UBC Theses and Dissertations

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UBC Theses and Dissertations

Design of a submillimeter gas laser Sahay, Vishnu 1967

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THE DESIGN OF A SUBMILLIMETER GAS LASER  Toy  VISHNU SAHAY B . A . S c , U n i v e r s i t y of B r i t i s h Columbia,  A THESIS SUBMITTED  1965  I N P A R T I A L FULFILMENT  OF  THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE  i n t h e Department of Electrical  We a c c e p t t h i s  Engineering  t h e s i s as conforming t o the  standards r e q u i r e d from degree o f Master  candidates f o r the  of Applied Science  Members o f t h e D e p a r t m e n t of E l e c t r i c a l E n g i n e e r i n g THE UNIVERSITY OF B R I T I S H COLUMBIA June,  1967  In  presenting  advanced  Library  agree  this  degree  shall  that  at  make  thesis  the  it  permission  in  University  freely  for  may  be  granted  by  tatives.  It  is  understood  financial  gain  not  of  the  that  be  Head  Date  4ou/v  3-S>, V^fcr"  British  allowed  Columbia  for  of  my  of  the  Columbia,  reference  copying  copying  Depa r t m e n t The U n i v e r s i t y o f B r i t i s h V a n c o u v e r 8, Canada  fulfilment  available  extensive  purposes  shall  partial  of  this  Department  or  without  requirements  I  agree  and  study.  thesis  or  publication  my w r i t t e n  by  of  for  that  I  an  the  further  for  scholarly  his  represen-  this  thesis  permission.  for  ABSTRACT A gas l a s e r has been designed .to :  e n t i r e f a r i n f r a - r e d spectrum.  'lase over t h e  This thesis discusses the  t h e o r e t i c a l and p r a c t i c a l c o n s i d e r a t i o n s t h a t a r e i n v o l v e d i n such a design. discussed  The t h r e e a s p e c t s  of design  that are  a r e t h e l a s e r c a v i t y , t h e e x c i t a t i o n mechanism, and  the d e t e c t i o n apparatus.  E v e r y e f f o r t i s made t h r o u g h o u t  to keep t h e system as simple  as p o s s i b l e .  Water v a p o r i s used i n t h e l a s e r as a t e s t g a s , s i n c e i t i s known t o have t r a n s i t i o n s i n t h e f a r i n f r a - r e d region.  I t was f o u n d t o l a s e i n s e v e r a l l i n e s most o f w h i c h  have b e e n i d e n t i f i e d w i t h l i n e s d i s c o v e r e d Two l i n e s , h o w e v e r , a p p e a r t o be new: with a possible error of -  by o t h e r  133.65P-,  workers.  a n d 145.75m  1.65u.  C h a r a c t e r i s t i c v a r i a t i o n s o f o u t p u t power w i t h pressure  and c u r r e n t d e n s i t y h a v e b e e n o b t a i n e d  f o rthe l a s e r  u s i n g water vapor. A t t e m p t s a t o b t a i n i n g l a s e r a c t i o n w i t h a c e t o n e and a l c o h o l proved  unsuccessful.  TABLE OP CONTENTS Page ABSTRACT  i i  TABLE OP CONTENTS  i i i  LIST OP ILLUSTRATIONS  iv  LIST OP TABLES  v i  ACKNOWLEDGEMENTS  v i i  1.  INTRODUCTION  1  2.  LASER MECHANISM  5  3.  4.  5.  6.  2.1  Population  Inversion  5  2.2  E x c i t a t i o n o f Gas L a s e r s  10  2.3  Line width  17  2.4  Gaseous D i s c h a r g e  21  RESONATOR DESIGN  23  3.1  Introduction  23  3.2  R e s o n a t o r Tube  33  3.3  M i r r o r s and t h e i r M o u n t i n g s . . . . .  45  3.4  External Mirrors  49  3.5  Mode S e l e c t i o n  50  COUPLING AND DETECTION  55  4.1  Coupling  55  4.2  Measurement o f O u t p u t S i g n a l I n t e n s i t y . .  65  4.3  Frequency Measurements  73  TESTS ON LASER.  82  5.1  T e s t s on L a s e r  82  5.2  Test Data  82  5.3  Discussion  of Results  86  CONCLUSIONS  95  REFERENCES  97 iii  L I S T OF ILLUSTRATIONS Figure  Page  2.1  Three L e v e l l a s e r  2.2  Hypothetical  P o t e n t i a l Energy Curves..  16  3.1  D i f f r a c t i o n L o s s o f Low O r d e r Modes...  26  3.2  Medium-Mode  30  3.3  A l i g n m e n t T o l e r a n c e o f Double Concave Cavity  3.4  7  Coupling  34  Alignment Tolerance of Piano-Concave Cavity  34  3-5  S t a b i l i t y Diagram  36  3.6  R e l a t i v e L o c a t i o n o f Modes  42  3.7  Cavity Structure  44  3.8  Fixed M i r r o r Housing  46  3.9  T r a n s m i s s i v i t y of Polyethylene  47  3.10  Movable M i r r o r Arrangement  47  3.11  M i r r o r Alignment Procedure  48  3.12  Aperture Limited Cavity Configuration.  52  3.13  Spot S i z e o f Concave C a v i t y  52  4.1  F i e l d I n t e n s i t y f o r 0 0 , 0 1 , 02 Modes, N=1.6 F i e l d I n t e n s i t y f o r 1 0 , 11 Modes, N=l .6  4.2 4.-3 4.4  Field N=1.6  58 58  I n t e n s i t y f o r 2 0 , 30 Modes, 59  F i e l d I n t e n s i t y f o r Low L o s s Modes W i t h C o u p l i n g A p e r t u r e , N=1.6 and N = 0 . 0 1 . .  60  4.5  C r i t i c a l A p e r t u r e F r e s n e l Numbers  61  4.6  Golay C e l l D e t e c t i o n Apparatus  68  4.7  Golay C e l l Detector  70  4.8  E b e r t - F a s t i e Monochromator  74  q  iv  4.9  J a r r e l - A s h Mono chroma t o r  76  5.1  T o t a l O u t p u t Power, Cavity  84  5.2 5.3 5.4  Near-Confocal  O u t p u t Power i n 118u L i n e , Near focal Cavity  Con85  T o t a l O u t p u t Power, P i a n o - C o n c a v e C a v i t y , 1mm C o u p l i n g A p e r t u r e T o t a l O u t p u t Power, P l a n - C o n c a v e 2mm C o u p l i n g A p e r t u r e  v  85 Cavity, 86  LIST OF TABLES Table  Fage  2- 1  Af v s M o l e c u l a r Weight  20  3- 1  S u b m i l l i m e t e r Gas L a s e r s  39  3-2  Low D i f f r a c t i o n L o s s Modes  43  3- 3  Modes E x c i t e d b y 118u, L i n e  43  4- 1  C r i t i c a l F r e s n e l Numbers  62  4-2  Transmission C o e f f i c i e n t s with a 2 mm C o u p l i n g H o l e  64  4- 3  Water Vapor T r a n s i t i o n L i n e s  80  5- 1  Monochromator Scans  91  5-2  Wavelength A n a l y s i s  92  vi  ACKNOWLEDGEMENT The f o l l o w i n g f i n a n c i a l support i s g r a t e f u l l y acknowledged : 1.  N a t i o n a l Research C o u n c i l B l o c k G r a n t s , NRC-A68 f o r 1965-66 and NRC-A3287 f o r 1966-67-  2.  B r i t i s h Columbia Graduate Student S c h o l a r s h i p f o r 1965-66.  5-  U n i v e r s i t y o f B r i t i s h Columbia F e l l o w s h i p f o r 1966-67. I would l i k e t o express my s i n c e r e thanks t o  Dr. D.P.' A k i t t f o r h i s i n v a l u a b l e guidance d u r i n g t h e e n t i r e project. I would a l s o l i k e t o thank Dr. L. Young f o r r e a d i n g the m a n u s c r i p t and h i s u s e f u l  comments.  :.. Thanks a r e due t o Mr. C. S h e f f i e l d f o r h i s t e c h n i c a l a s s i s t a n c e w i t h the c i r c u i t r y , and t o M i s s D. Mackenzie f o r typing the manuscript of t h i s t h e s i s .  F u r t h e r thanks a r e  g i v e n t o my f e l l o w s t u d e n t s who h e l p e d p r o o f - r e a d and assemble the t h e s i s .  THE DESIGN OP A SUBMILLIMETER GAS LASER 1.  INTRODUCTION  One of the few r e g i o n s of the e l e c t r o magnetic spectrum t h a t remains unexplored suhmillimeter region. terahertz.  i s the f a r i n f r a - r e d or the  The frequency  range i s from 0.3 t o 3  I n t e r e s t i n d e v e l o p i n g t h i s r e g i o n has been mounting  because i t o f f e r s p o t e n t i a l b e n e f i t s which combine those o f the microwave and of the o p t i c a l r e g i o n s .  These b e n e f i t s w i l l  p a r t i c u l a r l y be f e l t i n t h e f i e l d s of m i l i t a r y astronomy and  communications,  spectroscopy.  Two a s p e c t s of the development of t h i s r e g i o n a r e the g e n e r a t i o n and the d e t e c t i o n of s u h m i l l i m e t e r r a d i a t i o n . Development of one l e a d s t o the development o f the o t h e r .  At  the present time much of the r e s e a r c h e f f o r t i s d i r e c t e d towards d e v e l o p i n g s u h m i l l i m e t e r sources.  I t i s i n t h i s effort..that  l a s e r s a r e p r o v i n g themselves. Attempts have been made, l a r g e l y u n s u c c e s s f u l , t o develop these sources by e x t e n d i n g t h e p r i n c i p l e s behind :  c o n v e n t i o n a l microwave g e n e r a t o r s .  The s h o r t e s t wavelength-  k l y s t r o n t h a t has been made i s one by V a r i a n A s s o c i a t e s of Canada L i m i t e d and- i t operates  a t 1.76 mm (.170 GHz).  The only-  present n o n - l a s e r source of s u h m i l l i m e t e r waves i s developed by CFS of P a r i s , c a l l e d t h e C a r c i n o t r o n .  I t yields  output-  powers of m i l l i w a t t s - f o r wavelengths as s h o r t as 400p. (750 GHz). However, C a r c i n o t r o n s a r e extremely l i f e t i m e s are short. emissions  expensive  d e v i c e s and t h e i r  T h e r e f o r e , the phenomenon of s t i m u l a t e d  i s being exploited f o r f a r i n f r a - r e d  sources.  The was  phenomenon o f s t i m u l a t e d e m i s s i o n o f R a d i a t i o n  p r e d i c t e d and  e x p l a i n e d hy E i n s t e i n  1  i n 1917,  who  used  i n 1927,  who  used  2  2 t h e r m o d y n a m i c a l a r g u m e n t s , and  hy D i r a c  t h e t h e e r y o f quantum m e c h a n i c s .  However, i t was  1 9 5 3 " t h a t a p p l i c a t i o n f o r t h e phenomenon was  •5  m i c r o w a v e r e g i o n hy Weber , Townes e t a l  4  Prokhorov  .  Since then, e f f o r t s to apply  of" t h e e l e c t r o m a g n e t i c Maiman^, i n I 9 6 0 , ruby c r y s t a l .  by B a s o v  i t i n other  and regions  spectrum have proved s u c c e s s f u l .  a p p l i e d i t to the o p t i c a l r e g i o n u s i n g a  Subsequently,  have b e e n f o u n d and  more and more l a s e r m a t e r i a l s  used f o r the g e n e r a t i o n of  I n f a c t , so much w o r k has now  proposed i n the  and  5  only i n  radiation.  b e e n done i n t h i s f i e l d  possible to c l a s s i f y lasers i n four categories  that i t i s according  to the 'materials used. (a) " S o l i d S t a t e L a s e r s :  (b)  Organic  Gas  Lasers  Lasers To d a t e , gas  research purposes. gas  Laser  Lasers  (c) "Semi-conductor (d)  s u c h a s t h e Ruby  l a s e r s c a n be  the output  and  for  T h i s i s l a r g e l y because l a s e r a c t i o n i n s t i m u l a t e d by  beam c a n be  as f r e q u e n c y  l a s e r s h a v e b e e n t h e most p o p u l a r  a l a r g e v a r i e t y o f methods  stabilized  power a r e  and  t o a h i g h d e g r e e , i n so f a r  concerned. 7  S i n c e l a t e 1961,  when J a v e n e t a l  discovered  the  Helium-Neon L a s e r , a h o s t of gaseous m a t e r i a l s have been used for lasers.  L a s e r s u s i n g t h e s e m a t e r i a l s c a n be  i n t o t h r e e t y p e s , a c c o r d i n g t o the type  o f gas  classified  used.  3  (a)  N e u t r a l Atom Gas  (b)  I o n i c Gas  (c)  M o l e c u l a r Gas  lasers  Lasers Lasers  The g e n e r a t i o n of r a d i a t i o n a t f a r i n f r a - r e d f r e q u e n c i e s i s , a t p r e s e n t , the s o l e p r o v i n c e of m o l e c u l a r gas  lasers.  I n v e s t i g a t i o n of these l a s e r s has o n l y l a t e l y begun.  The  f i r s t o b s e r v a t i o n of s t i m u l a t e d e m i s s i o n i n the f a r i n f r a - r e d g  s p e c t r a of molecules was made i n 1964 and deuterium  oxide.  , u s i n g water vapour  S i n c e t h e n , r e s e a r c h f o r more and more  m o l e c u l a r gases w i t h s t i m u l a t e d e m i s s i o n a t f a r i n f r a - r e d f r e q u e n c i e s has proved f r u i t f u l . has as y e t been undertaken  However, no d e t a i l e d a n a l y s i s  t o determine  the exact mechanisms  i n v o l v e d i n the phenomenon. I n t h i s .thesis'',-a. .gas l a s e r i s designed'' which '•'. can ,be used t o c o n t i n u e the s e a r c h f o r hew m o l e c u l a r gas  :  m a t e r i a l s usable f o r l a s e r a c t i o n at f a r i n f r a - r e d frequencies. I t s h a l l then be t e s t e d u s i n g water vapour which i s known t o have t r a n s i t i o n s w i t h i n t h i s r e g i o n .  The range of wavelengths  over which the l a s e r so designed w i l l  a c t u a l l y operate can o n l y  be' determined  by a c t u a l e x p e r i m e n t a t i o n .  To determine  this  range, other m a t e r i a l s which are known to have t r a n s i t i o n s i n t h i s r e g i o n must be used i n the l a s e r . Whether any g i v e n m a t e r i a l w i l l have t r a n s i t i o n s i n the f a r i n f r a - r e d r e g i o n cannot be p r e d i c t e d . p r e d i c t e d whether the l a s e r designed  Nor can i t be  i n this project w i l l  e x c i t e a l l the t r a n s i t i o n s w i t h i n t h i s range s i n c e some of these t r a n s i t i o n s may  not be s t r o n g enough t o overcome the  losses inherent i n the laser.  However, t h e r e i s l i t t l e  doubt  t h a t w i t h t h i s l a s e r c e r t a i n new t r a n s i t i o n s c a n b e d i s c o v e r e d . The t h e s i s i s d i v i d e d i n t o f o u r p a r t s : (1)  t h e e x c i t a t i o n mechanism, i n w h i c h t h e p r o c e s s l a t e d e m i s s i o n and t h e p r o c e s s e s  of stimu-  that are involved i n  o b t a i n i n g t h i s i n a gas a r e d e s c r i b e d , (2)  t h e r e s o n a t o r d e s i g n , i n w h i c h t h e t h e o r e t i c a l and p r a c t i c a l considerations involved i n the design of the resonator are described,  (3)  t h e d e t e c t i o n p r o c e d u r e , i n w h i c h t h e d e t e c t i o n mechanism u s e d f o r power and f r e q u e n c y m e a s u r e m e n t s , a n d how t h e r e s u l t s c a n be i n t e r p r e t e d a r e d e s c r i b e d : , .  (4)  r e s u l t s a n d c o n c l u s i o n s , i n which' t h e r e s u l t s f r o m t h e e x p e r i m e n t a l d a t a a r e d e r i v e d and comments made o n them. The r e s o n a t o r d e s i g n i s c h o s e n a s s i m p l e a s p o s s i b l e  and  no a t t e m p t  stability.  i s made t o o p t i m i z e o u t p u t  power a n d f r e q u e n c y  5 2.  LASER MECHANISM  Before attempting t o d e s i g n the l a s e r c a v i t y , i t i s e s s e n t i a l t o u n d e r s t a n d t h e mechanisms w h e r e b y l a s e r a c t i o n i s obtained.  I n t h i s c h a p t e r , a q u a l i t a t i v e summary o f t h e s e  mechanisms i s g i v e n a s a p r e l i m i n a r y t o d e s c r i b i n g t h e method used t o e x c i t e the l a s e r . i n t r o d u c e d w h i c h may  Furthermore, c e r t a i n items are  i n some s u b s e q u e n t work l e a d t o p r e d i c t i o n s  o r h y p o t h e t i c a l e x p l a n a t i o n s o f t h e phenomena 2.1  Population  Inversion  I n a g i v e n system- o f p a r t i c l e s , exist  each p a r t i c l e can  i n one o f s e v e r a l quantum s t a t e s c h a r a c t e r i z e d by  energy l e v e l s . is  that are observed.  The number o f s t a t e s h a v i n g t h e same e n e r g y  c a l l e d the m u l t i p l i c i t y of t h a t energy l e v e l .  A  particle  c a n jump f r o m one e n e r g y l e v e l t o a n o t h e r by a b s o r b i n g o r e m i t t i n g energy e q u a l t o t h e energy d i f f e r e n c e between the levels involved.  The t r a n s i t i o n c a n t a k e p l a c e i n two ways:-  (a)  by y i e l d i n g e n e r g y t o o r a b s o r b i n g i t f r o m o t h e r p a r t i c l e s ,  (b)  by e m i t t i n g o r a b s o r b i n g a p h o t o n o f r a d i a t i o n  energy  whose f r e q u e n c y , V , i s g i v e n b y  h . where h = P l a n c k ' s c o n s t a n t E^= e n e r g y o f h i g h e r e n e r g y E = 2  energy o f l o w e r energy  level level  There i s a c e r t a i n p r o b a b i l i t y t h a t r a d i a t i o n a t f r e q u e n c i e s s u r r o u n d i n g v"  c a n be a b s o r b e d o r e m i t t e d when a  6  t r a n s i t i o n occurs.  T h i s p r o b a b i l i t y i s determined by a  known as the l i n e Shape, g ( ^ ) , which has  the  a resonance curve.  i t s own  linewidth  and  Each t r a n s i t i o n has  function  g e n e r a l shape of characteristic  t h i s determines the p r o b a b i l i t y t h a t a p a r t i c l e  w i l l undergo t h a t t r a n s i t i o n . A p a r t i c l e can undergo a t r a n s i t i o n e i t h e r or i t can he  s t i m u l a t e d to do so by i n c i d e n t  appropriate frequency.  spontaneously  r a d i a t i o n of  Spontaneous t r a n s i t i o n s can  an  occur o n l y  when a p a r t i c l e drops from a h i g h e r t o a lower l e v e l .  