h r o i s m would r e s u l t i n a f i x e d e r r o r i n estimating due  A,  which would :.tend to  to the p h o t o r e f r a c t i v e e f f e c t .  c a n c e l i n examining changes  A change i n d i c h r o i s m  p h o t o r e f r a c t i v e e f f e c t would produce an e r r o r .  due  to  the  Multiple reflections  w i l l l e a d to f u r t h e r e r r o r s i n d e t e r m i n i n g A ( q u i t e a p a r t  from  the  problem of i n t e r p r e t i n g A ) . From F i g . 3.7 thickness  i t can be  seen t h a t f o r a c r y s t a l o f  the change i n A i s n e a r l y l i n e a r w i t h the change i n b i r e -  fringence.  D i f f i c u l t i e s i n i n t e r p r e t i n g A are due  to the v a r i a t i o n  of the s e n s i t i v i t y of the e l l i p s o m e t e r w i t h the t h i c k n e s s at.the point being  3.10  of the  sample  probed.  Measurements on C r y s t a l s Heated i n L i ^ C O ^ 3.10.1  Introduction Measurements were made on c r y s t a l s b e f o r e  i n I^CO^ and  constant  after  to i n v e s t i g a t e the e f f e c t s of the treatment on the  on the p h o t o r e f r a c t i v e p r o c e s s .  treatment on hologram w r i t i n g and reported  and  heating  birefringence  P r e v i o u s l y , some e f f e c t s of  on the o p t i c a l a b s o r p t i o n  ( S t a e b l e r et a l . 1 9 7 4 , P h i l l i p s et a l . 1974)  t h a t the treatment reduced i r o n i o n s from Fe  3+  to Fe  had  the been  which i n d i c a t e d 2+  .  The  experiments  69  to be d e s c r i b e d i n d i c a t e t h a t the I ^ C O ^ treatment a f f e c t s the b i r e f r i n gence o f t h e c r y s t a l by d e c r e a s i n g the v a l u e o f t h e e x t r a o r d i n a r y i n d e x . I t i s p o s t u l a t e d t h a t t h i s i s due t o i n - d i f f u s i o n o f Li^O' i n t o the c r y s t a l , which,'in a d d i t i o n to causing i r o n r e d u c t i o n , serves to destroy shallow traps. 3.10.2  E x p e r i m e n t a l Procedures and R e s u l t s An undoped c r y s t a l grown from a s t o i c h i o m e t r i c melt was  heated i n a i r t o 520°C f o r 40 hours w h i l e packed  i n I ^ C O ^ powder.  T h i s treatment i s c l a i m e d t o c o n v e r t more than 96% o f t h e i r o n  impurities  to the d i v a l e n t s t a t e ( P h i l l i p s e t a l . 1974).  The c r y s t a l was  a l o n g the c - a x i s a f t e r the Li2C0.j treatment.  The v a r i a t i o n i n the  p o l a r i z e r .".reading i s shown by the lower curve i n F i g . 3.19. upper  The  curve i s a r e p r o d u c t i o n o f F i g . 3.11 which shows t h e p o l a r i z e r  v a r i a t i o n b e f o r e the treatment.  The p e r i o d i c n a t u r e o f the r e a d i n g s  has been removed and the c u r v e has s h i f t e d downwards.  An attempt  to f i t the lower curve i n F i g . 3.19 i s shown i n F i g . 3.20. gradient i n n 6  e  and the nominal v a l u e o f n  e  The  were s m a l l e r than the v a l u e s  used t o f i t the curve measured p r i o r t o the I ^ C O ^ treatment. fit  scanned  ,A b e t t e r  c o u l d p r o b a b l y be a c h i e v e d by assuming a n o n l i n e a r change i n n  a l o n g the sample.  g  T h i s would be c o n s i s t e n t w i t h uneven d i f f u s i o n o f  l i t h i u m i n t o the sample a l o n g the c - a x i s .  When more h e a v i l y doped  samples a r e heated i n I ^ C O ^ t h i s uneven d i f f u s i o n i s r e a d i l y  seen.  The treatment causes the samples t o t u r n brown and the e f f e c t  i s more  pronounced  near the u n p o l i s h e d edges o f the sample. O p t i c a l damage due t o a narrow s l i t  produced  same shape as were found f o r the u n t r e a t e d sample.  p a t t e r n s o f the  However, the damage  at d i f f e r e n t p l a c e s a l o n g the c - a x i s was more u n i f o r m a f t e r  treatment.  70  no  40  r  I  0  «  '  1  1  >  DISTANCE ALONG  1  2 C - AXIS  '  I  l  i 4  (mm)  F i g . 3.19 The change i n the p o l a r i z e r r e a d i n g ( c r y s t a l #4) caused by h e a t i n g i n L ^ C C ^ . TOP: b e f o r e heat treatment (same as F i g . 3.11). BOTTOM: a f t e r heat t r e a t m e n t .  DISTANCE  ALONG  C-AXIS  (mm)  F i g . 3.20 The c i r c l e s a r e the p o l a r i z e r r e a d i n g s shown by the bottom c u r v e i n F i g . 3.19. The s o l i d c u r v e was c a l c u l a t e d w i t h the f o l l o w i n g assumed parameters: t h i c k n e s s = (1.0 mm - 0.19 wavelengths)+ 1.92 wavelengths/cm; n = 2.20642 + 1.25 x 10- /cm; n = 2.29058. (compare w i t h F i g . 3.13). 5  e  Q  71  F i g . 3.21(a) shows the change observed due  in polarizer  readings  to o p t i c a l damage produced by i d e n t i c a l exposures a t v a r i o u s p l a c e s  a l o n g the c - a x i s b e f o r e treatment. L^CO^  treatment  T h i s v a r i a b i l i t y was  as shown i n F i g . 3.21(b).  removed by  the  The v a r i a t i o n i s b e l i e v e d  to i n d i c a t e the combined e f f e c t of m u l t i p l e r e f l e c t i o n s and  the g r a d i e n t  in stoichiometry. Thermal decay of the o p t i c a l damage i n undoped LiNbO^ b e f o r e and a f t e r L ^ C O ^  treatment  was  measured by t a k i n g repeated  the c - a x i s over a p e r i o d of a few days. i n the p o l a r i z e r r e a d i n g AP  F i g . 3.22  v a r i e d w i t h time.  The  scans  shows how  along  the change  e l a p s e d time  from  the end of the exposure c r e a t i n g the damage to the measurement of b i r e f r i n g e n c e a t the peak i n AP  i s g i v e n b e s i d e the c u r v e s .  The  the curves  do not a l l have the same b a s e l i n e as shown. ( T h i s was  normalized  i l l u s t r a t e the decay more r e a d i l y . )  (P < 1 ) were  The  sma 11 s h i f t s  to  a t t r i b u t e d to the temperature not b e i n g e x a c t l y the same when each scan was  taken.  polarizer  E f f e c t i v e l y , a s m a l l i n c r e a s e i n temperature lowers readings. In F i g . 3.23  a g a i n s t time and approximately  the l o g a r i t h m of the change i n AP  i s plotted  shows an e x p o n e n t i a l decay w i t h a time c o n s t a n t of  46 hours.  The  same experiment was  undoped c r y s t a l a f t e r the L ^ C O ^ decay had  the  treatment.  repeated  f o r the same  A f t e r 30 hours,  negligible  occurred.  3.10.3  Discussion  The L ^ C O ^  treatment  i n t r o d u c e d by P h i l l i p s and  Staebler  a f f e c t s not o n l y the a b s o r p t i o n of LiNbO^ but a l s o the b i r e f r i n g e n c e . In a d d i t i o n , thermal decay of the o p t i c a l damage was  diminished  after  72  20,  DISTANCE  ALONG  C-AXIS  (mm)  (a)  DISTANCE  ALONG  C-AXIS  (mm)  (b) F i g . 3.21 Change i n polarizer reading due to i r r a d i a t i o n of three places a l o n g the c-axis with a one-dimensional Gaussian beam giving an average o f 110 J/cm at a wavelength of 441.6 nm. (a) before and (b) a f t e r l i t h i u m carbonate treatment.  73  Ar  1 DISTANCE ALONG  2 C - AXIS  3 (mm)  F i g . 3 . 2 2 Thermal decay o f o p t i c a l damage i n an undoped l i t h i u m n i o b a t e c r y s t a l b e f o r e h e a t i n g i n L i 2 C 0 3 . The times i n d i c a t e t h e e l a p s e d time from t h e end o f i l l u m i n a t i o n t o t h e measurement o f t h e peak i n each c u r v e (± 1 min).  74  F i g . 3.23 L o g a r i t h m of the change i n AP as a f u n c t i o n o f time. The e x p e r i m e n t a l p o i n t s c o r r e s p o n d t o the peak a m p l i t u d e s of t h e c u r v e s i n F i g . 3.22.  75  treatment.  A decrease i n the c o n c e n t r a t i o n of empty t r a p s ( F e )  will  J T  i n c r e a s e the m i g r a t i o n  (or d i f f u s i o n ) l e n g t h of e l e c t r o n s and  t h e r e f o r e , enhance hologram w r i t i n g , o p t i c a l e r a s u r e and  will,  thermal decay.  T h i s i s e a s i l y seen by n o t i n g t h a t the f a r t h e r e l e c t r o n s move, the g r e a t e r the e f f e c t i n a l l t h r e e c a s e s . The seen cannot, t h e r e f o r e , be due  diminished  thermal decay  to the r e d u c t i o n of i r o n  I f , however, the Li2CC>  3  treatment served  centres.  to d e s t r o y  shal-  2+ low  t r a p s as w e l l as to reduce i r o n c e n t r e s to the Fe  would account f o r a l l the above o b s e r v a t i o n s . captured  by the s h a l l o w  state,- t h i s  E l e c t r o n s would  t r a p s d u r i n g hologram w r i t i n g and would con-  t r i b u t e to the hologram (or o p t i c a l inhomogeneity), but escape more r e a d i l y by iron centres. decay. before  be  thermal a c t i v a t i o n than those  D e s t r u c t i o n of the shallow  they would  trapped  i n the  t r a p s would d i m i n i s h  thermal  S i n c e i t would i n c r e a s e the d i s t a n c e t r a v e l l e d by f r e e e l e c t r o n s trapping  (as would a l s o occur w i t h the r e d u c t i o n of i r o n  i t would t h e r e f o r e a i d i n i n c r e a s i n g o p t i c a l w r i t i n g and explanation i s consistent with previous t h a t thermal decay o c c u r s  i n two  reports  centres)  erasure.  This  (e.g. Chen et a l .  1968)  s t a g e s , an i n i t i a l r a p i d decay f o l l o w e d  by a slower decay. As to why it  treatment i n I ^ C O ^  should produce these  effects  i s w e l l known t h a t o u t - d i f f u s i o n of l i t h i u m (Kaminow et a l .  can be used to produce o p t i c a l wave g u i d e s . a non-stoichiometric to 0.50  form, ( I ^ O ) . ^ (Nb 0^) 2  moles ( C a r r u t h e r s - e t a l . 1971).  index, n , Q  i s independent of  o r d i n a r y index, n , o  v  t  1973)  LiNbO^ can c r y s t a l l i z e i n , where \> ranges from  I t i s b e l i e v e d t h a t the  0.48  ordinary  but w i t h i n the g i v e n range the e x t r a - '  i n c r e a s e s almost l i n e a r l y • as v d e c r e a s e s  (Bergman et  76  al.  1968).  suggested  I n the p r o d u c t i o n  o f o p t i c a l wave g u i d i n g  (Kaminow e t a l . 1973)  that L ^ O  l a y e r s , i t was  was r e l e a s e d when the c r y s t a l  was heated i n vacuum, thus i n c r e a s i n g n . e When LiNbO^ i s heated w h i l e packed i n L ^ C O ^ , reasonable to postulate  i t seems  t h a t L i ^ O i s d i f f u s e d i n t o the c r y s t a l .  Intro-  2duction of 0  would d e s t r o y  of t h e i r o n c e n t r e s  serves  oxygen v a c a n c i e s .  to m a i n t a i n  I f the o x i d a t i o n  e l e c t r o n e u t r a l i t y then  intro-  d u c t i o n o f e x t r a L i would e x p l a i n the r e d u c t i o n o f i r o n c e n t r e s . +  introduction of L ^ O fit  i s consistent with  the d a t a o f F i g . 3.19.  the d e c r e a s e o f n  No e x p l a n a t i o n  &  state  The  required to  f o r t h e r e d u c t i o n o f the i r o n  c e n t r e s was g i v e n by P h i l l i p s and S t a e b l e r ( 1 9 7 4 a ) but i t i s understood ( p e r s o n a l communication) t h a t they had a l s o c o n s i d e r e d explanation.  the above  77  CHAPTER 4 THE USE OF FABRY-PEROT FRINGES TO OBSERVE THE PHOTOREFRACTIVE EFFECT  4.1  Introduction Multiple  two  i n t e r n a l r e f l e c t i o n s o f a l a s e r beam between t h e  o p t i c a l l y p o l i s h e d s u r f a c e s o f a c r y s t a l produce l i g h t and d a r k  f r i n g e s , depending on t h e o p t i c a l t h i c k n e s s o f t h e c r y s t a l . s i t u a t i o n i s s i m i l a r t o t h a t found i n a Wolf 1959)•  The  F a b r y - P e r o t e t a l o n (Born and  The o p t i c a l p a t h change r e q u i r e d t o move a d a r k  to the p o s i t i o n of the next adjacent dark f r i n g e  fringe  i s A/2 where X i s  the w a v e l e n g t h o f i l l u m i n a t i o n . The  geometry o f t h e f r i n g e s  i s an i n d i c a t i o n  a t i o n of the o p t i c a l thickness of the c r y s t a l .  Optical  g e n e i t i e s c a n e a s i l y be seen w i t h t h i s t e c h n i q u e . made t o move by h e a t i n g t h e s a r p l e , i n d e x changes.  of the v a r i inhomo-  The f r i n g e s  o r by o p t i c a l l y - i n d u c e d  c a n be  refractive  Changes i n t h e o r d i n a r y and e x t r a o r d i n a r y i n d i c e s c a n  be viewed i n d e p e n d e n t l y and t h e magnitude o f t h e o p t i c a l change e s t i mated.  This technique i - e s p e c i a l l y  useful  of t h e s p a t i a l v a r i a t i o n o f o p t i c a l l y - i n d u c e d  4.2  for visual  inspection  inhomogeneities.  Experimental Procedures The  fringes  a r e e a s i l y v i s i b l e t o t h e eye when t h e r e f l e c -  t i o n o f an expanded l a s e r beam f r o m t h e s u r f a c e o f t h e c r y s t a l i s viewed.  The o p t i c a l arrangement f o r t h e p h o t o g r a p h s t a k e n i n t h i s  Chapter i s shown i n F i g u r e 4.1.  78  BEAM SPLITTER-  BEAM EXPANDER  CRYSTAL  ]-CAMERA  F i g . 4.1 O p t i c a l arrangement interference fringes.  f o r taking  photographs o f t h e F a b r y - P e r o t  79  The beam from a l a s e r  ( e i t h e r He-Ne or argon i o n ) was  s p a t i a l l y f i l t e r e d and expanded to i l l u m i n a t e the e n t i r e c r y s t a l .  A  beam s p l i t t e r was p l a c e d b e f o r e the c r y s t a l to d e f l e c t the r e f l e c t e d beam towards the camera.  4.3  Experimental Results Photographs of the F a b r y - P e r o t f r i n g e s a r e shown i n  Fig.  4.2.  F o r F i g 4.2(a) - 4.2(d), an o s c i l l o s c o p e camera was used  w i t h a d i f f u s e r p l a c e d where the scope f a c e would u s u a l l y be. c r y s t a l was  i l l u m i n a t e d w i t h an argon i o n l a s e r  two photos of F i g s . 4.2(e) and 4.2 without a l e n s .  The l i g h t  (A=  541.5nm).  The  ( f ) were taken w i t h a 35mm camera  source was a He-Ne l a s e r  The photos on the l e f t  The  (Fig.  ( A = 632.8nm).  4.2(a), 4 . 2 ( c ) , 4.2(e) c o r r e s -  pond to the e x t r a o r d i n a r y index and those on the r i g h t  (Fig.  4.2(b),  4.2(d), 4 . 2 ( f ) ) to the o r d i n a r y index.  F i g . 4.2(a) and 4.2(b) show  the  c r y s t a l a f t e r any o p t i c a l l y - i n d u c e d  inhomogeneity has been annealed  out  of the c r y s t a l by h e a t i n g i t f o r a few hours a t 270°C.  v e r t i c a l band  The  towards the r i g h t end of the photos i s p a r t i a l l y due to  f a u l t y p o l i s h i n g of the s u r f a c e and p a r t i a l l y due t o o p t i c a l  inhomo-  g e n e i t i e s i n the b u l k produced d u r i n g growth. The photos i n F i g . t h i n v e r t i c a l l i n e on the l e f t  4.2(c) and 4.2(d) show two e f f e c t s :  The  i s the r e s u l t of i r r a d i a t i n g the c r y s t a l  w i t h a narrow s t r i p of l i g h t as d e s c r i b e d i n Chapter 3.  The  spatial  e x t e n t of the index change i s a p p r o x i m a t e l y as wide as the beam.  In the  c e n t r a l a r e a of the c r y s t a l , the f r i n g e s have been h e a v i l y d i s t o r t e d a number of holograms have been s t o r e d i n the c r y s t a l . are  These e f f e c t s  due to the b u i l d - u p of l a r g e dc space charge f i e l d s w i t h i n the  after  <•>  CO  Fig. 4.2. Fabry-Perot fringes In an Fa-dcpad crystal shoving optically-induced changes i n the r e f r e c t i v s indices, ( a ) , (c) (e) vera Bade with extraordinary polarised light and show tha variation i n rx . ( b ) , (d) „ (f) were ssada with ordinary polarized light and show tha variation i n n . &  81  crystal.  The s i n u s o i d a l v a r i a t i o n s i n index t h a t produce  diffraction  would be too s m a l l t o be seen. F i g . 4.2(e) and 4.2(f) show o p t i c a l damage due t o i r r a d i a t i o n w i t h a s i n g l e beam o f c i r c u l a r symmetry.  These p a t t e r n s a r e analogous  to the e x p e r i m e n t a l r e s u l t s o f Chen (1969) except t h a t here t h e v a r i a t i o n in n  e  and n^ a r e seen s e p a r a t e l y r a t h e r than the v a r i a t i o n i n the b i r e -  fringence.  The damaged p o r t i o n shown i n F i g . 4.2(f) was a p p r o x i m a t e l y  the same s i z e as the beam.  The damage i n F i g . 4.2(e) extends  beyond the edges o f t h e l i g h t beam.  well  This i s i n contrast to the t h i n  line  shown i n F i g . 4.2(c) and 4.2(d). Damage i s more apparent  f o r the e x t r a o r d i n a r y index  the e l e c t r o - o p t i c c o e f f i c i e n t i n v o l v e d  C ^)  l a r g e as f o r the o r d i n a r y case ( ^-j) •  The change i n the o r d i n a r y index  r  F i g . 4.2(f) w i l l  1  i s about  because  t h r e e times as  i n c r e a s e w i t h i n c r e a s e d exposure and tend toward the  s p a t i a l v a r i a t i o n already present i n F i g . 4.2(e).  When c r y s t a l s were  i l l u m i n a t e d w i t h a t h i n s t r i p o f l i g h t p a r a l l e l t o the c - a x i s from one c - f a c e t o the o t h e r , no s p a t i a l change i n the f r i n g e s was observed. The l i g h t  i n t e n s i t y , i n t h i s c a s e , would v a r y s p a t i a l l y , p e r p e n d i c u l a r t o  the c - a x i s , and be e s s e n t i a l l y u n i f o r m a l o n g the c - a x i s .  4.4  Discussion The f r i n g e changes,  were observed i n a Fe-doped  produced by the p h o t o r e f r a c t i v e  effect,  (0.015 mole %) c r y s t a l , 2.5mm t h i c k .  e f f e c t s were seen i n o t h e r Fe-doped c r y s t a l s 1.5mm  t h i c k and 10mm  Similar thick,  however no changes c o u l d be seen i n the f r i n g e p a t t e r n s o f an undoped crystal  (3mm t h i c k ) .  T h i s i n d i c a t e s t h a t the f i e l d s induced i n  undoped c r y s t a l s a r e much s m a l l e r than those induced i n doped  crystals.  82  An e s t i m a t e  o f the magnitude o f t h e space charge f i e l d s i n  doped and undoped c r y s t a l s can be o b t a i n e d  from these p h o t o s .  To move a  d a r k f r i n g e t o t h e p o s i t i o n o f the next d a r k f r i n g e , t h e o p t i c a . ! t h i c k n e s s must change by A/2. And  =  A/2  and An = A/2d.  space charge f i e l d  e  sc  =  -  -  2  - = 3 33 e A  6.0 kV/cm  n  r„n  = 2.24 and r„„ = 30.8 x 1 0 ~ 33 The  An = 1 0 ^ .  -4 An = 10 is  to give E  where n  F o r A= 500 nm and d = 2.5 mm,  then  -4 -4 An > 10 and i n undoped c r y s t a l s , An < 10  I n doped c r y s t a l s then, The  I f t h e t h i c k n e s s , d, remains c o n s t a n t  1 0  cmV . _1  absence o f p h o t o r e f r a c t i v e p r o c e s s e s  when t h e c r y s t a l was  i l l u m i n a t e d w i t h a s t r i p o f l i g h t p a r a l l e l t o t h e c - a x i s can be a t t r i b u t e d to t h e n a t u r e The  o f the e l e c t r o - o p t i c t e n s o r as was d i s c u s s e d  same s i t u a t i o n a r i s e s when hologram s t o r a g e  i n Chapter 2.  i s attempted w i t h the  p l a n e o f i n c i d e n c e o f the r e f e r e n c e and o b j e c t beams p e r p e n d i c u l a r t o the c - a x i s .  I n b o t h cases  the l i g h t  c - a x i s and i s e s s e n t i a l l y c o n s t a n t the o p t i c a l f a c e c o n t a i n e d transmitted along  i n t e n s i t y v a r i e s normal t o t h e  along  the c - a x i s .  I n our c r y s t a l s ,  t h e a - a x i s and t h e c - a x i s , and t h e l i g h t was  the b - a x i s .  Space charge f i e l d s c r e a t e d a l o n g t h e  a - a x i s would cause o n l y a s m a l l r o t a t i o n o f t h e o p t i c a l i n d i c a t r i x and the r e s u l t i n g change i n index would be v e r y  small.  83  CHAPTER 5 EXPERIMENTAL CONSIDERATIONS FOR  5.1  Elementary  HOLOGRAM FORMATION  Equations  To probe the mechanism of hologram s t o r a g e i n LiNbO^, the most elementary chosen.  h o l o g r a p h i c p a t t e r n , the s i n u s o i d a l g r a t i n g , was  T h i s p r o t o t y p e hologram c o n f i g u r a t i o n i s q u i t e g e n e r a l  s i n c e any a r b i t r a r y i n t e n s i t y v a r i a t i o n can be separated p a t t e r n s through formed when two crystal. may  One  Fourier coherent  decomposition.  sinusoidal  T h i s type of hologram can  the r e f e r e n c e wave and  by R = Re {r e x p ( i $ ) exp(icot)}  (5.1)  r  The  o t h e r wave which i s commonly c a l l e d  be r e p r e s e n t e d  be  plane waves i n t e r f e r e w i t h i n the volume of the  of these waves i s commonly c a l l e d  be r e p r e s e n t e d  into  the s i g n a l or o b j e c t wave  may  exp(iut)}  (5.2)  i n a s i m i l a r manner by S = Re{  s exp(i$ ) g  where w has a s i n g l e v a l u e which i s e q u a l f o r b o t h waves, and Re{  }  i n d i c a t e s the r e a l p a r t of the complex q u a n t i t y w i t h i n the b r a c k e t s . For convenience, the Re{  Eq. 5.1  and  5.2  a r e u s u a l l y d i v i d e d by exp(iwt)  } symbol dropped l e a v i n g R = r  exp(i$ ) r  and  (5.3) S = s exp(i$ ) g  The  and  .  i n t e n s i t y I , i n the r e g i o n of i n t e r f e r e n c e , i s found by t a k i n g the  s c a l a r product  of the sum  of the two  amplitude  vectors  I = (R + S).(R + § ) * = r . r + s.s + r . s  exp(i($  -*  )} + e x p ( - i ( $  )}  84  or I = R + S + 2r.s cos(« - * ) s r  (5.4)  where R and S a r e t h e i n t e n s i t i e s o f t h e i n d i v i d u a l waves. The t h i r d term i n E q . 5.4 i s the i n t e r f e r e n c e term which c o n t a i n s phase i n f o r m a t i o n .  the r e l a t i v e  F i g . 5.1 shows t h e i n t e r f e r e n c e o f two p l a n e waves.  For an a n g l e 20 between the wave normals, t h e p e r i o d , & , o f t h e s i n u s o i d a l i n t e n s i t y d i s t r i b u t i o n i s g i v e n by 2 £sinO = X where x i s t h e wavelength o f t h e l i g h t light  (5.5)  i n t h e medium i n w h i c h t h e  i s propagating.  Kx)  —£9 F i g . 5. 1  Interference  p a t t e r n o f two p l a n e waves.  To w r i t e a hologram i n LiNbO^, t h e c r y s t a l i s p l a c e d region of the i n t e r f e r e n c e p a t t e r n .  i n the  The s p a t i a l v a r i a t i o n o f t h e l i g h t  i n t e n s i t y induces a s p a t i a l v a r i a t i o n i n the r e f r a c t i v e i n d i c e s o f the c r y s t a l which c o n s t i t u t e s a volume hologram.  To r e a d  out t h e i n f o r m a -  t i o n s t o r e d i n t h e hologram, t h e c r y s t a l i s i l l u m i n a t e d w i t h a p l a n e wave ( t h e r e f e r e n c e wave) and t h e volume d i f f r a c t i o n g r a t i n g the l i g h t  i n a manner t h a t r e c o n s t r u c t s  scatters  t h e o b j e c t o r s i g n a l wave used  85  t o form the g r a t i n g .  