Radiation  from "such t r a n s i t i o n s w i l l emerge from the v a r i o u s p a r t i c l e s i n the  system i n random phase and  S t i m u l a t e d t r a n s i t i o n s , on the downward and  is.therefore  incoherent.  o t h e r hand, can he upward or  w i t h e q u a l p r o b a b i l i t y , the p r o b a b i l i t y b e i n g  dependent on the d e n s i t y of the  stimulating  radiation.  The  r a d i a t i o n emitted by s t i m u l a t e d downward t r a n s i t i o n s i s always coherent w i t h the  incident  r a d i a t i o n and  i s the  basis f o r l a s e r  amplification. I f a system of p a r t i c l e s can be l e v e l s i n thermal equilibrium  i n one  a t temperature, T,  of two the  energy  particles  w i l l populate these l e v e l s a c c o r d i n g to Maxwell-Boltzmann s t a t i s t i c s i n such a way \N-^,  t h a t the  p o p u l a t i o n of the l o w e r l e v e l ,  i s g r e a t e r t h a n t h a t of the upper l e v e l , Ng.  t h e r e f o r e , more p a r t i c l e s a v a i l a b l e than t h e r e are f o r downward. a b s o r p t i o n of the equilibrium  stimulating  9  was  are,  f o r upward t r a n s i t i o n s  T h i s would r e s u l t i n a. net energy.  However, i f t h e r m a l  c o u l d be d i s t u r b e d by some means and  l e v e l population, H ,  There  the  upper  caused to exceed the lower l e v e l  7 p o p u l a t i o n , N^, i n c i d e n t r a d i a t i o n o f t h e a p p r o p r i a t e  frequency  w o u l d s t i m u l a t e more downward t h a n upward t r a n s i t i o n s .  The  n e t r e s u l t i s t h a t r a d i a t i o n w o u l d he e m i t t e d w i t h  intensity  w h i c h d e p e n d s b o t h on t h e p o p u l a t i o n d i f f e r e n c e , and on t h e Q  i n t e n s i t y of the incident r a d i a t i o n . a net gain  There i s , t h e r e f o r e ,  given;by: Gain- = (^-n-^) u  quanta/second  where u = i n c i d e n t r a d i a t i o n i n t e n s i t y ~&2\ = E i n s t e i n c o e f f i c i e n t f o r s t i m u l a t e d  emission  b e t w e e n l e v e l s 2 and 1. T h i s c o n d i t i o n , where t h e p o p u l a t i o n o f t h e u p p e r l e v e l i s higher than that of the lower l a t i o n Inversion". c a n be a c h i e v e d  The e x t e n t  level i s called  "Popu-  t o which population i n v e r s i o n  determines the s u i t a b i l i t y of a m a t e r i a l f o r  use  i n laser action.  I n order t o discuss the various  and  parameters t h a t l e a d t o p o p u l a t i o n i n v e r s i o n , i t i s i n s t r u c -  t i v e to,-study t h e s i m p l e The  system w i t h t h r e e energy  conditions  levels.  p e r t i n e n t l e v e l s a r e shown i n f i g u r e 2.1 a n d t h e f o l l o w i n g  a n a l y s i s o f t h e s y s t e m c a n be made. \  \  \  \  •^3 \  N  \ £ 2 E  "=1  E  n.2 n1 Population (a) E q u i l i b r i u m C o n d i t i o n  3  x  F i g u r e 2.1  i n ,n^n, Population (b) E x c i t e d C o n d i t i o n x  Three L e v e l  Laser  8 At e q u i l i b r i u m , a Boltzmann p o p u l a t i o n d i s t r i b u t i o n o b t a i n s f o r t h e e n e r g y l e v e l s E-^, E g , E are given  .  The  populations  by? TS. -(E.-E.)/kT _x = e x 2 v  • N.  2  assuming u n i t m u l t i p l i c i t y . l e v e l s Eg and ng> at  n-^.  P o p u l a t i o n i n v e r s i o n between  c a n be a c h i e v e d by d e p o p u l a t i n g E-^ so t h a t  I n the case  frequency  of the Three L e v e l - , l a s e r , i n c i d e n t r a d i a t i o n  = E^-E.^ w i l l l e a d t o t h e f o l l o w i n g  processes;  h (l)  s t i m u l a t e d a b s o r p t i o n w i t h atoms i n l e v e l E^ r i s i n g level  (2)  E^,  s t i m u l a t e d e m i s s i o n w i t h atoms i n l e v e l E^ l e v e l E-^,  (3)  decaying.to  and  random s p o n t a n e o u s e m i s s i o n f r o m l e v e l E^ t o l e v e l All  E^.  t h e s e a r e r a d i a t i v e t r a n s i t i o n s , and w i l l  u n t i l n-^ = n^. n-^ and  to  With  t h i s s i t u a t i o n , ng may  proceed  be g r e a t e r V-^  a weak s t i m u l a t i n g r a d i a t i o n a t f r e q u e n c y  than  =  E  2" 1 E  h will The at  result  i n coherent  stimulating field a n  d  emission of r a d i a t i o n at frequency  may  be p r o v i d e d by t h e s p o n t a n e o u s  a l s o by p r e v i o u s l y s t i m u l a t e d e m i s s i o n .  ^  -y^-  emission  In a  l a s e r , m i r r o r s r e f l e c t t h i s r a d i a t i o n b a c k i n t o t h e e x c i t e d gas volume p r o d u c i n g f u r t h e r s t i m u l a t e d e m i s s i o n . A f a s t t r a n s i t i o n b e t w e e n l e v e l s E„  and  E„  3  t h a t the p o p u l a t i o n  i s g r e a t e r t h a n n-^.  Such a  s i t i o n t a k e s p l a c e by y i e l d i n g t h e e n e r g y ( E ^ - E^) crystal lattice,  i n t h e case  of s o l i d s ,  or.by  ensures  2  tranto  the  various'collisions  i n t h e case o f gases and o t h e r f l u i d s . W i t h t h e e l e m e n t a r y p i c t u r e p r e s e n t e d i n t h e preceding;.p a r a g r a p h s , i t i s now p o s s i b l e t o make some s t a t e m e n t s c o n c e r n i n g the attainment of p o p u l a t i o n i n v e r s i o n . ll)  The l e v e l  ..... - j _ s  n  c  e  must h a v e a w i d e l i n e w i d t h .  This i s necessary.  t h e r e i s u s u a l l y n o t enough e n e r g y a v a i l a b l e  from  o r d i n a r y s o u r c e s o f r a d i a t i o n i n a n a r r o w . f r e q u e n c y band. It  s h o u l d be n o t e d t h a t r a d i a t i v e t r a n s i t i o n s f r o m  E^ t o l e v e l 'E^ may n o t a l w a y s he p o s s i b l e  level  due t o t h i s  r e q u i r e m e n t , a s i n t h e c a s e o f gas l a s e r s .  Alternate  -methods, t o be d i s c u s s e d l a t e r , musx t h e n be a d o p t e d . (2)  W h i l e t h e t r a n s i t i o n 3-2 may o r may n o t be r a d i a t i v e , t h e i m p o r t a n t f a c t i s t h a t i t be f a s t compared t o t h e t r a n s i t i o n 2-1.  T h i s would  lead t o a population of l e v e l  i n e x c e s s o f t h a t o f E-^ and a p o p u l a t i o n i n v e r s i o n i s t h e n -achieved.  Note t h a t t h i s i m p l i e s t h a t a f a s t  transition  ' 3-2 h a s a n a r r o w b a n d w i d t h , a c c o r d i n g t o t h e U n c e r t a i n t y P r i n c i p l e AE.. A T ^ h where AE = b a n d w i d t h and AT = l i f e t i m e o f l e v e l E^. (3)  I n a d d i t i o n t o t h i s , l e v e l E-^ must d e c a y f a s t e r t h a n E^.  T h i s may b e done b y d i r e c t t r a n s i t i o n ,  level  radiative  o r o t h e r w i s e , t o l e v e l E^ a s i n f i g u r e 2.1 o r t o a n even "lower e n e r g y l e v e l whence p a r t i c l e s a r e t r a n s f e r r e d ~ u p t o l e v e l E,,.  i.  10  2.2  E x c i t a t i o n o f Gas  2.2.1  Lasers  Introduction Except f o r the  t r a n s i t i o n i n which stimulated  i s d e s i r e d , none need n e c e s s a r i l y he p a r t i c u l a r l y important i n the ative absorptions  c a n be  c a s e o f gas  are d i f f i c u l t ,  o b t a i n i n gaseous media.  radiative.  a c h i e v e d i n s e v e r a l ways, a l l o f w h i c h may  ease w i t h w h i c h n o n - r a d i a t i v e  frequent  inter-atomic  This  c o l l i s i o n s , are  to  inversion  contribute i s because  obtained.  of  the  I n gases  a c h i e v e d i n any  of  f o l l o w i n g ways ^: 1  (i)  O p t i c a l or R a d i a t i o n E x c i t a t i o n  (ii)  E l e c t r o n Impact  (iii)  I n e l a s t i c Atom-Atom  (iv)  Molecular  o b s e r v e d and  there  exist forbidden  are u s e f u l i n determining certain frequencies.  These r u l e s  However, t o a p p l y  Laser  .  them, t h e  However, i n t h e known and  the  above f o u r w i l l be  degree of t h e i r u s e f u l n e s s  c a n n o t be  at  spectroscopic  i n the c l a s s i c a l search  example  for  new  e x a c t mechanism  i n v e r s i o n i s a c h i e v e d i s open t o  C e r t a i n l y , a l l of the  are  whether l a s e r a c t i o n i s p o s s i b l e  l a s e r t r a n s i t i o n s , these are not whereby p o p u l a t i o n  Selection Rules  transitions.  c o n f i g u r a t i o n must be known, a s t h e y a r e o f t h e H e l i u m - N e o n Gas  Collision  Dissociative E x c i t a t i o n Transfer  I n each of t h e s e methods, the  the  radi-  t r a n s i t i o n s , c a u s e d by  t h e n , i n t e r - e n e r g y - l e v e l t r a n s f e r s c a n be the  impossible,  lasers, population  t o t h e i n v e r s i o n p r o c e s s t o some d e g r e e . the  is  l a s e r s , since  though not  I n gas  This  emission  speculation.  c a l l e d into play, predicted.  In  but order  11 to o b t a i n some i n s i g h t i n t o t h i s , a c l o s e r l o o k at each e x c i t a t i o n mechanism w i l l prove p r o f i t a b l e . 2.2.2  Radiative  Excitation  As mentioned on page 9, r a d i a t i v e t r a n s i t i o n s s t i m u l a t e d by an e x t e r n a l  source r e q u i r e  case of a gas  p r e s s u r e , the l i n e w i d t h  a t low  a wide l i n e w i d t h .  In  the  i s l a r g e l y deter-  mined by the Doppler e f f e c t - a phenomenon r e s u l t i n g from the r e l a t i v e motion o f the gas ver. end  p a r t i c l e s w i t h r e s p e c t to the  (A q u a l i t a t i v e d i s c u s s i o n of t h i s c h a p t e r . )  of l i n e w i d t h s  i s g i v e n at  O r d i n a r y s o u r c e s of r a d i a t i o n  i n a wide range of f r e q u e n c i e s - wide compared t o the determined by t h i s e f f e c t . radiation  T h e r e f o r e , the  w i t h i n the l i n e w i d t h ,  obserthe  radiate linewidth  i n t e n s i t y of  incident  i s i n s u f f i c i e n t t o r a i s e enough  p a r t i c l e s from the ground l e v e l t o l e v e l E^ t o permit the m a t i o n of p o p u l a t i o n i n v e r s i o n .  for-  T h e r e f o r e , r a d i a t i o n from  o r d i n a r y s o u r c e s cannot be the main source of e x c i t a t i o n f o r a gas  laser.  Radiative  e x c i t a t i o n does occur to a v e r y s m a l l  e x t e n t , however, owing t o spontaneous e m i s s i o n a t e x t e n t t o which t h i s i s u s e f u l cannot be  ^  ^he  determined.  A second l a s e r of a p p r o p r i a t e frequency may, be used t o e x c i t e the gas  laser.  however,  Since the output power of  t h i s l a s e r i s c o n t a i n e d w i t h i n a narrow frequency band, i t i s s u f f i c i e n t l y i n t e n s e to cause a p p r e c i a b l e p o p u l a t i o n I f the s p e c t r o s c o p i c c o n f i g u r a t i o n  of the gas  inversion.  i s known and  if  a l a s e r o f a p p r o p r i a t e frequency;.:c:ahl hei foHhd, R a d i a t i v e - e x c i 1  v  ;  t a t i o n can t h e n be the main method of e x c i t a t i o n .  In attempting  12  t o d i s c o v e r new  t r a n s i t i o n s i n v a r i o u s gases, p a r t i c u l a r l y  those whose s p e c t r o s c o p i c  c o n f i g u r a t i o n i s unknown, a second  l a s e r can he u s e f u l o n l y hy chance. not s t i m u l a t e the new  transitions.  A g i v e n l a s e r may Therefore,  or  may  a more g e n e r a l  form o f e x c i t a t i o n i s r e q u i r e d which can s i m u l t a n e o u s l y  excite  a l l the d e t e c t a b l e t r a n s i t i o n s . 2.2.3  E l e c t r o n Impact This i s the most g e n e r a l form of e x c i t a t i o n used f o r  atomic gases.  P o p u l a t i o n i n v e r s i o n by t h i s means occurs  due  t o the e x c i t a t i o n of atoms by c o l l i s i o n s w i t h e l e c t r o n s of h i g h k i n e t i c energy.  I n an e l e c t r i c d i s c h a r g e  f r e e e l e c t r o n s are formed.  of a gas,  These are a c c e l e r a t e d by  f i e l d t h a t c r e a t e d the d i s c h a r g e  and  n e c e s s a r y h i g h k i n e t i c energy.  In a discharge,  ions  and  the  the e l e c t r o n s a c q u i r e  the  the f o l l o w i n g  energy exchange p r o c e s s e s take place': (i)  ^electron c o l l i s i o n s of the f i r s t k i n d i n which an atom g a i n s energy from an e l e c t r o n . ,  ( i i ) e l e c t r o n c o l l i s i o n s of the  second k i n d i n which an e x c i t e d  atom l o s e s energy t o an e l e c t r o n , ( i i i ) spontaneous e m i s s i o n  of r a d i a t i o n from an e x c i t e d atom.,  ( i v ) a b s o r p t i o n of r a d i a t i o n by an atom, (v)  stimulated emission The  of r a d i a t i o n by an atom.  advantage t h a t these processes o f f e r over the  r a d i a t i v e method of o b t a i n i n g p o p u l a t i o n i n v e r s i o n i s t h a t the e l e c t r o n e x c i t a t i o n c r o s s - s e c t i o n i s much w i d e r than the a b s o r p t i o n l i n e w i d t h of gases.  Thus, a l t h o u g h the S e l e c t i o n  13 R u l e s r e m a i n t h e same f o r t r a n s i t i o n s , a n atom i s more to~-he e x c i t e d hy i n c i d e n t  t o a p e r m i s s i b l e l e v e l hy e l e c t r o n  radiation.  impact  likely than  However, t h e s i t u a t i o n i s now more  complicated than the simple picture tro t h e h i g h e r p r o b a b i l i t y  presented, e a r l i e r , owing  of various transitions.  obtain population inversion  using a single  I n order t o  g a s , some  additional  r u l e s must be o b s e r v e d . Suppose t h a t l a s e r a c t i o n E^ and E „  i s r e q u i r e d between l e v e l s  Under t h e r m a l e q u i l i b r i u m  2  l a t i o n s are given b y  _2  _2,  H  T  2  where  conditions,  t h e popu-  ;  1 1  exp  (  9j  -  3  2  )  kT  ±  2  1*. = S p o n t a n e o u s r a d i a t i o n transitions  lifetime of  b e t w e e n l e v e l E^ and t h e  g r o u n d l e v e l ( i = 3 , 2 ). = Transition  l i f e t i m e o f a n atom g o i n g  f r o m l e v e l E ^ t o t h e g r o u n d l e v e l when the  atom i s s u b j e c t e d o n l y t o c o l l i s i o n s  with electrons of a given density i n equilibrium  amongst t h e m s e l v e s a t  t e m p e r a t u r e T. T h i s f o r m u l a assumes t h a t t h e r e i s no d i r e c t action the  inter-  b e t w e e n l e v e l s E^ and E , b u t b e t w e e n t h e s e l e v e l s and 2  g r o u n d l e v e l , E.^.  of E , i . e .  H  2  ?21 72^  >  F o r t h e p o p u l a t i o n o f E^ t o e x c e e d  that  2  f2i T  3  '(2.D  14 I n the case  Q  R u l e s , the r a t i o r  i n a single" gas,  •il i  o f t r a n s i t i o n s a l l o w e d by t h e S e l e c t i o n i s t h e same f o r a l l i * .  Clearly  population inversion i s impossible to obtain  u n l e s s the l e v e l E g i s not r a d i a t i v e l y connected permitted t r a n s i t i o n s .  I n s u c h an e v e n t , T  t o ground  cannot  a f f e c t e d by r e a b s o r p t i o n o f s p o n t a n e o u s e m i s s i o n . t h e o t h e r h a n d , c a n s t i l l be  so a f f e c t e d .  were i n c r e a s e d , r e a b s o r p t i o n due emitted by T ^. -  then,  o t h e r gas c a n become i m p o r t a n t  be  T^,  on  I f t h e gas  t o s t i m u l a t i o n by  by  density  photons  enough t o  decrease  T h u s , i n o r d e r t o g e t N ^ > N g , a h i g h d e n s i t y o f gas  is  required. I n a r e a l gas, the presence  of other energy l e v e l s  b e s i d e s the t h r e e u s e d - f o r the above e l e m e n t a r y lead to complications.  Atoms u n d e r g o i n g  a n a l y s i s can  transitions  from  these l e v e l s can populate the lower l e v e l i n p r e f e r e n c e  to  E^.  this  The  p o p u l a t i o n i n v e r s i o n w i l l t h e n be l o s t .  For  r e a s o n , gas d i s c h a r g e l a s e r s i n v o l v i n g a m o n a t o m i c gas p o p u l a t i o n i n v e r s i o n i s t o be a c h i e v e d are comparatively r a r e .  s o l e l y be  i n which  e l e c t r o n impact  I n a few n o t a b l e c a s e s , Neon,  Krypton,  12 A r g o n and X e n o n  , t r a n s i t i o n s have indeed been  W i t h two e n e r g y l e v e l o f one  gases present gas  observed.  i n the d i s c h a r g e ,  and i f an  i s n e a r l y t h e same as an e n e r g y l e v e l  o f t h e o t h e r , p o p u l a t i o n i n v e r s i o n i s more r e a d i l y o b t a i n e d . *A c o n c l u s i o n d r a w n by B.A. Lengyal"*""'" f r o m t h e Quantum T h e o r y of T r a n s i t i o n s .  15 For  a m i x t u r e - o f two g a s e s , a and b, t h e e n e r g y l e v e l s a r e :  gas  a:  gas  b:  E  0,  l  =  E g , E^.  E-^ = 0 ,  E^ = E^ o f g a s a.  The c o n d i t i o n f o r p o p u l a t i o n i n v e r s i o n  is"*""*":  T  > where t h e 9's a r e s t i m u l a t e d t r a n s i t i o n l i f e t i m e s are  32  and t h e  T's  s p o n t a n e o u s t r a n s i t i o n l i f e t i m e s , and  1 = _1_ + _1_ ^3 ~^31 ^32 t, ba  = l i f e t i m e of t r a n s i t i o n s  a t l e v e l E^ b e t w e e n t h e  3  two g a s e s . The H e l i u m - N e o n l a s e r  i s a t y p i c a l example o f s u c h  7  a system . 2.2.4  I n e l a s t i c Atom-Atom C o l l i s i o n " * " ^ In a d i a t o m i c gas, p o p u l a t i o n i n v e r s i o n  i n one atom, Y, w i t h l a s e r  action  appropriate t o the spectro-  s c o p i c c o n f i g u r a t i o n o f t h a t atom. the  o t h e r atom, X, i n a n e x c i t e d  may be t r a n s f e r r e d X* + Y  may-be o b t a i n e d  The p r o c e s s may  state,  X*, and t h i s  t o Y by c o l l i s i o n s . Y* + X + AE  start  with  excitation  16 The  e n e r g y d i f f e r e n c e , - AE,  w a l l s or i n f u r t h e r c o l l i s i o n s . b u t may  he., e x p l a i n e d  may  The  he a b s o r b e d by  process  i s net  the  w e l l known,  i n terms of the p o t e n t i a l energy  curves.  u(R)  X* ,Y AE X,Y*  R o Distance Figure 2.2 The and R  Q  the  (X,Y*)" a r e  between atoms, R  H y p o t h e t i c a l P o t e n t i a l Energy Curves  p o t e n t i a l energy curves shown i n f i g u r e 2 . 2 .  b e t w e e n the"" two system" (X*,Y)  atoms,- t h e r e  o f t h e two  system  A t some c r i t i c a l  (X*,Y) distance  is a certain probability  can s w i t c h over t o the  that  system (X,Y*).  The  atom Y* w i l l t h e n r e v e r t t o i t s u n e x c i t e d  s t a t e w i t h the  of r a d i a t i o n .  also yield laser  N o t e t h a t t h e atom X* may  a c t i o n i n r e v e r t i n g t o an u n e x c i t e d  s t a t e , but t h e o u t p u t  not f a l l w i t h i n the d e s i r e d d e t e c t i o n range of O t h e r w i s e , i t s i m p l y r e v e r t s by n o n - r a d i a t i v e For  "new"  a r e not  may  frequencies. transitions.  g a s e s t h i s phenomenon c a n n o t be  s i n c e the p o t e n t i a l energy curves  emission  known.  predicted,  17 2.2.5  Dissociative E x c i t a t i o n Transfer This consists  molecule,  o f a n e x c i t e d atom c o l l i d i n g w i t h a  r a i s i n g the molecule  sequently f l i e s  t o an e x c i t e d  s t a t e , which sub-  apart w i t h t h e emission o f energy, r a d i a t i v e or  otherwise. X* + Y The  excited  Again, very l i t t l e it gas 2.3  atom Y* w i l l y i e l d t h e d e s i r e d  laser  i s known a b o u t t h i s mechanism and when  i s applicable.  I t c e r t a i n l y w i l l be i n v o l v e d  action. exactly  when a m o l e c u l a r  i s . e x c i t e d by a d i s c h a r g e . Linewidth The  two  ~ Y* + Y + X + AE  2  reson'ant  l a s e r system c o n s i s t s  o f t h e i n t e r a c t i o n between  s y s t e m s : t h e t r a n s i t i o n s and t h e c a v i t y .  t h e s e h a s i t s own c e n t e r f r e q u e n c y  and r e s o n a n c e c u r v e s .  resonance of the t r a n s i t i o n system i s c h a r a c t e r i z e d frequency  by the  o f t r a n s i t i o n and t h e l i n e w i d t h . E v e r y t r a n s i t i o n has a n a t u r a l l i n e w i d t h .  follows  Each of  This  as a r e s u l t o f t h e U n c e r t a i n t y P r i n c i p l e AE . A t £s where AE = s p r e a d  _h 2at of.energy  l e v e l s due t o l i n e w i d t h ,  At - l i f e t i m e i n a g i v e n  state,  = _1_ A  A  mn  mn  = spontaneous e m i s s i o n c o e f f i c i e n t , ^  The  18 T h e r e f o r e , A f = AE =  fmn  h The  2*  linewidth  natural linewidth i s generally very small, of  the o r d e r o f a few h e r t z .  I n a gas,  the molecules are i n  p e r p e t u a l m o t i o n and t h i s has t h e e f f e c t o f b r o a d e n i n g linewidth. (a)  T h e r e a r e two mechanisms w h i c h a c h i e v e  D o p p l e r B r o a d e n i n g and ( b )  Pressure  this  this:  Broadening.  D o p p l e r B r o a d e n i n g i s a c o n s e q u e n c e o f t h e random r e l a t i v e m o t i o n o f t h e m o l e c u l e s , o f m o l e c u l a r w e i g h t , M, w i t h respect t o the observer.  Af = 1.48 v f -  T h i s g i v e s a l i n7e w i d t h  mn  = 7.15 x 10" /TY f \m)  m  13  :  n  (2.2)  A s m a l l m o d i f i c a t i o n t o t h i s c a n be made i f t h e m o l e c u l e s a r e i o n i z e d and a c c e l e r a t e d by t h e e x c i t i n g  potential.  Pressure Broadening i s a g e n e r a l term f o r broadening caused by i n t e r - m o l e c u l a r c o l l i s i o n s .  At low pressure,  .Af = _ l where. T = mean t i m e b e t w e e n =  collisions,  1 nv  N = molecular density, v = mean v e l o c i t y o f c o l l i d i n g m o l e c u l e s , a-  = c o l l i s i o n cross section, 2 •-=  Ttb  h = molecular diameter. Therefore,  A-f = H v b At  2  (2.3)  a f i x e d temperature,- N v a r i e s w i t h p r e s s u r e a n d v  and b a r e c o n s t a n t .  Hence, A f i s p r o p o r t i o n a l t o p r e s s u r e .  19 With v a r y i n g temperature,  the v a r i a t i o n of Af i s complicated  s i n c e n-^, v and e v e n b a r e t e m p e r a t u r e  dependent.  C o l l i s i o n s w i t h tube w a l l s a l s o have a e f f e c t i f the dimensions mean f r e e p a t h .  of the tube a r e o f the order o f the  The l i n e w i d t h i s g i v e n b y  (TV  A f = 20 r \Mj where if  broadening  (2.4)  KHz  r = tube r a d i u s ,  t h e mean f r e e p a t h , 1,  f r e e p a t h , 1,  i s s m a l l compared t o r .  The mean  i s g i v e n by I =  1 2jtb R 2  where  N = m o l e c u l a r dens i t y = % P, RT  N  where  = A v o g a d r o s number = 6.023 x 10 1  (2.5) 23  ,  P = Pressure, R = U n i v e r s a l gas constant, = 8.32  j o u l e s / m o l e °k, 400 °k,  T = Temperature o f gas y i e l d s N = 3.21  z 10  1 6  molec/cnr , 5  I f the moleeular diameters  f o r P = 1mm  a r e o f t h e o r d e r o f an  Angstrom, I = 7.2 x 10" 2  cm.  I f t h e tube r a d i u s i s o f t h e o r d e r o f a few c e n t i m e t e r s , it  i s .much l a r g e r t h a n I .  I n s u c h a c a s e , t h e l i n e w i d t h due t o  c o l l i s i o n s w i t h w a l l s w i l l be s m a l l e r t h a n g i v e n b y e q u a t i o n The v a r i o u s l i n e w i d t h s g i v e n b y e q u a t i o n ( 2 . 2 ) , (2.4)  a r e g i v e n i n T a b l e 2-1,  c u l a r weight.  (2.4).  (2.3),  showing l i n e w i d t h s versus mole-  C o l l i s i o n l i n e w i d t h s a r e o b t a i n e d a s s u m i n g r = 4 cm.  20 Table  2-1  l i n e w i d t h v s M o l e c u l a r Weight, M  (Af)  < 'walls Af  M  ^ ^Doppler A f  press  f mn =3xl0  (approx)  f  1IL  mn  =10  (KHz)  (KHz)  (MHz)  5  46.5  319  1.92  19-15  10  .32.1  240  1.36  13-55  15  27.0  196  1.11  11.05  20  23.4  170  0.97  9.68  25  20.9  152  0.86  8.57  30  19.1  139  0.78  7.83  35  17.7  130  0.74  7.36  40  16.5  120  0.68  6.78  45  15.6  113  0.64  6.38  50  14. 8  112  0.61  6.06  Note:  (Af) i s a t p=l Torr. press * i s p r o p o r t i o n a t e l y decreased. 2  f  m  mn  n  = 2.54 x 1 0  1 2  = 1.37 x 1 0  1 2  , (Af)  d o p p  , (Af), ' dopp v  (MHz)  F o r l o w e r p, ( A f ) ^' 'pres  v  For H 0, f  y  = 8.55  MHz.  = 4.6  MHz.  From T a b l e 2-1, i t i s a p p a r e n t t h a t t h e D o p p l e r  effect  i s the predominant  l i n e b r o a d e n i n g e f f e c t i n gases o p e r a t i n g  at low pressures.  A t h i g h e r p r e s s u r e s , N i n e q u a t i o n (2.3)  would  i n c r e a s e t o f u r t h e r broaden  12  the l i n e .  T h e r e a r e o t h e r b r o a d e n i n g mechanisms w h i c h a r e weak 15 i n gases, but are predominant  i n solids  .  The s p i n - s p i n  a c t i o n and d i p o l e - d i p o l e i n t e r a c t i o n c a n b r o a d e n t h e l i n e more t h a n c a n t h e D o p p l e r e f f e c t and make t h e s o l i d  intermuch  material  21 suitable  f o r r a d i a t i v e pumping.  as t h e p a r t i c l e s p a c i n g s " will  The  later.  a range of f r e q u e n c i e s equal  i s t h e n by a gaseous  G-aseous  called  The  o n l y way  to the  Doppler  to i n c i t e  laser  discharge.  exception,  been o b t a i n e d  t h a t o f Cesium"""'"', l a s e r  u s i n g a gaseous  i n t o p l a y t o v a r y i n g e x t e n t s and  discharge. beepi  stimulated emission  a t a l a r g e number o f f r e q u e n c i e s .  safe to say, t h a t i f l a s e r a c t i o n  obtained  i s g o i n g t o be  of the e m i t t e d  i n a gaseous d i s c h a r g e .  radiation  has  I t i s thereobtained  f r o m some gas w i t h unknown s p e c t r o s c o p i c c o n f i g u r a t i o n , c e r t a i n l y be  say  sufficient  e x c i t a t i o n mechanisms d e s c r i b e d above h a v e  been achieved fore  notable  i n gases has  A l l -of t h e  output  Discharge  W i t h one action  on t h e l a s e r  of r a d i a t i o n cannot supply  width to i n c i t e l a s e r action.  2.4  rapidly  A t t h e moment, i t s u f f i c e s t o  t h a t the o r d i n a r y sources intensity within  off  increase.  e f f e c t of the Doppler w i d t h  be d i s c u s s e d  action  These e f f e c t s f a l l  The  i s o f .course unknown, b u t  i t will  frequency i t can  be  determined u s i n g appropriate d e t e c t i n g devices. A gas c a n be across state.  the tube, The  caused t o d i s c h a r g e  c a u s i n g t h e gas  p o t e n t i a l c a n be  (1)  rf  (2)  dc  (3)  Pulsed  As a r e s u l t through the discharge,  and  potential  t o b r e a k down i n t o a p l a s m a  i n one  of t h e s e ,  by a p p l y i n g a  of t h r e e  forms:  a c u r r e n t i s caused t o pass  e n e r g y i s a b s o r b e d by t h e gas  system.  22  Of t h e t h r e e methods o f i n d u c i n g a d i s c h a r g e , t h e p u l s e method is  p r e f e r r e d s i n c e i t has t h e p o t e n t i a l o f g r e a t e r  versatility.  I f a p u l s e of s h o r t d u r a t i o n i s a p p l i e d , i t i s  possible" t o o b t a i n the v a r i a t i o n of output cation (See  experimental  power a f t e r t h e  of the p u l s e w i t h the h e l p o f a f a s t - r e s p o n s e  section  on d e t e c t o r s ) .  T h i s would y i e l d  m a t i o n o f l i f e t i m e s o f t r a n s i t i o n s and a c t i o n b e t w e e n t h e atoms o r m o l e c u l e s  of the  detector,  interesting  the e f f e c t  appli-  of the  inforinter-  gas.  There a r e c e r t a i n t r a n s i t i o n s w i t h h i g h g a i n t h a t can excited  o n l y by p u l s e d d i s c h a r g e .  These a r e c a l l e d  Self-Termin-  a t i n g t r a n s i t i o n s . T h e s e are t r a n s i t i o n s that somewhat c l o s e r t o t h e g r o u n d t h a n t h e u s u a l l a s e r and  t h e l o w e r l e v e l may  action  then terminated  among l o w  and  because of f a v o r a b l e  c a n be b u i l t up i n a s h o r t  Laser  energy l e v e l s  Because of  f u n c t i o n s t o the l a s e r l e v e l from t h e ground s t a t e , population inversion  transitions,  as s o o n as t h e  b u i l d s up an a p p r e c i a b l e p o p u l a t i o n .  p r o x i m i t y of t h e ground s t a t e ,  occur  (i.e.,long lived).  i s o b t a i n e d by momentary i n v e r s i o n  d u r i n g a f a s t p u l s e , and state  be m e t a s t a b l e  be  lower the excitation  a very  time.  high  23 3. 3•1  RESONATOR DESIGN  Introduction In the previous  chapter  medium i s an a m p l i f i e r .  i t was shown t h a t t h e l a s e r g a s  I t has a center frequency of operation.,  where t h e g a i n i s a maximum, and a b a n d w i d t h .  With an a p p r o p r i -  a t e f e e d b a c k s y s t e m , t h i s a m p l i f i e r c a n be c a u s e d t o o p e r a t e a s an  oscillator.  S u c h a f e e d b a c k s y s t e m c a n be f u r n i s h e d b y c o n -  t a i n i n g "the g a s i n a g l a s s t u b e and p l a c i n g m i r r o r s a t e i t h e r end. be  . R a d i a t i o n w h i c h t r a v e r s e s t h e l e n g t h o f t h e tube would  a m p l i f i e d by t h e g a s , and r e f l e c t e d by t h e m i r r o r s , and would  t r a v e r s e t h e medium once a g a i n . w o u l d be f u r t h e r a m p l i f i e d . losses. field  After a finite  A t t h e same t i m e i t w o u l d  number o f r e f l e c t i o n s ,  a steady  how t h e s e c a n be u s e d t o d e s i g n a l a s e r w h i c h would  the theory  The c h a p t e r  and t h e n w i t h t h e p r a c t i c a l d e s i g n  f o r m u l a s w h i c h , a r e . i n v o l v e d , in.' t h e  of. t h e c a v i t y . those  Conditions  l a s e r t u b e may be r e g a r d e d a s a r e s o n a n t c a v i t y  i n t h e same s e n s e a s a c l o s e d c o p p e r b o x w i t h p o l i s h e d w a l l s i s a microwave c a v i t y . the is  with  c a v i t y des ign-.;are - q u o t e d .  O r t h o g o n a l Modes and R e s o n a n c e The  operate  deals f i r s t  t h e o r e t i c a l p a r t i s l a r g e l y q u a l i t a t i v e and o n l y  3.1.1  state  w i l l discuss the e f f e c t o f the m i r r o r s ,  w i t h i n the f a r i n f r a - r e d region.  The  incur  p a t t e r n w i t h i n t h e t u b e w o u l d be e s t a b l i s h e d . This chapter  and  I n the process the r a d i a t i o n  l a t t e r i s of the order of the order  inner  The d i f f e r e n c e i s t h a t w h e r e a s  of a few wavelengths long, the former  o f many t h o u s a n d s .  A n e x t r e m e l y l a r g e number  24 o f c a v i t y r e s o n a n c e s may c o n s e q u e n t l y be i n v o l v e d cavity.  These r e s o n a n c e s a r e s u s t a i n e d  i n a laser  by t h e p r e s e n c e o f t h e  a m p l i f y i n g medium,, w h i c h c o u n t e r b a l a n c e s t h e l o s s e s i n h e r e n t i n the  system.  The l o s s e s a r e c a u s e d b y i n h o m o g e n e i t i e s i n t h e  medium, r e f l e c t i o n o f f m i r r o r s w i t h f i n i t e  c o n d u c t i v i t y ; , and  d i f f r a c t i o n o v e r t h e edges o f t h e m i r r o r s .  16 Pox  and L i  showed t h a t a s t e a d y s t a t e c o n d i t i o n i s  r e a c h e d a f t e r many r e f l e c t i o n s . field  e x i s t s i n an i n f i n i t y  TEM modes.  I n t h i s state, the r a d i a t i o n  of near orthogonal  modes  T h e s e modes a r e c h a r a c t e r i s e d b y t h e i r  called transverse  f i e l d p a t t e r n s and a r e a s s i g n e d s u b s c r i p t s m and n , w h i c h a r e integers. The modes a r e t h e n n o t a t e d TEM modes. The f i e l d ° mn of the lowest  mode, T E M Q Q , i s c o n c e n t r a t e d  than are the f i e l d s  of higher  nearer to the a x i s  o r d e r modes.  Hence,, w i t h  mirrors  o f f i n i t e d i m e n s i o n s , e n e r g y l o s s e s due t o d i f f r a c t i o n o v e r edges, i s l o w e s t  f o r t h e T E M ^ Q mode.  The o t h e r  mirror  losses are  e q u a l l y h i g h f o r a l l modes w i t h i n a w i d e f r e q u e n c y range.D i f f r a c t i o n l o s s e s i n a l l modes depend o n t h e a c t u a l c a v i t y c o n f i g u r a t i o n , n a m e l y t h e s i z e o f t h e tube and t h e shape of the m i r r o r s o  T h e r e a r e s e v e r a l m i r r o r shape  configurations  t h a t c a n b e a n d have been u s e d f o r l a s e r c a v i t i e s . are both m i r r o r s  plane;  Among t h e s e  b o t h c o n c a v e ; one p l a n e a n d one c o n c a v e  o r c o n v e x ; one c o n c a v e and t h e o t h e r  convex.  Of t h e s e  configu-  r a t i o n s , t h e c o n c a v e - c o n c a v e i s known t o h a v e t h e minimum d i f f r a c t i o n l o s s e s f o r t h e d o m i n a n t mode ( T E M Q Q u s u a l l y ) , f o r the  same i n t e r - m i r r o r d i s t a n c e  and m i r r o r s i z e .  Pox and L i  17 and  D.E, McCumber  h a v e computed d i f f r a c t i o n l o s s e s f o r some  low  o r d e r modes i n c o n f o c a l  c a v i t i e s • ( c a v i t i e s whose m i r r o r  s p a c i n g equals t h e r a d i u s of c u r v a t u r e  25  of t h e i r m i r r o r s ) .  McCumher's r e s u l t s a r e reproduced i n the graph on page.26, f i g u r e 3°1* The  graph shows t h a t t h e d i f f r a c t i o n l o s s e s decrease  w i t h i n c r e a s i n g F r e s n e l Number N.  F o r t h e symmetrical  confocal  c a v i t y , " N is..given" by N = _a£ b\  (3.1)  where a = r a d i u s of m i r r o r  apertures  b = r a d i u s of c u r v a t u r e o f t h e m i r r o r s = l e n g t h o f tube A. = wavelength T h i s i n v e r s e dependence o f d i f f r a c t i o n l o s s on F r e s n e l number i s confirmed 18 Gordon  .  