T h i s i s shown i n F i g . 5.2.  \—l  1  a  -\  F i g . 5. 2 D i f f r a c t i o n o f t h e r e f e r e n c e wave by the hologram g r a t i n g .  Maximum d i f f r a c t i o n o c c u r s when Bragg's law (Eq. 5.5) i s s a t i s f i e d . The d i f f r a c t i o n e f f i c i e n c y r\, of t h e d i f f r a c t e d  o f the hologram i s the r a t i o  i n t e n s i t y t o the i n c i d e n t i n t e n s i t y . K o g e l n i k  has shown t h a t f o r t h i c k phase holograms  (1969)  (see Appendix A)  2 n = e x p ( - ad/cose) s i n (vd)  (5.6)  where a i s the a b s o r p t i o n , d i s t h e g r a t i n g t h i c k n e s s , and v= irAn/A  o  cos8 f o r p e r p e n d i c u l a r p o l a r i z a t i o n and  for p a r a l l e l polarization.  Here, A Q  v = TrAn cos28A  o  cos6  i s t h e vacuum wavelength and  An i s t h e a m p l i t u d e o f t h e s i n u s o i d a l r e f r a c t i v e i n d e x g r a t i n g . Eq. 5.6 n e g l e c t s m u l t i p l e i n t e r n a l r e f l e c t i o n s between t h e f a c e s o f t h e c r y s t a l . These e f f e c t s a r e d i s c u s s e d i n t h e next c h a p t e r . 5.2  The O p t i c a l  System  F i g . 5.3 shows a schematic o f t h e e x p e r i m e n t a l s e t u p u s e d . L i g h t from t h e l a s e r  ( e i t h e r w i t h a Coherent R a d i a t i o n Model 54 a r g o n  i o n , o r an RCA Model LD2186 two beams.  He-Cd) was s p l i t w i t h a beam s p l i t t e r i n t o  The t r a n s m i t t a n c e o f t h e beam s p l i t t e r was v a r i a b l e which  86  a l l o w e d adjustment of the r e l a t i v e beam powers. Two r o r s were used to d i r e c t  first  the two beams to cause them to  surface mirintersect  w i t h i n the volume o f the c r y s t a l . The geometry the  such t h a t the p a t h l e n g t h s of  two beams from the beam s p l i t t e r to the c r y s t a l were w i t h i n 1.0  of b e i n g e q u a l . the  of the setup was  T h i s ensured t h a t the path d i f f e r e n c e was  coherence l e n g t h of the l a s e r  tector  (10 cm).  the c r y s t a l i n l i n e w i t h the o b j e c t beam.  beam s h u t t e r was  than  A s i l i c o n p h o t o v o l t a i c de-: .  ( A l p h a m e t r i c s model dc 1010 w i t h a PI 110 broadband  placed a f t e r  less  cm  c l o s e d , the energy d i f f r a c t e d  probe)  was  When the o b j e c t  from the r e f e r e n c e beam  toward the d e t e c t o r c o u l d be measured, thus a l l o w i n g the d i f f r a c t i o n e f f i c i e n c y of the hologram F i g . 5.4 efficiency. of  to be determined.  shows another method used t o monitor the d i f f r a c t i o n  An a n c i l l a r y He-Ne l a s e r was  p o s i t i o n e d so t h a t the a n g l e  i n c i d e n c e of the beam s a t i s f i e d the Bragg c o n d i t i o n of the phase  g r a t i n g produced by the h i g h power argon i o n or He-Cd l a s e r s . hologram developed, more and more energy would be d i f f r a c t e d  As the from the  i n c i d e n t path of the He-Ne beam a l l o w i n g continuous measurement of the diffraction efficiency. model 132) was  chosen because  w i t h l i g h t of wavelength l e s s than 520  A low power(2 mw) He-Ne l a s e r  (Spectra Physics  the p h o t o r e f r a c t i v e e f f e c t  is inefficient  632.8 nm as compared w i t h l i g h t of wavelengths  nm.  Each of the above methods has i t s drawbacks e x p e r i m e n t a l l y . With the f i r s t method, the hologram read the d i f f r a c t i o n e f f i c i e n c y .  f o r m a t i o n must be i n t e r r u p t e d to  D u r i n g r e a d i n g , the r e f e r e n c e  w i l l cause some o p t i c a l e r a s u r e of the hologram. ments, the o p t i c a l . e r a s u r e on readout was  For c e r t a i n  beam  measure-  reduced by a t t a c h i n g a p a r -  87  F i g . 5.3 E x p e r i m e n t a l arrangement f o r measuring the d i f f r a c t i o n e f f i c i e n c y of p l a n e wave holograms by i n t e r m i t t e n t l y b l o c k i n g the S beam and measuring the i n t e n s i t y d i f f r a c t e d from the R beam.  F i g . 5.4 A l t e r n a t i v e arrangement f o r measuring t h e d i f f r a c t i o n by c o n t i n u o u s l y m o n i t o r i n g the a u x i l i a r y He-Ne beam.  efficiency  88  tially  s i l v e r e d g l a s s to an e l e c t r o m a g n e t i c s h u t t e r .  beam s h u t t e r was beam was  c l o s e d , to f a c i l i t a t e a measurement, the r e f e r e n c e  a t t e n u a t e d by a f a c t o r of approximately The  When the o b j e c t  second method does not  i n t e r r u p t i o n of i t s f o r m a t i o n but  100.  erase the hologram or n e c e s s i t a t e  i t does p r e s e n t o t h e r problems.  If  the a n g l e of i n c i d e n c e of the He-Ne beam i s not v e r y c l o s e to the Bragg a n g l e , then the d i f f r a c t i o n e f f i c i e n c y of the hologram  de-  termined w i t h t h i s beam i s much reduced from i t s t r u e v a l u e .  Not  o n l y i s the a l i g n m e n t v e r y  c r i t i c a l but d e t e r m i n a t i o n of the a c c u r a c y  the alignment  i s not an easy  t h i s alignment  problem s i n c e the r e a d i n g and w r i t i n g beams a r e the same.  Mechanical c r i t i c a l experimental  task.  The  of  f i r s t method does not have  s t a b i l i t y d u r i n g hologram f o r m a t i o n i s another consideration.  b e i n g r e c o r d e d determines  The h i g h e s t s p a t i a l  the v i b r a t i o n t h a t may  frequency  be t o l e r a t e d .  This  i s g e n e r a l l y of the o r d e r of the wavelength of the l i g h t used f o r r e cording.  The  r e c o r d i n g medium must not move more than a f r a c t i o n of  t h i s d i s t a n c e r e l a t i v e to the f r i n g e p a t t e r n b e i n g r e c o r d e d .  To keep  the r e c o r d i n g medium steady  fringe  i s not a problem, but to keep the  p a t t e r n s t a b l e s p e c i a l precautions are  necessary.  To keep the f r i n g e p a t t e r n steady r e f e r e n c e and mechanical  o b j e c t beams must remain c o n s t a n t .  To accomplish  bench.  The  T h i s means t h a t  t h i s , experiments were performed on an  o p t i c a l bench had been c o n s t r u c t e d by epoxying  a massive c o n c r e t e base (2.13  supported  the  v i b r a t i o n s , a c o u s t i c a l and thermal d i s t u r b a n c e s must be m i n i -  mized.  to  the o p t i c a l paths of  by two  between each row  x 1.72  x 0.15  columns of cement b l o c k s .  m).  The  optical  steel  table  strips  was  L a y e r s of f e l t were used  of b l o c k s to reduce the e f f e c t s of b u i l d i n g  vibrations.  89  To reduce thermal and a c o u s t i c a l d i s t u r b a n c e ,  a plexiglass  c o v e r was used t o e n c l o s e the components on the t a b l e top.  The l a s e r  was l e f t o u t s i d e t h e cover because o f the heat i t . g e n e r a t e d  during  operation. To check the e f f e c t s o f these p r e c a u t i o n s , ferometer  was s e t up as shown i n F i g . 5.5.  a simple  inter-  The d e t e c t o r was masked so  t h a t i t was i l l u m i n a t e d by a p o r t i o n o f one b r i g h t i n t e r f e r e n c e f r i n g e .  Mm  \  DETECTOR  BRIGHT FRINGE  LASER DETECTOR APERTURE  to S3  w  H S5  2  4  6  10  TIME / minutes  F i g . 5.5 TOP; Arrangement o f the i n t e r f e r o m e t e r used t o check s t a b i l i t y , BOTTOM: V a r i a t i o n i n the d e t e c t o r s i g n a l w i t h time. The l i n e w i t h the arrows i n d i c a t e s 20 % o f t h e e x c u r s i o n o f t h e s i g n a l when the f r i n g e s were made t o move p a s t t h e d e t e c t o r a p e r t u r e .  90  5.3  Hologram  Storage  With t h i s s e t u p , holograms were e a s i l y formed F i g . 5.6  shows the b u i l d - u p o f the e f f e c t i v e  ( r a t i o of d i f f r a c t e d of  4  intensity  efficiency  t o i n c i d e n t i n t e n s i t y ) , over a p e r i o d  minutes, o f a hologram i n a Fe-doped  saturation effect  diffraction  i n LiNbO^.  (0.015 mole %) c r y s t a l .  i s t y p i c a l of a l l holograms  The  found i n t h i s m a t e r i a l .  T h i s appears to be caused by the space charge f i e l d  reaching a value  where i t opposes the p r o c e s s which forms t h e hologram 1975, Moharam e t a l . 1975, G a y l o r d p e r s . comm.).  (Alphonse e t a l .  No attempt was made  t o e s t i m a t e the reduced d i f f r a c t i o n e f f i c i e n c y due t o u n s t a b l e f r i n g e problems. 30  0  60  120  180  240  TIME / s e c F i g . 5.6 B u i l d - u p o f the e f f e c t i v e d i f f r a c t i o n e f f i c i e n c y n, ( r a t i o of i n c i d e n t t o d i f f r a c t e d beam power) w i t h time i n an Fe-doped (0.015 mole %) c r y s t a l .  91  i Wo J/cm  . Source  ad  ,S  (cm /J)  2  2  Exposure t o g e t 1% n (mJ/ cm ) 2  G l a s s e t a l . 1975b Alphonse e t a l . 1975  0.1  0.225  S t a e b l e r e t a l . 1974a  0.122  0.1  .3  330  .444  225  1.224  1.22  81.6  (a)  Undoped C r y s t a l  0.0169  9.94  0.0462  0.367  2700  Fe doped  0.059  9.94  0.083  0.715  1400  0.0448  5.676  0.023  .343  292  0.029  0.8819  0.023  1.43  69.9  (ill)  0.0149  0.251  0.023  2.58  38.7  (iv)  0.079  0.251  0.023  13.68  7.3  (0.015M%)  Undoped ^ * Treated  * (ii)  in L1 C0 2  (1)  3  (b) T a b l e 5.1 (a)  S e n s i t i v i t y o f LiNbO- t o hologram s t o r a g e .  Miscellaneous published data;  (b)  d a t a o b t a i n e d from t h i s  study.  * (1)  Only t h e c e n t r a l p a r t o f the c r y s t a l was i l l u m i n a t e d , w i t h 0.0 V/cm a p p l i e d . (ii) Non-uniform i l l u m i n a t i o n o f whole c r y s t a l , w i t h 0.0 V/cm applied. (iii) C r y s t a l n e a r l y u n i f o r m l y i l l u m i n a t e d w i t h 0.0 V/cm a p p l i e d . (iv) C r y s t a l n e a r l y u n i f o r m l y i l l u m i n a t e d w i t h 3 kV/cm a p p l i e d . Measurements ( i ) t o ( i v ) a r e d e s c r i b e d i n Chapter 8.  92  In T a b l e 5.1 ( a ) , t h e p h o t o r e f r a c t i v e s e n s i t i v i t i e s o f LiNbO^ f o r v a r i o u s published data are l i s t e d . present  Measurements made d u r i n g t h e  study a r e g i v e n i n T a b l e 5.1 ( b ) . The change i n r e f r a c t i v e  index  An d u r i n g hologram r e c o r d i n g i s l i n e a r i n t h e i n c i d e n t energy d e n s i t y W  q  =  / i d t , i n the i n i t i a l  stages.  The s e n s i t i v i t y S f o r s m a l l  values of d i f f r a c t i o n e f f i c i e n c y n i s  ^  •  S =  W  (5.7)  r  ad o  where a i s t h e a b s o r p t i o n and d t h e c r y s t a l t h i c k n e s s . normalizes  t h e s e n s i t i v i t y f o r v a r y i n g amounts o f o p t i c a l a b s o r p t i o n i n  the c r y s t a l s . achieve  The (ad) f a c t o r  Tables  5.1 and 5.2 a l s o l i s t  1% d i f f r a c t i o n e f f i c i e n c y .  the d i f f e r e n t measurements.  There i s a wide v a r i a t i o n among t h e  Some o f t h e v a r i a t i o n may be because  m u l t i p l e i n t e r n a l r e f l e c t i o n s were n e g l e c t e d diffraction efficiency  t h e exposure n e c e s s a r y t o  (see Chapter 6 ) .  i n the c a l c u l a t i o n s of the  Other d i s c r e p a n c i e s may be i n t r o -  duced i f t h e u n i f o r m i t y o f t h e i l l u m i n a t i o n v a r i e d among t h e measurements (see Chapter 8 ) .  with  The most s e n s i t i v e measurement  2 7.3 mJ/cm ) was achieved  a p p l i e d across the c—faces.  (n = 1% o b t a i n e d  i n an "undoped" c r y s t a l w i t h  3 kV/cm  Presumably g r e a t e r s e n s i t i v i t y c o u l d be 2+  a t t a i n e d by i n c r e a s i n g t h e c o n c e n t r a t i o n o f Fe a larger f i e l d .  i o n s and by a p p l y i n g  93  CHAPTER 6 INFLUENCE OF MULTIPLE INTERNAL REFLECTIONS AND THERMAL EXPANSION ON THE EFFECTIVE DIFFRACTION EFFICIENCY OF HOLOGRAMS IN LiNbOg  6.1  Introduction A central  q u e s t i o n both f o r e n g i n e e r i n g a p p l i c a t i o n s  and f o r  s t u d y i n g the mechanisms of hologram f o r m a t i o n i s how much d i f f r a c t i o n efficiency  i s produced i n g i v e n c r y s t a l s by exposure to known amounts  of l i g h t .  I t i s shown i n t h i s c h a p t e r t h a t i t i s e s s e n t i a l  multiple internal  t o take  r e f l e c t i o n s between the c r y s t a l s u r f a c e s i n t o  when measuring d i f f r a c t i o n e f f i c i e n c y .  The i n t e n s i t y  of the l i g h t  i s d i f f r a c t e d by the hologram g r a t i n g i s v e r y s e n s i t i v e t h i c k n e s s of the c r y s t a l .  account that  to the o p t i c a l  Small changes i n temperature such as those  produced by the l a s e r beams used i n w r i t i n g  the hologram, or  fluctuations  i n the ambient temperature w i l l cause s i g n i f i c a n t changes i n the o p t i c a l thickness.  The e f f e c t s of m u l t i p l e r e f l e c t i o n s  d u r i n g the w r i t i n g  p r o c e s s , a l t h o u g h p r o b a b l y important, a r e not c o n s i d e r e d . the  effects  but  the problem i s more c o m p l i c a t e d f o r two-beam  6.2  for illumination  A n a l y s i s of  w i t h a s i n g l e beam was g i v e n i n Chapter 3, interaction.  Theory The  calculations  f o l l o w the method developed by K o g e l n i k  (1967) i n c o n n e c t i o n w i t h some problems i n v o l v i n g l i g h t by u l t r a s o n i c  waves.  For s i m p l i c i t y ,  the d i f f r a c t i o n of  the a n a l y s i s  to the case i n which the p l a n e s of c o n s t a n t r e f r a c t i v e constitute crystal.  i s restricted  index, which  the hologram grating,.".ave normal to the o p t i c a l f a c e of the  94  K o g e l n i k ' s (1969) coupled wave a n a l y s i s o f d i f f r a c t i o n i n t h i c k holograms shows t h a t f o r a beam o f u n i t power d e n s i t y , p o l a r i z e d in  t h e p l a n e o f i n c i d e n c e , i n c i d e n t a t the Bragg a n g l e 9^, t h e energy  exchange between the coupled :waves l e a d s to.'.a d i f f r a c t e d wave o f amplitude S(d) =  §  {exp(Y d) - e x p ^ d ) } 2  exp (-igd)  (6.1)  cos SJCYJ. - Y ) 2  y^,  where  y^ = -(a ± i§.)/cos 0 ^ = -(Trnj^/A) cos 2(9^^ - T T )  § 3  =  (2Trn  e  A  0,  ) cos  1  The c r y s t a l t h i c k n e s s i s g i v e n by d, the r e f r a c t i v e index by n , the g  amplitude o f t h e index m o d u l a t i o n a b s o r p t i o n o f the c r y s t a l by a. is  surrounded  forming t h e g r a t i n g by n^, and the T h i s e q u a t i o n assumes t h a t the g r a t i n g  by a medium w i t h t h e same average  refractive  index.  For g r a t i n g s formed i n c r y s t a l s , r e f l e c t i o n s w i l l occur a t the b o u n d a r i e s o f the g r a t i n g due t o the change i n t h e index a t t h e crystal surfaces. ted  F i g . 6.1 shows the i n t e r a c t i o n o f the m u l t i p l y - r e f l e c ^ t .  wave w i t h the hologram g r a t i n g .  transmission c o e f f i c i e n t e n t e r i n g the c r y s t a l .  At the f i r s t  boundary, the F r e s n e l  t ^ g i v e s "the amplitude o f the primary wave  : .  A f t e r one t r a v e r s a l o f the c r y s t a l , p a r t o f t h e  r e f r a c t e d wave i s r e f l e c t e d and a wavelet  o f amplitude  t ^ t S ( d ) emerges. 2  Both the primary wave and the r e f r a c t e d wave a r e r e f l e c t e d back i n t o the g r a t i n g and the i n t e r a c t i o n c o n t i n u e s .  The next r e f r a c t e d wavelet t o  emerge has t r a v e r s e d the g r a t i n g t h r e e times i n t o t a l and has an 2  amplitude at  t^t r 2  S(3d).  Here t  2  i s the F r e s n e l t r a n s m i s s i o n c o e f f i c i e n t  the second boundary, and r i s t h e F r e s n e l r e f l e c t i o n c o e f f i c i e n t f o r  beams i n c i d e n t on the s u r f a c e from w i t h i n the c r y s t a l .  The t o t a l  95  t t 1  F i g . 6.1  Multiple  2  S(d)  reflections  tj_t r  S(3d)  2  i n a hologram  grating.  of a l l the d i f f r a c t e d w a v e l e t s emerging from t h e c r y s t a l i s S. * = t , t ( S ( d ) + r S ( 3 d ) + r S ( 5 d ) + tot 1 2 2  4  0  Since t  2  = 1 + r , and t j = 1 - r , Eq. 6.2 S  w r i t t en (6.3)  (e -  9 )  tan (6 +  0 ) on the c r y s t a l  surface.  X  = 2  X  Here e i s t h e a n g l e a t which t h e beam i s i n c i d e n t I f Eq. 6.1  +...)  = (1 - R ) ( S(d) + R S(3d) + R S ( 5 d ) 2  tot tan  where R = r  can be  (6.2)  ...)  i s inserted  i n Eq. 6.3,  two g e o m e t r i c s e r i e s a r e o b t a i n e d  which can be summed to g i v e S ( d ) ( l - R) [ l + R e x p { d ( Y  tot  1 - R[exp{2d(Y  2  - 13)}+  exp{2d(Y  1  2  + Y  - 16)}] +R  2  x  - 2IB)}]  exp{2d(Y  2  (6.4) 4^-213)}  96  F i g . 6.2 E f f e c t i v e d i f f r a c t i o n e f f i c i e n c y of a hologram i n a l i t h i u m n i o b a t e c r y s t a l i s p l o t t e d a g a i n s t temperature change. F o r b o t h c u r v e s , n (T X = 2.252, X = 488 nm, d = 3 mm. The s o l i d c u r v e i s c a l c u l a t e d f a r no a b s o r p t i o n . The dashed l i n e i s c a l c u l a t e d w i t h ad = 0.28.  97  700  r  F i g . 6.3 E x p e r i m e n t a l l y o b t a i n e d r e f l e c t e d i n t e n s i t y o f an a r g o n i o n l a s e r beam i n c i d e n t on a 3 mm t h i c k c r y s t a l o f undoped LiNbO^ i s p l o t t e d a g a i n s t time o f exposure. T^he a n g l e o f i n c i d e n c e was 15 and t h e t o t a l beam i n t e n s i t y was 2360 W/m .  98  30„  J21 0.0  t  i '  1.0  t  i 2.0  i  i 3.0  i  j  4.0  AT (°C)  F i g . 6.4 E f f e c t i v e d i f f r a c t i o n e f f i c i e n c y of a hologram i n Fe-doped LiNbOg i s plotted against temperature. The "crosses" are experimentally obtained p o i n t s . The s o l i d l i n e i s calculated with n (T ) = 2.27351. e o d(T ) = 1.40 mm, X = 441.6 nm, ad = 0.252, T = 3 1 . 5 5 ° C , and SS* = 0.5. n  99  The  d i f f r a c t e d wave due t o m u l t i p l e S  tot  = T  r e f l e c t i o n s i s g i v e n by  ' ( > S  d  (6  where S(d) i s t h e wave d i f f r a c t e d i n t h e absence o f m u l t i p l e The  ' > 5  reflections.  e f f e c t i v e d i f f r a c t i o n e f f i c i e n c y , n , d e f i n e d as t h e r a t i o o f t h e  i n t e n s i t i e s of the incident f r a c t e d beam a f t e r l e a v i n g  beam e x t e r n a l t o t h e c r y s t a l the c r y s t a l , i s n  W i t h no m u l t i p l e  and t h e d i f -  e  = SS*TT*  (6.6)  r e f l e c t i o n s , t h e d i f f r a c t i o n e f f i c i e n c y would j u s t be  A  ss .  A  Since the transmittance f a c t o r TT  i s a function  of  the path  l e n g t h , t h e d i f f r a c t e d F o u r i e r components o f a r e a l hologram would be d i f f e r e n t l y affected  by m u l t i p l e  reflections.  I n the present case  however, t h e e f f e c t o f a change i n p a t h l e n g t h can be e a s i l y computed. The  e f f e c t o f a change i n t e m p e r a t u r e (T - TQ) can be accounted f o r by  writing  t h e e x t r a o r d i n a r y i n d e x n and t h e t h i c k n e s s d as n = n ( T ) ( l + 6<T-- T ) ) &  £  E  o  Q  ( 6 > ? )  and d = d ( T ) ( l + a'(T - T ) ) . o  Q  ( 6 > 8 )  -4 o Reported v a l u e s o f t h e t h e r m a l c o e f f i c i e n t s a r e 6 = 0.392 x 10  / C  (Boyd e t a l . 1967) a t 450 nm and a' = 16.7 x 10~ /°C (Nassau e t a l . 1966) 6  Hobden  and Warner (1966) a l s o  dence o f t h e r e f r a c t i v e The  g i v e a v a l u e f o r t h e t e m p e r a t u r e depen-  index.  s o l i d l i n e i n F i g . 6.2 shows t h e v a r i a t i o n i n t h e  e f f e c t i v e d i f f r a c t i o n e f f i c i e n c y w i t h changes i n t e m p e r a t u r e f o r a l o s s less d i e l e c t r i c grating grating  3mm t h i c k .  o f t h e same t h i c k n e s s .  o s c i l l a t i o n would be s m a l l e r .  The d o t t e d l i n e i s f o r an a b s o r b i n g  For a thicker grating  the period of  V e r y s m a l l u n i f o r m a b s o r p t i o n does n o t  100  affect  the p e r i o d o f the o s c i l l a t i o n s , but the maximum e f f e c t i v e  dif-  f r a c t i o n e f f i c i e n c y and the amplitude o f the o s c i l l a t i o n s a r e s m a l l e r f o r t h e same phase g r a t i n g . refractive 100%  index g r a t i n g  These r e s u l t s were c a l c u l a t e d  t h a t would g i v e a d i f f r a c t i o n e f f i c i e n c y o f  i n the absence o f m u l t i p l e r e f l e c t i o n s  and a b s o r p t i o n .  In some c i r c u m s t a n c e s , m u l t i p l e r e f l e c t i o n s may enhance the d i f f r a c t i o n e f f i c i e n c y . t h a t d i f f r a c t s 10% o f t h e i n c i d e n t diffract  fora  F i g . 6.3 i n d i c a t e s  actually  that a  grating  l i g h t w i t h no r e f l e c t i o n s can  15% o f the l i g h t f o r c e r t a i n  o p t i c a l paths.  6.3 E x p e r i m e n t a l R e s u l t s Two experiments were performed t o determine t h e e f f e c t s o f temperature on the d i f f r a c t i o n e f f i c i e n c y o f a simple g r a t i n g 3mm t h i c k ,  ina  undoped c r y s t a l o f LiNbO^. The  first  experiment was to determine i f the beams used t o  read and w r i t e holograms c o u l d heat the c r y s t a l s u f f i c i e n t l y t o a f f e c t the  diffraction efficiency.  time f o r an argon i o n l a s e r polarized  F i g . 6.4 shows the r e f l e c t e d (A = 488nm) i n c i d e n t  i n t e n s i t y vs  a t 15°. The beam was  w i t h i t s e l e c t r i c v e c t o r i n the p l a n e o f i n c i d e n c e and i t s 2  i n t e n s i t y was 2360 W/m The by  .  intensity  reflectance  o f a two-surfaced system i s g i v e n  (Heavens 1955) T  2 :1  + 2r r x  1 + 2r r x  where r ^ and r  2  2  cos ( 2 6 ^ + x\  cos ( 2 6 ^ + ^  2  2  r  (  (r  2  >  9  )  2 2  a r e the o r d i n a r y F r e s n e l c o e f f i c i e n t s  second s u r f a c e r e s p e c t i v e l y ,  6  f o r the f i r s t and  = - r ^ f o r t h i s case) "and  6j-=  2 1 0 1 ^ 0 0 3 ^  101  F i g . 6.4 due t o h e a t i n g .  i n d i c a t e s a change i n the o p t i c a l p a t h l e n g t h  The r a t e o f r i s e o f temperature i s i n i t i a l l y  s l o w i n g down as a steady s t a t e i s approached. w i l l affect r  1  and r  through Eq. 6.7,  2  compared t o the e f f e c t on 8^ an i n t e n s i t y  A second experiment was changes  i n the ambient  laser  3  suffer  out t o show t h a t  temperature w i l l change the e f f e c t i v e A hologram was  nm).  