by o t h e r workers, such as Boyd and  F i e l d a m p l i t u d e s and f i e l d i n t e n s i t i e s f o r v a r i o u s  modes f o r . d i f f e r e n t . v a l u e s of 'N have beer., evaluated of r e f e r e n c e s 16, 17 and 18.  by authors  As N i n c r e a s e s , t h e mode f i e l d  i s compressed n e a r e r t h e a x i s .  T h i s r e s u l t s i n a decrease i n  l o s s e s over t h e m i r r o r edges, ( i . e . d i f f r a c t i o n l o s s e s ) . F i g u r e 3.1 can a l s o be used t o determine d i f f r a c t i o n l o s s e s i n a non-confocal  cavity.  Boyd and Gordon have d e f i n e d  an e q u i v a l e n t c o n f o c a l c a v i t y f o r a n o n - c o n f o c a l  cavity.  They  base t h e i r d e f i n i t i o n on a q u a n t i t y c a l l e d t h e "Spot S i z e " . At any c r o s s - s e c t i o n o f t h e tube and w i t h i n a r a d i u s s m a l l compared t o the m i r r o r r a d i u s , t h e r a d i a t i o n a m p l i t u d e drops e x p o n e n t i a l l y away from the tube a x i s .  The: .spot s i z e i s d e f i n e d as t h e  •.:.;.<:•  d i s t a n c e from t h e a x i s t o t h e p o i n t where the amplitude f a l l s to l / e of i t s value a t the a x i s . non-confocal  F o r symmetrical,  concave,  c a v i t i e s , t h e spot s i z e a t t h e m i r r o r w i s  26  Figure  3.1 Low  Diffraction O r d e r Modes  Losses f o r  27 g i v e n by: w  s  2d b  = it  2'  - [d lb  (3.2)  where b = r a d i u s o f c u r v a t u r e  of both m i r r o r s  d = separation of mirrors and b ^  d„  Equation  (3.2) i s v a l i d  o n l y i f w «.'a. s i s a minjjnum. f o r . :.the- c o n f o c a l c a s e  W i t h a g i v e n d, w s (b=d) and i s g i v e n bys •  w  = bA *  s  Since w  (3.3) i s a" minimum ,.-f o r h t h e . c o n f o c a l c a s e i/.the..'.dif• '  s  f r a c t i o n losses are also smallest f o r that For the non-confocal  case.  c a v i t y , an e q u i v a l e n t  Presnel  Number c a n be d e r i v e d so t h a t N = l 2 d\ a  where, a,-^,^  =  |~2d  a  -  |d\ ~|^ 2  \ b j  r a d i i of mirror  d = mirror  '  (3.4)  J  aperatures  separation  b = radius of curvature  o f t h e two m i r r o r s .  The d i f f r a c t i o n l o s s c a n t h e n be d e t e r m i n e d f r o m f i g u r e 3.1 u s i n g t h i s v a l u e Aside  o f N»  from i n c u r r i n g d i f f r a c t i o n l o s s per r e f l e c t i o n ,  t h e r a d i a t i o n s u f f e r s a phase s h i f t . involved.  H e r e a l s o t h e modes a r e  Boyd and G o r d o n show t h a t t h e c o n d i t i o n f o r r e s o n a n c e  i s t h a t t h e r o u n d t r i p phase s h i f t be 2it t i m e s which has v a l u e s  zero through i n f i n i t y .  a r e l a t i o n s h i p between m  P  an i n t e g e r . q  T h i s c o n d i t i o n imposes  n, q a n d t h e w a v e l e n g t h . A......  Again,  t h i s p h a s e r e l a t i o n s h i p d e p e n d s on t h e c a v i t y c o n f i g u r a t i o n .  28 For t h e g e n e r a l concave-concave case, t h e phase r e l a t i o n ship i s : 4_d = 2q + (1 + m + n ) ( l - 4 t a n " h^d) A. % h+d  (3.5)  1  From equation(3.5 ) »it i s found t h a t t h e v a r i o u s modes ;  do n o t , i n g e n e r a l , operate a t t h e same frequency.  Two modes  would operate a t t h e same wavelength, A., i f A. =  4d  =  2 q^+ (l+m^+n-j^) K  K= 1 - 4_ t a n Tt  - 1  4d 2^TTl+m^+n^7K  b^d h+d  (3.6)  (q!-<l ) = 4-K (-(m +n ) - ( m ^ ^ ) ) = iK(A(m + n ) ) ( 3 . 7 ) 2  Since q^ and q  2  2  2  a r e i n t e g e r s , the q u a n t i t y , -£-K(A(m+n))  must a l s o he an i n t e g e r .  I f A(m+n) i s an odd i n t e g e r , then K  must he an even i n t e g e r .  However, f o r K t o he even, b=0 or.d=0,  n e i t h e r o f which cases a r e i n t e r e s t i n g .  T h e r e f o r e , i t i s not  p o s s i b l e f o r two modes whose A(m+n) i s an odd i n t e g e r t o be resonant a t the same frequency.  On t h e other hand, two modes  whose A(m+n) i s an even i n t e g e r may be. s i m u l t a n e o u s l y r e s o n a n t , s i n c e now K i s p e r m i t t e d t o be an odd i n t e g e r .  When K has t h e  odd i n t e g e r v a l u e s , l - 4 r , ( r = 0 , l , 2 3 . . . . , ) „ t h e n , d=b', .which i s , 5  c o u r s e , t h e c o n f o c a l case.  Thus, i n the c o n f o c a l case, a l l  t r a n s v e r s e modes (TEM ) whose (m+n) i s even operate a t one mn * f r e q u e n c y , w h i l e those whose (m+n) i s odd a l l operate a t some crther frequency. I f K were t o d i f f e r s l i g h t l y from an i n t e g e r , as i t does i n t h e n o n - c o n f o c a l case, two modes would not operate a t the same f r e q u e n c y , u n l e s s t h e i r (m+n)'s were t h e same.  Their  29  f r e q u e n c i e s , however, may he v e r y c l o s e t o each o t h e r , the p r o x i m i t y b e i n g determined  by t h e f a c t o r b-d. b+d  Thus, the modes  may be regarded as i n d i v i d u a l r e s o n a t o r s , each o p e r a t i n g a t some c e n t r a l frequency, f « by: n  The Q's o f t h e s e r e s o n a t o r s a r e g i v e n  Q = 2fffmn E Pd where E = energy s t o r e d i n the mode,  '(3.8)  P^= r a t e o f energy d i s s i p a t i o n i n mode per t r a n s i t . Note t h a t t h e mode r e s o n a t o r s a l s o have harmonic f r e q u e n c i e s , owing t o the i n t e g e r , q.  These a r e spaced by:  (from e q u a t i o n ( 3 . 2 ) ) Af = c_- , c = speed o f l i g h t i n a vacuum " 2d 3.1.2  (3.9)  I n t e r a c t i o n between C a v i t y Modes and A m p l i f y i n g Medium 'In t h e l a s e r c a v i t y , a c o m p l i c a t e d i n t e r a c t i o n takes  p l a c e between t h e a m p l i f y i n g medium and an i n f i n i t y o f resonant modes w i t h ' ' " c h a r a c t e r i s t i c s f and Q . - mn mn t e r i s t i c s f ^ and l i n e w i d t h Af^.  The medium has c h a r a c -  Prom e q u a t i o n ( 3 . 8 ) , the, Q's  of s e v e r a l modes a r e v e r y h i g h , p a r t i c u l a r l y t h e lower o r d e r modes.  The l i n e w i d t h of t h e gas i s determined  by t h e Doppler  e f f e c t and t h i s i s g e n e r a l l y much w i d e r t h a n Af . mn  There i s  hence a c o m p l i c a t e d c o u p l i n g among the. v a r i o u s . r e s o n a n t systems ( i . e . , the medium and t h e modes) i n w h i c h energy i s g i v e n up by t h e system w i t h the g r e a t e r energy and l o w e r Q t o those w i t h l e s s energy and h i g h e r Q. w i t h energy by t h e medium. between resonant systems,  Thus t h e modes a r e f e d  The mathematics o f t h e c o u p l i n g 19 o b t a i n e d by Wagner and Birnbaum, ,  30 d e s c r i b e s the manner i n which energy i s f e d i n t o the v a r i o u s modes. A q u a l i t a t i v e a n a l y s i s w i l l s u f f i c e here.  z  fmn F i g u r e 3-2  Medium Resonance Curve Mode Resonance Curves  fo Medium-Mode C o u p l i n g  I n f i g u r e 3.2, t h e resonance curves o f s e v e r a l modes are shown.  Assuming t h a t c o u p l i n g among the o r t h o g o n a l modes  i s n e g l i g i b l e , t h e modes w i l l be coupled w i l l be coupled  Energy  from t h e medium t o a mode, depending on t h e Q  of t h a t mode as w e l l as t h e d i f f e r e n c e , to equation  t o the medium.  |^o~^mnl "  Referring  (3.8) t h i s means t h a t most o f the energy i s f e d i n t o  the modes which a l r e a d y s t o r e most of t h e energy.  This  t h e i r Q w i t h t h e r e s u l t t h a t more energy i s coupled  i n t o these  modes.  m n  increases  F i n a l l y , a l l t h e energy goes i n t o those modes which  i n i t i a l l y had t h e h i g h e s t Q and whose f r e q u e n c i e s a r e nearer f o .  ,;  The mode w i t h the h i g h e s t Q i s the dominant mode, usually  TEMQQ^,  since the d i f f r a c t i o n losses are smallest f o r  31 t h a t mode.  However, i t i s p o s s i b l e t h a t o f t h e t o t a l l o s s ,  the d i f f r a c t i o n l o s s i s n e g l i g i b l e f o r s e v e r a l modes as w e l l a s , and  other t h a n , t h e  TEM^Q^  mode.  The Q's o f these modes w i l l  t h e n be n e a r l y as h i g h as t h a t o f t h e dominant mode. resonant f r e q u e n c i e s  The  may a l s o be v e r y c l o s e t o t h e resonant  f r e q u e n c y o f t h e dominant mode.  Thus, t h e energy w i l l be  coupled i n t o s e v e r a l modes and a l l o f these may o p e r a t e . R e f e r r i n g again t o equation  (3«5)» i n t h e c o n f o c a l  case,- KS=1, h=d and hence,  4d  A. = 2q  (3.10)  +(1 + m + n)  I t can he seen t h a t s e v e r a l modes,: i n c l u d i n g t h e dominant mode, have t h e same .-..resonant frequency.-  i n other  words, t h e resonant frequency i s "mode degenerate". A f i n a l r e s u l t of t h e medium-mode-coupling a n a l y s i s i s t h a t the s m a l l e r t h e gain, .of t h e medium., t h e fewer the] number of modes e x c i t e d .  I t i s , therefore, possible t o excite only  the dominant mode i n both t h e c o n f o c a l and t h e n o n - c o n f o c a l cases s i m p l y by l i m i t i n g the o v e r - a l l g a i n e x p e r i e n c e d by t h e i n c i d e n t radiation. The  o v e r - a l l g a i n t h a t the r a d i a t i o n w i l l e x p e r i e n c e  depends on t h e l e n g t h o f t h e tube.  Thus, the l e n g t h can be  chosen so as t o e x c i t e s e v e r a l modes, o r e l s e .only-the dominant mode.  I t can be a p p r e c i a t e d  t h a t i f the l e n g t h i s t o o s m a l l ,  no modes a t a l l w i l l be e x c i t e d .  T h i s i s c l e a r from t h e view-  p o i n t , mentioned e a r l i e r , t h a t t h e g a i n must c o u n t e r b a l a n c e the l o s s e s .  The l e n g t h of t h e tube must, t h e r e f o r e , be g r e a t e r  than some, minimum v a l u e .  The s i m p l e a n a l y s i s above must be m o d i f i e d when cons i d e r a t i o n i s g i v e n to t h e e f f e c t s t h a t t h e presence o f t h e a m p l i f y i n g medium has on t h e modes.  The degree o f m o d i f i c a t i o n  depends on t h e g a i n and the l i n e w i d t h of t h e t r a n s i t i o n and c a n be c o n s i d e r e d a source of e r r o r i n t h e d e t e r m i n a t i o n of t r a n s i t i o n frequency.  Mode-pulling,  f o r example, i s an e f f e c t due  to the v a r i a t i o n of r e f r a c t i v e index w i t h frequency and i t l e a d s t o modes w i t h i n t h e l i n e w i d t h b e i n g p u l l e d c l o s e r toward the c e n t r e frequency.  The r e s u l t i s t h a t the s p a c i n g between  a x i a l modes i s no l o n g e r c / 2 b .  Furthermore,, e f f e c t s such as  ""hole-burning" l e a d t o anomalous v a r i a t i o n s o f power i n a g i v e n mode as t h e mode frequency  i s s h i f t e d (by a l t e r i n g • the. m i r r o r  s e p a r a t i o n ) through t h e l i n e c e n t e r . N o n - l i n e a r i t y and s a t u r a b i l i t y o f g a i n l e a d t o an e f f e c t which almost c o n t r a d i c t s t h e s i m p l e a n a l y s i s o f f i g u r e 3 - 2 . W.W.  Rigro.d 20 found and Fox and L i21 confirmed  t h a t t h e dominant  output t r a n s v e r s e mode i s t h e h i g h e s t o r d e r mode p e r m i t t e d by a near conf o c a l c o n f i g u r a t i o n .  The r e a s o n f o r t h i s , as g i v e n by  Fox and L i i s t h a t h i g h e r o r d e r modes have l a r g e r beam diameters t h a n lower order modes. molecules  Thus, modes of a l l orders compete f o r  i n t h e c e n t r a l r e g i o n s of the beam,, but t h e h i g h e r  modes can s t i m u l a t e and r e c e i v e energy from molecules the diameter  of t h e lower order modes.  order  outside  I f the h i g h e r g a i n o f f -  s e t s t h e h i g h e r l o s s , t h e h i g h e r order modes may n o t o n l y be a b l e t o o s c i l l a t e , b u t may succeed i n s u p p r e s s i n g t h e lower modes by s a t u r a t i n g t h e g a i n i n t h e c e n t r a l r e g i o n .  order  This  e f f e c t may n o t he v a l i d f o r i n f r a - r e d m a t e r i a l s , but even i f i t was i t i s i m p o s s i b l e t o p r e d i c t whether domination  can be so  33 complete t h a t a l l lower  o r d e r modes w i l l he  i s l i k e l y t h a t s e v e r a l modes a r e different relative Fox resonators  It  excited simultaneously,  with  magnitudes. L i make t h e p o i n t t h a t t h e t h e o r y  gives, l o s s . v a l u e s  resonator. theory,  and  suppressed.  of  passive  which-.canobeausediin;;^  Thus i t i s p o s s i b l e t o d e s i g n a l a s e r u s i n g  always r e a l i z i n g t h a t the  the theory o f a g a i n - m o d i f i e d s u f f i c i e n t l y long to provide a t l e a s t one  mode.  I t may  this  o u t p u t w i l l be d e t e r m i n e d  cavity.  The  l a s e r should  by  be  enough g a i n t o overcome l o s s e s i n be  t h a t the a c t u a l g a i n w i l l  be  s u f f i c i e n t l y h i g h t o p r o v o k e e x c i t a t i o n o f s e v e r a l modes simultaneously,  and  i f so,  d i s t r i b u t e d among t h e s e 3.2  t h e o u t p u t power w i l l be  General The  modes.  Considerations c a v i t y c o n s i s t s of a c y l i n d r i c a l g l a s s tube  m i r r o r s a t e i t h e r end.  The  shape and  e a c h must be d e s i g n e d  The exceed  d i a m e t e r o f t h e t u b e and  dimensions of the m i r r o r s .  r e l a t e d and  primary  These a r e  closely  w i t h the others  see  i n the  cavity.  i s t o draw on t h e e x p e r i e n c e  However, s i n c e i t i s  of other  only  experimenters.  s u f f i c i e n t t o k e e p t h e l o s s e s t o a minimum and  i f t h e g a i n was The  choice  inter-  i n mind.  p o s s i b l e t o p r e d i c t t h e g a i n o f a g i v e n medium, t h e  I t w i l l be  the  c o n c e r n i s t h a t t h e g a i n i n t h e medium  the l o s s e s inherent  alternative  with  parameters i n v o l v e d i n d e s i g n i n g  t h i s c a v i t y a r e t h e l e n g t h and  to  ;  R e s o n a t o r Tube  3.2.1  not  -  indeed  h i g h enough t o c o u n t e r  r e f l e c t i o n l o s s e s c a n be m i n i m i z e d  of m i r r o r m a t e r i a l .  The  by  these  test losses.  appropriate  d i f f r a c t i o n l o s s e s can be  mini-  34 mized by u s i n g t h e c o n f o c a l c o n f i g u r a t i o n . There i s another v e r y v a l i d reason f o r choosing configuration.  This  i s the important  of m i r r o r alignment.  practical  this  consideration  I n a l a s e r c a v i t y , i t i s necessary  that  the a x i s of the m i r r o r s pass through the l a s e r tube and t h a t i t be f a r enough away f r o m t h e t u b e w a l l s t o a l l o w t h e T E M ^ Q 22  mode-room!to o p e r a t e  .  The e x t e n t t o w h i c h t h e m i r r o r a x i s  c a n be r o t a t e d w h i l e s t i l l  f u l f i l l i n g t h i s requirement  the  "Alignment Tolerance"  has  u s e d t h i s d e f i n i t i o n t o show t h a t A l i g n m e n t T o l e r a n c e i s  highest plane  of the m i r r o r system.  f o r a c o n f o c a l m i r r o r system.  p a r a l l e l m i r r o r system i s o f the order  shown i n F i g u r e s  3-3  and  0  o  Sinclair  The t o l e r a n c e o f t h e  worse t h a n t h a t o f t h e c o n f o c a l c a v i t y . are  D.C  defines  o f a hundred  Sinclair's  times  results  3-4.  O id  u H o  !H  Q) H o  -P  EH  CD •H  •H  lm 100m M i r r o r Radius F i g u r e 3.3 D o u b l e Concave Cavity (Mirror Separation = lm)  5!  