small  diffraction  formed  u s i n g two p l a n e waves  (A = 441.6  to the o b j e c t beam i n t e n s i t y was beams o f 27.5°.  i s negligible  fluctuations).  also carried  doped (0.015 mole%) c r y s t a l o f L i N b 0 He-Cd 15 mW  A change i n temperature  however the e f f e c t  e f f i c i e n c y due to m u l t i p l e r e f l e c t i o n s .  from a RCA  fast,  ( i . e . the l i g h t must be c o h e r e n t t o  change due t o temperature  8^  i n an Fe-  originating  The r a t i o o f the r e f e r e n c e  1.2 w i t h an a n g l e o f i n c i d e n c e between  Both beams were p o l a r i z e d w i t h the e l e c t r i c v e c t o r  p a r a l l e l t o the p l a n e of i n c i d e n c e which a l s o c o n t a i n e d the c - a x i s o f the  crystal.  controlled  The c r y s t a l was  p l a c e d i n a chamber w i t h the temperature  t o b e t t e r than ±0.02°C.  The hologram was  ±0.02°C u n t i l the e f f e c t i v e d i f f r a c t i o n e f f i c i e n c y A f t e r w r i t i n g the hologram,  formed a t 35.64  was  about  25%.  the e f f e c t i v e d i f f r a c t i o n e f f i c i e n c y  was  measured by momentarily e x p o s i n g the c r y s t a l t o the r e f e r e n c e beam ( a t reduced i n t e n s i t y ) from time t o t i m e .  F i g . 6.5 i n d i c a t e s t h a t the hologram  decayed s i g n i f i c a n t l y (due t o t h e r m a l r e l e a s e o f e l e c t r o n s from t r a p s ) i n the  first  t h i r t y minutes, a f t e r which the t h e r m a l decay was  enough not to a f f e c t  the measurements o f  interest.  A f t e r t h i s i n i t i a l p e r i o d , the d i f f r a c t e d monitored as the temperature was are  shown i n F i g . 6.6.  small  light intensity  a l l o w e d to s l o w l y f a l l ,  and the  was  results  The p o i n t s a r e e x p e r i m e n t a l and the s o l i d l i n e it  was  f i t t e d by v a r y i n g n  e  and SS  i n Eq. 6.6), w i t h the temperature  (the absolute d i f f r a c t i o n dependence o f n  efficiency  and d (from Eqs.  102  6.7 and 6.8) i n c l u d e d . sensitive  t o changes  The e f f e c t i v e d i f f r a c t i o n e f f i c i e n c y i s c l e a r l y  i n temperature as s m a l l as 1°C.  The e f f e c t i s  almost e n t i r e l y due t o a change i n t h e o p t i c a l path l e n g t h through -3 the c r y s t a l .  The a n g l e o f r e f r a c t i o n  T h i s would have n e g l i g i b l e  o n l y changed  about  e f f e c t on the Bragg c o n d i t i o n .  expansion i n the c - d i r e c t i o n  10  degrees. Thermal  i s e i g h t times s m a l l e r than i t i s i n the a  or b d i r e c t i o n s (Nassau e t a l . 1966) and i s , i n any c a s e , so s m a l l as t o cause n e g l i g i b l e  change i n t h e g r a t i n g  spacing.  In c o n c l u s i o n , i t has been shown t h a t a s m a l l change i n temperature w i t h i n the LiNbO^  c r y s t a l can s i g n i f i c a n t l y change the  e f f e c t i v e d i f f r a c t i o n e f f i c i e n c y o f a hologram  stored i n the c r y s t a l .  A temperature i n c r e a s e can be caused by t h e a b s o r p t i o n o f moderately i n t e n s e l a s e r beams used t o read and w r i t e holograms.  The e f f e c t i s  due t o thermal expansion i n c r e a s i n g t h e o p t i c a l path l e n g t h o f t h e crystal.  Multiple internal reflections  to o s c i l l a t e as t h e o p t i c a l t h i c k n e s s  cause the d i f f r a c t e d  changes.  intensity  103  - CHAPTER 7 PHOTOCURRENTS IN LITHIUM NIOBATE  7.1  Introduction P h o t o c u r r e n t s i n LiNbO^ may  externally applied f i e l d  (Chen 1969).  be measured i n the absence of an As was  o u t l i n e d ' i n Sec.  2.6,  G l a s s et al.(1974b ,1975a) have used the b u l k p h o t o v o l t a i c e f f e c t  to  explain t h i s .  photo-  In t h i s c h a p t e r , e x p e r i m e n t a l o b s e r v a t i o n s of the  c u r r e n t a r e g i v e n which support the t h e o r y t h a t p h o t o c u r r e n t s w i l l i n the absence of b u i l t - i n f i e l d s i n the The experiments  flow  crystal.  to be d e s c r i b e d show t h a t the r e l a t i o n between  the p h o t o c u r r e n t and the r a d i e n t i n t e n s i t y i s l i n e a r over the range considered. charge  C o o l i n g c r y s t a l s from a temperature  t h a t r e l a x e s space  f i e l d s , w i t h and without a s h o r t a p p l i e d to the c - f a c e s of the  c r y s t a l , d i d not a f f e c t the p h o t o c u r r e n t .  P h o t o c u r r e n t s were measured  d u r i n g hologram f o r m a t i o n i n doped and undoped c r y s t a l s .  An attempt  was  made to c o r r e l a t e the p h o t o c u r r e n t w i t h the induced change i n the refractive  7.2  index.  Experimental  Procedure  For s i n g l e beam measurements, the c r y s t a l s were i l l u m i n a t e d w i t h an argon i o n l a s e r nate the whole c r y s t a l .  ( A = 514.5  602  The beam was  expanded to  To make e l e c t r i c a l c o n n e c t i o n to the  g o l d e l e c t r o d e s were evaporated a f l a s h of chromium.  nm).  i n the c - f a c e s of the c r y s t a l s  The p h o t o c u r r e n t was  illumi-  crystals, over  measured w i t h a K e i t h l e y  electrometer. In the h o l o g r a p h i c measurements, the c r y s t a l s were i l l u m i n a t e d  104  in  the c e n t r a l  3 mm.  p o r t i o n o f t h e c r y s t a l w i t h a beam  The a n g l e between t h e beams (26) was 30°.  diameter  of  The e l e c t r i c v e c t o r o f  each beam and the c - a x i s o f t h e c r y s t a l were i n t h e p l a n e o f i n c i d e n c e . The p h o t o c u r r e n t was measured i n t h e same way as t h e s i n g l e beam experiments.  Both an argon i o n l a s e r  ( A = 480 nm) and a He-Cd  laser  ( X= 441.6 nm) were used t o w r i t e holograms.  7.3  Results When t h e c r y s t a l s were i l l u m i n a t e d ,  c u r r e n t and a p h o t o c u r r e n t were measured.  both a  pyroelectric  F i g . 7.1 shows t h e s h o r t  c i r c u i t c u r r e n t measurement on an undoped LiNbO^ c r y s t a l . peak i s t h e p y r o e l e c t r i c heating. exhibited  contribution  The steady s t a t e  The i n i t i a l  to the c u r r e n t caused by beam  current i s the photocurrent.  The p h o t o c u r r e n t  no decay a f t e r 43 hours o f c o n t i n u o u s i l l u m i n a t i o n .  When t h e  l i g h t was turned o f f , a p y r o e l e c t r i c  c u r r e n t o f o p p o s i t e p o l a r i t y was  measured  F i g . 7.2 shows t h e p h o t o c u r r e n t  as t h e c r y s t a l c o o l e d .  for' d i f f e r e n t  i n t e n s i t i e s measured on an undoped c r y s t a l .  ship i s c l e a r l y  The r e l a t i o n -  linear.  To t e s t t h e e f f e c t s o f p y r o e l e c t r i c  f i e l d s on t h e photo-  c u r r e n t an Fe-doped (0.015 mole %) LiNbO^ was s l o w l y c o o l e d from 375°C w i t h circuited.  ( i ) t h e c - f a c e s s h o r t e d and ( i i ) w i t h t h e c - f a c e s openI n each case the p h o t o c u r r e n t was measured a f t e r  reached room temperature.  The r e s u l t s o f t h r e e experiments  the c r y s t a l are given  i n T a b l e 7.1. F i g . 7.3 shows t h a t i n the i n i t i a l  stages o f hologram  form-  ic ation,  arcsin  ( n ) was l i n e a r i n exposure 2  F i g . 7.4 shows t h e same r e s u l t  f o r an undoped c r y s t a l .  f o r an iron-doped c r y s t a l .  From  105  LIGHT OFF  'LIGHT ON  F i g . 7.1 Time development of the p r y r o e l e c t r i c and photo c u r r e n t s d u r i n g i l l u m i n a t i o n and of the p y r o e l e c t r i c c u r r e n t a f t e r the l i g h t i s turned o f f . l.Or  INTENSITY F i g . 7.2 The p h o t o c u r r e n t intensities.  / (mW  cm ) -2  i n an undoped  LiNbO^ c r y s t a l f o r d i f f e r e n t  106  F i g . 7.3 I n i t i a l two wavelengths.  stage o f hologram f o r m a t i o n i n an undoped c r y s t a l a t A r c s i n ( / n ) i s p r o p o r t i o n a l t o t h e change i n i n d e x .  EXPOSURE /(mJ/cm ) 2  F i g . 7.4 I n i t i a l stage o f hologram f o r m a t i o n i n an Fe-doped(0.015 mole %) c r y s t a l a t two wavelenths.  107  Kogelnik's  (1969) d e r i v a t i o n o f t h e d i f f r a c t i o n e f f i c i e n c y f o r a s i n u -  s o i d a l g r a t i n g , a l i n e a r r e l a t i o n s h i p i s expected  s i n c e t h e amplitude  of t h e index modulation  (i/r\ ) •  doped c r y s t a l produced  i s p r o p o r t i o n a l to a r c s i n  The i r o n -  a g r e a t e r change i n t h e index than t h e undoped  c r y s t a l f o r the same exposure.  As shown i n F i g s . 7.3 and 7.4, t h e  p r o c e s s was more e f f i c i e n t a t A = 441.6 nm.  SEQUENCE  PHOTOCURRENT  ABSORPTION  I / a  pA  COEFFICIENT -1 cm  pA cm  sc  5.4  0.48  11.3  oc  3.6  0.31  11.2  sc  5.8  0.51  11.4  T a b l e 7.1 E f f e c t s o f s h o r t - c i r c u i t (sc) and o p e n - c i r c u i t (oc) c o o l i n g on t h e p h o t o c u r r e n t (A = 514.5 nm) . The a b s o r p t i o n was measured on a Cary Spectrophotometer w i t h i n c o h e r e n t l i g h t w i t h c o r r e c t i o n s made f o r reflections. The c r y s t a l s were c o o l e d from 375°C t o 25°C. D u r i n g these measurements t h e p h o t o c u r r e n t was measured a f t e r t h e p y r o electric transient.  The c u r r e n t s a r e l i s t e d  i n T a b l e 7.2.  PHOTOCURRENT (pA) CRYSTAL  A = 488 nm  A = 441.6 nm  Doped  0 .224  0.216  Undoped  1 .44  0.842  T a b l e 7.2 P h o t o c u r r e n t s measured d u r i n g hologram f o r m a t i o n i n an Fe-doped (0.015 mole %) and undoped c r y s t a l a t two d i f f e r e n t wavelengths.  108  7.4  Discussion The measurement o f the p h o t o c u r r e n t  it  i n LiNbO^ shows t h a t  does not decay w i t h time when the e n t i r e c r y s t a l i s i l l u m i n a t e d and  t h a t i t i s p r o p o r t i o n a l t o the i n t e n s i t y o f the i l l u m i n a t i o n . al.  Glass e t  (1974b) have r e p r e s e n t e d the p h o t o c u r r e n t d e n s i t y as J  = KCtl  (7.1)  where I i s the i n t e n s i t y , a the a b s o r p t i o n and K a c o n s t a n t depending on the i m p u r i t i e s i n the c r y s t a l ,  (see Sec. 2.6).  From the s l o p e o f F i g . 7.2  -1 -9 a = 0.115 cm , K = 1.14 x 10 Acm/W f o r the undoped  and w i t h  crystal —9  used.  T h i s i s comparable t o G l a s s e t a l . ' s v a l u e o f < = 3.0 x 10  Acm/W f o r a Fe-doped Although it  a new t r a n s p o r t mechanism i s thought  i s n o t immediately  be n e g l e c t e d .  crystal.  obvious  t o be i n v o l v e d ,  t h a t the e f f e c t s o f p y r o e l e c t r i c f i e l d s can  I t i s w e l l known t h a t i f no f r e e charges were e x t e r n a l l y  a v a i l a b l e , LiNbO^ c r y s t a l s  c o o l e d from  ~200°C w i t h no f i e l d p r e s e n t would  develop v e r y l a r g e i n t e r n a l and e x t e r n a l f i e l d s due t o the uncompensated change i n remanent p o l a r i z a t i o n ( A m o d e i e t a l . 1972b).  These f i e l d s  are so  l a r g e t h a t i t seems p o s s i b l e t h a t i n j e c t i o n o r e x t r a c t i o n o f e l e c t r o n s s h o u l d s e t up space scale fields  charges w i t h i n the c r y s t a l w i t h the r e s u l t t h a t l a r g e  remain i n the c r y s t a l even a f t e r a p p l y i n g an e x t e r n a l s h o r t .  S h o r t i n g the c - f a c e s o f the c r y s t a l d u r i n g c o o l i n g would p r e v e n t t h e development o f these space  charges.  p h o t o c u r r e n t was independent T h i s experiment suggests  failed  that b u i l t - i n  temperature  The d a t a i n T a b l e 7.1 shows t h a t t h e  o f the e l e c t r i c a l c o n d i t i o n d u r i n g c o o l i n g .  t o c o n f i r m the e x i s t e n c e o f a b u i l t - i n f i e l d s o f p y r o e l e c t r i c o r i g i n developed  range encountered  field.  It  over the  h e r e may be n e g l e c t e d and t h a t some o t h e r  mechanism i s r e s p o n s i b l e f o r the p h o t o c u r r e n t .  109  In attempting to correlate the photocurrent measured during hologram formation with the index modulation  required to give the  measured d i f f r a c t i o n e f f i c i e n c y , only the i n i t i a l region of l i n e a r index change was considered.  The holograms were considered to be  formed by electrons d r i f t i n g i n a f i e l d with the migration length being short compared with the grating spacing.  The space charge f i e l d  i s given by Eq. 2 . 7  E  = sc  where L = E y T . Q  eLg mt — cos kx e  (7.2)  The change i n the r e f r a c t i v e index i s given by Eq. 2 . 3 1 -n  *  3 e  r  E  33 sc 0 0  Using Eq. 5 . 5 and Eq. 6 . 6 the e f f e c t s of multiple r e f l e c t i o n s may be allowe for.  The measured build-up i n the d i f f r a c t i o n e f f i c i e n c y i s n  e  sinVf  = TT*  (  ^  d o  s  C e  °  S  2 9  )  (7.4)  o  * h If of  a r c s i n ( (n /TT K ) e  i s plotted as a function of time, the slope  the curve can be calculated from Eq. 7 . 2 to Eq. 7 . 4 to be 3  cos 26 r_.meg L cos kx  ird n S1  "--=  '27T~co's/o  "  0.5)  0  Eq. 7 . 5 may be solved f o r the expression g LQ  This may be compared with  the value of g L computed from the photocurrent i n the following way. Q  For a c r y s t a l with electrodes separated by a distance I, the average photocurrent measured at the electrodes i s assumed to be given by I = eg vf (7.6) p  o  110  where g V i s  t h e number o f  Q  illuminated  v o l u m e (V)  d i s t a n c e each e l e c t r o n and E q . 7.6  electrons(e)  generated per second i n  and L / £  is,  travels  between the  on the a v e r a g e , the f r a c t i o n  independent measurements of Table 7.3 l i s t s  the  electrodes.  of  From E q .  the  7.5  g L can be made. Q  the v a l u e s of  g L c a l c u l a t e d by the °o c r y s t a l and a n undoped  two  J  methods f o r  Crystal  a doped (0.015 mole % i r o n )  _ 1 2 - 2 -1 g L/10 m s / 1 A  Wavelength  o  from  (nm)  Undoped  Doped  0.173  441.6  5.63  0.63  488  1.79  0.963  441.6  1.56  1.09  Q  g L for Q  g L, c a l c u l a t e d from t h e diffraction efficiency.  different  crystals  c a n n o t b e made b e c a u s e t h e i n t e n s i t y for  all  the  d i s c r e p a n c y between the v a l u e s of  ent  methods.  the measurements.  The d i f f r a c t i o n  any  the  efficiency  9.62  -Table 7.3 A comparison of to g L c a l c u l a t e d f r o m t h e  of  from d i f f r a c t i o n  photocurrent  488  A comparison of  magnitude  of  crystal.  the  " d c " change i n the  of  and d i f f e r e n t  illumination  T h e r e a r e a number o f  efficiency  photocurrent  wavelengths  was n o t  Q  index modulation.  It  same  possible reasons  g L c a l c u l a t e d by the  measurement  the  g i v e s an  does not  i n d e x w h i c h may be p r o d u c e d .  two  for  differ-  estimate  account  A s w i l l be  for shown  ,  Ill  i n the next c h a p t e r , the geometry o f i l l u m i n a t i o n o f the c r y s t a l a f f e c t s t h e r a t e a t which holograms a r e formed.  In a d d i t i o n , the  o p t i c a l and thermal h i s t o r y o f the c r y s t a l may be important. i n c l u s i o n o f TT  The  i n Eq. 7.4 t o account f o r m u l t i p l e r e f l e c t i o n s p r o -  v i d e s o n l y an approximate  c o r r e c t i o n since the o p t i c a l thickness of  the c r y s t a l i s n o t known t o a f r a c t i o n o f a wavelength.  Subsequent  to t h e s e measurements a method has been developed t o circumvent problem  this  (Moharam, C o r n i s h and Young 1975) . O p t i c a l e r a s u r e o f the hologram  reduce the r a t e a t which the hologram  d u r i n g i t s f o r m a t i o n may  forms.  The o p t i c a l e r a s u r e  would c o n t r i b u t e t o the p h o t o c u r r e n t but would decrease the index grating.  T h i s would cause a d i s c r e p a n c y between g L measured u s i n g Q  these two methods. In c o n c l u s i o n , the p h o t o c u r r e n t was l a r g e r than would be expected from the hologram measurements.  A better correlation  might  be a c h i e v e d i f some o f the problems l i s t e d above -»were taken i n t o account.  112  CHAPTER 8 THE  EFFECTS OF  8.1  INTERNAL AND  APPLIED FIELDS ON  HOLOGRAMS STORED IN  LlNb0  Introduction The  grams may  a p p l i c a t i o n o f an e x t e r n a l f i e l d  during  the w r i t i n g of  be an important method of c o n t r o l l i n g the p r o c e s s .  d i f f u s i o n , i n t e r n a l f i e l d s and r e f r a c t i v e process.  The  the b u l k p h o t o v o l t a i c  published  are i n apparent c o n t r a d i c t i o n . applied f i e l d  T h i s was  of  e f f e c t to the photo-  d a t a on which p r o c e s s e s a c t u a l l y o c c u r  S t a e b l e r et a l . found t h a t e i t h e r s i g n of  (± 2kV/cm (1972b) and  of w r i t i n g e q u a l l y .  ± lOkV/cm (1974a)) i n c r e a s e d  taken as i n d i c a t i n g d i f f u s i o n .  the  On  increased  of o p t i c a l damage. field and  T h i s was  and  the other  taken as i n d i c a t i n g t h a t d r i f t  o f p y r o e l e c t r i c o r i g i n was  o c c u r r i n g , as proposed by  the magnitude of the f i e l d was The  experiments by  and  on  Chen (1969)  et a l . on be  s i g n i f i c a n c e i n the l i g h t of  the  the b u l k p h o t o v o l t a i c e f f e c t , s i n c e a l t h o u g h p y r o e l e c t r i c  the b u l k p h o t o v o l t a i c  field  in k built-in '  Staebler  f i e l d s might be absent i n a p a r t i c u l a r c r y s t a l , i t i s not  The  generation  i n which holograms were found to  w r i t t e n by d i f f u s i o n o n l y , assume a new theory,  that  estimated.  r e s u l t s of the p r e v i o u s  the e f f e c t o f a p p l i e d v o l t a g e ,  new  reduced the r a t e of  rate  the  other hand, Ohmori et a l . (1974) and Yasojima et a l . (1972) found s i g n of f i e l d  holo-  I t i s also  an a t t r a c t i v e means of i n v e s t i g a t i n g the r e l a t i v e c o n t r i b u t i o n s  one  3  e f f e c t should  be  obvious  how  inoperative.  experiments to be d e s c r i b e d  show t h a t the r e s u l t s of a p p l i e d  experiments depend on the f r a c t i o n of the c r y s t a l i l l u m i n a t e d the i n t e n s i t y o f l i g h t .  hologram w r i t i n g and  In a d d i t i o n , d u r i n g r e p e a t e d c y c l e s of  r e a d i n g , w i t h consequent o p t i c a l e r a s u r e ,  the  \'  113  d i f f r a c t i o n e f f i c i e n c y of the holograms depends on the voltage applied during the previous cycles as w e l l as that applied during the current writing.  The explanation of the r e s u l t s i s that l a r g e - s c a l e "dc"  space charge f i e l d s (as w e l l as the s p a t i a l  "ac" f i e l d s which produce  the holograms) are b u i l t - i n by exposure to l i g h t .  The actual f i e l d i n  the c r y s t a l depends, therefore, on the f i e l d b u i l t - i n during the previous and current exposure, as w e l l as on the applied f i e l d . An experimental complication i s that applied f i e l d s of the magnitudes required i n these experiments can appreciably a f f e c t the o p t i c a l thickness of the c r y s t a l and hence can affect both reading and writing holograms due to multiple i n t e r n a l It  reflections.  i s w e l l known that exposure to l i g h t can "build i n " a  large scale "dc" f i e l d .  Although not e x p l i c i t y taken into account i n  previous work on the effect of applied voltage, there i s no dispute that such f i e l d s are created.  They are what i s observed i n compensator ex-  periments ( e . g . the o r i g i n a l work of Chen (1969)) and i n ellipsometer experiments (Chapter 3 ) . A f i r s t point concerns the s p a t i a l extent of the " d c " space charge fields relative earlier  to the illumination that produces them.  As was discussed  (sec. 2.3) Chen (1969) explained the r e s u l t s of h i s circular-beam  experiments with a dipole-type f i e l d which extended w e l l outside the i l l u m i nated area.  Chen referred to electrons released and retrapped "outside the  illuminated area".  This phrase has been quoted or s i m i l a r statements made  i n several papers (Johnston 1970, Yasojima et a l . 1972, Peterson et a l . 1971, Clarke et a l . 1973).  A c t u a l l y , the trapping process i t s e l f i s believed  114  to be independent o f the l i g h t  intensity.  Few e l e c t r o n s a r e t r a n s p o r t e d  o u t s i d e t h e i l l u m i n a t e d volume and then o n l y f o r s h o r t d i s t a n c e s .  This  was shown i n Chapter 3 by experiments i n which t h e l i g h t beam e f f e c t i v e l y v a r i e d i n i n t e n s i t y o n l y i n one d i m e n s i o n .  With t h i s geometry, t h e f i e l d  and hence the change i n b i r e f r i n g e n c e were e s s e n t i a l l y c o n f i n e d  to the  i r r a d i a t e d volume. The  next p o i n t concerns t h e e f f e c t o f how u n i f o r m l y t h e  c r y s t a l i s Illuminated.  F o r complete, u n i f o r m  i l l u m i n a t i o n of the c r y s t a l  (which i s i m p o s s i b l e w i t h t h e two p l a n e wave beams used f o r hologram production)  t h e f i e l d i n t h e c r y s t a l would be t h e a p p l i e d f i e l d p l u s t h e  "virtual" field.  With p a r t i a l i l l u m i n a t i o n a " d c " space charge f i e l d  a l s o be p r e s e n t .  Thus, w i t h as near a s p o s s i b l e t h e whole c r y s t a l  a t e d , i t i s expected t h a t an a p p l i e d f i e l d  e q u a l and o p p o s i t e  should  illumin-  t o the  " v i r t u a l " f i e l d would a l l o w hologram w r i t i n g by d i f f u s i o n o n l y . a p p l i e d w i t h e i t h e r p o l a r i t y about t h i s v a l u e  will  Fields  increase the r a t e  of hologram p r o d u c t i o n because o f i n c r e a s e d t r a n s p o r t l e n g t h .  If plots  of d i f f r a c t i o n e f f i c i e n c y v s . v o l t a g e show a minimum which i s n o t z e r o then d i f f u s i o n  8.2  may  Experimental 8.2.1 The  be s i g n i f i c a n t .  Procedures  Sample P r e p a r a t i o n and Hologram Measurements sample used was n o m i n a l l y  pure LiNbO^ (sample #4 o f  Appendix D) heated i n I ^ C O ^ a t 520°C f o r 40 h o u r s , a treatment due t o P h i l l i p s and S t a e b l e r .  The a b s o r p t i o n was 0.23 cm * a t 514.5 nm, -  grams were formed u s i n g an argon l a s e r  *The " v i r t u a l " f i e l d  Holo-  (A = 514.5 nm) p o l a r i z e d p a r a l l e l  (E^) i s t h e f i e l d due t o t h e b u l k p h o t o v o l t a i c  as d i s c u s s e d i n Sec. 2.9.1.  effect  115  t o t h e c - a x i s w i t h an a n g l e o f i n c i d e n c e  o f 1 0 ° . With t h e s e c r y s t a l s ,  decay o f o p t i c a l damage and o f holograms i s n e g l i g i b l e i n t h e d a r k (Chapter 3) a p p a r e n t l y  due t o t h e d e s t r u c t i o n o f s h a l l o w t r a p s b u t h o l o -  grams a r e r a p i d l y erased  by i l l u m i n a t i o n w i t h t h e r e f e r e n c e  p o s s i b l e and c o n v e n i e n t , t h e r e f o r e , acquire  information  beam.  It i s  t o make r e p e a t e d experiments and t o  on r e p r o d u c i b i l t y , which i s absent i n p r e v i o u s work.  A l l measurements o f t h e e f f e c t i v e d i f f r a c t i o n e f f i c i e n c y were made by w r i t i n g w i t h two p l a n e waves f o r a s p e c i f i e d exposure and then b l o c k i n g the s i g n a l beam and m o n i t o r i n g t h e r e f e r e n c e the hologram t o decay t o z e r o . tion efficiency,  beam u n t i l r e a d o u t caused  The magnitude o f t h e e f f e c t i v e d i f f r a c -  n, ( r a t i o o f d i f f r a c t e d i n t e n s i t y t o i n c i d e n t i n t e n s i t y )  was t h a t a c h i e v e d  immediately a f t e r t h e w r i t i n g and a t t h e commencement  o f o p t i c a l r e a d o u t ( F i g . 8.1). F i e l d s were a p p l i e d through aluminum e l e c t r o d e s c-faces  of the c r y s t a l .  applied f i e l d crystal.  The c o n v e n t i o n i s t h a t t h e d i r e c t i o n o f t h e  i s p o s i t i v e i f d i r e c t e d towards t h e - c f a c e o f t h e  This i s  to the p h o t o v o l t a i c 8.2.2  evaporated on t o t h e  i n t h e same d i r e c t i o n as t h e " v i r t u a l " f i e l d due effect.  Multiple Internal Reflections  In t h e i n i t i a l work a s e r i o u s p r o b l e m became apparent w h i c h i s not mentioned i n e a r l i e r work on t h e e f f e c t o f a p p l i e d v o l t a g e . that both applied voltage  and t h e l a r g e s c a l e  This i s  (as opposed t o s i n u s o i d a l )  space charge f i e l d s produced by exposure t o l i g h t m o d i f y t h e o p t i c a l thickness extent and  o f t h e c r y s t a l through t h e e l e c t r o - o p t i c e f f e c t t o a s u f f i c i e n t  t h a t , because o f m u l t i p l e i n t e r n a l r e f l e c t i o n s , b o t h t h e w r i t i n g  reading  e f f i c i e n c y a r e changed by a p p r e c i a b l e  that, i f t h i s e f f e c t i s neglected,  applied voltage  amounts.  T h i s means  c o u l d be i n t e r p r e t e d  4  3  s«  2  -  l  u  0 1 0  *  ' 10  I  t  20  I  t  «  30  '  40  i  '  50  •  .  t  60  TIME / sec F i g . 8«1 Measurement of one w r i t e , r e a d - e r a s e c y c l e . The hologram was w r i t t e n f o r 15 sec w i t h a s h u t t e r b l o c k i n g the d e t e c t o r . A s h u t t e r was then used t o b l o c k the S i g n a l beam and the hologram e r a s u r e m o n i t o r e d u n t i l the hologram decayed. The e f f e c t i v e d i f f r a c t i o n e f f i c i e n c y n g i v e n i n o t h e r f i g u r e s was t h a t measured a t the b e g i n n i n g of r e a d - o u t i . e . a t 15 sec f o r t h i s example. e  117  .551 I  S  i  i  i  .51  s  5  i  > i  i ' » i  i  l i  .45[  • i  -  1  APPLIED  j  0  1  _ i  1  FIELD  (kV/cm)  i  t i  Fig. 8.2 E f f e c t o f a p p l i e d f i e l d on t h e t r a n s m i t t a n c e o f LiNbOg. The c r y s t a l t h i c k n e s s was 1 cm; t h e a n g l e o f i n c i d e n c e o f the l a s e r beam was 1 0 ° w i t h X = 5 1 4 . 5 nm and e l e c t r i c v e c t o r p a r a l l e l t o c - a x i s . Top: c r y s t a l a f t e r t h e r m a l e r a s u r e o f damage a t 2 7 0 ° C . Bottom: t h e same c r y s t a l a f t e r hologram w r i t i n g . The t r a n s m i t t a n c e i s d i m i n i s h e d because some o f the l i g h t i s d i f f r a c t e d by t h e hologram. The phase s h i f t a l o n g the h o r i z o n t a l a x i s i s due t o t h e o p t i c a l l y - i n d u c e d " d c " space charge field. The b a r s show the e f f e c t o f s m a l l , t e m p e r a t u r e f l u c t u a t i o n s (<0.2°C).  118  as h a v i n g an e f f e c t on t h e p h y s i c s o f t h e e l e c t r o n t r a n s p o r t p r o c e s s when i n f a c t i t was a c t i n g o n l y through  the e l e c t r o - o p t i c e f f e c t .  The  importance o f m u l t i p l e i n t e r n a l r e f l e c t i o n s was p r e v i o u s l y p o i n t e d o u t i n c o n n e c t i o n w i t h the measurement o f d i f f r a c t i o n e f f i c i e n c y where they may account  (Chapter  6)  f o r some o f t h e c y c l i c v a r i a t i o n s o f d i f f r a c t i o n  e f f i c i e n c y w i t h exposure which have been r e p o r t e d i n t h e l i t e r a t u r e . The p r e s e n t e f f e c t has n o t p r e v i o u s l y been mentioned i n t h e l i t e r a t u r e . F i g . 8.2  shows t h e observed  t r a n s m i t t a n c e changes due t o  a p p l i e d v o l t a g e s i n a c r y s t a l 1 cm t h i c k .  The upper c u r v e i s f o r a  f r e s h c r y s t a l w i t h no o p t i c a l damage and the lower  c u r v e was r e c o r d e d  a f t e r a few holograms had been s t o r e d i n t h e c r y s t a l .  The e n t i r e  curve  i s lower because some o f t h e i n c i d e n t beam used t o r e c o r d t h e c u r v e was d i f f r a c t e d by t h e s t o r e d hologram.  The main p o i n t s o f i n t e r e s t a r e t h e  change i n t r a n s m i t t a n c e w i t h a p p l i e d v o l t a g e and t h e phase s h i f t between the two c u r v e s caused  by t h e e f f e c t s o f space charge f i e l d s  w h i l e w r i t i n g t h e holograms.  induced  The v e r t i c a l b a r s show t h e f l u c t u a t i o n s i n  t r a n s m i t t a n c e due t o s m a l l temperature f l u c t u a t i o n s  (<0.2°C).  One  s o l u t i o n t o t h e problem o f m u l t i p l e r e f l e c t i o n s , which was t r i e d ally,  i s t o r e s t r i c t measurements t o v o l t a g e s g i v i n g e q u a l p a t h  (modulo A/2),  The r e a d i n g and w r i t i n g v o l t a g e s w i l l change w i t h  t o t a l exposure and must be determined  and  lengths  i . e . e q u i v a l e n t p o i n t s i n F i g . 8.2, f o r example minima  i n transmittance.  reflectance.  initi-  by measuring t r a n s m i t t a n c e o r  An a l t e r n a t i v e way around t h e problem o f m u l t i p l e r e f l e c t i o n s ,  t h e method used i n t h e experiments t o be d e s c r i b e d , i s t o u s e  s u f f i c i e n t l y t h i n c r y s t a l s t h a t t h e change i n o p t i c a l t h i c k n e s s may be neglected.  I n t h i s case, the e f f e c t i v e d i f f r a c t i o n e f f i c i e n c y  still  119  1 2 SUCCESSIVE  3 WRITE-READ  4  5 CYCLES  F i g . 83 E f f e c t o f p r i o r exposure a t d i f f e r e n t v o l t a g e s on hologram w r i t i n g f o r p a r t i a l i l l u m i n a t i o n o f the sample. The i n c r e a s i n g t r a n s i e n t shows 3 s u c c e s s i v e w r i t e - r e a d c y c l e s " a t z e r o ^ a p p l i e d f i e l d a f t e r a 15 s e c exposure t o t h e r e f e r e n c e beam w i t h +3 kVcm a p p l i e d . The d e c r e a s i n g t r a n s i e n t shows 3 s u c c e s s i v e w r i t e - r e a d c y c l e s a f t e r a 15 s e c exposure to the r e f e r e n c e beam w i t h -3 kVcm a p p l i e d . The b a r s show the s t a n d a r d d e v i a t i o n o f 11 holograms formed a t zero a p p l i e d f i e l d . W r i t i n g and r e a d i n g c o n d i t i o n s were t h e same as f o r t h e lower c u r v e i n F i g . 8.4 .  120  -  3  -  2  - 1 APPLIED  0 VOLTAGE /kV  1  2  3  1/2 F i g . 8.4 N o r m a l i z e d v a l u e s o f a r c s i n n vs. applied voltage (for elect r o d e s 1 cm a p a r t ) . The r e l a t i v e a r e a o f i l l u m i n a t i o n i s shown by t h e c i r c l e s and t h e c r y s t a l f a c e (1 cm square) by t h e s q u a r e s . Curve A: t h e exposure corresponded t o p o i n t 3 on F i g . 8.5 and the i n t e n s i t y was 8.36 mW/cm . Curve B: t h e exposure c o r r e s p o n d e d t o p o i n t 2 o f F i g . 8.5 and t h e i n t e n s i t y was 44 mW/cm . Curve C: exposure and i n t e n s i t y , same as B. Curve D: t h e exposure c o r r e s p o n d e d t o p o i n t 1 o f F i g . 8.5 and t h e i n t e n s i t y was 378 mW/cm . e  2  2  121  d i f f e r s from t h e a b s o l u t e d i f f r a c t i o n e f f i c i e n c y , b u t the d i f f e r e n c e i s not a p p r e c i a b l y  changed by the a p p l i e d v o l t a g e or by space charge  I t s h a l l l b e assumed t h a t v a l u e s o f a r c s i n n e  r e l a t i v e amplitudes  8.3  1/2  fields.  a r e a measure o f t h e  o f the r e f r a c t i v e index g r a t i n g s .  Results The  d i f f r a c t i o n e f f i c i e n c y produced by a g i v e n exposure was  found  t o depend on t h e v o l t a g e a p p l i e d d u r i n g p r e v i o u s exposures as w e l l  as  t h a t a p p l i e d d u r i n g t h e c u r r e n t exposure.  T h i s e f f e c t was more  pronounced when o n l y a p o r t i o n o f the c r y s t a l was i l l u m i n a t e d , r a t h e r than the whole c r y s t a l .  The r e s u l t s shown i n F i g . 8.3 were o b t a i n e d  with  two beams o f 2.8 mm diameter i l l u m i n a t i n g the c e n t r a l p a r t o f the 1 cm square f a c e o f the c r y s t a l . w r i t i n g a t zero v o l t a g e  The i n c r e a s i n g t r a n s i e n t shows t h e r e s u l t of  (and then r e a d i n g u n t i l t h e hologram decayed)  t h r e e s e q u e n t i a l s t i m e s , a f t e r p r e v i o u s i l l u m i n a t i o n w i t h +3 kV/cm a p p l i e d . The d e c r e a s i n g  t r a n s i e n t shows the r e s u l t o f the same experiment b u t w i t h  -3 kV/cm a p p l i e d d u r i n g the p r e v i o u s exposure.  The b a r s r e p r e s e n t the  s t a n d a r d d e v i a t i o n o f the hologram e f f i c i e n c y o f e l e v e n s e q u e n t i a l runs performed a t zero a p p l i e d v o l t s . F i g . 8.4 shows t h e e f f e c t o f a p p l i e d v o l t a g e on the r e f r a c t i v e index g r a t i n g amplitude The  p e r u n i t exposure, f o r f o u r d i f f e r e n t i l l u m i n a t i o n s .  geometry o f i l l u m i n a t i o n f o r each curve i s shown by t h e c i r c l e s and  the r e l a t i v e s i z e o f t h e c r y s t a l i s r e p r e s e n t e d by the squares. each hologram formed a t ± a p p l i e d v o l t a g e , t h r e e or f o u r w r i t e ,  Before read-  erase c y c l e s were completed a t zero a p p l i e d v o l t a g e i n an attempt t o e s t a b l i s h s i m i l a r s t a r t i n g c o n d i t i o n s and t o check f o r f a t i g u e e f f e c t s . Curve A o f F i g . 8.4 was measured f o r exposures shown by p o i n t 3 on  122  F i g . 8.5 and w i t h the beams expanded w e l l beyond the c r y s t a l edges so t h a t the i n t e n s i t y was n e a r l y u n i f o r m a c r o s s the c r y s t a l .  F o r curve B, t h e  beams were expanded t o j u s t i l l u m i n a t e the whole c r y s t a l . f o r t h i s case corresponded  t o p o i n t 2 on F i g . 8.5.  The exposure  Curve C was measured  a t t h e same i n t e n s i t y and exposure as c u r v e B b u t w i t h o n l y the c e n t r a l p o r t i o n o f the c r y s t a l i l l u m i n a t e d . f o r F i g . 8.3.  T h i s geometry was the same as t h a t  Curve D was measured w i t h the same geometry as curve C  But a t h i g h e r i n t e n s i t y and exposure as i n d i c a t e d by p o i n t l l on F i g . 8.5. The r e s u l t s i n F i g . 8.4 show t h a t the e f f i c i e n c y o f w r i t i n g holograms depends on t h e geometry o f i l l u m i n a t i o n and on t h e i n t e n s i t y . a r e n o t symmetrical  The curves  about zero a p p l i e d v o l t a g e w i t h t h e asymmetry b e i n g  more pronounced a t h i g h e r i n t e n s i t y and w i t h o n l y p a r t o f the c r y s t a l illuminated. In one sequence o f experiments,  over 150 holograms were w r i t t e n  i n one r e g i o n o f t h e c r y s t a l and read but w i t h no n o t i c e a b l e f a t i g u e i n writing  8.4  efficiency.  Discussion In o r d e r t o i l l u s t r a t e the p r i n c i p a l f e a t u r e s r e q u i r e d t o e x p l a i n  the r a t h e r complex r e s u l t s d e s c r i b e d above, a v e r y s i m p l e model i s cons i d e r e d i n which t h e c r y s t a l i s u n i f o r m l y i l l u m i n a t e d by a s i n g l e beam over a l e n g t h L w i t h darkfcregions o f l e n g t h  2 a t each s i d e o f t h e  i l l u m i n a t e d r e g i o n . ' N e g l e c t i n g d i f f u s i o n , the c u r r e n t s i n the i l l u m i n a t e d and dark r e g i o n s , r e p e c t i v e l y , a r e J ( l i g h t ) = epnE + and  J(dark)  = eun E o a  K C I I  (8.1) (8.2)  123  EXPOSURE/Wsec  cm~2  F i g . 8.5 The time development o f a r c s i n n d u r i n g hologram w r i t i n g f o r the c o n d i t i o n s o f c u r v e D o f F i g . 8.4. Up t o 4 W s e c / c m the c u r v e s f o r the reduced i n t e n s i t i e s (curves A, B and C) i n F i g . 8.4 c o i n c i d e d . The numbers i n d i c a t e the exposures used i n F i g . 8.4. e  2  124  where t h e f r e e c a r r i e r c o n c e n t r a t i o n n = n in  o  + gx and n  i s the c a r r i e r c o n c e n t r a t i o n  o  the i l l u m i n a t e d  region field.  is E  3.  i n the i l l u m i n a t e d r e g i o n i s  region  where E  3-  i s E== E + E 3.  i s the a p p l i e d  SC  illuminated region  and the f i e l d  field  The d i s c o n t i n u i t y i n the c u r r e n t  i n the dark.  and E  SC  density  such  i n t h e dark  a t t h e edges o f t h e Q per u n i t  i n i t i a l value of Q i s Q  exposures.  The c o n s t r a i n t (E  where e E  g c  q  and i s t h e charge l e f t  + E  dt  o  for E dQ_ dt  The  from p r e v i o u s V  gives (8.4)  S u b s t i t u t i n g Eq. 8.1 and 8.2  gives  4^ = e y ( n + g x ) ( E + E  Substituting  (8.3)  )L + E & = V sc' a  = - Q and e i s t h e p e r m i t t i v i t y .  i n t o Eq. 8.3  '  of constant a p p l i e d voltage  a  area,  that  |2. = J ( l i g h t ) - J(dark) .  The  field  i s the space charge  produces s h e e t s o f spacecharge,  due t o t r a p p e d e l e c t r o n s  The  3-  and E  S  n  o  SC  T  a  sc  x a l - eyn E  ) +  o a  .  (8.5)  i n terms o f Q and V, eyQ £+Lj . E  +  eyjxV (A+L-) +  ^  ^  (  8  >  5  )  s o l u t i o n o f Eq. 8.6 i s  Q(t)  where  =  {1 - ( 1 - ^ )  t = o  o  n (J2.+L) eygx{l +  Substituting  exp(-t/t )}  the " v i r t u a l " f i e l d  — -  (8.7)  ' k.  E^ f o r K a l / e u g x , the steady s t a t e  space  125  charge f i e l d  is  E  . Q = -  ( =») t  . = -  . V + E (4+L) -/T N  H I +  (8.8)  + T  T t  °  )  T  gTL This simplified exponentially voltage, field  the  m o d e l shows t h a t  towards  its  intensity  either  final  of  the  " d c " space charge f i e l d  v a l u e w h i c h depends on the  illumination  increases or  and t h e  adjusts  applied  dark c o n d u c t i v i t y .  decreases from the v a l u e l e f t  from  The  previous  exposures. If (e.g.  a symmetrically p l a c e d , smoothly v a r y i n g  Gaussian) i s  assumed, then, w i t h zero dark  glecting diffusion, E where 1(0)  is  charge f i e l d  the is  distribution.  s c  the (x)  = -(E  space charge f i e l d  + E )(l v  I(x)/I(0))  (8.9)  "  electrodes.  This steady state  space  independent  of  the  intensity  of  light  for  a given  spatial  et  al.  theory  correct,  the  dependence  If  the G l a s s  crystal  first  c l u d i n g the  on i n t e n s i t y  implies  is  of  is  that his  space charge f i e l d  illustrated  exposure of  "virtual"  the  a crystal  With the field)  in F i g . 8.6, (i.e.  geometry is  an a p p l i e d f i e l d  which a s s i s t s the  for  an a p p l i e d  which j u s t  8.6(d)  field  for  field.  an a p p l i e d Diffusion  field  of  the  c r y s t a l s had a p p r e c i -  for  a  initial  condition the  field,  "virtual"  w h i c h opposes and i s  and i n  field  (exFig.8.6(b)  Fig.8.6(c)  and  greater  h a s b e e n n e g l e c t e d and t h e d a r k  is  field  d e v e l o p a s shown i n  "virtual"  cancels the  partially  i n a n i d e a l i z e d way  F i g . 8.6(a),  expected to  for  "virtual"  becomes  the  zero space charge).  Fig.  -  and n e -  conductivity.  illuminated the  conductivity  at  The d e v e l o p m e n t  for  a  intensity  intensity  f o u n d by Chen (1969) able dark  steady state  light  in  than  the  conductivity  126  c+  I i i i I  —  i  -  r  — i i  t  04-  (b)  0  (c) Ol  E -i i i — i -  (d)  F i g . 8.6 Idealized i l l u s t r a t i o n of the development of the "dc" space charge f i e l d ( ) during the f i r s t exposure of a c r y s t a l . (a) geometry of i l l u m i n a t i o n . (b) for an applied f i e l d which a s s i s t s the " v i r t u a l " field. (c) for an applied f i e l d which j u s t cancels the " v i r t u a l " f i e l d , (d) for an applied f i e l d which opposes and i s greater than the " v i r t u a l " f i e l d . The applied f i e l d i s shown by the s o l i d l i n e ( ).  127  has  been taken as z e r o . For p a r t i a l o r non-uniform i l l u m i n a t i o n o f the c r y s t a l , i f the  s p a t i a l v a r i a t i o n o f l i g h t i n t e n s i t y c o u l d be made the same f o r e r a s u r e and w r i t i n g , and i f the dark c o n d u c t i v i t y was n e g l i g i b l e , then t h e steady s t a t e space charge f i e l d tially  l e f t by the e r a s u r e p r o c e s s should  compensate the " v i r t u a l " and a p p l i e d  fields.  The more s p a t i a l l y  l i m i t e d the beam, t h e more exact would be t h e compensation. would be w r i t t e n by d i f f u s i o n , not d r i f t  essen-  The hologram  (except f o r the feedback e f f e c t  o f the s i n u s o i d a l space charge f i e l d ) and a p p l i e d v o l t a g e  should have  l i t t l e effect. With n o n - n e g l i g i b l e  dark c o n d u c t i v i t y the s a t u r a t i o n  charge f i e l d would depend on t h e l i g h t i n t e n s i t y . account q u a l i t a t i v e l y f o r the d i m i n i s h e d the e x p e r i m e n t a l c o n d i t i o n s Fig.  These  considerations  e f f e c t o f an a p p l i e d f i e l d f o r  o f curve D i n F i g . 8.4.  For curve C of  8.4 t h e reduced i n t e n s i t y may have produced o n l y p a r t i a l  s a t i o n o f t h e " v i r t u a l " and a p p l i e d f i e l d s . b y t h e space charge thus showing more dependence on t h e a p p l i e d The  space  compenfield,  field.  l a r g e s c a l e space charge f i e l d s c e r t a i n l y account f o r the  effects of previously applied voltages.  When t h e steady s t a t e  voltage  i s changed, the p r e v i o u s steady s t a t e space charge f i e l d no l o n g e r sates  f o r the a p p l i e d and " v i r t u a l " f i e l d s .  and w r i t i n g a r e r e q u i r e d Fig.  compen-  A few c y c l e s o f e r a s u r e  t o r e a c h a steady s t a t e response, as shown i n  8.3. From the p o i n t o f view o f a p p l i c a t i o n s i n r e a d - w r i t e memory  systems, t h e above shows t h a t b e n e f i c i a l r e s u l t s would be o b t a i n e d by s u i t a b l e changes i n a p p l i e d v o l t a g e  d u r i n g w r i t i n g and e r a s u r e c y c l e s .  128  Curves B and A o f F i g . 8.4 show t h e r e s u l t s o f s u c c e s s i v e l y more u n i f o r m i l l u m i n a t i o n o f the c r y s t a l . greater,  The w r i t i n g e f f i c i e n c y i s  the more n e a r l y u n i f o r m the i l l u m i n a t i o n beacuse the " d c "  space charge f i e l d which develops t o oppose the w r i t i n g p r o c e s s i s n o t as l a r g e .  The v o l t a g e  as n e a r l y u n i f o r m l y f i e l d s a r e minimal)  which g i v e s minimum e f f i c i e n c y w i t h t h e c r y s t a l  illuminated asspossible allows  (so t h a t space charge  the " v i r t u a l " f i e l d  t o be e s t i m a t e d ,  since  the minimum should  correspond t o a c a n c e l l a t i o n o f the a p p l i e d and  "virtual" fields.  V a l u e s o f 0.05 t o 1 kV/cm were o b t a i n e d  which a r e not  out o f l i n e i n view o f t h e wide range (1.5 and 40 kV/cm) r e p o r t e d by Glass  e t a l . (1974b, 1975a) f o r d i f f e r e n t c r y s t a l s .  The f a c t t h a t the  minimum e f f i c i e n c y o f hologram w r i t i n g w i t h as n e a r l y . a s i l l u m i n a t i o n was n o t zero  i n t h e above experiments i n d i c a t e s t h a t  d i f f u s i o n may be s i g n i f i c a n t . s i n c e the s p a t i a l p a t t e r n s  p o s s i b l e uniform  However, some q u e s t i o n  of erasure  e x i s t s on t h i s  and w r i t i n g beams a r e n e c e s s a r i l y  d i f f e r e n t and t h e i l l u m i n a t i o n can.be u n i f o r m i i n n e i t h e r case. b e l i e v e d , t h e r e f o r e , t h a t the r e s u l t s a r e i n g e n e r a l hologram w r i t i n g due t o d r i f t  It is  agreement w i t h  i n a p p l i e d , space charge and " v i r t u a l "  f i e l d s , p o s s i b l y w i t h some c o n t r i b u t i o n from d i f f u s i o n .  129  CHAPTER 9 LUMINESCENCE DUE  9.1  TO IRON CENTRES  Introduction Luminescence i n l i t h i u m n i o b a t e has been observed due  to  chromium i m p u r i t i e s , (Burns e t a l . 1966, G l a s s 1969, 1973, H o r d v i k  1972,  1973), but n o t , a p p a r e n t l y , due t o i r o n , which i s the i m p o r t a n t dopant f o r the hologram  storage a p p l i c a t i o n s of t h i s m a t e r i a l (Peterson et a l .  1973, Amodei e t a l . 1972). i t was  A s e a r c h was made f o r luminescence because  thought t h a t t h i s might h e l p towards u n d e r s t a n d i n g t h e p r o c e s s of  hologram w r i t i n g , w h i c h appears t o i n v o l v e a new mechanism, s p e c i a l t o f e r r o e l e c t r i c s  electron transport  ( G l a s s e t a l . 1975b).  A b s o r p t i o n of  l i g h t produces a p h o t o c u r r e n t d i r e c t l y , r a t h e r than foy m e r e l y  liberating  e l e c t r o n s , w h i c h t h e n produce c u r r e n t by d r i f t i n g o f d i f f u s i n g .  