lm 100m R a d i u s o f Concave M i r r o r F i g u r e 3.4  Flano-Concave Cavity (Mirror Separation = lm)  35  are, however, certain disadvantages to using a confocal cavity. One of them is that it has a very low mode volume. T h i s is defined by: mode volume = j j rdrdedz (3.11) where w(zj = spot size at any point, z, l' 2 ^ P ^ l axis b etween which the mode volume is desired, r,9,z = are cylindrical cordinates. Sinclair s hows that power obtainable from the cavity depends on this mode volume. Hence, to obtain maxm i um power output, a cavity with maxm i um mode vou l me is desired. The small mode volume of the confocal cavity is, therefore,, a disadvantage. The seriousness of. this shortcoming is reduced by the requirements of this experiment - nameyl that the output power should merely be high e nough that it can be detected. ,-, A far more critical disadvantage appears when the There  z  z  =  a  n  y  W 0  o i n  s  o  n  a s e r  23  of the cavity is considered. Boyd and K o g e l n i k have defined "unstable regions" as the ranges of mirror .separ a t i o n , d, in which the diffraction losses are high. . They have proved the existence of these ranges. T h e i r stability diagram is reproduced in figure 3-5. In figure 3-5, it is apparent that the confocal point, d=b-^=b2 is one of critical stability. An error in the radius of curvature of either mirror can prohibit laser action due to high diffraction loss. Hence, the mirror separation for a system with identical mirrors should have d^b. However, the Reparation (d-b) should not be too large, since the confocal stability  36  system s t i l l y i e l d s minimum d i f f r a c t i o n l o s s e s as w e l l as maximum alignment tolerance,,  F i g u r e 3.5  S t a b i l i t y Diagram  I t has now been r e s o l v e d t h a t t h e m i r r o r c o n f i g u r a t i o n should be n e a r - c o n f o c a l .  I t remains t o determine t h e a c t u a l  dimensions o f t h e t u b e .  As was s t a t e d e a r l i e r , these can o n l y  a r b i t r a r i l y be chosen, on t h e e x p e r i e n c e o f others„  However,  some d i s c u s s i o n o f the f a c t o r s i n v o l v e d i s useful,. 1.  Lengths I n s e c t i o n  3°l°ls>  i t was s t a t e d t h a t t h e  g a i n was p r o p o r t i o n a l t o the tube l e n g t h .  A l s o , from \.  McCumber's r e s u l t s ( f i g u r e 3 - 1 ) , t h e d i f f r a c t i o n l o s s e s i n crease as t h e F r e s n e l Number, B, d e c r e a s e s ,  H i s given f o r a  s y m m e t r i c a l c o n f o c a l system by: N = a£ b\  '  2a = diameter o f m i r r o r b = d i s t a n c e between m i r r o r s .  (3.1)  37 I f t h e m i r r o r d i a m e t e r , 2a, t h e t u b e d i a m e t e r , and as t h e  c l e a r l y , the d i f f r a c t i o n l o s s e s  roughly  p r o p o r t i o n a l t o the  must be  a compromise b e t w e e n g a i n and D i a m e t e r : The  the l e n g t h of the a r e known.  same as  the i n t e r - m i r r o r d i s t a n c e about the  tube l e n g t h , then,  2o  i s chosen the  tube l e n g t h .  tube d i a m e t e r c a n  t u b e and  the  In determining  are  Hence t h e t u b e  diffraction  same  length  loss,  be d e t e r m i n e d i f  permissible d i f f r a c t i o n losses  the p e r m i s s i b l e d i f f r a c t i o n l o s s ,  i t must be remembered t h a t t h e l a s e r c a v i t y i s r e q u i r e d t o o v e r t h e w a v e l e n g t h r a n g e o f 0,1 fraction losses  should,  mm  l o s s of the  mm.  D e s i r a b l y , >the•: d i f -  be w e l l b e l o w t h e m i r r o r  l o s s e s o v e r t h i s r a n g e , so as n o t all  t o 1,0  cavity.  t o add  Prom t h e  serve  reflection  a p p r e c i a b l y to the  expression,  (3.1), f o r  over-  the  F r e s n e l Number, i t i s s e e n t h a t t h e l o s s e s d e c r e a s e w i t h i n creasing mirror radius,  a.  However, t h e m i r r o r r a d i u s , a, c a n n o t be of a n  indefinitely large size,  number o f p a r t i c l e s  t h a t c a n be  Laser  a c t i o n d e p e n d s on  induced i n t o an  l a t i o n s i t u a t i o n , w h i c h d e p e n d s on  chosen to  to keep t h i s a r e a  the c u r r e n t d e n s i t y o f  tube,  t o a minimum.  the  i n v e r t e d popu-  discharge., which, i n t u r n , i s i n v e r s e l y p r o p o r t i o n a l t o area of c r o s s - s e c t i o n of the  be  the  the  . I t i s , therefore, desirable Thus t h e r a d i u s ?  c h o s e n as a compromise b e t w e e n c u r r e n t d e n s i t y and  a, s h o u l d  be  diffraction  loss, 3. C o u p l i n g s of the  Output c o u p l i n g e n t e r s  c a v i t y because i t represents  i n t o the  a source of l o s s .  d i s c u s s i o n o f t h i s i s g i v e n i n the n e x t c h a p t e r  9  but,  design Further for  the  3§ p r e s e n t , l e t i t be mirrors w i l l  s t a t e d t h a t a s m a l l a p e r t u r e i n one  of  a l l o w some o f t h e power t o emanate f r o m t h e  to  a d e t e c t i n g apparatus.  to  d i s t u r b t h e mode f i e l d  The  the cavity  e f f e c t of t h i s a p e r t u r e w i l l  c o n f i g u r a t i o n i n s i d e the  be  cavity.  17 However, a c c o r d i n g t o D.E.  McCumber,  i f t h i s a p e r t u r e i s kept  s m a l l compared t o m i r r o r s i z e , . t h e ' e f f e c t ' w i l l ' be a s m a l l , p e r turbation.  The  transmission coefficient w i l l  then simply  the r a t i o of the aperture area to the area determined  by  he  the  spot s i z e , i . e .  T = (r / w )  (3.12)  2  where T = t r a n s m i s s i o n c o e f f i c i e n t , r = r a d i u s of aperture. a ' w = spot s i z e , s Equation mode.  (3.12) i s p r i m a r i l y a p p l i c a b l e t o the dominant  C e r t a i n modes may  not  e v e n be t r a n s m i t t e d .  because of the p a r t i c u l a r f i e l d  This i s  p a t t e r n o f t h e s e modes, a s  w i l l be f u r t h e r m e n t i o n e d i n t h e c h a p t e r on c o u p l i n g and d e t e c t i o n . 24Equation 3.2.2  ( 3 . 1 2 ) was  Dimensions In  in  f i r s t u s e d by P a t e l e t a l .  the p r e v i o u s s e c t i o n , the 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  the choice of dimensions  were g i v e n .  Since the  gain  c h a r a c t e r i s t i c s o f any g i v e n l a s e r gas medium a r e unknown, t h e design c o n s i d e r a t i o n s reduce to choosing a convenient l e n g t h and  thence  laser  determining the other l a s e r parameters.  o r d e r t o s t a r t f r o m some b a s e , a l o o k a t w o r k s done by i s helpful. 25 A k i t t et a l have d e s c r i b e d a water v a p o r  other  experimenters  laser  In  39 o p e r a t i n g a t 118 m i c r o n s w a v e l e n g t h .  F l e s h e r and M u l l e r  26  have  a l s o designed a l a s e r w i t h which they obtained:.::laserqactiohnin w a t e r v a p o r a t w a v e l e n g t h s 79m able to detect and  1 1 8 u , and 2 20u.  suhmillimeter lines  i n CH^CN a t 3 1 3 ^ and 337(i.  i n D^O a t 84M., 108p,, and 117  T a b l e 3-1 g i v e s a summary-  c o m p a r i s o n o f t h e two l a s e r s o are  In this table, d i f f r a c t i o n losses  i n d i c a t e d w i t h a dash i f they a r e n e g l i g i b l e  to the r e f l e c t i o n losses  (<0v01%) compared  (~2%). Table  Suhmillimeter Reference 25:  •3.66 m  Tube L e n g t h  They a l s o were  3-1 Gas L a s e r s Reference 26  Present Desig]  2. 15: im  2.44; ii 7.62 <  Tube D i a m e t e r  10.15  cm  Mirror  10.15  cm  7.5 cm 5. 73 cm  m  2. 69 m  3.0 i  3.77 3.19 1. 71  5.85 4.96 2.66 1.74 1.17 0,98  Diameter  M i r r o r Radius of Curvature P r e s n e l Number (Equation 2.10), =100u =118-1  =220u  =337(i  =500\x =600u =700p. =800u =900u =1 mm. D i f f r a c t i o n Loss I n TEM Mode, =100u =118u =220p. n  u  u  =337^  =500|i =600u =700u. =800u =900u =1 mm  4.0  6,9  5.85  3.14  2.05 1.38 1.05 0.98 0.86 0.78 0.69  1. 12 0. 76 0. 63 0. 54 0. 47 0.42 0. 38  —  — 0.02% 0.05% 0.20% 0.45% 1.10%  0,84; 0.732 0.65  0.59  --  -  -  7.62 <  0. 6% 1. 5% 4.5% 8 % 10 %  30  %  -  0.01% 0.08% 0.25%  0.9 %  2.5 % 6 %  40 T a b l e 3-1  shows t h a t a l a s e r w i t h F r e s n e l Number  b e t w e e n 3 = 77 and 6.9 a t A. = lOOu- c a n s u s t a i n l a s e r a c t i o n up to  a w a v e l e n g t h o f a t l e a s t 400u i n H © , 2  gas i s suspected nearer still  D 0 2  and CH^CN.  t o h a v e l i n e s b e y o n d 400p,, a F r e s n e l Number  6.9 a t lOOp. i s n e e d e d and w h e t h e r l a s i n g w i l l  was a i m e d f o r .  to  occur  will  depend on t h e g a i n c h a r a c t e r i s t i c s o f t h e medium,, at X -  W i t h t h e above a n a l y s i s , a l a s e r w i t h N=6  and  If a  72 i n c h e s  A heavy g l a s s tube,  3 inches  i n s i d e diameter  l o n g , was r e a d i l y a v a i l a b l e and was  be a c o n v e n i e n t  considered  size f o r the laboratory operations.  w i t h g l a s s Tees c o n n e c t e d t o t h e ends o f t h i s t u b e , spacing  c a n be a r r a n g e d t o be  near-confocal  3 inches  were o b t a i n e d .  Along  the mirror  o r 2.44 m e t e r s .  m i r r o r s y s t e m i s d e s i r e d and a c o n v e n i e n t  radius of curvature mirrors,  96 i n c h e s  i s three meters.  lOOp,  A mirror  C o n s e q u e n t l y , two c o n c a v e  i n d i a m e t e r and 3 meters r a d i u s o f  curvature  They a r e made o f q u a r t z and a l u m i n u m  surfaces  which r e f l e c t  9&f° o f i n c i d e n t r a d i a t i o n i n t h e w a v e l e n g t h r a n g e  4(i t o 900)io  The d i f f r a c t i o n l o s s e s a r e shown i n T a b l e 3 - 1 ,  third  columno The l a s e r s o d e s i g n e d  for  w i l l now  sustain laser action  t r a n s i t i o n s up t o 500|_i w a v e l e n g t h , p r o v i d e d  that these  tran-  s i t i o n s h a v e t h e same g a i n f e a t u r e a s t h e 118u- l i n e o f watejr vapor.  Higher wavelength a c t i o n w i l l ,  sustained i f the gain  i s correspondingly  of course, higher  a l s o be  for this  wave-  length. For of i n t e r e s t  the l a s e r , thus constructed, c e r t a i n q u a n t i t i e s  c a n be d e r i v e d .  41 The  s e p a r a t i o n b e t w e e n a x i a l modes i s o f i n t e r e s t i n  o r d e r t o d e t e r m i n e t h e number o f modes t h a t c a n be s i m u l t a n e o u s l y excited i n the laser.  The l i n e w i d t h o f t h e t r a n s i t i o n s was  i n s e c t i o n 2.3.  determined  S e p a r a t i o n b e t w e e n modes whose (m+n)  a r e d i f f e r e n t b y one i s o b t a i n e d f r o m e q u a t i o n M c  f  m  (3.5). (3.5)  = 2q + (l+m+n)K  n  K = IU4_ t a n " l b^d = 0.869 % b+d f  , - f I'. 1  m  r  >  = cK = 27 MHz, m +n -m+n = 1 4d  S e p a r a t i o n b e t w e e n t h e h a r m o n i c s o f a g i v e n TEM mode * ° mn i s g i v e n by equation f  »,n  t < l +  The  l  (3-9):  " m,n, f  q  -Jj =  c h a r t , f i g u r e 3-6, shows t h e r e l a t i v e p o s i t i o n s o f  t h e v a r i o u s modes w i t h r e s p e c t t o some h a r m o n i c , q, o f t h e TEMQQ, mode. It i s a matter  o f some i n t e r e s t t o s e e how many o f t h e s e  modes c a n be e x c i t e d a t t h e same t i m e a s t h e T E M ^ Q mode.  Table  3-2  l i s t s modes w i t h d i f f r a c t i o n l o s s e s n e g l i g i b l e compared t o t h e m i r r o r r e f l e c t i o n l o s s o f 2$.  D.E. McCumber's g r a p h o f f i g u r e  s h o w i n g power l o s s p e r p a s s due t o d i f f r a c t i o n f o r s e v e r a l modes i s used. and  S i n c e h i s g r a p h shows l o s s v a l u e s down t o o n l y 0.1$  F r e s n e l numbers up t o 2.25,  polation.  Table  3-2  i s o b t a i n e d by e x t r a -  The " n e g l i g i b l e " v a l u e o f d i f f r a c t i o n l o s s i s t a k e n  a r b i t r a r i l y a s 0.01$.  T a b l e 3-3  shows t h e number o f modes t h a t  c a n b e e x c i t e d s i m u l t a n e o u s l y w i t h t h e T E M ^ mode f o r v a r i o u s l i n e w i d t h s , a s s u m i n g A. = 118u-. 3.2.3  Structure of Cavity With the dimensions o f the c a v i t y tube  determined,  3.1  (oo)  (01) (10)  (02)(11) - (2Q)  (30)(12) (03)(21)  ^}{}l}{ -(04)(31) .  {  22)  (60)(51)(42)(33)" (06)(15)(24).  o  (50) (41) (32) (05)(14)(23)  (60)(51)(42)(33) (06)(1 )(24) 5  combinations?^^ > » ^ J f  m  • 8  n  9 1  10 12  1  *  io  13  KHZ_  F i g u r e 3.6 R e l a t i v e - l o c a t i o n of Modes 4^  ro  43 Table  3-2  Low D i f f r a c t i o n Loss Modes* N 100  LOW D i f f r a c t i o n Loss Modes  5.85  00, 10, 20, 01, 30, 11, 40, 21, 02, 50,  31, 60, 12, 70, 22, 03, 51, 32, 13 118  4.96  -do-  except 13  220  2.66  00, 10, 20, 01, 30, 11, 40, 21, 02, 50  337  1.74  00, 10, 20,' 01  500  1.17  00  600  0.975  -**  700 800  0.835 0.732  -** -**  900 1000  0.65 0.59  -** -**  *Reference D.E. McCumber **See Table 3-1  Table 3-3 Modes e x c i t e d , by 118u l i n e * Doppler Width ' (MHz) 10 15 "  Modes E x c i t e d (Aside from (00)) n i l 70  20 25 30 35  20, 11, 02, 70 -do-do- p l u s 40, 50, 31, 22 -do-  40  a l l low loss(modes except 10, 01  55  a l l low l o s s modes  * R e f e r t o Table 3-2  i t now remains t o s o l v e the p r a c t i c a l problems o f i n s e r t i n g the l a s i n g gas and o f e x c i t i n g l a s e r a c t i o n .  44  Gas i n s e r t i o n  can be a c h i e v e d by u s i n g a c o n t r o l l i n g v a l v e and a vacuum pump. The l a s e r i s e x c i t e d by h a v i n g d i s c h a r g e e l e c t r o d e s a t e i t h e r end.  A l l these a r e i n s e r t e d i n t o t h e mouth o f g l a s s Tees which  are a t t a c h e d t o t h e ends o f the 72 i n c h tube. for  See f i g u r e 3-7  details.  Power Input E l e c t r o d e Zl -Mirror  Power Ground E l e c t r o d [ Gas Input Valve-  C o u p l i n g Hole P i g u r e 3.7  Cavity Structure  A few words about t h e v a r i o u s components a r e i n o r d e r . The vacuum pumping i s done i n two stages  initially.  The f i r s t one uses a d i f f u s i o n pump t o evacuate t h e system down to a p p r o x i m a t e l y 2x10"^ T o r r .  T h i s i s necessary i n order t o  d e t e c t l e a k s i n t h e tube and t h e r e b y prevent a i r from n a t i n g the l a s i n g gas.  contami-  The second stage uses an o r d i n a r y r o t a r y  pump so as t o m a i n t a i n t h e gas a t l a s i n g p r e s s u r e s . p r e s s u r e s a r e o f the order o f 0.5 T o r r t o 1.0 T o r r .  Lasing (See  r e f e r e n c e 25 and 26.) The d i s c h a r g e i s caused by a 5022-line type p u l s e modulator whose output i s f e d through p o l i s h e d aluminum e l e c t r o d e s  45  The modulator c a n d e l i v e r 2 microsecond p u l s e s up t o 200 times per second, w i t h a peak v o l t a g e o f 7 k v and c u r r e n t , 280 amps. C o u p l i n g i s achieved hy a s m a l l a p e r t u r e i n t h e grounded end m i r r o r .  The a p e r t u r e i s 2mm i n diameter,  and the through  t u n n e l i s l i m i t e d t o 3mm l o n g i n an e f f o r t t o reduce the waveguide e f f e c t t h a t such a t u n n e l would cause.  No attempt i s  made here t o determine q u a n t i t a t i v e l y t h e matching problem due to t h e waveguide e f f e c t . The mountings o f the m i r r o r s a r e a v e r y  important  p a r t o f the d e s i g n and the next s e c t i o n w i l l be devoted t o t h i s . 3.3  M i r r o r s and t h e i r Mountings  3.3.1  Mountings The m i r r o r s must be mounted so t h a t t h e r e i s great  f l e x i b i l i t y i n their setting.  The axes o f t h e two m i r r o r s must  not o n l y be a l i g n e d w i t h •each': other,- they must a l s o be c o i n c i - ... d e n t a l w i t h the a x i s o f the tube.  T h i s means t h a t the m i r r o r s  must be a b l e t o r o t a t e about any a x i s i n the t r a n s v e r s e  plane.  The s p a c i n g between t h e two m i r r o r s a l s o determines the resonant (3.5). frequency  frequency  equation  By a d j u s t i n g t h e i n t e r - m i r r o r d i s t a n c e , d, the resonant o f t h e dominant mode can be made t o c o i n c i d e w i t h t h e  transition-frequency. mode.  o f the c a v i t y , i n accordance w i t h  This would ensure maximum power i n t h i s  (See s e c t i o n 3.1.1.)  Hence, the m i r r o r mountings must  be such t h a t t h e m i r r o r s p a c i n g i s a d j u s t a b l e .  T h i s means t h a t  a t l e a s t one o f t h e m i r r o r s should be a b l e t o move a x i a l l y . These r e q u i r e m e n t s a r e met by the use o f b e l l o w s , two micrometers and a screw, as i n f i g u r e 3.8.  The f i g u r e shows a  46  mechanism f o r r o t a t i n g the m i r r o r s about any a x i s i n the t r a n s verse  plane.  F i g u r e 3.8  F i x e d M i r r o r Housing  The m i r r o r i s a f f i x e d t o ( l ) , w i t h p r o v i s i o n s f o r the c o u p l i n g h o l e .  A window f i x t u r e over t h i s h o l e  a s e a l i n g f o r vacuum purposes.  provides  The window m a t e r i a l can be  changed so as t o be t r a n s p a r e n t t o the o p e r a t i n g  frequency.  H i g h d e n s i t y p o l y e t h y l e n e i s used i n t h e f a r i n f r a - r e d . window i s 1/8 i n . t h i c k .  From F i g u r e 3 • 9 , . t h i s  t o 50$ l o s s between lOOu- and 600p.. t o 22\x s u f f e r s i m i l a r l o s s e s .  