9.2  Experimental Procedures The samples were e x c i t e d a t room temperature u s i n g chopped  r a d i a t i o n a t 325, 488 o r 515 nm from a He-Cd or an A r g o n - i o n l a s e r w i t h e l e c t r i c v e c t o r a l o n g t h e c - a x i s . "As an i n d i c a t i o n o f the i n t e n s i t y , luminescence was j u s t o b s e r v a b l e w i t h the naked eye from undoped s p e c i mens t r e a t e d w i t h l i t h i u m c a r b o n a t e .  The l u m i n e s c e n t r a d i a t i o n  was  c o l l e c t e d w i t h an e l l i p s o i d a l m i r r o r and f o c u s s e d on the e n t r a n c e o f a P e r k i n - E l m e r 98G monochromator as shown i n F i g . 9.1. used t o p r e v e n t l a s e r l i g h t e n t e r i n g t h e monochromator and e l i m i n a t e i n c o h e r e n t l i g h t from t h e e x c i t i n g l a s e r beam. mator was  slits  F i l t e r s were a l s o , to The monochro-  f i t t e d w i t h a g r a t i n g w i t h 300 lines/mm, b l a z e d a t 640 nm i n  MONOCHROMATOR 3  ELLIPSOIDAL MIRROR  3  TTtT"  S-20 SAMPLE  NOVA-2 COMPUTER and INTERFACE  INTEGRATOR i  LOCK-IN AMPLIFIER  ITS? CHOPPER LASER  F i g . 9.1  Schematic o f t h e apparatus used t o measure t h e photoluminescence i n LiNbO  LO O  131  the f i r s t was  order.  The  luminescence p a s s i n g  d e t e c t e d w i t h a c o o l e d S-20  detector. averaging  9.3  The and  through the monochromator  p h o t o m u l t i p l i e r tube and  phase-sensitive  spectrometer i s i n t e r f a c e d to a NOVA-2 computer f o r s i g n a l a n a l y s i s o f data,  R e s u l t s and  F i g . 9.2  (Thewalt, 1975).  Discussion  (top) shows the luminescence s p e c t r a observed f o r a  congruent c r y s t a l doped w i t h 0.015  mole % i r o n b e f o r e and  the c r y s t a l i n a i r to 520°C f o r 20 h w h i l e packed i n L i C 0 2  d e f i n e d peak a t 770 nm Li C0 2  3  treatment  appears f o l l o w i n g treatment.  of u n i n t e n t i o n a l i r o n present  the peak i s due  3 >  heating  A well-  I n F i g . 9.2  (bottom)  of an "undoped" c r y s t a l i s shown to i n t r o d u c e a s m a l l  amount of e x t r a luminescence a t 770 nm, few ppm  after  presumably c o r r e s p o n d i n g  the  i n t h i s c r y s t a l . I t i s concluded t h a t  to the presence of i r o n .  background luminescence was  to  I t i s not understood why  so s m a l l i n the u n t r e a t e d  the  doped sample.  The  2+ Li C0 2  3  treatment reduces i r o n c e n t r e s to the Fe  state.  i n c r e a s e i n o p t i c a l a b s o r p t i o n i s shown i n F i g . 9.3 used. Li C0 2  A peak or shoulder 3  treatment.  adding i r o n and  The  The r e s u l t a n t  f o r the  appears i n the r e g i o n of 470 nm  crystals  following  a b s o r p t i o n edge moves t o l o n g e r wavelengths  again following L i C 0  fact that  the  luminescence peak i s so much i n c r e a s e d on c o n v e r t i n g the i r o n to  the  2  3  treatment.  The  on  2+ Fe  s t a t e suggests t h a t i t i s due  to e x c i t a t i o n of these  ever, the luminescence a t 770 nm was  l a r g e r with  undoped c r y s t a l than w i t h the u n t r e a t e d , 2+ a b s o r p t i o n at the Fe  peak a t 470 nm,  centres.  I t has  How-  the L i ^ O ^ - t r e a t e d ,  doped c r y s t a l which showed more  and,  therefore, probably  2+ more Fe  centres.  a l r e a d y been.mentioned .  contained  132  WAVELENGTH 800  n  (nm)  700  600  500  j  1  1  ' PHOTON  ENERGY  400 r~  (eV)  F i g . 9.2 Photoluminescence s p e c t r a o f LiNbO, a t 300 K. The " e x c i t a t i o n wavelength was 325 nm w i t h a power o f about 5 mW. TOP: 0.015 mole % Fe-doped LiNbO^ b e f o r e and a f t e r a n n e a l i n g treatment i n I ^ C X ^ . The v e r t i c a l bars represent the standard d e v i a t i o n s f o r the data a f t e r four scans. BOTTOM: Undoped LiNbO-j b e f o r e and a f t e r a n n e a l i n g treatment i n Li^CX^. Due t o the d i f f i c u l t i e s i n r e p r o d u c i n g t h e o p t i c a l alignment f o r d i f f e r e n t samples, t h e r e l a t i v e i n t e n s i t i e s f o r t h e f o u r s p e c t r a a r e a c c u r a t e t o o n l y 30 %. I n t h i s and l a t e r f i g u r e s no c o r r e c t i o n has been made f o r the S-20 response o f t h e f i l t e r s . U  133  F i g . 9.3 A b s o r p t i o n spectrum f o r undoped and f o r 0.015 mole % Fe-doped L i N b 0 b e f o r e and a f t e r h e a t i n g i n L i C 0 a t 520 C f o r 20 hours as measured w i t h a Cary s p e c t r o p h o t o m e t e r . 3  2  3  134  t h a t the treatment d e s t r o y s c i e s ) as w e l l - a s  reducing  shallow  traps  (perhaps due  the i r o n c e n t r e s  to oxygen v a c a n -  (see Chapter 2-).  I t may  be  t h a t the luminescence, i n f a c t , i n v o l v e s the t r a p p i n g of e l e c t r o n s  by  3+ Fe  c e n t r e s and  t h a t the removal of s h a l l o w  t r a p s means t h a t a  higher  3+ p r o p o r t i o n of e x c i t e d e l e c t r o n s a r e c a p t u r e d F i g . 9.4  by  the Fe  shows t h a t a c t i v a t i o n u s i n g  centres.  l i g h t of wavelengths  t y p i c a l l y used f o r hologram w r i t i n g a l s o gave the same luminescence 2+ peak.  In t h i s c a s e ,  should  be  the Fe  centre absorption  i n v o l v e d as opposed to the a b s o r p t i o n  et a l . 1974a, C l a r k e t a l . 1973. Glass  i n the r e g i o n o f 470 edge t r a n s i t i o n  R e d f i e l d e t a l . 1974).  et a l . (1974b,1975'a) on a b s o r p t i o n  of l i g h t  (Phillips  According  electrons are  nm  to  expelled  2+ from Fe c e n t r e s w i t h momentum i n one d i r e c t i o n a l o n g the c - a x i s . The q u e s t i o n a r i s e s as to whether e l e c t r o n s e n t e r the c o n d u c t i o n band, or 3+ whether they r e a c h  an Fe  site directly  through i n t e r v a l e n c e t r a n s f e r .  Hush (1967) d e f i n e s i n t e r v a l e n c e t r a n s f e r as  "an  which i n v o l v e s t r a n s f e r of an e l e c t r o n from one to an a d j a c e n t  one,  sess more than one  the donor and  acceptor  transition  nearly localized  site  b e i n g m e t a l i o n s which pos-  accessible oxidation state".  e l e c t r o n i s t r a n s f e r r e d between a donor and element  optical  In the c a s e where an  acceptor  (homonuclear i n t e r v a l e n c e t r a n s f e r ) no  i o n o f the same  luminescence i s expected  (Hush 1967).  T h i s , then would not appear to be the case f o r o p t i c a l t r a n s 2+ 3+ s i t i o n s i n LiNbO^ i n v o l v i n g Fe and Fe ions. C l a r k et a l . (1973) 2*f* C1 have suggested t h a t i n t e r v a l e n c e t r a n s f e r o c c u r s  between Fe  and  ions  (heteronuclear  i n t e r v a l e n c e t r a n s f e r ) so t h a t the a b s o r p t i o n  cess  i s represented  as Fe  2 +  (e) + Nb^  Fe  3 +  +  Nb *^) 5  Nb pro-  13 5--  WAVELENGTH  (nm)  700  gQO  PHOTON  ENERGY  sm  (eV)  F i g . 9.4 P h o t o l u m i n e s c e n t s p e c t r a o f 0.015 mole % Fe-doped LiNbO-j a t 300°K f o r two d i f f e r e n t wavelengths o f e x c i t a t i o n : 488 nm and 515 nm. The sample was t r e a t e d i n L^CO-j. The power o f t h e e x c i t a t i o n l i g h t was 0.4 W. The r e l a t i v e i n t e n s i t i e s o f t h e two s p e c t r a a r e a c c u r a t e t o w i t h i n 10 %. F i l t e r s were used t o b l o c k t h e e x c i t i n g l a s e r l i g h t , and a l s o t o b l o c k any background l u m i n e s c e n c e .  136  They p o s t u l a t e  t h a t e l e c t r o n s a r e then f r e e t o move i n the c o n d u c t i o n 3.  band made up of the niobium d o r b i t a l s u n t i l they a r e ions.  retrapped  I n t h i s case, the luminescence which was observed would  when the e x c i t e d e l e c t r o n s were In c o n c l u s i o n ,  by Fe  occur  retrapped.  t h e observed luminescence due t o i r o n  would appear t o i n d i c a t e t h a t e l e c t r o n s a r e d i s t r i b u t e d by means 2+ 3+ than homonuclear i n t e r v a l e n c e t r a n s f e r between Fe  and Fe  centres other  sites.  The d e t a i l s o f the p r o c e s s which a r e i n v o l v e d however,are n o t p r e s e n t l y understood. The ..occurrence o f homonuclear i n t e r v a l e n c e t r a n s f e r o f c o u r s e i s not r u l e d o u t , p a r t i c u l a r l y a t h i g h e r i r o n c o n c e n t r a t i o n s .  137  CHAPTER 10 CONCLUSIONS  The  purpose of t h i s work was to study the mechanisms o f the  p h o t o r e f r a c t i v e e f f e c t t o f u r t h e r the u n d e r s t a n d i n g of the p r o c e s s ; f o r engineering Initially, and  applications.  The c o u r s e of the work was b r i e f l y as f o l l o w s .  the phenomenon was i n v e s t i g a t e d t o c l a r i f y  d i f f u s i o n as charge t r a n s p o r t mechanisms.  photovoltaic  the r o l e o f d r i f t  L a t e r , when the b u l k  e f f e c t was proposed as a t r a n s p o r t mechanism, f u r t h e r ex-  periments were c a r r i e d out to i n v e s t i g a t e t h i s e f f e c t . s t u d i e s were made to extend the u s e f u l n e s s probing  the p h o t o r e f r a c t i v e p r o c e s s .  In a d d i t i o n ,  of automated e l l i p s o m e t r y i n  The e f f e c t s of a p p l i e d f i e l d s on  the p h o t o r e f r a c t i v e e f f e c t , and the e f f e c t s of m u l t i p l e i n t e r n a l r e f l e c t i o n s on t e c h n i q u e s used to probe t h i s e f f e c t , w e r e The  also investigated.  c o n t r i b u t i o n s which were made to the s u b j e c t may be sum-  marized as f o l l o w s : a)  A t h e o r e t i c a l treatment o f t h e development of r e f r a c t i v e i n d e x  g r a t i n g s through d r i f t short migration  and d i f f u s i o n was made w i t h o u t the r e s t r i c t i o n of  length.  The p r i n c i p a l r e s u l t was t h a t the e f f i c i e n c y  of hologram w r i t i n g i n c r e a s e s  f o r increased migration  l e n g t h up to a  certain limit.  I t was a l s o shown t h a t the i n c r e a s e d m i g r a t i o n  would not l i m i t  the r e s o l u t i o n o f the r e c o r d i n g medium.  b)  An e x p l a n a t i o n  was p r o v i d e d  e x i s t e d i n the p u b l i s h e d  f o r the apparent c o n t r a d i c t i o n which  d a t a from a p p l i e d f i e l d experiments.  shown t h a t the r e s u l t s of such experiments depend on the f i e l d during previous the c u r r e n t  exposure t o l i g h t as w e l l as on the f i e l d  experiment.  length  I t was applied  applied  during  In a d d i t i o n , the measurements depended on the  138  p o r t i o n of the c r y s t a l i l l u m i n a t e d s i n c e t h i s a f f e c t e d the magnitude of the space charge f i e l d  t h a t c o u l d be developed.  s i s t e n t w i t h holograms formed by d r i f t , voltaic effect. increase  I t was  No v a l u e  The  r e s u l t s were conthe b u l k photo-  found t h a t e i t h e r s i g n of the a p p l i e d f i e l d  asymmetry was  but  the e f f e c t was  a t t r i b u t e d to the p h o t o v o l t a i c  of the a p p l i e d f i e l d would t o t a l l y i n h i b i t hologram  i n d i c a t i n g t h a t d i f f u s i o n was c)  d i f f u s i o n and  the e f f i c i e n c y of hologram f o r m a t i o n  symmetrical.  The  Further  effect.  e v i d e n c e was  I t was  p r i m a r i l y due  partially  could  not effect.  formation  responsible.  g i v e n f o r the e x i s t e n c e  of the b u l k  photovoltaic  shown t h a t the p h o t o c u r r e n t i n l i t h i u m n i o b a t e  to p y r o e l e c t r i c f i e l d s developed d u r i n g  was  c o o l i n g of  not the  crystals. d)  The  importance of m u l t i p l e i n t e r n a l r e f l e c t i o n s on the i n t e r p r e t a t i o n  of e x p e r i m e n t a l d a t a was  recognized.  I t was  d i f f r a c t i o n e f f i c i e n c y measured o u t s i d e from the a b s o l u t e  shown t h a t the e f f e c t i v e  the c r y s t a l can v a r y  significantly  d i f f r a c t i o n e f f i c i e n c y of the phase g r a t i n g .  changes i n temperature such as those produced by  Small  exposure to medium i n t e n -  s i t y l a s e r beams produce s u f f i c i e n t change i n c r y s t a l t h i c k n e s s a significant effect. tant i n applied f i e l d  M u l t i p l e r e f l e c t i o n s were a l s o shown to be experiments and  i n the i n t e r p r e t a t i o n of  and  adjustable-compensator measurements.  e)  The  and  o p t i c a l l y induced changes i n the b i r e f r i n g e n c e of l i t h i u m  advantages of u s i n g an e l l i p s o m e t e r  c r y s t a l s were i n v e s t i g a t e d . meter was  . T h i s was  to probe the  impor-  ellipsometry  birefringence  p r a c t i c a b l e s i n c e the  automatedt'through' computer c o n t r o l .  e l l i p s o m e t r y , i t was  to have  niobate ellipso-  In a d d i t i o n to  using  shown t h a t l a r g e s c a l e changes i n the r e f r a c t i v e  i n d i c e s c o u l d be r a p i d l y i n s p e c t e d  i f the c r y s t a l was  made to a c t as  a  139  Fabry-Perot f)  interferometer.  I t was shown t h a t when l i t h i u m n i o b a t e  c r y s t a l s a r e heated i n  l i t h i u m c a r b o n a t e , t h e treatment reduces i r o n i m p u r i t i e s  , changes t h e  b i r e f r i n g e n c e o f t h e c r y s t a l and d e c r e a s e s t h e r a t e a t which induced space charge f i e l d s decay. proposed t h a t t h e treatment d e s t r o y s  optically  To e x p l a i n t h e s e r e s u l t s , i t was shallow traps.  g)  Luminescence due to i r o n c e n t r e s was observed f o r t h e f i r s t  The  s p e c t r a l b e h a v i o u r o f t h e luminescence was n o t u n d e r s t o o d b u t  would be r e l a t e d t o t h e r e d i s t r i b u t i o n o f o p t i c a l l y e x c i t e d among  traps.  10.1  Suggestions f o r Further Further  time.  electrons  Research  investigations are required  t o c h a r a c t e r i z e more  c o m p l e t e l y the mechanisms o f t h e p h o t o r e f r a c t i v e e f f e c t .  Some o f t h e  parameters i n v o l v e d i n charge t r a n s p o r t which a r e n o t p r e s e n t l y known a r e the quantum e f f i c i e n c y o f p h o t o - e x c i t a t i o n ,  the l i f e t i m e of  f r e e c a r r i e r s , t h e c a p t u r e c r o s s s e c t i o n o f t r a p s , and t h e m i g r a t i o n length of free electrons. by  the concentration  These parameters a r e undoubtedly  influenced  o f d e f e c t s and i m p u r i t i e s i n t h e c r y s t a l .  A d d i t i o n a l work i s r e q u i r e d on t h e n a t u r e o f t h e d e f e c t s and t h e i r control.  I t was suggested i n Chapter 3 t h a t h e a t i n g  l i t h i u m carbonate d e s t r o y s  shallow traps.  l i t h i u m niobate i n  I d e n t i f i c a t i o n o f these  t r a p s and how they i n f l u e n c e the p h o t o r e f r a c t i v e e f f e c t would be useful. The  luminescence s t u d i e s o u t l i n e d i n t h i s t h e s i s c o u l d  f u l l y be extended.  use-  I n f o r m a t i o n on the l i f e t i m e o f e x c i t e d e l e c t r o n s and  the energy l e v e l s o f the t r a p s i n v o l v e d  c o u l d p o s s i b l y be  obtained.  140  In a p p l i c a t i o n s where i n c r e a s e d p h o t o r e f r a c t i v e s e n s i t i v i t y i s necessary, research  into optimizing  electrons i s required.  the m o b i l i t y and  P o s s i b l y , m a t e r i a l s other  would have an advantage i n t h i s  instance.  l i f e t i m e of f r e e  than l i t h i u m n i o b a t e  141  REFERENCES  Abrahams, S.C., Reddy, J.M. Chem. S o l i d s 27, 997.  and B e r n s t e i n , J . L . 1966a J . Phys.  Abrahams, S.C., H a m i l t o n , W.C. Chem. S o l i d s 21_, 1013.  and Reddy, J.M.  A l p h o n s e , G.A., A l i g , R.C., 1975 RCA Rev. 36, 213.  S t a e b l e r , D.L.  Amodei, J . J . 1971a RCA Rev.  32,  Amodei, J . 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Reports  1316.  496. 589. and C o r n i s h ,  W.D.  1974  147  APPENDIX A FURTHER PROPERTIES OF LITHIUM NIOBATE  A.1  Miscellaneous P h y s i c a l Properties The  s t r u c t u r e of the f e r r o e l e c t r i c c r y s t a l l i t h i u m n i o b a t e  i s rhombohedral, p o i n t group symmetry 3m w i t h a = 0.5499 nm and a = 55° 52'  (Nassau  e t a l . 1966a).  A t room temperature  the..crystalline  s t r u c t u r e c o n s i s t s o f p l a n a r sheets of oxygen atoms i n a p p r o x i m a t e l y hexagonal c l o s e p a c k i n g .  The r e s u l t i n g o c t a h e d r a l i n t e r s t i c e s a r e  t h i r d o c c u p i e d by Nb and o n e - t h i r d by L i w i t h the remainder (Abrahams et a l . 1966a,1966b). A l l the. oxygen o c t a h e d r a . a r e a r e two v a l u e s each f o r the L i - 0 and Nb-0  distances.  one-  vacant d i s t o r t e d and t h e r e  Abrahams e t a l .  conclude t h a t l i t h i u m n i o b a t e i s not p r i m a r i l y an i o n i c c r y s t a l but one i n which c o v a l e n t bonds dominate. The pure c r y s t a l has v e r y l i t t l e a b s o r p t i o n from 350 nm t o 5um.  I t i s a u n i a x i a l c r y s t a l w i t h o r d i n a r y and  i n d i c e s a t 500 nm r e p o r t e d to be n = 2.34 o The d i s p e r s i o n and  temperature  extraordinary r e f r a c t i v e  and n = 2.24 e  a t 25°C.  dependence of the r e f r a c t i v e i n d i c e s  has  been r e p o r t e d (Boyd et a l . 1964,'1967,Miller et a l . 1965,Hobden et a l . 1966,Nelson et a l . 1974).  The d i e l e c t r i c  c o n s t a n t h a s been measured-for - d i r e c t i o n s -  p e r p e n d i c u l a r t o the c - a x i s as 78,and a l o n g the c - a x i s as 32 (Nassau al.  1966).  Jorgensen  High temperature and B a r t l e t t  c o n d u c t i v i t y occur.  a t 1 atm of oxygen and  t r a n s p o r t p r o c e s s e s have been measured by  (1969) who found  The  et  t h a t b o t h i o n i c and  electronic  e l e c t r i c a l c o n d u c t i v i t y i s completely  1000°K, w h i l e f o r low oxygen p a r t i a l  the c o n d u c t i v i t y a t 1000°K becomes c o m p l e t e l y e l e c t r o n i c . c o n d u c t i v i t y i s p r o p o r t i o n a l to p  n  *.  ionic  pressures The  electronic  148  The e l e c t r o n m o b i l i t y was c a l c u l a t e d 1000°K i n a 50% CO/50% C 0 dependence.  atm and e x h i b i t s a i' ^  The i o n i c c o n d u c t i v i t y i s c a t i o n i c and i s most p r o b a b l y  m e l t i n g p o i n t about 1260°C  The C u r i e temperature i s 1210°C and  (Nassau e t a l .  ature the c r y s t a l i s a s t a b l e f e r r o e l e c t r i c . ent  i s 10~  temperature  1  2  due t o t r a n s p o r t by l i t h i u m i o n s . the  t o be 1.7 cm^/Vsec a t  1966).  A t room  temper-  The p y r o e l e c t r i c  yC/(m deg) i n t h e r e g i o n o f 100°C  coeffici-  (Roitberg e t a l .  1970).-  The c o e f f i c i e n t s o f thermal e x p a n s i o n a r e 16.7 x 1 0 ^ p e r °C i n t h e -  a - a x i s d i r e c t i o n and 2 x 10 ^ p e r ° C i n t h e c - a x i s  A. 2  Crystal  direction.  Growth Nassau et a l . ( 1 9 6 6 b ) have d e s c r i b e d t e c h n i q u e s used t o grow  single c r y s t a l s of lithium niobate. t e c h n i q u e w i t h an e l e c t r i c f i e l d  The most common i s t h e C z o c h r a l s k i  a p p l i e d d u r i n g growth  c r y s t a l i s r o t a t e d as i t i s p u l l e d from t h e m e l t . a p p l i e d d u r i n g growth a m u l t i - d o m a i n c r y s t a l  (Fig.  A.l).  The  I f no f i e l d i s  forms.  E i t h e r p o l a r i t y may  be a p p l i e d , however i f p o l a r i t y i s r e v e r s e d d u r i n g growth a 180° domain w a l l i s produced.  C r y s t a l s which a r e n o t p o l e d d u r i n g  may be p o l e d a f t e r w a r d s , b u t o n l y a t temperatures above  A.3  growth  1C00°C.  Thermal B l e a c h i n g and F i x i n g o f Holograms i n LiNbO^ O p t i c a l e r a s u r e o f holograms which u s u a l l y o c c u r s d u r i n g  out  can be a v o i d e d i f t h e holograms a r e f i x e d  S t a e b l e r e t a l . 1972a).  (Amodei e t a l .  read-  1972a,  When a c r y s t a l i n which a hologram has been  stored  i s heated t o 100°C f o r 20 o r 30 minutes and then c o o l e d , i t i s found t h a t the  hologram has been b l e a c h e d .  The phase g r a t i n g may be r e s t o r e d by  i l l u m i n a t i n g t h e c r y s t a l w i t h l i g h t o f wavelengths 400 t o 500 nm.  The  149  • PULLING  MECHANISM  / ) o-iomA  Pt/Pt-Rh jl T H E R M O C O U P L E 11 IN G R O U N D E D I Pt S H I E L D  MOLTEN LlNbOj  Jl.O  CM  . A . l Apparatus f o r the C z o c h r a l s k i growth of l i t h i u m an e l e c t r i c f i e l d (Nassau e t a l . 1966b).  niobate  150  r e s t o r e d g r a t i n g cannot be o p t i c a l l y b l e a c h e d . Amodei e t a l . have proposed t h a t t h e hologram i s b l e a c h e d n o t by t h e r m a l l y a c t i v a t e d e l e c t r o n s which a r e r e d i s t r i b u t e d  uniformly, but  by some k i n d o f i o n i c movement which compensates t h e space charge. the c r y s t a l i s c o o l e d and then i l l u m i n a t e d , o p t i c a l l y e x c i t e d redistribute  uniformly.  Qualitatively,  electronic  Further  to l i g h t .  t h i s explanation  investigation  accounts f o r t h e e x p e r i -  o f t h e mechanisms i n v o l v e d i n  and i o n i c t r a n s p o r t a r e r e q u i r e d b e f o r e d e t a i l s o f t h e  thermal p r o c e s s e s  i n lithium niobate  can be f u l l y u n d e r s t o o d .  i o n i c motion a t lOO^C i s due t o l i t h i u m compensation i s caused by l i t h i u m hedral i n t e r s t i c e s normally When t h e c r y s t a l i s c o o l e d the c r y s t a l  electrons  The phase g r a t i n g reappears due t o t h e i o n i c  d i s p l a c e m e n t s which a r e i n s e n s i t i v e  mental r e s u l t s .  When  lattice.  i o n s , i t may be t h a t t h e charge  ions migrating  present  I f the  t o v a c a n t oxygen o c t a -  i n the c r y s t a l  (Abrahams e t a l . 1966a).  t h e s e i o n s a r e f r o z e n i n t h e i r new s i t e s i n  151  APPENDIX B ELECTRO-OPTIC BEHAVIOUR OF LITHIUM NIOBATE The p r o p a g a t i o n o f . e l e c t r o m a g n e t i c waves i n an d i e l e c t r i c c r y s t a l i s dependent on the p r o p a g a t i o n and direction  anisotropic  polarization  o f the wave w i t h r e s p e c t t o the c r y s t a l axes.  The d i e l e c t r i c  p r o p e r t i e s a t o p t i c a l f r e q u e n c i e s a r e g i v e n by D  = e  i  o  e.. E.  (B.1)  i j 3  where D" i s the d i s p l a c e m e n t , E i s the e l e c t r i c f i e l d , of f r e e  space and e_^_. t h e t e n s o r p e r m i t t i v i t y  e  the p e r m i t t i v i t y  Q  o f t h e medium.  Combining  Eq. 1 w i t h Maxwell's e q u a t i o n s l e a d s t o t h e c o n c l u s i o n t h a t two waves o f d i f f e r e n t v e l o c i t i e s may, i n g e n e r a l , propagate  through  the c r y s t a l f o r  a g i v e n wave normal (Nye 1960).  indices  o f t h e two waves  The r e f r a c t i v e  may be o b t a i n e d by drawing an e l l i p s o i d known as t h e i n d i c a t r i x . x  2  and x^ a r e the p r i n c i p a l d i r e c t i o n s  o f the p e r m i t t i v i t y  I f x^,  tensor, the  i n d i c a t r i x i s d e f i n e d by the e q u a t i o n 2  2  2 3C«  Xi  "V n  l  ^2 n  2  + ^ = 1 n  (B.2)  3  TL^ = /e^, n^ = / E ~ .  where n^ =  If a straight  l i n e i s drawn from t h e c e n t r e of t h e e l l i p s o i d  p a r a l l e l t o the wave normal o f t h e p r o p a g a t i n g wave, then an e l l i p s e may be formed by c l e a v i n g the e l l i p s o i d through this l i n e .  The semi-axes of. t h i s  polarization  which may propagate.  i t s centre, perpendicular to  e l l i p s e d e f i n e the two d i r e c t i o n s The i n d i c e s  of r e f r a c t i o n  of  seen by the  two p r o p a g a t i n g waves a r e then g i v e n by the l e n g t h o f t h e semi-axes. I f an e l e c t r i c f i e l d  i s present, the r e f r a c t i v e  index o f the  152  c r y s t a l Is a l t e r e d  and the new I n d i c a t r i x i s i n g e n e r a l d e s c r i b e d by  . 1 „ t-S i,j;k,£ n  +  z  ijk k E  +  R  i  j  k  *  k *  E  E  where the I n d i c e s i,j,k,£ r u n from 1 t o 3.  ' ' '  +  x  i j = x  1  ( B  -  The c o e f f i c i e n t s z.., and  ljk  J  R  ijk£  a  r  e  t  *  i e  H  n  e  a  r  a n <  *  t  n  quadratic  e  electro-optic  coefficients.  C o n t r a c t i o n s i n the i n d i c e s a r e u s u a l l y made as f o l l o w s : and  R mn  3 )  r , •«-*• z,..*, mk (ij)k  E . , . , „, where m and n r u n from 1 t o 6 and m i s r e l a t e d to (ij)(k£) w  ( i j ) and n t o (kJl) as f o l l o w s :  1 + 11, 2 + 22, 3 + 33, 4 + 23, 5 + 13,  6 + 12. Certain  systems cannot e x h i b i t  the l i n e a r e l e c t r o - o p t i c  effect  (such as those w i t h a c e n t r e o f symmetry) w h i l e a l l m a t e r i a l s e x h i b i t the quadratic e f f e c t . effect.  Lithium niobate exhibits  Symmetry c o n s i d e r a t i o n s r e q u i r e  o p t i c c o e f f i c i e n t s a r e e q u a l and t h a t following  matrix  (class  :  0  r  2  = 28 x 10  1  0  3  :  42  -r  4  electro-  22  22  3  3  :  13  :  33 0  42 0  0  0  0  = 8.6 x 10  cm/volt, r  13  0  0  r  some of t h e l i n e a r  some a r e zero as shown by the  - r 22  0  1  that  electro-optic  3m).  0  where (Turner 1966) r  the l i n e a r  -10  cm/volt, r „ = 3.4 x 10 22  = 30.8 x 10  1  0  cm/volt,  -10  cm/volt,  153  A further  property  of LiNbO^ i s  w i t h x ^ c o n s i d e r e d as the p o l a r a x i s . s o i d of r e v o l u t i o n  a n d two o f  that i t  is a uniaxial  Hence, the  indicatrix  crystal  i s an  ellip-  the t h r e e p r i n c i p a l semi-axes a r e e q u a l so  that o  n  The i n d i c a t r i x  ( _ i  n  +  is  " 22  2  r  E  =  n  l  =  n  2'  e  n  =  thus g i v e n by  2  +  V  13  r  l  X  2  T  ( J  +  o  (  T n e  J  r  +  + 2(r  33  E  E ) x  4 2  2  3  )  3  X  x  2  From t h i s present,  2  +  2 (  " 22 r  + 2(r  3  l  E  }  E ) x  4 2  1  equation i t  +  n  22  r  E  2  +  r  V  13  Since a l l  l  X  X  x  g  2  = 1.  ±  (B.4)  can be seen t h a t i f  the i n d i c a t r i x  sent , the equation of  (-T The e f f e c t  occur.  +  r  V  13  E„ i s 3  in  the x  the i n d i c a t r i x  X  l  2  ^2  +  to  +  n  o  of  the only  the major  axes  If  however E^ or E  field  is of are  2  present  occurs.  F o r a wave p r o p a g a t i n g  n  E^ i s  t h e c r o s s terms w o u l d be z e r o , no r o t a t i o n  the p r i n c i p a l axes of then a r o t a t i o n  *2  o  then only an e x t e n s i o n or c o n t r a c t i o n of  possible.  fractive  3*  n  introduce  2  d i r e c t i o n , w i t h o n l y E^ p r e -  reduces  r  V  33  to  X  3  2  =  1  (  B  -  5  )  e  c h a n g e s , An  °  a n d An  o  e  i n t h e two  re-  indices. M a n i p u l a t i o n of n  . A n  o  The change i n  3 o  r 2  =  index i s  13  equation E„ 3  B . 5 shows  , a  n  d  n  , A n  that  e  then p r o p o r t i o n a l  3 r E_ e . 33 3 0 0  2  =  to  the  field.  (-) B 6  154  APPENDIX C COUPLED WAVE THEORY FOR K o g e l n i k (1969) has waves by version  THICK HOLOGRAM GRATINGS  treated  t h i c k phase holograms u s i n g of h i s treatment w i l l be  conditions  and  b i s e c t o r o f the  f o r the two  the Bragg d i f f r a c t i o n of p l a n e c o u p l e d wave t h e o r y .  outlined  f o r the  A  c a s e of p e r f e c t  i n c i d e n t beams R and  S, as i n d i c a t e d  a n a l y s i s assumes monochromatic l i g h t to be  gram g r a t i n g of t h i c k n e s s plane of incidence. f e r e n c e wave R and  Bragg  case where the g r a t i n g p l a n e s a r e p a r a l l e l to  d,  grating  i n c i d e n t on a phase h o l o -  d a t an a n g l e 0 p o l a r i z e d p e r p e n d i c u l a r  Only two  waves a r e assumed t o be p r e s e n t :  the s i g n a l wave S.  o b e y i n g the Bragg c o n d i t i o n .  The  the  in Fig. C.l.  F i g . C . l Model of a t h i c k hologram g r a t i n g o f t h i c k n e s s s p a c i n g I and Bragg a n g l e , i n the medium, 9.  The  condensed  These two  waves a r e  the  to the  the re-  o n l y waves  assumption l i m i t s the a n a l y s i s  to  thick  155  holograms. (Storck and W o l f f  (1975) have shown t h a t , i n the case o f low  d i f f r a c t i o n e f f i c i e n c y , the a n a l y s i s i s a l s o v a l i d f o r t h i n holograms). Wave p r o p a g a t i o n i n t h e g r a t i n g i s d e s c r i b e d by V E.+ K E = 0 2  The e,  (C.l)  2  propagation constant  i s r e l a t e d t o the r e l a t i v e d i e l e c t r i c  and the c o n d u c t i v i t y a, by 2 K  co = — e c 2  (C.2)  - iioua  where c i s the v e l o c i t y o f l i g h t , y i s t h e p e r m e a b i l i t y and  constant  o f the medium  u t h e a n g u l a r frequency o f t h e e l e c t r i c f i e l d E ( x , z ) .  The f r i n g e s  of the phase g r a t i n g r e s u l t from a s p a t i a l m o d u l a t i o n o f e : e =  •?  (C.3)  E , cos kx  +  o  1  i s the amplitude o f the s p a t i a l m o d u l a t i o n and E  where  d i e l e c t r i c constant.  q  i s the average  (The s p a t i a l m o d u l a t i o n i n . t h e c o n d u c t i v i t y i s  assumed t o be n e g l i g i b l e ) .  The g r a t i n g v e c t o r k, i n the case under  c o n s i d e r a t i o n has o n l y an x-component and i s g i v e n by  (C.4)  k = -y  where JI i s the g r a t i n g p e r i o d and i s r e l a t e d t o t h e wavelength o f l i g h t X by X = 2 £ s i n 0 . E q s . C . 2 and C.3 K  2  can be combined t o g i v e = B  2  - 2iaB + 2 ' B ( e K  where B i s the average p r o p a g a t i o n constant constant:  + i k x  + e"  and a  i k x  )  the average  (C.5) absorption  ±  .  6 =  2TTE —'—5  X  2  o  yea a =  2e  JL  2  o  (C.6)  156  The  coupling constant  K' i s d e f i n e d as  .-.ire, K.  (C.7)  =  2XE  The  c o u p l i n g c o n s t a n t d e s c r i b e s the c o u p l i n g between the r e f e r e n c e and  the s i g n a l wave. O p t i c a l media may  be c h a r a c t e r i z e d by t h e i r r e f r a c t i v e i n d e x n,  when the f o l l o w i n g c o n d i t i o n s a r e 2Trn  »  a;  Here n i s the average modulation.  n»n  (C.8)  1  r e f r a c t i v e index and n^ the amplitude  These c o n d i t i o n s w i l l be assumed t o be met,  3= The  A  '  K  =  The  i n the r e f r a c t i v e index,forms S and  complex amplitudes  total electric E  field  P =  x =  causes an exchange of energy  • x) + S ( z ) exp(-i£ • x)  The r e s u l t s o f t h i s a n a l y s i s may s u b s t i t u t i n g K " f o r K'where  (CIO)  sin(-0)  6  0  cos 0  cos(-0)J  - i  20  absorp-  sin 6  be a p p l i e d  and C.10  / -ip.x  By comparing terms w i t h e q u a l e x p o n e n t i a l s (e  cos  be-  S(z)  i n t e r c h a n g e and because of  s o l v e the c o u p l e d wave e q u a t i o n s , Eq. C l , C.5  K  a grating  of these two waves, R(z) and  (x,z) = R(z) expC-iP^  =  case  i n the g r a t i n g i s  where  To  spatial  (C.3)  v a r y a l o n g z as a r e s u l t o f the energy tion.  i n which  A  s p a t i a l modulation  The  of the  Trn,  2Trn  which c o u p l e s the two waves R and tween them.  met.  ,  and  a r e combined. -i£.x". „ ;  e  )  to p a r a l l e l p o l a r i z a t i o n  by  157  we a r r i v e a t R"  - 2iR'g cos G - 2ia6R +  S"  - 2iS'B  =0  2K'£S  (C.ll)  and cos 9 - 2ia|3S +  ( S  2  - a )S + 2  2K'BR  where the primes i n d i c a t e d i f f e r e n t i a t i o n w i t h r e s p e c t t o z. i n t e r a c t i o n between the R and S beams i s slow then t h e R' may be n e g l e c t e d .  S' cos 6 + aS = - i K R  (C.14)  exp(a z) +  1  1  expfo^z) + s  exp(a z)  (C.15)  exp(a z)  (C.16)  2  2  2  The c o n s t a n t s  may be o b t a i n e d by s u b s t i t u t i n g Eq. C-15 and C.16 i n t o the coupled The s o l u t i o n i s a, , = 1,2  cos8  (a ± 12K)  (C.17)  f i n d r ^ and s^ the boundary c o n d i t i o n s f o r t r a n s m i s s i o n hologram a r e  introduced.  The r e f e r e n c e wave R i s assumed t o s t a r t w i t h u n i t  tude a t z = 0. it  K'S) and due t o a b s o r p t i o n (aR, a S ) .  c o n s t a n t s r ^ and s^ depend on the boundary c o n d i t i o n s .  wave e q u a t i o n s .  To  a l o n g z due t o  g e n e r a l s o l u t i o n to the coupled wave e q u a t i o n s i s  S(z) =  ±  and S'' terms  (C.13)  R(z) = r  o  I f the  R' cos 0 + aR = flic's  c o u p l i n g t o the o t h e r wave ( K R ,  The  (C. 12)  E q . C . l l and C.12 can be r e w r i t t e n i n t h e form  P h y s i c a l l y , the R and S waves change t h e i r amplitude  The  1  0  =  As i t propagates  through  ampli-  the phase g r a t i n g i t decays as  c o u p l e s energy i n t o S which i s assumed t o be zero a t z = 0.  The  boundary c o n d i t i o n s a r e  R(0) = 1,  S(0) = 0  S o l v i n g f o r r ^ and s^ and s u b s t i t u t i n g i n Eq.C.16 t h e amplitude s i g n a l wave as i t l e a v e s the g r a t i n g i s g i v e n by  (C18) of the  158  S ( d )  where y^  2  -  =  -(a  cos ^) 1  ± l<)/cos  9.  ( e X p (  V  }  -  6  X  p  (  Y  l  d  )  >  (  C  '  1  9  )  The d i f f r a c t i o n e f f i c i e n c y o f the g r a t i n g  n i s d e f i n e d as n = SS* . I n the p r e s e n t  (C.20)  c a s e Eq. C.20 r e d u c e s t o n = exp( v  ^7 )sin vd cos 0 2  2  1  (C.21) cos 29  where v = Trn^/X cos 9 f o r p e r p e n d i c u l a r p o l a r i z a t i o n and v = 7rn^ ^ for parallel  polarization.  C  Q  S  Q  159  APPENDIX D SOURCES OF THE LITHIUM NIOBATE  CRYSTALS  The c r y s t a l s used i n t h i s study were o b t a i n e d from C r y s t a l Technology_  I n c . , Mountain View, C a l i f o r n i a and from Harshaw Chemical  Company, S o l o n Ohio.  Table D . l l i s t s  the nominal dimensions,  and i m p u r i t y doping of the c r y s t a l s .  orientation  C r y s t a l s 1, 2 and 3 were c u t from  C r y s t a l Technology b o u l e #10-375 which was grown a l o n g t h e c - a x i s . C r y s t a l 4 was c u t from b o u l e #10-286 which was grown a l o n g t h e b - a x i s . The f i f t h c r y s t a l was purchased from Harshaw. All  the c r y s t a l s were  grown by the C z o c h r a l s k i t e c h n i q u e .  The c o m p o s i t i o n of the melt from which the c r y s t a l s were grown i s g i v e n i n Table D . l . gruent melt  A . s t o i c h i o m e t r i c melt c o n t a i n s more.Li  ( R e d f i e l d e t a l . 1974).  than does a con-  I n our c r y s t a l s , the s t o i c h i o m e t r i c  melt was 49.0 mole% L i 0 w h i l e the congruent melt was 48.6 mole % L i Q . o  Crystal  Dimensions a  9  (mm)  Polished face  Iron-doping (mole %)  Composition o f the melt  b  c  10  10  a  0.015  congruent  1  10  2  10  2.5  20  b  0.015  congruent  3  10  1.5  20  b  0.015  congruent  4  10  1.0  10  b  undoped  stoichiometric  5  15  3  20  b  undoped  congruent  Table D . l L i t h i u m n i o b a t e c r y s t a l s used i n t h i s study.  160  APPENDIX E THE  APPLICATION  OF LITHIUM NIOBATE  IN A HOLOGRAPHIC MEMORY SYSTEM  Read-write o p t i c a l memories based on hologram s t o r a g e e r a s a b l e medium are of i n t e r e s t because they large storage  capacity with l i t t l e  speed random a c c e s s i b i l i t y . b a s i s w i t h p o s s i b l y 10  5  o f f e r the p o s s i b i l i t y  or no m e c h a n i c a l motion and  f o r a h o l o g r a p h i c memory a r e shown i n F i g . E . l .  high  to be  stored.  b a s i c components  An a r r a y o f l i g h t  s t o r a g e medium by beam d e f l e c t o r s .  beam would be d i f f r a c t e d on to a sensor could occur  simultaneously  For reading,  a r r a y by  the  would be e l e c t r i c a l l y a d d r e s s a b l e  The  page composer and  by t h e  d e f l e c t o r i s more c o m p l i c a t e d  sensor  may  The  i t i s slower.  acc-isto-optic The e l e c t r o - o p t i c  presently requires high  operating  system i s arranged  so t h a t a l l t h e s t o r e d holograms  the r e f e r e n c e beam on t o a s i n g l e d e t e c t o r a r r a y .  be an a r r a y of p h o t o d i o d e s produced as an i n t e g r a t e d  Economically  (Korpel  Chen 1970). The  diffract  and  but  arrays  t h e beam  Both these d e v i c e s can be made w i t h LiNbO^ c r y s t a l s  et a l . 1966,  Erasure  computer.  electro-optic deflectors.  d e f l e c t o r i s the s i m p l e r of t h e two  voltages.  reference  the hologram.  P o s s i b l e d e v i c e s t h a t c o u l d be used to d e f l e c t and  holo-  d u r i n g the r e a d i n g or w r i t i n g c y c l e s or  c o u l d be accomplished s e p a r a t e l y .  are acousto-optic  valves  F o r w r i t i n g , the s i g n a l and  r e f e r e n c e beams a r e d i r e c t e d to the a p p r o p r i a t e p o s i t i o n on the graphic  of  A c c e s s to d a t a would be on a page-by-page  b i t s read or w r i t t e n i n p a r a l l e l . The  composes the page of data  i n an  i t may  be more f e a s i b l e to make up  The  detector  circuit.  the d e t e c t o r a r r a y  with  161  X-Y  DEFLECTORS LASER  MIRROR  BEAM SPLITTER  READ-OUT ARRAY  MIRROR  STORAGE MEDIUM  (a)  DEFLECTED LASER BEAM  LiNb0  PHOTODETECTOR ARRAY 3  CRYSTAL  (b)  F i g . E . l . (a) Schematic o f a r e a d , w r i t e , e r a s e i n - s i t u h o l o g r a p h i c o p t i c a l memory. I n t h i s c o n f i g u r a t i o n , the page composer i s used i n reflection. Page composers may a l s o be used i n t r a n s m i s s i o n , (b) Schematic o f readout i n a p a g e - o r g a n i z e d h o l o g r a p h i c memory.  162  a number o f s m a l l i n t e g r a t e d The  circuits.  l a s e r power r e q u i r e d  i s determined by t h e number o f  elements i n a page and the e f f i c i e n c y o f t h e o p t i c a l system. instance,  i n a system i n which the h o l o g r a p h i c  was 10 % and t h e t r a n s m i s s i o n  e f f i c i e n c y o f a l l other  20%-then o n l y 2% o f the l a s e r power  efficiency  components was  would r e a c h t h e d e t e c t o r  4 was then shared between 10 d e t e c t o r  array. I f t h i s  -6 elements o n l y about 10 % o f t h e  l a s e r power would r e a c h each element. 1 pJ of l i g h t , a reading  diffraction  For  For a detector  that  required  speed o f ly's p e r hologram would r e q u i r e a l a s e r  w i t h a power o f 1 W. The  page composer e n v i s i o n e d  i n t h i s type o f system would  c o n s i s t o f an a r r a y o f elements t h a t c o u l d be switched between a t r a n s parent c o n d i t i o n and an opaque c o n d i t i o n t o correspond t o ones and z e r o s . A number o f d i f f e r e n t types o f page composers have been i n v e s t i g a t e d b u t o n l y p r o t o t y p e s have been b u i l t . have used nematic l i q u i d 1974).  Some e x p e r i m e n t a l h o l o g r a p h i c  c r y s t a l s (Stewart e t a l . 1973, d ' A u r i a  systems et a l .  These r e q u i r e a b u f f e r memory and a t l e a s t one e l e c t r i c a l  connection  f o r each b i t .  I n a d d i t i o n , they a r e i n h e r e n t l y slow,  r e q u i r i n g several m i l l i s e c o n d s to switch such as PLZT have a l s o been c o n s i d e r e d  states.  typically  F e r r o e l e c t r i c ceramics  f o r use i n page composers.  Transparent electrode s t r i p s a r e deposited  on each f a c e o f a s l i c e  w i t h p a r a l l e l s t r i p s on t h e one s i d e b e i n g  o r t h o g o n a l t o those on t h e  other  side.  Coincident  the c r o s s e d  electrodes.  addressing  connections are required. c r y s t a l s , a t present  changes t h e b i r e f r i n g e n c e between  F o r an N x N a r r a y o f elements o n l y 2N e l e c t r i c a l Although the devices  a r e f a s t e r than  liquid  t h e PLZT f a t i g u e s b o t h e l e c t r i c a l l y and o p t i c a l l y .  163  Carlsen ing  (1974)  the d i g i t a l d a t a .  has  proposed an a l t e r n a t i v e method f o r  In h i s system d a t a b i t s would be s t o r e d  recordsequen-  t i a l l y as they a r r i v e d from the computer thus a l l e v i a t i n g the need f o r a l a r g e page composer. the d a t a  to be  s t o r e d i n any  The  advantages of p a r a l l e l i n p u t a r e l o s t  s t o r e d i n one one  page i s p r e a r r a n g e d .  O t h e r w i s e the  s e q u e n t i a l i n p u t , the computer c o u l d t a g the d a t a  a g i v e n page. achieved.  data  page would be so d i v e r s e t h a t t h e r e would not be much  advantage i n r e t r i e v i n g i t a l l i n a p a r a l l e l output mode. access  unless  W i t h random f o r storage  In t h i s manner, p a r a l l e l output of r e l a t e d d a t a c o u l d  C a r l s e n proposed t h a t each b i t i n a page be  to y i e l d a m u l t i p l e exposure hologram.  Each page would be  d i f f e r e n t l o c a t i o n i n the r e c o r d i n g medium. holograms, the need may  that t h i s i s p o s s i b l e .  Huignard e t a l .  the same o b j e c t a g a i n but w i t h  i n phase by u.  another  stored i n a  some of the  (1975)  To  super-  have demonstrated  U s i n g LiNbO^ as a s t o r a g e medium, they  s t o r e d a number of holograms i n s u p e r p o s i t i o n . they r e c o r d e d  a  I n u s i n g m u l t i p l e exposure  a r i s e to s e l e c t i v e l y e r a s e  imposed b i t s but not o t h e r s .  be  stored with  d i f f e r e n t a n g l e w i t h a l l b i t s i n a page superimposed upon one  in  first  erase a given  hologram  the r e f e r e n c e wave s h i f t e d  T h i s produced a complimentary s p a t i a l m o d u l a t i o n i n the  r e f r a c t i v e i n d e x thus e l i m i n a t i n g t h a t p a r t i c u l a r hologram.  From a  p r a c t i c a l p o i n t of view t h i s method would n o t be v e r y u s e f u l s i n c e extreme s t a b i l i t y would be It other has  required.  i s of i n t e r e s t to compare h o l o g r a p h i c  memory systems w i t h  systems to determine what r o l e they might p l a y .  shown t h a t h o l o g r a p h i c  Kiemle  (1974)  memories u s i n g a s i n g l e d e t e c t o r a r r a y  and  g a s i n g l e hologram p l a t e a r e l i m i t e d  i n storage  c a p a c i t y to about  10  164  bits.  New  memory t e c h n i q u e s  b u b b l e domains may cheaper s o u l t i o n s . magnetic drums and  such as c h a r g e - c o u p l e d  be c a p a b l e  d e v i c e s and  of t h i s c a p a c i t y range and may  Conventional  magnetic  provide  r e c o r d i n g t e c h n o l o g i e s such as  d i s k s w i l l probably  be improved.  Development o f  h o l o g r a p h i c memories t h e r e f o r e s h o u l d s t r i v e t o complement t h e s e o t h e r t e c h n o l o g i e s because i t i s u n l i k e l y t h a t they w i l l r e p l a c e them. to  and  completely  I t i s e n v i s i o n e d t h a t h o l o g r a p h i c memories w i l l be  p r o v i d e c a p a c i t i e s comparable to those of magnetic tape  systems, but w i t h much s h o r t e r a c c e s s  able  storage  times.  8 The  c a p a c i t y l i m i t mentioned above, of 10  memories u s i n g a s i n g l e d e t e c t o r a r r a y and  b i t s for holographic  recording plate, arises  because t h e a n g l e a t which the d e t e c t o r a r r a y can be limited.  illuminated i s  T h i s determines the maximum s i z e of the r e c o r d i n g p l a t e .  K i e m l e (1974) however has  i n v e s t i g a t e d t h e concept  of u s i n g modules w h i c h  each c o n t a i n a page composer, hologram s t o r a g e medium and memory system would have one of  p a s s i v e beam  virtually  dividers.  l a s e r , one x-y beam d e f l e c t o r and T h i s concept  unlimited capacity.  memory systems.  detector.  The  a number  would a l l o w random a c c e s s  to  In T a b l e E . l a comparison i s made of some  MEMORY T Y P E  CAPACITY  Semiconductor  10 -10 9  Core  io  Disk  10  M a g n e t i c Tape ( I B M TBM S y s t e m )  10  1 2  io  Magnetic  Bubbles  10 -10  >io  '  5  15 s  2.5x10  . 5 - 5 ms  16 x l O  6  bits/cm  2  1 y s - 1 ms  10  8  bits/cm  2  Table  memory  bits/cm  2  6  E.l  some c o m p u t e r  5  bits/cm  systems.  Hodges  (1975)  Rajchman  (1970)  Matick  (1972)  Wildmann  (1975)  2  2.4x10  8  A comparison of  • '•  > 5 s  1 3  1 3  •-•  3 bits/cm  1.4x10  1 2  6  2000  REFERENCE  100 ms  8  -10  DENSITY  < 1 ms  1 0  1 ys  System  Memories  RANDOM ACCESS TIME  6  IBM 3850  Holographic  (bits)  o  bits/cm  Harris  et  al.(1975)  Bobeck et  al.(1975)  Kiemle  (1974)  (  166  '  APPENDIX F ELLIPSOMETER  The  ALIGNMENT  ellipsometer i s a geometrical  instrument  which depends  on t h e r e l a t i v e alignment o f i t s components f o r i t s a c c u r a c y .  