The  corresponds  L i n e s below t h i s , down  I t i s t o be r e c o g n i z e d t h a t  the .atmosphere, m a y i a b s o r b y c e r t a i h  lineslatlinfra^rediifrequen-  cies. The s p a c i n g can be a l t e r e d by moving the m i r r o r which does not have the c o u p l i n g a p e r t u r e . i n the same way as the o t h e r .  T h i s m i r r o r i s housed  The d i f f e r e n c e i s that the m i r r o r  47  T r  e  100  i i o  n  0*  . 0  — . — — — .  100  200  .  ,  1  .  »  300  400  500  600  700  Wavelength (u) F i g u r e 3.9  T r a n s m i s s i v i t y of Polyethylene 2mm  Thick  2 7  i s no l o n g e r mounted on t h e end p l a t e , hut on a s e p a r a t e p l a t e which i s a t t a c h e d t o a p l u n g e r . end p l a t e as i n f i g u r e 3.10. s t e a d y r a t e by use o f a motor.  The plunger i s mounted on the I t can be moved i n and out a t a A d i f f e r e n t i a l micrometer  p l u n g e r i s p l a c e d i n b e a r i n g c o n t a c t w i t h t h i s plunger and t h e . micrometer screw i s t u r n e d w i t h a synchronous motor.  F i g u r e 3.10  Moveable M i r r o r Arrangement  48  With t h i s mounting i n p l a c e , t h e l a s e r c a v i t y i s A l l j o i n t s a r e vacuum-sealed w i t h 0 - r i n g s .  complete.  It  remains t o a l i g n t h e m i r r o r s and t h e n t o perform t h e t e s t s on the  laser.  3.3.2  M i r r o r Alignment ;The m i r r o r s a r e mounted so t h a t t h e i r o r i e n t a t i o n i s  f l e x i b l e , p r i m a r i l y t o f a c i l i t a t e t h e i r alignment.  It is  d e s i r e d t h a t t h e axes o f the two m i r r o r s be c o - l i n e a r and the common a x i s should c o i n c i d e w i t h t h e a x i s o f t h e l a s e r tube. The  alignment procedure which f o l l o w s i s based on t h e f a c t t h a t  for  s p h e r i c a l m i r r o r s a beam w h i c h t r a v e l s a l o n g t h e m i r r o r a x i s  i s a l s o r e f l e c t e d along that a x i s .  Sheet  Sheet  F i g u r e 3.11  M i r r o r .Alignment Procedure.  I n f i g u r e 3.11, an aluminum sheet i s placed i n f r o n t of m i r r o r #1.  The sheet has a s m a l l a p e r t u r e  a x i s o f t h e tube. of m i r r o r #2.  i n i t at the  A sheet o f p o l y s t y r e n e i s p l a c e d i n f r o n t  A He-Ne L a s e r beam i s caused t o pass a l o n g the  49 tube a x i s v i a t h e c o u p l i n g h o l e and through t h e h o l e i n t h e aluminum sheet. i s seen.  Where the beam h i t s t h e p o l y s t y r e n e a r e d spot  The beam i s r e f l e c t e d o f f m i r r o r #1 and, i f t h e m i r r o r  a x i s does not c o i n c i d e w i t h t h e tube a x i s , i s b l o c k e d by t h e aluminum sheet.  U s i n g t h e micrometer, t h e m i r r o r i s o r i e n t e d  so t h a t the r e f l e c t e d beam passes through the h o l e i n t h e aluminum and forms a second spot::on the p o l y s t y r e n e . caused t o c o i n c i d e w i t h t h e f i r s t .  T h i s spot i s then  The a x i s of m i r r o r #1 i s  now a l i g n e d w i t h t h e tube a x i s . The it  beam now h i t s m i r r o r # 2 , w i t h t h e c e n t r a l p a r t of  shooting, out .the c o u p l i n g h o l e and ' an , annular' r i n g g i s , - r e f l e c k e d r  back t o the p o l y s t y r e n e sheet.  This a n n u l a r r i n g i s caused t o  c o i n c i d e w i t h t h e o r i g i n a l spot.  Now m i r r o r #2 i s a l s o a l i g n e d .  Note t h a t w i t h v e r y s l i g h t misalignment,  many spots w i l l be seen  on the p o l y s t y r e n e , owing t o o f f - a x i s r e f l e c t i o n s from both mirrors. When t h e aluminum and t h e p o l y s t y r e n e sheets a r e removed,"the alignment c a n be checked when t h e l a s e r i s l a s i n g . A t w i s t on one o f t h e micrometers w i l l r e s u l t i n .a sharp decrease i n output s i g n a l l e v e l . 3.4  External Mirrors A simple c a v i t y d e s i g n t h a t was c o n s i d e r e d a l o n g w i t h  the d e s i g n j u s t d e s c r i b e d c o n s i s t s o f h a v i n g t h e m i r r o r s o u t s i d e the tube.  The tube would c o n t a i n t h e l a s e r gas, t h e d i s c h a r g e  e l e c t r o d e s and the gas-pumping mechanisms, w h i l e t h e concave m i r r o r s a r e mounted o u t s i d e .  The ends o f the tube are g l a s s -  s e a l e d a t t h e B r e w s t e r angle.  T h i s "Brewster Angle C o n f i g u -  50 r a t i o n " was f i r s t i n t r o d u c e d by R i g r o d I n s p i t e of the v e r y simple  28 et a l . structure, this  r a t i o n i s not f e a s i b l e f o r a m u l t i - f r e q u e n c y infra-red region.  configu-  l a s e r i n the f a r  The s e a l i n g ends are e l l i p t i c a l  p l a t e s whose  areas a r e : A = Jtp£  Cos 9  = 3tX9_  ~0.5  = 56.5  in  2  .  This a r e a i s so l a r g e t h a t i t i s d i f f i c u l t t o m a i n t a i n u n i f o r m i t y over the s u r f a c e of the g l a s s end p l a t e s .  Also, to  keep the ends s t u r d y , the g l a s s has t o be v e r y t h i c k .  This  causes d i e l e c t r i c " l o s s , which i s v e r y h i g h f o r s u b m i l l i m e t e r wavelengths.  .:ho ."H..'  The B r e w s t e r Angle C o n f i g u r a t i o n i s s u i t a b l e f o r tubes of s m a l l e r d i a m e t e r , but i s not f e a s i b l e f o r the wide f a r i n f r a red tube. 3.5  Mode S e l e c t i o n For s e v e r a l r e a s o n s , such as s t a b l e s i n g l e f r e q u e n c y  o p e r a t i o n , i t i s d e s i r a b l e t o operate a l a s e r i n a s i n g l e mode. 29 30 31 S e v e r a l ways have been suggested f o r t h i s , has been s u b j e c t e d techniques,  '  '  and the m a t t e r  t o i n c r e a s i n g i n t e r e s t over t h e y e a r s .  however, a r e r a t h e r s o p h i s t i c a t e d and i n v o l v e  The exten-  s i v e m o d i f i c a t i o n on the simple l a s e r system designed i n t h i s chapter.  The s i m p l e s t way of e l i m i n a t i n g a l l but a s i n g l e mode  i s by i n c r e a s i n g t h e d i f f r a c t i o n l o s s e s of a l l modes.  A com-  promise must, of course, be reached between mode s e l e c t i v i t y and  output power, and p r e c a u t i o n s must be t a k e n t h a t l o s s i s not  h i g h enough t o p r e c l u d e  laser action altogether.  51 E s s e n t i a l l y , the problem reduces t o d e c r e a s i n g the F r e s n e l Number o f the l a s e r .  A c c o r d i n g t o the p r e v i o u s  defini-  t i o n o f " n e g l i g i b l e d i f f r a c t i o n l o s s " , £j«0.01%, the d e s i r a b l e E r e s n e l Number, from f i g u r e 3.1, i s N=1.2, s i n c e t h e  w i l l be t h e o n l y mode w i t h n e g l i g i b l e d i f f r a c t i o n l o s s .  This  ( 3 . 1 ) , t h a t a l o n g , narrow l a s e r i s  i m p l i e s , from e q u a t i o n required.  mode  TEMQQ  However, the present l a s e r i s meant t o s u s t a i n  o s c i l l a t i o n s over a wide f r e q u e n c y range and hence the l a s e r s i z e must remain c o n s t a n t .  S u b s t i t u t i n g mirrors of d i f f e r e n t s i z e s  f o r d i f f e r e n t wavelengths i s u n f e a s i b l e from t h e p o i n t o f v i e w of the " n e a r - c o n f o c a l " requirement, and o f expense.  Therefore,  the f o l l o w i n g two simple methods may be adopted. 3.5.1.  Aperture  Limiting  Prom equation?  ( 3 . 4 ) , N can be reduced s i m p l y by  r e d u c i n g a-^ o r a^ o r both.  Since r e d u c t i o n o f the m i r r o r s i z e  i s not f e a s i b l e , a^ can be' reduced by b l o c k i n g o f f the outer edges o f the m i r r o r .  I n t h e l a s e r o f f i g u r e 3-7, a diaphragm  can be i n s e r t e d through one mouth o f the Tee on t h e grounded end.  The c o n f i g u r a t i o n would be as i n f i g u r e 3.12.  ,  I n t h i s f i g u r e , i f d'^< d, the m i r r o r a p e r t u r e ban be Prom f i g u r e 3.1, N=1.2 w i l l l e a d . t o  t a k e n as ag.  l o s s i n a l l but t h e (00) mode.  a where N  p  =N  No  a  significant  To o b t a i n N=1.2,  = 1.8/N  (3.13)  0  = P r e s n e l Number o f t h e c a v i t y w i t h no diaphragm. Y;.^:,.-tiv,.'1  52  F i g u r e 3.12 3.5.2  Aperture Limited Cavity Configuration  Piano-Concave  Cavity  D i f f r a c t i o n l o s s e s can a l s o Toe i n c r e a s e d by r e p l a c i n g one m i r r o r by a f l a t m i r r o r .  Ah added b e n e f i t o f f e r e d by t h e  plano-concave c a v i t y i s t h a t a w i d e r mode volume i s a v a i l a b l e so t h a t m o l e c u l e s i n a w i d e r beamwidth c o n t r i b u t e toward t h e g a i n o f t h e l o w e r o r d e r modes. 32  E o g e l n i k and L i ^ show t h a t i n a s y m m e t r i c a l concave l a s e r w i t h m i r r o r r a d i i o f c u r v a t u r e , R, the spot s i z e of the beam v a r i e s as i n f i g u r e  F i g u r e 3.13  3.13-  Spot S i z e of Concave C a v i t y  For a s y m m e t r i c a l  53  cavity, "2  w  ~ %  V 2R-D/ —,  2d R w  _  2  (3.14) —i  X\ d (2R-d) 4  2 o =  2  '  \2  '?  1 2  2d  \2rcd V R 2 U \d R 2 at d From e q u a t i o n  2d R  (3.15)  (3-4), 2  2d R  a  d\ w  2 a o = N  2  a  N  2d R 2  2JCW  R 2red  R 2 d  2d R  2  2d R  (3.16)  By symmetry, a f l a t m i r r o r p l a c e d a t d/2 w i l l n o t a l t e r the beamwidth.  Hence, a plano-concave c a v i t y w i t h m i r r o r  separa-  t i o n , d may be regarded as a concave-concave c a v i t y w i t h m i r r o r s e p a r a t i o n , d' = 2d and a p e r t u r e , a, and r a d i i Substituting  i n t o equations  of c u r v a t u r e , R=b.  (3.15) and (3.16), and remembering  t h a t d i s r e p l a c e d by 2d, and c a n c e l l i n g out w  Q  i n equation  (3.16)  the F r e s n e l Number o f t h e plano-concave c a v i t y becomes a Id 2d\ R 2 c1 a R ~ d\ 2  _  2d R, 2  n i  J  (3.17)  W i t h r e s p e c t t o t h e o r i g i n a l c a v i t y of F r e s n e l Number, N , o'  54  N =H  d R  IRI  -  2d R  N = F_  (3-18)  dR 2dR -  Note that now,  d'  d must he l e s s than 1. R  In the present  c a v i t y , with d=2.44m and R=3m, N = 0.4N  (3-19)  55 4.  COUPLING AND DETECTION  The p r e v i o u s two c h a p t e r s d e a l t w i t h t h e d e s i g n and the e x c i t a t i o n o f t h e l a s e r .  I t now remains t o couple out the  s i g n a l generated by t h e l a s e r and then t o measure t h e frequency and i n t e n s i t y o f t h i s s i g n a l .  T h i s chapter d i s c u s s e s t h e  v a r i o u s c o u p l i n g and d e t e c t i o n mechanisms t h a t c a n he used and i n d i c a t e s t h e ones b e s t s u i t e d f o r t h e present e x p e r i m e n t a l set-up. 4•1 4.1.1  Coupling Types o f Coupling: The t h r e e most common ways o f c o u p l i n g t h e l a s e r power  to an o u t s i d e system a r e T r a n s m i s s i o n C o u p l i n g , D i f f r a c t i o n C o u p l i n g and A p e r t u r e C o u p l i n g .  Each o f these types o f f e r s i t s  own advantages t o a g i v e n l a s e r system and the c h o i c e o f which t o i n c o r p o r a t e depends on the system i t s e l f . T r a n s m i s s i o n C o u p l i n g i s a c h i e v e d by d e s i g n i n g one m i r r o r o f t h e l a s e r t o be p a r t i a l l y t r a n s p a r e n t .  The Ruby L a s e r ^  i s a n o t a b l e example o f a l a s e r u s i n g t h i s type o f c o u p l i n g . The p a r t i a l t r a n s p a r e n c y of t h e m i r r o r does not i n t e r f e r e w i t h the mode p a t t e r n s o f t h e l a s e r r e s o n a t o r and i t i s expected t h a t most o f t h e output power would be c o n t a i n e d w i t h i n t h e spot s i z e of the cavity.  F o r t h e c a v i t y Resigned, from e q u a t i o n  the spot s i z e s a r e l a r g e over t h e e n t i r e wavelength A.=100p, t o \=1000u.  (3.2^,  range,  T r a n s m i s s i o n c o e f f i c i e n t s a r e kept low  ( t y p i c a l l y 10-25%) so as not t o s t o p l a s e r a c t i o n i n t h e c a v i t y . T h e r e f o r e , i n o r d e r t o have a p p r e c i a b l e output power, t h e p o l y e t h y l e n e window d e s c r i b e d i n s e c t i o n 3.3-1 should be a t l e a s t  56  of the same d i a m e t e r as the spot s i z e .  The  then be r a t h e r l a r g e and hence i n c o n v e n i e n t  window s i z e would i n a vacuum system,.  An a d d i t i o n a l o b j e c t i o n t o T r a n s m i s s i o n  Coupling i s  t h a t the p a r t i a l l y t r a n s p a r e n t m i r r o r i s c o n s t r u c t e d  using  d i e l e c t r i c l a y e r s , s i n c e p a r t i a l l y s i l v e r e d m i r r o r s have a p p r e c i a b l e ohmic l o s s .  The  p r o p e r t i e s of d i e l e c t r i c m i r r o r s  however, f r e q u e n c y dependent.  Thus, s e v e r a l m i r r o r s may  needed to cover the e n t i r e s u b m i l l i m e t e r range. unfeasable  are, be  This i s obviously  from the p o i n t of view of p r a c t i c a b i l i t y and  cost.  A l s o , such a d i e l e c t r i c has t o be p o s i t i o n e d o u t s i d e the d i s charge tube so as t o p r o t e c t i t from the l a s i n g gas. may  The  mirror  be c o r r o s i o n r e s i s t a n t t o most gases, but s i n c e the l a s e r i s  intended  f o r use w i t h v a r i o u s d i f f e r e n t gases, i t i s s a f e s t to  keep them away.  Such a p r e c a u t i o n a r y measure r e q u i r e s the  use  of the B r e w s t e r Angle C o n f i g u r a t i o n which has a l r e a d y been deemed u n s u i t a b l e f o r the present  laser. 33  D i f f r a c t i o n C o u p l i n g was  proposed by L a t o u r e t t e et a l .  They designed one m i r r o r s m a l l e r than the other and the output c o n s i s t s of the r a d i a t i o n t h a t d i f f r a c t s over the s m a l l m i r r o r edge.  The  d i f f r a c t i o n l o s s e s i n a l l the o p e r a t i n g modes i n the  l a s e r were thus i n c r e a s e d and the r e s u l t of t h i s was the output t o be c o n t a i n e d  i n a s i n g l e mode.  to cause  However, s i n g l e  mode o p e r a t i o n i s not the prime c r i t e r i a of 'the p r e s e n t  laser.  A l s o , d e s i g n d i f f i c u l t i e s would be encountered, s i n c e a means must be e s t a b l i s h e d t o c o l l e c t the d i f f r a c t e d r a d i a t i o n . would complicate s e c t i o n 3.3.1  This  the simple m i r r o r h o u s i n g d e s i g n d e s c r i b e d i n  w i t h a system of f o c u s s i n g l e n s e s .  The  Brewster  Angle C o n f i g u r a t i o n w i l l e l i m i n a t e the h o u s i n g problem, but  will  57 l e a d t o l o s s e s as mentioned i n s e c t i o n 3.4.  Therefore,  Dif-  f r a c t i o n C o u p l i n g i s not c o n s i d e r e d a p p r o p r i a t e f o r t h e present laser. A p e r t u r e C o u p l i n g i s a c h i e v e d by p u t t i n g a s m a l l h o l e i n t h e c e n t e r of one m i r r o r . i n • t h e present l a s e r .  I t i s the simplest t o incorporate  The s m a l l h o l e does, however, e f f e c t t h e  mode p a t t e r n s w i t h i n t h e l a s e r , and may even change it's o p e r a t i n g modes.  I t i s a m a t t e r of some importance  modes s i n c e t h i s w i l l f a c i l i t a t e  the determination of the t r a n -  s i t i o n f r e q u e n c i e s of t h e m a t e r i a l s . f o r e , devoted  t o know t h e o p e r a t i n g  The next s e c t i o n i s , t h e r e -  t o A p e r t u r e C o u p l i n g and i t s i n f l u e n c e on t h e out-  put mode p a t t e r n s . 3.1.2  Aperture  Coupling  Due t o the f a c t t h a t t h e d i f f e r e n t modes o f the o s c i l l a t i o n system have d i f f e r e n t f i e l d p a t t e r n s , a n a p e r t u r e i n a m i r r o r w i l l couple out power more i n some modes than i n o t h e r s . Furthermore,  t h e presence of t h e a p e r t u r e w i l l a f f e c t t h e f i e l d  c o n f i g u r a t i o n w i t h i n the c a v i t y and t h e r e b y a f f e c t t h e l a s e r o u t 17 put.  D.E. McCumber  has made an a n a l y s i s of t h e e f f e c t o f an  a p e r t u r e i n both m i r r o r s o f a c o n f o c a l , symmetric c a v i t y w i t h F r e s n e l Numbers r a n g i n g from 0.6 t o 2.0.  He bases h i s a n a l y s i s  on t h e f a c t t h a t t h e a p e r t u r e s a r e p e r t u r b a t i o n s on t h e nona p e r t u r e case.  McCumber's r e s u l t s do not a p p l y d i r e c t l y t o t h e  present l a s e r s i n c e t h i s has a n o n - c o n f o c a l c a v i t y w i t h o n l y one a p e r t u r e and the F r e s n e l Number range i s 0.595 t o 5.95 f o r wavel e n g t h s 0.1 mm t o 1.0' mm.  