Errors  may a r i s e from zero e r r o r s i n t h e azimuth s c a l e s o f t h e p o l a r i z e r , q u a r t e r wave p l a t e and a n a l y z e r , from a zero e r r o r i n t h e a n g l e o f i n c i d e n c e s c a l e and from i m p e r f e c t i o n s  i n the o p t i c a l  elements,  e s p e c i a l l y t h e q u a r t e r wave p l a t e . The Studna (1971).  alignment method used was t h a t d e s c r i b e d by Aspnes and They p o i n t e d o u t t h a t t h e u s e o f a t r a n s p a r e n t  surface eliminated the e f f e c t of f i r s t order p o l a r i z e r and a n a l y s e r . alignment.  i n the  These e f f e c t s can produce e r r o r s i n t h e  The procedure o f a t y p i c a l alignment was as f o l l o w s . The  arm  ellipticities  reflecting  light  source  (He-Ne L a s e r ) was a d j u s t e d w i t h  i n the s t r a i g h t - t h r o u g h p o s i t i o n .  the analyser  With t h e q u a r t e r wave p l a t e i r i s  stopped down t o i t s s m a l l e s t p o s i t i o n , and w i t h no a p e r t u r e a n a l y s e r arm, t h e d i r e c t i o n o f t h e l a s e r beam was a d j u s t e d  i n the to give a  maximum s i g n a l from t h e d e t e c t o r . Next t h e a n g l e o f i n c i d e n c e zero e r r o r was checked.  Apertures  were i n s e r t e d i n b o t h ends o f the a n a l y s e r arm t o d e f i n e t h e a x i s o f t h i s arm. and  The a n a l y s e r arm was then moved i n O.of  s t e p s about 90°  t h e a n g l e o f i n c i d e n c e was p l o t t e d v s . t h e d e t e c t o r s i g n a l .  r e s u l t i n g curve was symmetrical  The  about i t s maximum and peaked a t 89.97°,  i n d i c a t i n g an e r r o r o f -0.03° i n t h e s c a l e ( F i g . F . l ) . The  z e r o e r r o r s i n t h e p o l a r i z e r and a n a l y s e r  s c a l e s were  checked w i t h t h e q u a r t e r wave p l a t e removed, and w i t h t h e a n g l e o f i n c i d e n c e a t 7 0 ° . An o p t i c a l l y f l a t  q u a r t z s l a b was used a s a r e f l e c t o r .  167  to u to u to  o  O  Pi  o H U W H W  J  I  I  89.9  i  L  .1  i  .95  i  i  i  .05  90.  ANGLE OF INCIDENCE  i  / deg  F i g . F . l Zero c o r r e c t i o n f o r the a n g l e o f i n c i d e n c e  scale.  2.0;92  I  -cj—o"  .8  X  /  X X  /  .4  X  /  .2h  1.0;91  0 90  .2  .6 P /  .8  1.0 91  deg  F i g . F.2 C o r r e c t i o n s t o the a n a l y s e r and p o l a r i z e r s c a l e s , (o-o-o) b a l a n c i n g t h e a n a l y s e r near 0? f o r s e t v a l u e s o f P n e a r 90°(outer s c a l e s f o r a b s c i s s a and o r d i n a t e ) . (x-x-x) b a l a n c i n g t h e p o l a r i z e r near 0° f o r s e t v a l u e s o f A near 90° ( i n n e r s c a l e s f o r a b s c i s s a and o r d i n a t e ) . The c o r r e c t c o r r e c t i o n f a c t o r s a r e : A = -0.69?,P = - 1 . 8 5 ° .  168  The  s l a b was  surface  t h i c k enough to exclude the r e f l e c t i o n from i t s near  from e n t e r i n g  a p p r o x i m a t e l y 90°,  the a n a l y s e r  arm.  the p o s i t i o n of the  maximum s i g n a l from the d e t e c t o r . front surface P  and  the P and  that  the s u r f a c e  A arms a l l l i e i n one  s l a b was  P and  A set  the a x i s of r o t a t i o n of  around, and  to  adjusted f o r a  T h i s procedure ensures t h a t  of the r e f l e c t o r l i e s on  A arms, and  With both  the the  l o n g i t u d i n a l axes of  p l a n e , thus e s t a b l i s h i n g the p l a n e of  incidence. The P about 90° polarizer obtain shift  analyser  was  then n u l l e d near A = 0  f o r s e t v a l u e s of  to o b t a i n a s t r a i g h t l i n e p l o t of A v s . P . was  n u l l e d f o r P near 0  another s t r a i g h t l i n e . i n the o r d i n a t e  and  +TT/2 s h i f t  m i s s i o n axes of the a n a l y s e r perpendicular  o  the  f o r set v a l u e s of A about 90  i n the a b s c i s s a  the p o i n t  and  of the  of i n t e r s e c t i o n the  p o l a r i z e r are  to the p l a n e of i n c i d e n c e .  made by  Then  These l i n e s were p l o t t e d w i t h a  c u r v e , as shown i n Fig-E,".^.. At  s c a l e s was  o  The  s e t t i n g the p o l a r i z e r and  o  -TT/2  second trans-  either p a r a l l e l  or  c o r r e c t i o n i n the analyser  , to  two  to the i n t e r o  s e c t i o n v a l u e s and or  then r o t a t i n g the  s h a f t encoders to read 90.00  0.00°. To  determine the  the p o l a r i z e r was  zero e r r o r i n the q u a r t e r wave p l a t e o o s e t to 0.00 and the a n a l y s e r set to 90.00 .  q u a r t e r wave p l a t e r o t a t e d  The  about 0.00° to l o c a t e the p o s i t i o n of  minimum s i g n a l at the d e t e c t o r . first  scale,  When the s i g n a l i s a minimum,  the  a x i s of the q u a r t e r wave p l a t e i s p a r a l l e l to the p o l a r i z e r  m i s s i o n a x i s and found .(Fig.  F.3).  so the e r r o r i n the q u a r t e r wave p l a t e s c a l e can  transbe  I o  •MINIMUM  2.0  1.0 QUARTER WAVE PLATE ANGLE /deg"'  F i g . F.3  Zero c o r r e c t i o n f o r the q u a r t e r wave p l a t e  scale.  170  For a l l o f t h e measurements made w i t h the e l l i p s o m e t e r , the q u a r t e r  wave p l a t e was p o s i t i o n e d  a t -45° .  An i d e a l  wave p l a t e would have a r e l a t i v e phase r e t a r d a t i o n , A and  a t r a n s m i t t a n c e r a t i o , T , o f 1.0° c  i s advisable  t o have as p e r f e c t a q u a r t e r  To a d j u s t straight-through  A  c  , o f 90.00°  Small d e v i a t i o n s  v a l u e s can produce l a r g e e r r o r s i n t h e e l l i p s o m e t r y it  quarter  and T , the a n a l y s e r  from these  r e a d i n g s and so  wave p l a t e as p o s s i b l e . arm was f i x e d i n t h e  p o s i t i o n w i t h P a t 0.00°, A a t 90.00°, and t h e q u a r t e r  wave p l a t e a t 315.00°.  The t u n i n g micrometer screw on the S o l e i l -  Babinet compensator was turned and t h e p o s i t i o n s which gave e x t i n c t i o n were noted. 4TT. . ..  These p o s i t i o n s correspond to r e t a r d a t i o n s  Quarter wave r e t a r d a t i o n  (i.e.  o f 0, 2 T ,  mr/2) i s found by adding  onequarter o f t h e d i f f e r e n c e between e x t i n c t i o n s e t t i n g s t o any one of t h e s e t t i n g s . : The f i n a l s e t t i n g of t h e q u a r t e r accomplished u s i n g  the ellipsometer  Inconel-coated glass s l i d e . the e l l i p s o m e t r y of  and A  .  wave p l a t e was  readings of a c a r e f u l l y aligned,  For a p e r f e c t l y aligned  instrument,  r e a d i n g s i n zones 1 and 3 w i l l g i v e the same v a l u e s  The micrometer on t h e compensator was a d j u s t e d  minimize t h e spread i n t h e m ' s and A ' s .  I t was found t h a t the p o s i t i o n  * The  r e l a t i o n s between zones 1 and 3 a r e : Zone 1  A = 90  + 2P, 1  i|> = A  135 >  90 >  ±  P > -45 1 A >0 ±  -45 A Z  o  n  e  3  = 2P  y =180  3  - 90 - A  3  225 > 180 >  P A  to  3  3  > 45 > 90  McCrackin(1963) g i v e s a d e s c r i p t i o n o f a l l the zones,  1711'  of minimum d i f f e r e n c e i n ijj was not the same as t h e p o s i t i o n o f minimum d i f f e r e n c e i n A . s  A s e r i e s o f r e a d i n g s were taken f o r d i f f e r e n t  p o s i t i o n s and u s i n g the program o f McCrackin(1969) calculated.  The s e t t i n g chosen gave A  A  c  =90.0 77° and T  and T  c  were  = 0.99959.  APPENDIX G * ELLIPSOMETRIC INVESTIGATION OF THE EFFECTS IN ANODIC T a ^  G.  1  ELECTRO-OPTIC AND  ELECTROSTRICTIVE  FILMS ( C o r n i s h & Young  Introduction E l l i p s o m e t r y may  be used to d e t e c t and measure s e p a r a t e l y  the s m a l l changes i n r e f r a c t i v e index and  t h i c k n e s s which o c c u r  t h i n d i e l e c t r i c f i l m s when a f i e l d  i s applied.  birefringence i s also detectable.  The  s and  The  occurrence  components have the e l e c t r i c v e c t o r p e r p e n d i c u l a r and  r e f l e c t i v i t i e s f o r the two R /R = ( t a n i|> ) e x p ( i A ) . p s  of  a m p l i t u d e changes i n the  p components of l i g h t on r e f l e c t i o n from the f i l m .  p l a n e of i n c i d e n c e r e s p e c t i v e l y .  in  e l l i p s o m e t r i c technique  c o n s i s t s i n measuring the r e l a t i v e phase and  was  1973)  I f R^  and R  components, one  g  The  s and  p a r a l l e l to  a r e the  p  the  complex  o b t a i n s ^ and  A where  In the p r e s e n t work, a PDP8-E computer  used to perform the e l l i p s o m e t e r b a l a n c i n g procedure as w e l l as  r e c o r d c u r r e n t s , v o l t a g e s and  elapsed  In p r e v i o u s work on these discovered  to  time.  f i l m s , Holden and  Ullman(1967,1969)  the m o d u l a t i o n of i n t e n s i t y r e f l e c t i o n on a p p l y i n g  a.c.  f i e l d s to the f i l m s u s i n g a monochromator w i t h a l o c k - i n a m p l i f i e r d e t e c t i o n technique. ness m o d u l a t i o n . to  They e x p l a i n e d  Frova and M i g l i o r a t o ( 1 9 6 8 , 1 9 6 9 ) a t t r i b u t e d  r e f r a c t i v e index changes and  i n c r e a s e d and had  They were a b l e to show t h a t the  the index decreased  p r e v i o u s l y been m i s t a k e n l y  effect those  crystals.  Hopper and Wang(1972) were the f i r s t to a p p l y  metry to t h i s problem.  the  compared t h e i r c o e f f i c i e n t s t o  o f oxygen-octahedra f e r r o e l e c t r i c Ord,  t h e i r r e s u l t s i n terms o f t h i c k -  ellipso-  thickness  on i n c r e a s i n g an a p p l i e d f i e l d .  It  assumed t h a t the f i l m s would become  * T h i s appendix r e p r e s e n t s a c o n t i n u a t i o n and r e f i n e m e n t of work subm i t t e d f o r the M.A.Sc. degree and l e d to the p u b l i c a t i o n l i s t e d . The method developed has s i n c e been a p p l i e d to Nb-Oj. by Yee and Young(1975) .  173  thinner.  These authors  dependence on f i e l d , as to  reported  the b a s i s of  d a t a on the b a s i s o f  since only a narrow range of  g i v e f i l m growth ( i o n i c  t r a c k e d by t h e i r  their  conduction)  at  automated e l l i p s o m e t e r .  an i s o t r o p i c  applied  (M.A. Hopper, p e r s o n a l  The e f f e c t s cations  i n f a b r i c a t i n g modulators a l s o of  interest  optical  the e f f e c t  i n unpublished work, anisotropy  possible interest  with  circuits,  in  appli-  where they c o u l d be used  ( F r o v a and M i g l i o a t o ( 1 9 6 8 , 1 9 6 9 ) .  s i n c e they give information  They  on t h e s t r u c t u r a l  example, on the changes w h i c h l e a d to  for  history  effects  i n the i o n i c conduction process which occurs i n  growth.  Also,  electrostriction effect  (Young 1963 ) a s one s o u r c e o f vation  energies for It  the quadratic  i o n i c motion  field  (Young 1960  may r e a s o n a b l y b e a s s u m e d t h a t  are  changes  i n these f i l m s ,  a quadratic  on  communication).  i n question are of  such as i n t e g r a t e d  such  a r a t e w h i c h c o u l d be  H o p p e r a n d De Smet h a v e c o n s i d e r e d t h e q u e s t i o n o f a field  linear  f i e l d was u s e d ,  They t r e a t e d  index change but  a  strong film  was s u g g e s t e d terms i n the  acti-  ). the f i l m s ,  which have  i  n o r m a l l y been c o n s i d e r e d to be amorphous, c o n s i s t o f of  one of  investigated  i n a s e r i e s of  papers  appear to be c o m p l i c a t e d sequences of  of  fused pentagonal bipyramids or d i s t o r t e d  It  has been supposed t h a t  the h i s t o r y  process indicate both point defect distortion  of  e x p l a n a t i o n of  1972  ).  form  t h e v a r i e t i e s o f c r y s t a l l i n e Ta20^ w h i c h S t e p h e n s o n and R o t h  have r e c e n t l y structures  a disordered  the l a t t i c e . those effects  ( e . g . 1971  herringboned  octahedral  effects  ).  i n the  chains  bipyramids.  ionic  conduction  c o n c e n t r a t i o n changes and  However, t h e r e  These  general  i s controversy over  the  ( D e l l ' O c a , P u l f r e y and Young 1972) ; Dignam  174  G.2  Experimental  Procedures...  The automated e l l i p s o m e t e r was t h a t used by Ord was  et a l . ( 1 9 7 2 ) . A Rudolf  s i m i l a r i n general design  to  (type 43603-200E) e l l i p s o m e t e r  m o d i f i e d by the a d d i t i o n of s t e p p i n g motor d r i v e s (I.M.C. Magnetic  Corp. type 008-008) on the a n a l y s e r and p o l a r i z e r .  Anti-backlash  (W.M.  Berg,._Inc.) were used, w i t h one motor step c o r r e s p o n d i n g  0.01°  r o t a t i o n of the o p t i c a l elements.  motors was  employed.  One  gears  to a  Software a c c e l e r a t i o n of  d i f f e r e n c e from the d e s i g n of Ord  the  e t a l . was  t h a t a b s o l u t e , b r u s h - l i k e s h a f t encoders (Theta Instrument Company) were used to read the a n a l y s e r and p o l a r i z e r a n g l e s . ellipsometer balance,  A f t e r each  the changes i n the p o l a r i z e r and  analyser  angles  as i n d i c a t e d by the s h a f t encoders were compared w i t h the e s t i m a t e those a n g l e s as c a l c u l a t e d by the computer by a l g e b r a i c a l l y output  p u l s e s sent to the motors.  An e r r o r warning was  of  summing  printed  i n d i c a t i n g any d i s c r e p a n c i e s , such as would o c c u r , f o r example, i f a motor d i d not respond vproperly to every p u l s e . source a t 632.8nm was Corp.) was RCA  931,  used.  8645) was  a c l o c k and time was  I t was  preceded  by  thus a l l o w i n g o r d i n a r y room i l l u m i n a t i o n .  i n t e r f a c e to a PDP8-E computer was  D i g i t a l Corp. components.  (Gaertner  A p h o t o m u l t i p l i e r (type  used as d e t e c t o r .  a narrow band o p t i c a l f i l t e r , The  He-Ne l a s e r  A S o l e i l - B a b i n e t compensator  used as the q u a r t e r wave p l a t e .  l a t e r RCA  A 1 mW  constructed using  standard  I t p r o v i d e d d i g i t a l and analogue i n p u t s ,  a l s o r e l a y c o n t r o l s to i n i t i a t e c u r r e n t flow.  not minimized but was  t y p i c a l l y 2.2s.  The  Balance  ellipsometer  was  a l i g n e d u s i n g the method of M c C r a c k i n , P a s s a g l i a , Stromberg & S t e i n berg  (1963). In s i t u measurements were made w i t h a t r i a n g u l a r p r i s m  cell  175  made by j o i n i n g o p t i c a l g l a s s f l a t s w i t h epoxy r e s i n . incidence  (63.46°) was f i x e d by t h e need f o r normal i n c i d e n c e on  the c e l l f a c e s . at  The a n g l e o f  298K.  The s o l u t i o n was 0.2M s u l p h u r i c a c i d and was c o n t r o l l e d  The cathode was p l a t i n i z e d p l a t i n u m .  Tantalum specimens  ( M a t e r i a l s Research Corp.) were s i n g l e c r y s t a l s l i c e s e l e c t r o p o l i s h e d i n 10% by volume 48% by mass HF i n 98% by mass H S 0 2  4  Measurements were made a t i n t e r v a l s i n two zones f o r c a l i b r a t i o n purposes. were c o r r e c t e d G'. 3  I n t r a c k i n g , one zone o n l y was used.  C e l l window e r r o r s  for.  Results Since  the f i l m s a r e s o l i d , and, a l s o , f o r t h a t m a t t e r ,  they a r e a t t a c h e d  to a s o l i d s u r f a c e ,  i t i s t o be expected t h a t  would become a n i s o t r o p i c ( b i r e f r i g e n t ) on a p p l y i n g a f i e l d .  since they  One  would expect t h a t the f i l m s would become u n i a x i a l w i t h t h e o p t i c axis perpendicular  to the f i l m s u r f a c e .  Since  the f i l m s a r e grown by  the a p p l i c a t i o n o f h i g h f i e l d s - t h a t i s i n t h e a n i s o t r o p i c s t a t e and, f u r t h e r m o r e , s i n c e t h e growth p r o c e s s i s i t s e l f  d i r e c t i o n a l , i n that  the i o n s t r a v e l normal t o t h e f i l m , one might even expect t h a t , on removal o f t h e f i e l d , frozen-in.  Despite  some a n i s o t r o p y  o f the same type might remain  the f a i l u r e to detect  s t r u c t u r e i n these f i l m s  i n d i f f r a c t i o n experiments t h e r e f o r e , they need n o t be c o m p l e t e l y of m i c r o s t r u c t u r e The absorbing  o r be c o m p l e t e l y  isotropic.  e l l i p s o m e t r y a n g l e s ty, A f o r homogeneous i s o t r o p i c , non-  f i l m s f o l l o w a closed loop  anisotropy represented  free  ( a t l e a s t , modulo 2TT i n A) .  With -  o f t h e expected k i n d , t h e r e f r a c t i v e index would be by an o p t i c a l i n d i c a t r i x which was an e l l i p s o i d  of r o t a t i o n  176  about the f i l m normal.  I f so,  the  s - l i g h t responds to n  the  Q  radius  of the c i r c u l a r p r i n c i p a l s e c t i o n .  The  p l i g h t responds to n^,  where  i f <()^ i s the a n g l e of i n c i d e n c e  n^  the index of the ambient,  the  and  a n g l e of r e f r a c t i o n fy^ i s g i v e n by n^  s i n <j>^ = n^  s i n §^ w i t h the  indi-  are then c a l c u l a b l e i n the  usual  c a t r i x d e t e r m i n i n g a r e l a t i o n between  n  The way  and  2 2 2 2 2 2 s i n cb /n + n cos d> / p 2 e p 2 o n  0  T  s  and  R  1.  =  0  T  reflectivities R  n^;  p  except t h a t d i f f e r e n t i n d i c e s n^ and  n^ a r e used.  The  result i s  t h a t , f o r an a n i s o t r o p i c f i l m , the d a t a s p i r a l e i t h e r upwards or downwards (depending on the  s i g n of the b i r e f r i n g e n c e )  domain i n s t e a d of f o l l o w i n g a c l o s e d l o o p . w i t h a n i s o t r o p i c f i l m s was EigV G . l  considered  The  problem of  balanced d u r i n g  (with the f i e l d  the growth p r o c e s s  periodic interruptions removed, the d a t a l i e  (with the f i e l d  a curve f o r an  caption. cycle.  on,  on)  and  removed).  The  an a n i s o t r o p i c f i l m .  With  the cycles  d a t a f o r zero  non-absorbing w i t h i n  figure  each  films  some l i m i t s  o f f , but becoming markedly a n i s o t r o p i c  homogeneous through t h e i r t h i c k n e s s )  field  f i t computed c u r v e s f o r  Thus, the d a t a a r e c o n s i s t e n t w i t h the  b e i n g i s o t r o p i c , homogeneous and  was  again  the c u r v e t r a c e s a h i g h e r path on  data f o r constant a p p l i e d f i e l d  w i t h the f i e l d  ellipsometer  i s o t r o p i c f i l m w i t h c o n s t a n t s as shown i n the  With the f i e l d The  The  on a s i n g l e c u r v e f o r s u c c e s s i v e  of growth (see legend f o r o p t i c a l c o n s t a n t s ) . fit  ellipsometry  shows the lower p a r t of ^, A domain f o r f i l m s which thicknesses.  field  , A  r e c e n t l y by E n g e l s e n (1971).  were grown s u c c e s s i v e l y to g r e a t e r  during  i n the  when the f i e l d was  (though on.  still  17.7  Fig. G . l Lower p a r t of ip,A domain f o r i n c r e a s i n g t h i c k n e s s o f f i l m s on t a n t a l u m up t o t h r e e c y c l e s . Lower curve (dashed) i s computed f o r an i s o t r o p i c o x i d e and the e x p e r i m e n t a l p o i n t s a r e f o r z e r o f i e l d : B , f i r s t c y c l e ; © , second c y c l e ; A , t h i r d c y c l e . Upper t h r e e c u r v e s ( s o l i d l i n e s ) r e p r e s e n t an a n i s o t r o p i c f i l m w i t h e x p e r i m e n t a l p o i n t s f o r f i e l d a p p l i e d : • , f i r s t c y c l e ; o >second c y c l e ; A , t h i r d c y c l e . Optical constants: thantalum n - i k = 2.46-i2.573; i s o t r o p i c o x i d e , n = 2.195; a n i s o t r o p i c o x i d e , n -n = -0.090; n -n = 8(n -n ) , w i t h $-1.6. ' o n ' e n o n n  r  Fig.  G.2  Upper p a r t o f if>, A domain.  Key as f o r F i g . G . l .  178  F i l m s grown i n the p r e s e n t e l e c t r o l y t e do not show d e t e c t a b l y the e f f e c t s seen f o r f i l m s grown i n p h o s p h o r i c a c i d which c o n s i s t of two  layers  due  to i n c o r p o r a t i o n of phosphate; t h i s l a y e r i s b e l i e v e d to grow due  to metal  ( D e l l ' O c a & Young 1970).  The o u t e r l a y e r has a lower  i o n motion as opposed to oxygen i o n motion.  index  This effect,  however, g i v e s a q u i t e d i f f e r e n c t k i n d of s p i r a l l i n g of the ^, A plot. Fig.  G.2  shows s i m i l a r r e s u l t s f o r the top p o r t i o n of the I c u r v e s , c o n f i r m i n g the behaviour demonstrated by F i g . G.l.. To proceed the changes produced w i t h no f i e l d  f u r t h e r i t was  assumed t h a t i f  by a f i e l d E and  if  e  and  n  o  are  i s the index of the o x i d e  a p p l i e d , then 8 =  A n /A n = e o  i s a c o n s t a n t independent  (n -n ) / (n -n ) n e n o  of E.  The method of s e p a r a t e l y d e t e r m i n i n g  changes of t h i c k n e s s and of index i s i l l u s t r a t e d shows, on the if) , A  plane,  by  F i g . G.3.  contours of equal t h i c k n e s s and  c a l c u l a t e d f o r our a n g l e of i n c i d e n c e and assuming determined  n  B = 1.6  by o b t a i n i n g the b e s t f i t of computed c u r v e s and  This  equal  n , Q  as experimental  d a t a i n F i g . G . l and G.2. A l s o shown a r e e x p e r i m e n t a l d a t a f o r a g i v e n 2 f i l m to which a sequence of f i e l d s was The d e c r e a s e i n index and Fig.  G.3  a p p l i e d up to 5.07  -1  x 10 MV  m  the i n c r e a s e i n t h i c k n e s s can be r e a d o f f i n  f o r each v a l u e of the f i e l d .  In the p r e v i o u s work by  Ord  et a l . ( 1 9 7 2 ) the f i l m s were assumed i s o t r o p i c , i . e . i n c a l c u l a t i n g s i m i l a r c h a r t s the v a l u e of B was  taken as 1.  f i l m do not e x c l u d e such treatment. measured o n l y by growing the f i l m  The d a t a f o r a s i n g l e  The a n i s o t r o p y i s d e t e c t e d  so as to cover more than one  and cycle.  179  n=2.1947  I  \  zero field  2.1930  W/deg  F i g . G.3 Contours ( ) of constant index n ( w i t h 3 = 1.6) and contours ( ) o f c o n s t a n t f i l m t h i c k n e s s on t a n t a l u m w i t h s u b s t r a t e c o n s t a n t s as i n F i g . G . l . The e x p e r i m e n t a l p o i n t s a r e f o r a f i l m on t a n t a l u m w i t h a range o f f i e l d a p p l i e d as shown and m a i n t a i n e d u n t i l s t e a d y - s t a t e changes were e s t a b l i s h e d . The f i e l d s were such t h a t negl i g i b l e i o n c u r r e n t was produced and hence n e g l i g i b l e growth.  180  APPENDIX H PROGRAMS USED TO CONTROL THE  H.l  ELLIPSOMETER SYSTEM  Introduction There were seven main programs used t o c o n t r o l the automated  e l l i p s o m e t e r and  to c o l l e c t d a t a .  The programs were w r i t t e n i n a com-  b i n a t i o n of F o r t r a n , a n d assembly language t o be compatible w i t h the o p e r a t i n g system used by the PDP-8E computer.  U s i n g the programs  i n T a b l e H . l , the p o l a r i z e r and a n a l y s e r r e a d i n g s c o u l d be w h i l e the c r y s t a l was  scanned through  the p r o b i n g beamr.  0S8  listed  accumulated The d a t a  was  s t o r e d on the Dectape U n i t f o r output v i a the t e l e t y p e or the i n c r e m e n t a l plotter.  Table  H.2  l i s t s the s u b r o u t i n e s used by the main programs.  The most f r e q u e n t l y used programs were c a l l a b l e from a monitor  program (SKEY,SV).  the keyboard through  The  f u n c t i o n s t h a t c o u l d be performed  monitor were ( i ) step the xy motors which moved the  the p r o b i n g beam;  ( i i ) p o s i t i o n the pen of the xy  ( i i i ) b a l a n c e the e l l i p s o m e t e r ; and  keyboard from crystal  plotter;  ( i v ) scan the c r y s t a l h o r i z o n t a l l y  and r e c o r d the p o l a r i z e r a n g l e , a n a l y s e r a n g l e , and p o s i t i o n of the crystal. board  A f t e r f i n i s h i n g a command, the program r e t u r n e d to the key-  monitor. Other programs (DIFFA.SV and.DIFFP.SV) were used  e i t h e r the a n a l y s e r or p o l a r i z e r r e a d i n g s o f two and  to p l o t  the d i f f e r e n c e on the xy p l o t t e r .  and POLA.SV p l o t t e d scan.  DATA.SV was  from one  scan was  to s u b t r a c t  scans a l o n g the  The  crystal  two programs ANAL.SV  the a n a l y z e r and p o l a r i z e r r e a d i n g s from a s i n g l e used  t o type out the c o n t e n t s o f a f i l e where the d a t a  stored.  MAIN PROGRAMS  SUBROUTINES  CALLED  FUNCTION  1. S K E Y . S V  S R U N , S B E N , S S T E P , SPLTXY S X Y P E N , SMOT2, S B E l , SRDA SRPHOT, S R E V , STEPN  Keyboard monitor  2.  PLOT.SV  SAXES  Draws a x e s and c a l c u l a t e s s c a l e for plotting  3.  POLA.SV  SAXES,  4.  ANAL.SV  S A X E S , SDEGR,  SPLTXY  P l o t s a n a l y s e r r e a d i n g s ".from ' o n e and t y p e s r e s u l t s  5.  DIFFA.SV  SAXES,  SPLTXY.  S u b t r a c t s a n a l y s e r r e a d i n g s f r o m two f i l e s , p l o t s and t y p e s t h e d i f f e r e n c e  6.  DIFFP.SV  S A X E S , SDEGR,  SPLTXY  S u b t r a c t s p o l a r i z e r r e a d i n g s f r o m two f i l e s , p l o t s and t y p e s t h e d i f f e r e n c e  7.  DATA.SV  SDEGR  SDEGR,SPLTXY  SDEGR,  program  factors  Plots p61ar.izer.:readings:fronrone and t y p e s r e s u l t s  Types c o n t e n t s of  a file  T a b l e H . l Main programs used to c o l l e c t data and c o n t r o l the automated e l l i p s o m e t e r .  on t h e  file  file  teletype  FILE  C A L L I N G NAME  FUNCTION  1.  SBE1  BEI  W r i t e s P and A o n t h e  2.  STEPN  STEPN  Steps the d e s i g n a t e d motor  3.  SREV  REV  Reverses the d i r e c t i o n  4.  SSTEP  STEP  Stops the d e s i g n a t e d motor  5.  SRUN  RUN  Scans the c r y s t a l and r e c o r d s t h e P and A  positions  6.  SMOT2  M0T2  M o v e s XY m o t o r s  crystal  7.  SAXES  AXES(IYR,  8.  SBEN  BE(P,  9.  SDEGR  DEGR(IL, I H ,  10.  SPLTXY  PLTXY(I, X,  11.  SXYPEN  XYPEN  12.  SRDA  RDA(IL.  I X R , I Y M U L , IXMUL)  ANGLES)  IY)  ANGLES)  times  the d e s i g n a t e d  motor  once  to r e p o s i t i o n  ellipsometer  the  once  C o n v e r t s d o u b l e p r e c i s i o n o c t a l number t o d e c i m a l number (ANGLES)  (IL,  IH)  P l o t s o n e p o i n t o n XY p l o t t e r Moves t h e p l o t t e r  IH,  of  10  Draws a s e t o f a x e s . I Y R and I X R a r e t h e l e n g t h s o f t h e Y and X a x e s . IYMUL a n d IXMUL are the s c a l i n g f a c t o r s c a l c u l a t e d Balances the  A)  teletype  pen to a d e s i g n a t e d  location  Reads t h e s p e c i f i e d s h a f t encoder and r e t u r n s a n g l e a s a d o u b l e p r e c i s i o n o c t a l number ( I L . I H ) a n d a s a d e c i m a l number (ANGLES)  13. SRPHOT  FUNCTION  CALLING NAME  FILE  PvPHOTO (ERR)  T a b l e H.2  Reads the e r r o r s i g n a l from the d e t e c t o r o f the e l l i p s o m e t e r  S u b r o u t i n e s used by the main programs l i s t e d  i n Table H.l  H.2  1.  Main Programs  SKEY.SV C  KEYBOARD '  COMMON  COMMAND  PROGRAM  I D I P * 11 A L , I I A H , I I P L J I I P H  S  '<5T#CLA RFAPC ! j?)! !^T  2  F C M A T < ' : ' A2>  3 4  C A L L 8F.1 COVTIV'.'E IF( TMCT_c;.c; ) C A L L MOTS CONTINUE I F C I N S T - l 17.1 CALL hljrvj COVTIN'LE  5  I F < IN<?T-133 ) 4 j 3 , 4  a  /  •  .  5 10  :  7 6  5 , t pi  IF<IMST-1036>9,8»9 <? 9  C A L L YYPF.N CONTINUE J M P ST  5  2.  EMI  POLT.SV C 1 ' .  2, 3  ;  . ' r>"A" AXES AMD CLACULATE SCALE FACTOR? WPITf(1,1) FORMAT C "7.-EP0 PLOTTER ' ) READC U H J I Y ' • FORMATC " Y ^ANGE IM DEGRFF.S = 'I3> READC1,3)IXR FORMATC' X "flMfiE = 'I3> CALL AXFSClYR,T.X?.,IYMTrL,IXMt)L> CALL EXIT END  185  3.  POLA.SV C C  1.  P L O T P O L A R I Z E R TRADINGS FOTIND IN F I L E E N T E R E D .SR OPT ION: I F S«11 = 1 5 T Y P E OUT R E S U L T S A L S O . DIMF.-VSIO'J I A H S M ) . IARCRPIO) DIMENSION D P ( P 0 0 ) , I X ( 2 P 1 ) DPH=-370. ' DPL=3 7 P . .READ*1,1)FILF.l FORMAT*"ENTER 1ST DATA F I L K NAME: "A6) READ<1,3)\' • FORMAT ( ' MO. OF DATA L T V F S = ' I 3 ) XY R L O T T F R I N I T I A L I S A T I O N  v  3 C  .WRITE*  .14  S  4 '  ,  1 , 1 / 4 ) '  FORMAT* "PLOTTER READY? PRESS COMT. SRI 1=01 FOR A X E S • ) HLT • ' • _ IXA=« IYY=0 C A L L !OPEN* * DTA1 * > F I L E 1 ) R F A D ( 4 , Z i ) C I A l C.J), I AP C J ) , I A 3 , I A 4 , IXC J ) , I A S , J = 1 , N ) FO"MAT < 6 A 3 ) DO ft. 1 = 1 ,'M IAL=IA1CI) IAH=IA!?CI) C A L L DEfJR C I A L , I AH, A ) DPCI)=PA IFCDPH-DPCI))7,8,8 DPH=DP(I) CO^TIMtiH IF(DPL-DPCI))6,5,5 ' .. D P L = D P < I ) CONTINUE '•TRITE* 1 , 1 S ) D P H , DPL FORMAT*"PLOT L I M I T S : Y H I G H = " F 6 . 2 " YLOV="F6•2 ) RFAP* 1, 18)rPH,pD! .. FORMAT*"SET YHIGH=*FS.9," V L O V = " F 6 . ? ) IYM=TFIxcr.PH-.pPL) • ' IXM=IXCN) P L O T AXES AND S E T S C A L E A3 = F L 0 A T *IYM)/10• '•'RITE* 1 ,9 ) A3 FORMAT* "EACH Y D I V I S I O N ='F'4.2' D E G R E E S ' ) . C A L L A X F ^ d V M , IXM, t Y M f l L , IXMfJL) YM"L=FLOAT*IYMUL) S C A L E DATA AND PLOT- POIMTS DO 10 1=1,M 1X1=IX*I)*IXMUL PP=(DP(I )-DPL)*10.*YM(jL IPP=IFIX(PP) IDX=IXI-IX> IDY=IPP-IYA IXA=IXI . D  7 R 5 6 15.  J  18  C  9 C  IYA=IPP CALL PLTXY(IDX,IDY) "RITE*1,11) FORMAT*"TYPE R E S U L T S ? Y E S : S F 1 1 = 0 1 ; P R E S S HLT CLA » . . •  10 11  S S S S S S  740*  .  S 12 S  .  AMD <K1 S7A C L A JMS T Y R E CALL EXIT TYPE,P l.'RITF* 1, 1P)< I X ( I ) , D P ( I ) , 1=1,N) FORMAT(13,F8•3) JMP I T Y P E  •' END  . '  COMT")  PLOT SR  ANALYSER  OPTION:  READINGS  I FSR11=1;  DIMENSION  FOUND TYPE  I A 1 C 2 0 0 ) , I A S C S 0 0 )  DIMENSION  I N F I L E  ENTERED  OUT RESULTS  ALSO.  '  D P C S 0 0 ) , I X C 8 0 0 )  DPH=-370. DPL=3~70. R E A D C 1 , 1 ) F I L E 1 FORMATC'ENTER  1 S TDATA  F I L E  NAME:,  'A6>  R E A D C 1 , 3 ) N F O P M A T ('NO. XY  O F DATA  PLOTTER  L I N E S * ' 1 3 ) -  ...  I N I T I A L I S A T I O N  W.RITEC 1* 1 4 )  ' '  FORMAT('PLOTTER  READY?  PRESS  C O N T . . S R I 1 = 01  FOR AXES')  HLT. IXA = 0 IXY =0  ••  CALL  IO P E N C  "  *D T A 1 ', F I L E 1 ) .  R E A D C 4, 4 ) C IA 3 , IA4 , I A 1 CJ ), IA S CJ ), IX CJ ), I A5 , J = 1» N ) " FORMATC 6 A S ) DO  IS I = 1 , N  I A L = I A 1 C I ) I A H = I A 2 C I ) CALL  P E G R C I A L , I A H , P A )  '.  .  •  D P C I ) = 3 A 0 . - P A I F C D P H - D P C I ) ) 7 , 8 , 8 DPH=DPCI)  •  CONTINUE IFC DPL-DP  C I ) ) 6 , 5 J 5  DPL=D?CI) CONTINUE  '  '.•'RITEC l , ' l  5>DPH,DPL  FORMATC'PLOT  L I M I T S :  YHIGH='F6.2'  YL0W='F6.2)  READC1,1H)DPH,DPL FORMATC'SET  YHIGH='F6•2 » '  YL0W='F6.8)  IYM=IFIXCDPH-DPL) IKM=.IXCN) PLOT  AXES  A N D S E T SCALE  A 3 - F L 0 A T CIYM)/10• <.'!R I T E C 1 , 9 ) A 3 FORMATC 'EACH CALL  Y  D I V I S I O N  AXES CIYM,IX  ='F4.2'  DEGREES')  W,IYMUL,IXMUL)  YMUL=FLOATCIYMUL) SCALE DO  1  DATA  o.  A N D PLOT  POINTS-  I= 1 ,N  I X I = I X C I ) * I X M U L P P = C D P C I ) - D P L ) * 1 0 . * Y M U L I P P = I F I X C P P ) I D X = I X I - I X A .  .  I D Y = I P P - I Y A IXA=IXI I Y A = I P P CALL  P L T X Y C I D X , I D Y )  W P I T E C 1 , 1 1 ) . FORMATC 'TYPE  RESULTS?. YES:  SR11=015  HLT  PRESS '  .  CONT') .  CLA 7406 AND C K 1 S7A  C L A ,  JMS  T Y P E  CALL  E X I T  .  '' .  TYPE,0 V R I T E C 1 , I S ) C I X C I ) , D P C I ) , 1 =1 ,N) FORMATCI3,F8.2) JMP  END  I  .  T Y R E  •  .  ,  '  •  187  criRTRftOT A\JL.' R*"APT \ir;c FO'A'P IM T H E P F I L E S ENTR ED PLOT THE PI E"E\'CF .»« . PI S T A N C E ALUM'i C R Y S T A L C O OPTir»\j. t r " 1 1 = 1: T Y p O f y qjrcrjLTS A L O . D I M E N S i Q V i a t ( o m n ) . rA >f9n"i),inicP''iri)»iPP(?rip) DIMENSION C ( P " i > » IXCPCIP) r  c  ,  c  nCrf=-T7n. DPL=37P. RFAPC1.1)rIL=M K0PN1T( • v \ i c i « DATA F I L E NAME: ' A* ) R«n( 1 ,P)FILFP F'|C».AT( ' f . v T « P\'D PAT A F I L E \JAMF8 ' A* > PPAPC 1 , -> ) V ITOPv;AT( • MO . OF DATA L I N FS = ' I 3 ) •YV P L O T T E R J \i I T T AL I t 0\J '">!TP(|,|Zl) Vf)RMAf( 'PLOTTER R F A P Y ? D K t r c e CONT. SB 1 1=01 HLT lvn = T IXY = o T F  T  7  FOR  AXES')  !ncr.\'( •  CALL PTA1 ' . F l L F 1 > REAP{ /), /O ( I A3 . I A'i, I A I ( J ) , I APC J ) , I * ( j >. I A^, J=-l » N ) r.lPijuT C « A P )  C A L L 1 O D V - v < • PTA 1 ' , K I L E P ) B V U n C f l . / i ) < l AT, T A/i . t * t ( ,J) , t 'IPC .J) . I A<5. I A « , J = t , N) F I N P MA" AMD MIN <7AL"E? OF PR PO « I = 1» M lAL=iaiCI) TAH=IAP(M C A L L PE<~.R( I A L . T AH. PA) IP'.= i r < i < n inH=I^P<1) C A L L PFRC ( IBt,» I"H, P'U P CI»-DA-PM I FC P P ( I ) - - \ r . )P ! , p n , p,^ ;.TDT T V ( 1 , J o > t * ( T >, PRC I ) REAPC1,93)PP(I) FORMAT < • S ET D EL A = ' F f • P ) COMTIN"E IF<PR'-t-r ( I ) )7.5(»n p D H = riD(I) CONTIIFCPP!.-PPt I ) X , ^. S ppt., = r>P( I ) CONTIV'E wn?( i , impoH.r P L FORMAT ( ' PLOT L ' M I T C ? Y H ! T 4 = ' F * . P ' YLOM= • f * . ? ) R E A P ( I » 3 s 1 P.PH. P P L P O C M A T C ' R T V H I ^ H : ' t e n , • vt_QW= » F f . ? ) IYV iuiXCPRH-tRL) D  c  -  C  =  PLOT A X E AND SCALE .»1=FLOATC i v - ^ j / i p i . WPlTEtl,0)^T FnoviAT (• c-ACH v P P H « I ' V M -s'F/i.P' C A L L AVFS ( I YM t I XM , I YM'JL. I X*T!L ) Vv!Tt!. i.-| nAT( I Y M " D S C A L E PATA A\!p .PLOT POINTS PO 1 'A I = 1 , N I V ! = I Y C I ) * I xyi!L pp- ( r,P< I ) - PPL ) * 1 0 • + YM"L IPP=IFIX(PP) I D X = I Y t - I XA trtv=IDP-TYA 41  =  IXA=IXI  DWfcF.S ' >  j  •  188  IVA=IPD  \6 \\.  c.M.i*  PLTXVC inv,  VRITF(l.ll) FOR/ATf'TYRR  \VY,  R""LTS?  YES:  SR.l=fll8  PRESS  COMT')  KL CLA 7/>'*«. 4\!P ( H I 57« CLA j y s TVPF \ C A L L FX I T TVPF.o ' M R I T F f 1 . I P ) C t x c I ) . TP<I )•1 = 1 » M V P O P MAT ( P > F ^ i P ) JMP I TYPF T  s 5 S  s 12  s  6.  END  DIFFP.SV C C C  cnnT'-ACT P O L . RFADT NGS FOUMD IN T H E P F I L E S ENTERED PLOT T H E D I F F E R E N C E D I S T A N C E ALONG C R Y S T A L SP OPTIONS I F <!P11=1J T Y P E OUT R E S U L T S A L S O . DIMTCJS I ON lftl(P«l».)» I A-2( P.V..B) , I P l CP'/.".), I ™ S ( 2553 > DIMENSION DR<S0E1>» IK<8?-0) DPH=-37S. D L = 3 7*). D  READ< 1.- D F I L E 1 1 p, 3 C 1/1 S  4  C  FORMAT< ' SN'TF." 1ST DATA F I L E . NAME: * Afi) T»5M5< 1, P. ) F I L E R FORMAT ('ENTER 2ND DATA F I L E NAME: ' A6> READ<1,3)N FORMATC 'NO• OF DATA L I N E S = ' ! 3 ) XV P L O T T E R INITIALISATION '•'PITEf 1, 14) FORMAT C 'PLOTTER READY? P E S S CONT. SRI 1=01 D  FOP  AXES')  HLT IXA=0 * IXY=0 . ' CALL IORENC'DTA1',FILF1) F.EADC.4, 4 ) C IA1 C.J), IA2C J ) , I A 3 , I A / l , IXC J ) , I A 5 , J= 1 , N ) FORMAT(*AS) CALL IOPENC'DTA1',FILES) P E A D ( C I B 1 C-J), ISC< J ) , I " 3 , I A/|, I A 5, I A C , J=1,M) F I N D MAX AND MIN V A L U E S OF DP DO 6 1=1,M IAL=1A1(I) IAH=IA?.CI) C A L L DEG' ( I A L , I AK, P A ) IBL=IB1(I) 3  -  IBH=IBP.<I) CALL DEGRCIBL,IBH,PB) DPC1)=PA-PB IFCDPH-DPC I ) )7, F., FS 7 8 5 6  DPH=DR(I) CONTINUE I F C D P L - D P C I ) ) 6 , 5, 5 DRL = r.R<n CONTTNO; V R I T E C 1 , 1 5 ) D P H , DPL  15 30  C  FORMATC'PLOT L I M I T S : YH1GH='F6.P* YL0V='F6.8> PEADC1,30)DPH, D°L • FORMATC ' S E T YHI 0H= ' F 6 . 2, ' S E T YLO'>'= ' F 6 . 2 ) . IVM=I F I X ( D P H - D P L ) IXM=IXCN) P L O T AXES AND S E T S C A L E A3 = F L 0 A T ( I M ) / 1 ' I . V  T  .  '  189  VRITEC1L9)A3 9  .  FORMAT ('EACH Y D I V I S I O N ='F4.2 • CALL AXESCIYM,IXM,IYMUL,IXMUL) YMUL-FLOATCIYMUL) . ' S C A L E DATA AND RLOT P O I N T S D O Iff 1 = 1, M I X I = IX ( I ) * I Vi'i' !L PR=CDPCI )-DPL)*10.*YMUL IPP=I F I X ( P P ) IDX=IXI-IXA IDY=I?p-lYA  C  11 S S  IXA=Ixt IYA=I? HALL C L T V y c I P X , I D Y ) '•' I T'" ( 1 » ! 1 ) F O R M A T C ' TYPE RESULTS? YES : HLT CLA  c. c  AND ( H I S7 A C L A  S R  JMS T Y P E CALL EXIT T Y P E , P>  IP  W P I T F . ( 1 , 1 P ) ( I X ( I ) , D P ( I ) , I = 1,N) FORMAT I I 3 , F « . P )  DEGREES')  .  C  10  p  c,  7.  r  JMP END  I TYPE i  SPll=31J  -  .  PRESS  CONT ' )  •  DATA.SV C 0  READ C O N T E N T S O F F.N AM E AND T Y P E A N G L E S A R E C O N V E R T E D TO DECIMAL DIMENSION P ( 2 ~ 0 ) , ACSPfO DIMENSION  ON T T Y FOR O U T P U T  I P L C P ^ H ) , I P H C P P U , I AL ( P ? - ) » l A H ( P . O O ) , I Y C 2 0 0 )  READC1,13)FMAME 13  FORMAT<•ENTER P.EADC1,1)N  1  FOPMATv'NO. OF L I N E RF.ADC 1, 1 4 ) N 1 , N 2  14  . '3 " S  DATA  FILE IN  NAME:  •Afi)  FILE='I3)  F O R M A T C ' L I S T L I N E S » I 3 ' T O '13) • C A L L IOPENC 'DTA1 ',FN.AME) DO 3 I = 1, N R E A D ( / i , S ) I P L C I ) , IPHC I ) , I ALC I ) , IAHC I ) , I Y ( I ) , I X CONTINUE ' FORMAT<6AP) DO  4  I=N1,N2  IAl = I P L C I) IA2=IPHCI) C A L L  D E G R CI A 1 , I A P , A M G )  PCI)=ANO IA1 = 1 A L C I ) I A P = I A H C I )  A 10  C A L L DEGR C 7 A 1 , I A 2 , A N G ) AC I ) = 3 6 0 • - A N G CONTINUE  WRITEC1,!!?) FORMATC ' DO  12 11  11  P  A  Y  X')  I=N1,N2  V P I T E C 1 , 1 2 ) P C I ) , A C I ) , IYC I ), I X F O R M A T C F . ' J . P - IX,F6.?., IX, 1 3 , I X , 1 3 ) CONTINUE CALL EXIT E N D  190  H.3  1 .  Subroutines C a l l e d  by the Main Programs  S B E 1  B A L A N C E E L L I P S O M E T E R AND PRINT SUBROUTINE BEI C A L L BE<P,A> VRITEC l . D P . f l FORMATC ' P = • F 6 . 8 , 8 X , ' A = ' F 6 « S ) RETURN END  2.  STEPN S T E P Y MOTOR N T I M E S SUBROUTINE STEPN CLA DO 1 1=1,10 CALL STEP TAD WAIT DCA w WT, ISZ V • JMp  TO ACCOUNT  .  r.TI*  CONTINUE RETURN WAIT,5000 M, 0 END  3.  P&A.  SREV  s s s s s s s •s s s s  RF.UERRF. MOTOR D I R E C T I O N S U B R O U T I N E REV COMMON I D I R CLA TAD \ I D I R ' AND <K5 CMA AMD <K5 DC A CHDIR TAD \ I D I R AND CK6772 TAD ( K i o n o TAD CHDIR DC A \ I D I R RETURN CHDIP,P! END  '  FOR GEAR  REDUCTION  SSTEP c  s s •s s s s 5 c  S 5 S  s s s c  s s s s s. s s s s s s s s s s s s s s s s s s 5  s  STEP  MOTOR  ONCE  SUBROUTINE STEP COMMON I DIP, , CLA TAD M D I R • AND C K 1 0 0 0 S7A C L A JMP ACCST TAD A C C S T P ' S.7.A C L A JMP ACCNTU JM3 S T E P I RETURN A C C S T , I AC S7 A JMP A C C S f TAD (K1000 . CM A AND \ I D I R DC A M D I R T A D CK-P.0 DC A A C C S T P TAD ( K 5 7 0 0 DCA W T I M E ACCNTU,JMS STEP1 TAD " T I M E TAD CK1Q0 DCA N T I M E TAD " T I M E B, I AC sr. A JMP B ' ISZ ACCSTP RETURN RETURN ACCSTP,0 •. " T I M E , 0STEP1.0 r  6334  CLA TAD UT C, I A C S2A JMP C J M P I ST E P I WT,7000 END  192  SCAN T H E C R Y S T A L . SUJIROUTI NE RIIN COMMON I D l , I I A L , I I AH,I I P L , I I F H D I M E N S I O N I A L C 1 O O ) , I A H C 1 0 0 ) , I PLC 1 0 0 ) , I P H C 1 0 0 ) , I Y C 1 0 0 ) R E A D C 1 , 1 ) 1 I X , I IY FORMAT C'START IMG P O S I T I O N : x='I 3,' • Y=•I 3 ) R E A D C 1 , 2 ) M 1 , I MCI FORMAT C'1 ST S E C : M='I3,' INC='I2). R E A D C 1 , 3 ) N 2 , INC2 FORMATC•2ND S E C : M= * I 3, ' INC='I 2 ) XY P L O T T E R I N I T I A L I S A T I O N IXA=fl I YA=G 6503 • • . READC 1 , 3 0 ) 1 X M M l . , I YM'TL FORMATC'PLOTTER: IXM'.FL= ' 12, ' I Y M U L = ' I 2 ) READC1,33)P1 FORMATC'SET Y - Z E P O = ' F 6 . 2 ) READC1,32)FNAMS FORMATC ' DATA. STORAGE F I L E C6 L E T T NAME) = 'A6> WRITEC1,31) FORMATC 'SR AND P L O T T E R S E T ? PRESS C O N T ' ) HLT YM!!L= F L O A T C IYMI7L) CALL 00RENC'DTA1",FNAME) KK=100 J=l ' • . CALL DECP,A) IALCJ)=IIAL IAHCJ)=IIAH , IPLCJ)=IIPL IPHCJ)=IIPH IYCJ)--0 JMS P L O T N=N1 INC=INC1 JMS SCAN N=N2 • ' INC=INC2 JMS SCAN N=N1 ' . \ INC=INC1 JMS SCAN KK=J • JMS T A P E CALL OCLOSE W R I T E C 1 , 1 0 ) I I X , I I Y , P , A .. FORMATC'FINISHED: x = ' I 3 , ' Y = ' I 3 , ' P='F6.2,' Y='F6.2//) RETURN SCAN,0 DO I = 1, N J=J+1 DO 7 1 2 = 1 , I N C , CLA TAD CK60 6332 CALL STEPN IIY=IIY+INC IYCJ)~IIY CALL BECP,A) IALCJ)=IIAL n  y  i>.  193  C S  S S  S C C  S' •  S  S• S Sfl 21 23  S  .1AHC J ) = 11 AH IPLCJ)=IIPL IPHCJ)=IIPH IS ? R 0 9 = 1 , PLOT C I I Y , P ) 7604 AMD CK/i srA CLA JMS PLOT IF SP 1 1 = I t-'RITE P,.A IF  '•  SP10=1,HALT  CLA 7604 AMD <K3 PCA \ I S " IKCIS"PS.?n VRITEC 1, 81 )?,.A, I IY F0PMATCPF7.2,14) GO T 0 C 9 5 , 8 3 , 8 3 ) I S P CONTINUE HLT  *  .  .  . .  IF  S S  7604 AMD CK100 S2A CLA RETURN CONTIN"E AFTER 1 " I 0 READINGS, OUTFUT TO TAPE  25 C  .  .  "  •  C  S  SR05=1,  " .,  RETURN  IF<1W0-JJ5,5,4  5 S 4 5 S  CONTINUE JMS TAPE CONTINUE JMP I SCAN TAPE, 0 DO 9  9 8  K=1*KK  WITEC 4,8)IPLCK),IFHCK),IAL(K),IAHCK),IYCK), FORMAiC 6AP) J = 0  S S  JMP I TAPE PLOT,0 IYI=II *IXMUL V  .  P P = < P - P 1 ) * 1 0 . * Y « T . T L  S  IPP=IFIXCFP) IDX=JYI-IXA IDY=IPP-IYA IXA=7YI IYA=IPP CALL PLTXYCIDX,IDY) JMP I PLOT END  , .  IIX  SM0T2 C  S t . 2 C 3 S S S 4  5 S S 5 C 6 7 S S S 8 9 S S S S S S S S 10 S S S S S 11 .S  . '  .  MOVE X , Y MOTORS FROM T H E K E Y BOARD S U B R O U T I N E MOT?. COMMON I D I R I D I F = 'D DCA " A I T READC1,1)MY FORMATC ^ = ' 1 4 ) • READC1,P)NX FORMATC ' X = • I/i) MOVE Y MOTOR IF CMY>3,4,5 'N=IABSC"-JY) CLA TAD CK/lO JMS.MOVEY GO TO 6 N=NY CLA TAD CX60 • o JMS MOWEY MOVE X MOTOR IF<NX)7,H,9 N=IARSCNX> CLA TAD CKP.Ofl JMS MOVE RETURN N=NX CLA , ' TAD C K 3 0 0 JMS MO»E RETURN '• MOVERS 633« CLA DO 10 1 = 1 , N CALL STEP WT, 1ST. '-'AIT 'JMP . CONTINUE J M P I MOVE "AIT,0 • M0VEY,0 6332 CLA DO 11 I = 1 , M C A L L STE°N J M P I MOVEY END  195 7.  SAXES  • C  DBA'.' A X E S A N D C L A C U L A T E S C A L E SU3R0UTINE AXESC IYR,I X R , I Y ' ^ I J 6500 ' CLA CLL 6506 IY = I Y P * 1 0 * IMAX=2000 IMAY=I700 IXM'JL=INAX/'IXR  S  S S  FACTORS IXMUL)  D  4 5 S S  .  S S S  15  S S 11 S S 12  C  S S 13 10  S S 14 16  S S S S S S S  S S 17 S S S' S S ? S S S S S  S S  S S S  I Y M U L = I MAY /1 Y P <-'RITF.( 1 , 4 ) IX;.;T;L, I Y M U L F O R M A T ? ' I XM'.1.= * 1 4 , * CLA 7604 AND CK1 SZA C L A " JMS AXIS RETURN AXIS,0 MOCE=0 IP=IYR IMUL=IYM"L IMC=IR*IMUL/10 DO 1 0 1 = 1 , 1 0 DO 1 1 J = 1 , I M C TAD LDDNY JMS XLATF. CONTINUE DO I P N = l , 3 0 TAD LUDE* JM XLATE CONTINUE DO 1 3 . K = l , 2 0 TAD LDD"X JMS XLATE CONTINUE CONTINUE IR=IR*IMUL DO 1 4 I = 1 > I P TAD LUDSY JMS *LATE • CONTINUE IF(MODE)16,16, 17 M0DE=1 IR=IXR IMUL=IXMUL CLA TAD LDDEX DCA LDDNY. TAD LUDNY DCA LUDEX TAD LDDSY ' DCA LDDUX TAD L"D"X DCA LUDSY GOTO.15 CONTINUE JMP I AXIS' LDDEX,IP LUDEX,11  •  LDDUX,* LUD'JX, 5 LDDNY,PP LUDNY#21 LDDSY* 42 LUDSY,41 XLATE,0 XA*6501 JMP X A 6506 CLA C L L JMP I XLATE INCT.0  • END  .  IYMUL= ' 14 ) .  •  196  8.  SBEN  C  31 S  S S S S S S S 38 S S  C C 5  t  S :9. 5 C C 3 6 4 C 5 7  S  8 C  9 C 12 10  BALANCE ELLIPSOMETER ONCE. SUBROUTINE BE CP,A) COMMON IDIR,I IAL,I I AH,I I PL,I IPH DIMENSION ESC20) IBAL=0 IBAL=IBAL+1 CLA TAD CK3 JMS SETM JMS BAL CLA TAD (K4O10 JMS SETM . JMS BAL GO T0C31,32)I3AL CONTINUE CALL RDACI IAL,I I AH,A) CLA 6338 A=360.-A CALL PDA CI I P L , 1 1 P H , P ) RETURN BALANCE,SPECIFIED UNIT BAL,0 NSTEP=0 MINF=0 . ' • • W=16 CONTINUE JMS SUM SUM1=S CONTINUE JMS SUM SUM8=S I F MINF=1» APPROACHING A MIN IF<MINF)3,3,4 - REVERSE MOTOR I F NOT APPROACHING A MIN IF(SUM2-SUM1>5,5,6 CALL REV MINF=1 GO TO 1 IFCSUM2-SUMU5i7,7 PASSED THRU MIN? GO TO 7 SUM1=SUM2 GO TO 2 CONTINUE JMS SUM SUM1=S , CALL REV J=2*N DO 8 1=1,J CALL STEP NSTEP=NSTEP+1 BUILD SUM2 UNTIL IT EQUALS SUM1 SUM2=0 DO. 9 1 = 1, N CALL PPHOTOCERR) CALL STEP NSTEP=NSTEP+1 ESC I ) = EPP SUM8=SUM2+EPR DROP LAST AND ADD NEW READING IN CIPCULAR BUFFER 1=1 CALL STEP NSTEP=MSTEP+1 v  C A L L RPHOTOCF.RR) SUM2 = SUMP.+EPP-ES< I ) F.St I > = F.PP I F < S U M 9 - s n M i ) l 1,13*13 1=1+1 N1=N+1 I F ( I-.Ml ) 10, 13, IP GO TO 10 J=MSTEP/2 CALL PEV DO 14 I = 1 , J CALL  STEP I n.AL S ETM,0 TAD ( K 1 0 0 0 633?. JMP  DCA M D I R JMP I S E T M SUM* 0 S = 0. DO 4 0 I S = 1 » M C A L L RPHOTO C E R R ) CALL STEP S=S+ERR JMP I SUM END  CONCERT R E A D I N G S TO A N G L E S SUBROUTINE DEGR(IL*IH*ANGLE) CLA TAD I M L DCA ANGL TAD I \ I H DCA ANGH TAD ANGL AND ( K 1 7 DCA M A I T A D ANGL RTR RTR AND CK17 DCA \ I A 9 TAD ANGL  RTL RTL  RAL AND C K 1 7 ' DCA M.A3 TAD ANGH AND CK17 EC A M A 4 " TAD ANGH ' RTR RTR AND <K17 DCA \ I A 5 A =.01*FLOATCIA1)+.1*FL0ATCIA2)+FL0ATCIA3> ANGLE=A+10.=-FLOAT< I A 4 ) + 1 0 0 . * F L O A T C I A 5 > RETURN ANGL* 0 ANGH,0 , END  198 10.  SPLTXY C  PLOT ONE POINT SUBROUTINE PLTXYCIX,IY> IDX=IX IDY=IY IF CIDX) 5,6,7 CONTINUE PA,TAD LUDWX JMS XLATE IS7, \IDX JMP PA GO TO 6 IDX=-IDX PB,TAD LUDEX JMS XLATE ISZ \IDX JMP PB CONTINUE IF ( IDY) 8,9, 10 CONTINUE PC,TAD LUDSY JMS XLATE 1SZ \IDY •JMP PC GO TO 9 IDY=-IDY PD/TAD LUDNY • JMS XLATE ISZ \IDY JMP PD CONTINUE JMS WAIT 6505 JMS WAIT 6503 RETURN XLATE,0 XA,6501 JMP XA 6506 CLA CLL JMP I XLATE • LUDWX,0 5 LUDEX,11 LUDSY,41 LUDNY,21 WAIT,0 XB,6501 JMP XB / 6502 JMP i WAIT END  5 S S S S 7 S S S 5 6 8 S S  S S  10 S S ' S  S  9 S S S S  S S S S S S S S S S S S S S S  11.  SXYPEN C  1  MOUE  '  THf  XV  D I . O T T "  SUBROUTINE XYPEN PEATH 1 , 1 ) I X , J v F0"vtAT< ' XIMC= CALL P L T X Y C I X , I Y ) RETURN END  o r \ |  FPOM TTY  YINC=  ' I4>  199  12.  SRDA C  READ T H E S H A F T ENCODER S P E C I F I E D S U B R O U T I N E RDA < I L , I H , A N G L E ) CLA C L L  S  s  fisos  S S S S  DCA ANGH 6304 DCA ANGL TAD ANGL AND C K 1 7  S S  DCA  S  TAD ANGL"  S  M A I  RTR  RTR AND < K 1 7 DCA MA2 TAD ANGL RTL RTLRAL AND-(Kl7 DCA \ I A 3 TAD ANGH AND (Kl7  S S S.  S  '  S S S  S S  S S S  S S S S S  '  •S S  S S  M A 4  TAD RTR RTR  ANGH  AND  <K17  .  DCA MAS A = • 01 * F L O A T ( I A l ) + . l * F L O A T C I A S ) + FLOAT C I A 3 ) ANGLE=A+10.*FLOATCIA4)+100.*FLOATCIA5) TAD ANGL DCA I M L TAD ANGH DCA I MH RETURN ANGL,0 ANGH,0 END  S S  DCA  ,  13. SRPHOT C  READ  THE  ERROR  SUBROUTINE «5  CLA  S  TAD  S  6323  S  SIRNAL  RPHOTO  (K17 .  A,63?!  f  JIVJP  S  A  63P4  S  CMA  .S  DCA ERR  M E R R =FLOAT.( I E R R )  RET'TRN ..  END  <ERR>  

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