However, i n t h e absence o f l i t e r a t u r e  analyzing situations d i r e c t l y applicable to this laser, h i s  r e s u l t s can be used t o o b t a i n a q u a l i t a t i v e p i c t u r e  of t h e  e f f e c t of t h e a p e r t u r e on the mode p a t t e r n s . F i g u r e s 4 . 1 t o 4.3 show the f i e l d i n t e n s i t y of some low l o s s modes i n the unperturbed system.  2.0  F i g u r e 4.1  F i e l d I n t e n s i t y f o r 00, 01, 02 modes, N = 1.6  59  2.0  rm  1.5 1.0 0.5 0  0  F i g u r e 4-3  0.2  0.4  0.6  0.8  1.0  1.2  F i e l d I n t e n s i t y f o r 20, 30 modes, N = 1.6  At f i r s t g l a n c e , i t would appear t h a t an a p e r t u r e c e n t r e d a t r=0 w i l l couple out most power i n t h e (00) mode. However, as t h e a p e r t u r e s i z e i s i n c r e a s e d , the t o t a l d i f f r a c t i o n l o s s e s o f t h e (00) mode, i n c l u d i n g those over the m i r r o r edge and those t h r o u g h t h e a p e r t u r e , e q u a l those of t h e (01) mode.  Furthermore,  mode m i x i n g b e g i n s t o become s i g n i f i c a n t .  Mode m i x i n g may be regarded as. an attempt by t h e f i e l d i n t h e low l o s s  (00) mode t o reduce i t s i n t e n s i t y a t r=0 and t h e r e b y  reduce t h e t o t a l (00) l o s s .  The excess f i e l d i n t e n s i t y i s  d i s t r i b u t e d amongst the o t h e r modes, p a r t i c u l a r l y t h e (02) mode. F o r McCumber's system, t h e new f i e l d  i n t e n s i t y i s shown  i n f i g u r e 4.4. An a p e r t u r e of r a d i u s r  Q  w i l l i n t h i s case  output  m o s t l y (02) modes a l o n g w i t h some ( 0 1 ) , (03), (00) and a l s o o t h e r h i g h e r o r d e r modes.  The l a t t e r w i l l be i n v o l v e d t o a  g r e a t e r e x t e n t i f the a p e r t u r e s i z e i s i n c r e a s e d f u r t h e r .  Thus,  as the a p e r t u r e s i z e i s i n c r e a s e d , t h e l a s e r output should change  60 for  a g i v e n m i r r o r F r e s n e l Number from t h e (00) mode t o t h e (01)  and t h e n t o t h e (02) modes and subsequently t o modes o f h i g h e r 4.0  F i g u r e 4.4  F i e l d I n t e n s i t y f o r low l o s s modes w i t h C o u p l i n g A p e r t u r e , N = 1.6 and N = 0.01 q  order.  There a r e , t h e r e f o r e , c r i t i c a l v a l u e s o f a p e r t u r e  F r e s n e l Numbers, N , f o r which these t r a n s i t i o n s occur. o The c r i t i c a l F r e s n e l Number f o r t r a n s i t i o n t o t h e (01) mode i s d e r i v e d by McCumber and h i s r e s u l t s a r e shown i n f i g u r e 4-5. For a g i v e n m i r r o r F r e s n e l Number, i f N - i s below t h e o curve i n f i g u r e 4-5, t h e dominant mode i s t h e (00) mode.  For  v a l u e s above, i t i s the ( 0 1 ) j o r , depending upon t h e e x t e n t t o which they a r e above, the (02) mode. As was s t a t e d e a r l i e r , t h e f i g u r e s i n t h i s s e c t i o n are d i r e c t l y a p p l i c a b l e .• to the c o n f o c a l c a v i t y w i t h a p e r t u r e s i n b o t h m i r r o r s and F r e s n e l Numbers r a n g i n g from 0.6 to. 2.0.  61  0.6  F i g u r e 4.5  0.8 1.0 1.2 1.4 1.6 F r e s n e l Number N m C r i t i c a l a p e r t u r e F r e s n e l Number N for which d i f f r a c t i o n l o s s e s of (00) mode e q u a l those of (01) mode/versus F r e s n e l Number N . q  A p p l i c a t i o n t o systems w i t h n o n - c o n f o c a l  c  configuration with  an a p e r t u r e i n o n l y one m i r r o r can then o n l y be done as a crude estimate.  F o r the l a t t e r system, the curve of f i g u r e 4.5  can be s h i f t e d to the r i g h t s i n c e the l o s s e s through a s i n g l e a p e r t u r e would be s m a l l e r than through two such a p e r t u r e s . With t h i s i n mind, the a 2 mm  a p e r t u r e system can be s t u d i e d .  A t a b l e of C r i t i c a l F r e s n e l Numbers i s shown i n Table  4-1.  62 Table 4-1 A, (mm)  C r i t i c a l F r e s n e l Numbers N  N  m  N  0  oc  ( A  1 1  P  p ;  0.1  5.7  0.0042  IO"  0.2  2.85  0.0021  IO  0.3  1.9  0.0014  IO"  0.4  1.43  0.0011  0.00001  0.5  1.14  0.00084  0.00015  0.6  0.95  0.0007  0.001  0.7  0.81  0.0006  0.005  0.8  0.71  0.00055  0.015  0.9  0.63  0.00047  0.025  1.0  0.57  0.00042  0.03  - 8  6  The c r i t i c a l a p e r t u r e F r e s n e l Numbers a r e read d i r e c t l y from f i g u r e 4.5.  An e x a m i n a t i o n o f Table 4-1 would  indicate  t h a t t h e dominant output mode w i l l be the (00) mode from about A, = 0.5mm t o l o n g e r wavelengths,  i f a l l o w a n c e i s . made f o r t h e  r i g h t - s h i f t o f t h e curve i n f i g u r e 4.5. the (01) mode and subsequent  Below t h a t wavelength,  h i g h e r modes become dominant.  Bennett *^ has d e r i v e d a f o r m u l a f o r the optimum t r a n s 1  mission c o e f f i c i e n t , T  ^, which w i l l y i e l d the maximum output  power i n t h e (00) mode. T  opt =  t  4  -  where G- = g a i n p e r pass o f the system L = d i f f r a c t i o n l o s s per pass. T h i s f o r m u l a assumes t h a t t h e (00) mode I s t h e domi-  1  *  63 nant mode.  T h i s r e q u i r e s t h a t the c o u p l i n g aperture, he s m a l l  enough t h a t the l a s e r o s c i l l a t i o n s are not pushed i n t o the  (01)  or h i g h e r modes.  this  requirement  An a p e r t u r e of diameter 2mm  f o r A,<0.5mm.  will fulfil  Below t h a t , a h i g h e r o r d e r mode w i l l  dominate. I t i s not p o s s i b l e to determine  the optimum a p e r t u r e  s i z e f o r a gas whose g a i n , G , i s not known when the l a s e r i s b e i n g designed.  Furthermore,  s i n c e the d i f f r a c t i o n l o s s e s , L,  depend upon the frequency of o s c i l l a t i o n s , so does the optimum t r a n s m i s s i o n c o e f f i c i e n t , as seen i n e q u a t i o n ( 4 . 1 ) .  There-  f o r e , t h e r e i s l i t t l e t o be gained by a i m i n g f o r o p t i m a l c o u p l i n g a t any one f r e q u e n c y i n a l a s e r designed to be used over a wide range of f r e q u e n c i e s .  I n d e s i g n i n g the c a v i t y ,  i t i s s a f e s t t o use a s m a l l a p e r t u r e and t o check e x p e r i m e n t a l l y i f an output s i g n a l i s o b t a i n e d . l,arger a p e r t u r e i s r e q u i r e d . of a 2mm  aperture.  I f no s i g n a l i s d e t e c t e d , a  T h i s was the b a s i s f o r the c h o i c e  The g a i n can be determined  power, P , i s measured e x a c t l y from Bennett's P  =  p 0  where  P  Q  P  T  =  P  (G  ^  I  - T)  w-ji) -  C(V&  and  C  output  formula:  T  - :-  2  t  i f the  L ;  = c o n s t a n t , assuming t h a t the  output power i s p r o p o r t i o n a l to the net g a i n of the medium, •'G-(IJ-T).  A g a i n , the c o n s t a n t  C  i s an unknown q u a n t i t y .  The t r a n s m i s s i o n c o e f f i c i e n t can r o u g h l y be for  estimated  a g i v e n h o l e s i z e by t a k i n g t h e r a t i o of the a p e r t u r e area  to the spot s i z e areas T = a 2 r  (3.12)  T h i s f o r m u l a was suggested and used by P a t e l e t a l A t a b l e of t r a n s m i s s i o n c o e f f i c i e n t s i s g i v e n below ( r e f e r t o e q u a t i o n (3.2)) f o r an a p e r t u r e 2mm i n diameter. Table 4-2 A. (mm)  T r a n s m i s s i o n C o e f f i c i e n t s w i t h a 2mm C o u p l i n g Hole 2 w 2 s r (mm )  T  ?  0.1  1.0  7.8xl0  0.2  1.0  15.6xl0  0.3  1.0  23.4xl0  0.4  1.0  31.2xl0  0.5  1.0  3.9xl0  5  0.026%  0.6  1.0  4.7xl0  3  0.021%  0.7  1.0  5.5xl0  5  0.018%  0.8  1.0  6.2xl0  5  0.016%  0.9  1.0  7.0xl0  5  0.014%  1.0  1.0  7.8x10  3  0.013%  0.13%  2  3  0.064%  3  0.043%  5  0.032%  Note t h a t t h e t r a n s m i s s i o n c o e f f i c i e n t s g i v e n i n t h e above t a b l e a r e f o r t h e u n d i s t u r b e d (00) mode.  The t o t a l out-  put power w i l l c o n s i s t o f those modes whose f i e l d i n t e n s i t y i s not zero a t t h e m i r r o r c e n t e r .  Furthermore,  the spot s i z e  f o r m u l a (3.2) assumes peak f i e l d i n t e n s i t y i n t h e (00) mode a t the m i r r o r c e n t r e .  The a p e r t u r e may cause the i n t e n s i t y t o  change so t h a t t h i s c o n d i t i o n i s no l o n g e r f u l f i l l e d .  There-  fore, the transmission c o e f f i c i e n t s i n t h i s table lose t h e i r v a l i d i t y as t h e wavelength wavelengths,  i s reduced below 0.5mm.  F o r these  t h e modes ( 0 1 ) , ( 0 2 ) , (03) w i l l a l s o couple out  65  s i g n i f i c a n t amounts o f power and i f t h e i r spot s i z e s were known, the o v e r - a l l t r a n s m i s s i o n c o e f f i c i e n t can he determined.  No  attempt i s made t o determine these h e r e , s i n c e t h e problem i s more complex than t h i s r e p o r t w a r r a n t s .  Besides t h i s , i t w i l l  make no major c o n t r i b u t i o n t o t h e o b j e c t o f the present t h e s i s . 4•2  Measurement of Output S i g n a l I n t e n s i t y The f a r i n f r a - r e d r e g i o n of t h e frequency spectrum.,  300 GHz t o 3000 GHz has o n l y r e c e n t l y been t h e s u b j e c t o f i n t e n s i v e study.  The frequency r e g i o n s s u r r o u n d i n g t h i s one, namely  the u l t r a v i o l e t , t h e o p t i c a l , the near i n f r a - r e d and t h e m i c r o wave r e g i o n s , have a l l been w e l l s t u d i e d and t h e i r p r o p e r t i e s documented.  T h i s i s l a r g e l y b e c a u s e s i g n a l s a t these f r e q u e n 1  c i e s have been f a i r l y s i m p l e t o d e t e c t .  High s e n s i t i v i t y , low  n o i s e e q u i v a l e n t power, and f a s t time response have c h a r a c t e r i s e d the d e t e c t i o n methods used i n these r e g i o n s .  With advancing  t e c h n o l o g y , e s p e c i a l l y i n the f i e l d s o f semiconductors and o f magnetism, these d e t e c t i o n methods have been extended i n t o t h e submillimeter regions.  To d a t e , t h i s e x t e n s i o n has been  accomplished o n l y a t t h e l a b o r a t o r y l e v e l . A b r i e f account of these t e c h n i q u e s i s g i v e n below t o determine whether t h e y can he o f use i n t h e present p r o j e c t . The paramount c r i t e r i a f o r s u i t a b i l i t y w i l l once a g a i n be s i m p l i city.  A t t h e p r e s e n t stage of i n v e s t i g a t i o n , a simple d e t e c t o r  i s o f g r e a t e r requirement t h a n a complex one, even though the l a t t e r may have s u p e r i o r s e n s i t i v i t y and n o i s e c h a r a c t e r i s t i c s .  66 4.2.1  E x t e n s i o n of t h e Microwave and the Near I n f r a - R e d D e t e c t i o n Techniques The h i g h e r f r e q u e n c i e s o f t h e microwave spectrum  are g e n e r a l l y d e t e c t e d by p o i n t c o n t a c t r e c t i f i e r s . f a s t , s e n s i t i v e d e t e c t o r s which operate a t room  These a r e  temperature.  34 They a r e a l s o e a s i l y b u i l t .  C A . Burrus  has g i v e n a compre-  hensive r e p o r t on the use o f d e t e c t o r s f o r the wavelengths between 1mm and 10mm.  Present p o i n t c o n t a c t r e c t i f i e r s - formed by  h i g h p r e s s u r e s p r i n g loaded c o n t a c t between a m e t a l p o i n t and a semiconductor  s u r f a c e - have a lower wavelength l i m i t of 0.5mm.  Research i s c u r r e n t l y b e i n g conducted u s i n g v a r i o u s  semiconductor  m a t e r i a l s t o extend t h i s to the s m a l l e r wavelengths of t h e subm i l l i m e t e r range.  Such r e s e a r c h has not y e t been e n t i r e l y  successful. Par i n f r a - r e d r a d i a t i o n can a l s o be d e t e c t e d by e x t e n d i n g techniques used f o r near i n f r a - r e d r a d i a t i o n .  These d e t e c t o r s  are f a s t response, h i g h s e n s i t i v i t y and low n o i s e d e v i c e s and, therefore, very d e s i r a b l e f o r experimentation.  P h o t o c o n d u,35,36 ctivity  i s the most commonly 37used phenomenon i n i n f r a - r e d d e t e c t i o n ' I n 1961, E.H. P u t l e y  found t h a t d e t e c t i o n was p o s s i b l e w i t h  InSb doped w i t h group I I I o r V i m p u r i t i e s i n c o n c e n t r a t i o n s o f 10  1 4  cm^ i f a magnetic f i e l d o f 5000 Gauss i s a p p l i e d .  temperatures  Low  a r e r e q u i r e d - o p t i m a l l y 1.8°K, and the d e t e c t i o n  range i s 0.2mm t o 2mm.  The range, 0.1 t o 0.2mm must be d e t e c t e d  u s i n g a d e t e c t o r which employs a d i f f e r e n t phenomenon - the E l e c t r o n Bolometer o r the Hot E l e c t r o n E f f e c t (see Smith ). Here, v e r y pure samples o f Ge or InSb a t 4°E a r e used.  67 The above method, u s i n g p h o t o c o n d u c t i v i t y and r e l a t e d phenomena p r o v i d e s a f a s t , s e n s i t i v e and low n o i s e response. However, a combination  of two d e t e c t o r s i s r e q u i r e d , b o t h  o p e r a t i n g a t v e r y low temperatures.  I n the present s i m p l e l a s e r  system, the advantages i n response o f f e r e d by t h i s d e t e c t i o n system can be dispensed  w i t h i n favor of a simpler detector, i f  available. Another c l a s s of d e t e c t o r s c o n s i s t s of d e v i c e s s e n s i t i v e t o the h e a t i n g e f f e c t of r a d i a t i o n . known as Bolometers.  The  Such t h e r m a l d e t e c t o r s are  s e n s i t i v i t y of these d e v i c e s , though  i n f e r i o r to the photoconducting  devices, i s high.  time i s , however, r e l a t i v e l y l o n g .  The  response  (For a comparison of photo-  ns • c o n d u c t i v e and t h e r m a l conductors, see P u t l e y .) The t h e r m a l d e t e c t o r s : the S i n g l e C r y s t a l , Superconducting,  various Cooled,  Carbon and G-ernamium Bolometers are d i s c u s s e d i n the a r t i c l e 35 Smith  and  by  i n P u t l e y ' s e x c e l l e n t summarising a r t i c l e on f a r  infra-red detection  .  Bolometers are  s e n s i t i v e t o a wide  range of f r e q u e n c i e s and t h i s i s a p r o p e r t y t h a t i s important f o r an experiment s e e k i n g new  laser transitions.  However,  these  Bolometers l i s t e d above operate a t c o o l e d temperatures and,  there-  f o r e , are here d i s c a r d e d i n f a v o r of a Bolometer which w i l l  detect  r a d i a t i o n a t room temperature. The most s u i t a b l e d e t e c t o r f o r the present e x p e r i ment i s the Golay C e l l operates  5 9 , 4 0  .  ' I t s main v i r t u e s are t h a t i t  a t room temperature and  detection.  i t has a' wide bandwidth f o r  I t s s e n s i t i v i t y i s i n f e r i o r to t h a t of the c o o l e d  d e t e c t o r s , as i s i t s n o i s e f i g u r e .  The time response i s about  68 millisecondsi  150  The m a i n u s e t o w h i c h i t c a n be p u t i s t o  d e t e c t t h e t o t a l s i g n a l power e m a n a t i n g all  o r any o f t h e v a r i o u s modes and  radiation.  f r o m t h e gas l a s e r , i n  f r e q u e n c i e s of the  output  B e c a u s e o f i t s s l o w r e s p o n s e , i t c a n n o t be u s e d  to  measure t i m e r e s p o n s e o f t h e v a r i o u s t r a n s i t i o n s t o t h e p u l s e s o f t h e e x c i t i n g power.  T h i s would  e l a b o r a t e d e t e c t i o n arrangements 4.2.2  10 Hz and  is The  mentioned  earlier.  Golay C e l l D e t e c t i o n System R a d i a t i o n emanating  Cell  r e q u i r e some o f t h e more  from the l a s e r  c h a n n e l l e d i n t o the Golay C e l l  i s chopped a t  "eye".  The  Golay  c o n v e r t s t h e r a d i a t i o n power t o an e l e c t r i c a l s i g n a l  compared t o a r e f e r e n c e s i g n a l o f 10 Hz  which  i n a Lock-in Amplifier.  o u t p u t o f t h i s o p e r a t i o n shows t h e v a r i a t i o n o f t h e  C e l l output w i t h r e s p e c t to the r e f e r e n c e s i g n a l .  Golay  Figure  4.6  shows a s c h e m a t i c d i a g r a m o f t h e d e t e c t i o n a p p a r a t u s .  Reference  Signal  Chopper  Lock-Ln  Laser Beam  Golay  Cell  Sig.  Amplifier  Ref.  Recorder F i g u r e 4.6  Golay C e l l D e t e c t i o n Apparatus  Output  I n t h e f o l l o w i n g paragraphs, the v a r i o u s components of the d e t e c t i o n apparatus a r e d e s c r i b e d and t h e i r purposes and principles  mentioned, (i)  The Golay C e l l  ;  .  The C-olay C e l l i s a pneumatic d e t e c t o r s  t h a t i s , one  t h a t depends on the change i n volume o f a gas caused by t h e incident radiation.  The laser- beam i s caused t o f a l l on a  r a d i a t i o n a b s o r b i n g element which i s housed i n a s m a l l chamber. One w a l l of t h e chamber i s a f l e x i b l e m i r r o r w i t h t h e r e f l e c t i n g s u r f a c e on t h e o u t s i d e .  The shape o f t h e w a l l responds t o  v a r i a t i o n s i n t h e volume o f t h e gas i n the chamber.  A beam o f  o r d i n a r y l i g h t i s r e f l e c t e d o f f t h e m i r r o r onto a p h o t o c e l l . Interposed  i n t h e path o f t h i s beam i s a l i n e g r i d so t h a t t h e  image of one h a l f o f t h e g r i d i s , upon r e f l e c t i o n o f f t h e m i r r o r , superimposed on the other h a l f .  With the use o f l e n s e s , v a r i -  a t i o n s i n t h e bulge of t h e m i r r o r w i l l determine t h e amount o f l i g h t which w i l l s p i l l over t h e second h a l f of t h e g r i d and. r e a c h the p h o t o c e l l .  I n t h i s way, the l i g h t f l u x i n c i d e n t on  the p h o t o c e l l depends on t h e d i s t e n s i o n o f t h e m i r r o r , which i n t u r n depends on t h e r a d i a t i o n absorbed by the pneumatic chamber. A s k e t c h showing the p r i n c i p l e o f the G-olay C e l l i s shown i n f i gure 4 . 7 . The Golay C e l l used h e r e , f o r s u h m i l l i m e t e r wavelengths, has an a p e r t u r e o f s i z e 1.8 i n . 10 ^ volts/watt. +  The s e n s i t i v i t y i s a p p r o x i m a t e l y  The p h o t o c e l l i s b i a s s e d w i t h +90 v o l t s and  the lamp used 2.5 v o l t s a t 1.5 amperes.  The output o f t h e  Golay C e l l i s connected t o the L o c k - i n A m p l i f i e r .  7apere&rfrf/ustingScrew  F i g u r e 4.7  Golay Infra-Red D e t e c t o r  o  71  (ii)  Chopper  The e l e c t r i c a l s i g n a l from a G-olay C e l l r e p r e s e n t s the  d i f f e r e n c e between t h e i n c i d e n t r a d i a t i o n and some ambient  r a d i a t i o n , such as t h e l i g h t i n g i n the room. r a d i a t i o n may d r i f t  The ambient  i n v a l u e and t h e r e b y cause an erroneous  s i g n a l t o be r e a d . However, i f t h e beam i s chopped, t h i s d r i f t w i l l not e f f e c t t h e Golay C e l l o u t p u t . the  Whenever the beam i s i n t e r r u p t e d ,  c e l l i s i n e f f e c t r e s e t t o a z e r o v a l u e , and the output  s i g n a l w i l l r e p r e s e n t the r a d i a t i o n t h a t was not b l o c k e d by the  chopper. I f t h e beam i s i n t e r r u p t e d f o r a s u f f i c i e n t l y l o n g  time, t h e Golay C e l l output would s t a r t f a l l i n g t o t h e ambient value.  T h e r e f o r e , t h e r a t e o f chopping should be such t h a t  the  beam i s b l o c k e d f o r a time l e s s t h a n the time c o n s t a n t o f  the  instrument.  T h i s l a s t i s 0 . 1 5 sec.  A c i r c u l a r b l a d e which  i s c u t such t h a t t h e a l t e r n a t e quadrants o n l y permit t h e passage of t h e beam, and which r o t a t e s a t 5 Hz w i l l chop t h e beam a t 10 Hz. The beam i s t h e n b l o c k e d f o r 0 . 1 seconds, which i s l e s s t h a n the  time c o n s t a n t of t h e i n s t r u m e n t .  A 115 v o l t , 60 Hz synchronous  motor i s used f o r t h i s purpose. 1  Another advantage o f chopping i s t h a t t h e f r e q u e n c y dependent noise  i n t h e i n s t r u m e n t s can be reduced.  Other  sources of n o i s e i n t h e d e t e c t i o n apparatus a r e reduced u s i n g a Lock-In A m p l i f i e r . (iii)  Lock-In A m p l i f i e r  This i s a device that allows d e t e c t i o n of small i n t e n -  72  s i t y signals buried i n n o i s e . 4 1  from v a r i o u s sources.  Noise e n t e r s i n t o the system  Johnson n o i s e i n t h e r e s i s t o r s and shot  n o i s e i n vacuum tubes and semiconductors spectrum which depends on the bandwidth.  produce a white  noise  Gain m o d u l a t i o n or*  f l i c k e r n o i s e i s a s s o c i a t e d w i t h a m p l i f i e r c i r c u i t s and i t v a r i e s as l / f , i . e . maximum n o i s e a t d c .  Other sources o f n o i s e a r e  power l i n e p i c k - u p and r f i n t e r f e r e n c e . F l i c k e r n o i s e i s reduced because t h e o p e r a t i n g i s 10 Hz r a t h e r t h a n dc, by proper s h i e l d i n g . Amplifier.  frequency  I n t e r f e r e n c e can o n l y be e l i m i n a t e d  White n o i s e i s reduced u s i n g a l o c k - I n  The bandwidth i s reduced t o zero by t h i s d e v i c e u s i n g  a harmonic mixer.  I n t h i s , the chopped s i g n a l i s beat w i t h a  r e f e r e n c e s i g n a l o f t h e same frequency and t h e upper s i d e band e l i m i n a t e d by a low pass f i l t e r o f a r b i t r a r i l y s m a l l bandwidth. The lower s i d e band i s then a m p l i f i e d w i t h a dc a m p l i f i e r and the output f e d t o a r e c o r d e r . (iv)  Reference S i g n a l  The r e f e r e n c e s i g n a l i s o b t a i n e d by chopping a beam of l i g h t i n c i d e n t on a p h o t o r e s i s t o r c i r c u i t u s i n g the same chopper as t h e output beam o f t h e l a s e r .  T h i s ensures t h a t  the r e f e r e n c e s i g n a l i s o f t h e same frequency  (though not neces-  s a r i l y t h e same phase) as t h e chopped s i g n a l . (v)  L i g h t Cone  Owing t o d i f f r a c t i o n e f f e c t s a t t h e c o u p l i n g a p e r a t u r e , t h e output beam d i v e r g e s .  A l i g h t cone i s necessary t o  channel t h i s r a d i a t i o n i n t o t h e Golay C e l l a p e r t u r e . 1  D.E. W i l l i a m s o n  4-2  has shown t h a t t h e cone must have p r e c i s e  73  dimensions t o ensure t h a t no r a d i a t i o n i s r e f l e c t e d hack o f f the i n s i d e s u r f a c e of the cone.  U s i n g an e x t e n s i o n of h i s methods,  a cone o f d i m e n s i o n 1 i n . diameter and 5 i n . l e n g t h ; i s made. The cone i s made o f copper and w i t h proper p o l i s h i n g of t h e i n s i d e w a l l s can t r a n s m i t 99$ o f i n c i d e n t r a d i a t i o n . The mouth o f the cone i s covered  b y a black high density poly-  e t h y l e n e sheet which prevents v i s i b l e l i g h t from e n t e r i n g t h e detector.  The p o l y e t h y l e n e i s t r a n s p a r e n t t o s u b m i l l i m e t e r  frequencies  (see f i g u r e 3 . 9 ) .  4.3 Frequency Measurements I t i s now ' p o s s i b l e t o use t h e Golay C e l l apparatus t o measure the t r a n s i t i o n f r e q u e n c y , material. and  o r frequencies, of the l a s e r  A monochromator i s i n t e r p o s e d between the output h o l e  t h e Golay C e l l .  By o b s e r v i n g t h e v a r i a t i o n of power as  the monochromator i s scanned and a l s o as t h e m i r r o r s e p a r a t i o n i s changed w h i l e k e e p i n g t h e monochromator s e t a t some v a l u e , the t r a n s i t i o n frequency  can be deduced.  i s , t h e r e f o r e , a n important  The monochromator  p a r t of the d e t e c t i o n system.  It  i s d i s c u s s e d i n t h e next s e c t i o n . 4.3.1  Monochromator A simple but adequate monochromator i s t h e E b e r t - F a s t i e  type monochromator.  I t s p r i n c i p l e i s i l l u s t r a t e d i n f i g u r e 4.8.  The i n p u t and t h e output s l i t s a r e i n t h e f o c a l plane of t h e l a r g spherical mirror.  T h i s causes t h e g r a t i n g t o be i l l u m i n a t e d by  p a r a l l e l r a d i a t i o n and a l s o t h e s c a t t e r e d r e g i o n of i n t e r e s t i s brought t o a focus on t h e output  slit.  P i g u r e 4,8  E b e r t - F a s t i e Monochromator  The monochromator uses an E c h e l e t t e g r a t i n g w h i c h can he b l a z e d f o r a c e r t a i n f r e q u e n c y i n any order. angle,is  The b l a z e  determined by the order d e s i r e d and by t h e d e s i g n  of the monochromator.  The i n p u t s l i t arrangement i s such t h a t  r a d i a t i o n r e f l e c t e d by t h e concave m i r r o r s t r i k e s t h e g r a t i n g i n a n e a r l y p a r a l l e l beam a t some a n g l e , 0 , w i t h r e s p e c t t o t h e a x i s of the m i r r o r .  The output s l i t i s so p o s i t i o n e d i n r e l a t i o n  t o the concave m i r r o r t h a t those r a y s s c a t t e r e d o f f t h e g r a t i n g i n a d i r e c t i o n making an a n g l e , 0 , w i t h t h e m i r r o r a x i s a r e focussed  t o the center  of t h e output s l i t .  An E c h e l e t t e g r a t i n g  s c a t t e r s maximum r a d i a t i o n i n t h e d i r e c t i o n of t h e s p e c u l a r r e f l e c t i o n o f f the facets of the g r a t i n g .  The s p e c u l a r d i r e c t i o n  can be caused t o c o i n c i d e w i t h t h e r e f l e c t e d d i r e c t i o n , 0 ,  simply  by r o t a t i n g the g r a t i n g so t h a t t h e f a c e t s a r e p a r a l l e l t o t h e f o c a l plane of t h e m i r r o r .  The angle 0, through which t h e  g r a t i n g must be r o t a t e d f o r t h i s c o n d i t i o n t o o b t a i n i s e q u a l t o  75 the b l a z e a n g l e , 6 ,  of the g r a t i n g .  I n the above r o t a t e d c o n d i t i o n , the g r a t i n g e q u a t i o n n\ = d ( s i n 9  i  - sin9 )  (4.1)  r  becomes  (4.2)  nX = 2dco,s0sino where  X = wavelength,, d = s p a c i n g between  grooves,  9^ = i n c i d e n t angle w i t h r e s p e c t t o normal t o grating, 9^ = r e f l e c t e d angle w i t h r e s p e c t t o normal t o grating,,, and  9^ = 9  0+  = 0 r ^  o ,  A .  The g r a t i n g i s s a i d t o have been b l a z e d f o r t h e .A. and n w h i c h s a t i s f y e q u a t i o n (4.2).  I n the general p o s i t i o n of  the g r a t i n g , t h e g r a t i n g e q u a t i o n (4.1), becomes nX. = 2dcos0sin9 Equation appear  (4-3)  (4.3) y i e l d s t h e wavelength and o r d e r which  a t t h e c e n t r e o f t h e output s l i t .  Thus, t h i s  a f f o r d s a means f o r c a l i b r a t i n g t h e monochromator instrument t o be used f o r t h i s experiment,  k  equation I n the  a 0.25 Meter E b e r t  Monochromator made by t h e J a r r e l - A s h Company (see f i g u r e 4-9), the c a l i b r a t i o n i s performed f o r a 6000A  0  grating i n f i r s t  order.  T h i s o p t i c a l system can be adapted t o t h e present s u h m i l l i m e t e r system by r e p l a c i n g t h i s g r a t i n g by an a p p r o p r i a t e g r a t i n g and c a l i b r a t i n g t h e monochromator u s i n g f o r m u l a  (4.3).  The s u h m i l -  l i m e t e r wavelengths a r e o b t a i n e d by u s i n g the c o n v e r s i o n  formula?  76  A/F B/E C D  = = = =  Entrance/Exit S l i t E n t r a n c e / E x i t 45° M i r r o r s Collimating Mirror Grating Selector  Figure 4.9  J a r r e l - A s h Monochromator  g i v e n by: n A  d o = _0 n A d s s s  (4.4)  0  where t h e s u b s c r i p t s " s " and "o" stand f o r s u b m i l l i m e t e r and optical respectively.  Equation  (4.4)  i s d e r i v e d from  assuming t h a t 0 and 9 a r e t h e same i n both systems. to t h i s e q u a t i o n , when \ =0, A =0. g  (4.3),  According  However, i f i n t h e process  of exchanging the g r a t i n g s , the new g r a t i n g i s s l i g h t l y m i s p l a c e d so t h a t A. ^0 when A =0, t h e A S  O  c a l c u l a t e d by u s i n g t h i s  equation  S  must be m o d i f i e d by (4-5)  n s AA.s = 2ds cos0cosOA9 where AO i s t h e e r r o r i n placement.  The v a l u e o f AO can be  found by a c t u a l experiment u s i n g a known t r a n s i t i o n l i n e .  77 In' tire monochromator, 0 i s estimated t h a t Cos0~O.99. Two  For the 6000 A  0  t o he ~ 8°,  b l a z e d g r a t i n g , n =1,  s u h m i l l i m e t e r g r a t i n g s are made on aluminum b l a n k s  d =0.01 s  i n . and  0.02  i n . respectively.  The  so  d =1/1180 mm, with  b l a z e angle i s  From e q u a t i o n (4.3 ),these g r a t i n g s are b l a z e d f o r 131p>  and  15°.  262\x  respectively.  The above d a t a can be s u b s i t u t e d i n t o e q u a t i o n s  (4.4) and  and a s u h m i l l i m e t e r c a l i b r a t i o n f o r the monochromator  (4.5)  w i l l be o b t a i n e d .  For the two g r a t i n g s , t h e n  n A. = 300X + 0 . 5 A 9 x l 0 s s o and  n X S  I t was  S  = 600A.  + l.OAQxlO  0  5  |i  (4.6)  u  (4.7)  r  5  R  s t a t e d e a r l i e r t h a t the concave m i r r o r  focus r a d i a t i o n s t r i k i n g i t a t an a n g l e , 0 , w i t h r e s p e c t the a x i s , a t the c e n t e r of the output s l i t .  will to  I n the same  manner, r a d i a t i o n t h a t i s s c a t t e r e d a t a n g l e s s l i g h t l y d i f f e r e n t from 0 w i l l be f o c u s s e d  on e i t h e r s i d e of t h i s c e n t e r .  Thus,  when the monochromator i s set f o r a c e r t a i n wavelength, i t w i l l not o n l y show t h a t wavelength a t the output s l i t , but a l s o s u r r o u n d i n g wavelengths w i t h i n a range, dA,.  The  range dA.,  called  the " r e s o l u t i o n " , depends on the s l i t width,, dx as i n e q u a t i o n dA. = 2dFcos0 ._ d  n  where  (4.8).  (4.8)  F = f o c a l l e n g t h of the concave m i r r o r n = order of spectrum For the two d\  and  g r a t i n g s , the r e s o l u t i o n s are r e s p e c t i v e l y  = 2xl0"^dx n  dA. = 4 x l O ~ d x n 3  (4.9) (4.10)  78 4.3-2  Frequency Measurement Procedures With t h e a i d o f the monochromator, t h e G-olay C e l l  apparatus can he used t o measure t h e t r a n s i t i o n f r e q u e n c i e s o f the gas.  There a r e two ways i n which t h i s can he done. The  f i r s t method i s t o scan through 9 w i t h t h e mono-  chromator, and t o note the v a r i a t i o n s of power as recorded on the r e c o r d e r .  The process  of scanning w i l l d i s t i n g u i s h t r a n -  s i t i o n l i n e s which a r e separated by wavelengths g r e a t e r than the r e s o l u t i o n o f t h e monochromator.  I n t h e s e a r c h f o r new  t r a n s i t i o n l i n e s , i t i s , t h e r e f o r e , advantageous t o have a h i g h r e s o l u t i o n u s i n g a narrow s l i t .  The s l i t w i d t h must, t h e r e -  f o r e , be a compromise between r e s o l u t i o n and d e t e c t a b l e power. I t i s t o be r e a l i z e d t h a t the r e a d i n g s g i v e n by the c a l i b r a t i o n equations  (4.9) and (4.10) y i e l d t h e product n X .  T h e r e f o r e , any peaks t h a t a r e observed as a r e s u l t of the monochromator s c a n n i n g may be due t o a h i g h e r o r d e r o f a s m a l l wavelength t r a n s i t i o n l i n e .  I n o r d e r t o r e c o g n i z e these  smaller  wavelengths, i t i s a d v i s a b l e , t o use s e v e r a l g r a t i n g s blazedfor  wavelengths such t h a t t h e s m a l l e r wavelength t r a n s i t i o n  l i n e s appear i n s t i l l h i g h e r  order.  W i t h i n t h e l i m i t s o f t h e monochromator r e s o l u t i o n and the v a r i o u s sources  of n o i s e , c e r t a i n l i n e s may be i n d i s t i n g u i s h -  a b l e from each o t h e r .  A l l wavelength r e a d i n g s obtained by t h e  scanning method a r e , t h e r e f o r e , c o r r e c t o n l y t o w i t h i n t h e resolution. The  second method o f measuring t h e t r a n s i t i o n l i n e s  i s by v a r y i n g t h e m i r r o r s e p a r a t i o n .  Resonances occur o n l y i f  79 e q u a t i o n 3.5 i s s a t i s f i e d : 4 d = 2q + (1+m+n) r i - ^ t a n " A. V  1  'b & \ b+d /  (3-5)  z  S i n c e t h e r e may be s e v e r a l t r a n s i t i o n l i n e s f o r a g i v e n m a t e r i a l , as t h e r e a r e f o r water v a p o r , t h e monochromator i s n e e d e d s o t h a t t h e s i g n a l d e t e c t i n g a p p a r a t u s " s e e s " o n l y one l i n e at a time.  I f j u s t one a x i a l mode h a s a l o s s l o w enough  t o be e x c i t e d , t h e t r a n s i t i o n w a v e l e n g t h  c a n be d e d u c e d b y  the equationA = 2Ad  (4.H)  where Ad = d i s t a n c e t h e m i r r o r moves b e t w e e n r e s o n a n c e s . There  i s a l i k e l y p o s s i b i l i t y t h a t more t h a n one  a x i a l mode i s e x c i t e d .  E f f o r t s t o minimize the l i k e l i h o o d of  t h i s were made i n s e c t i o n 3.5.  However, i t may be t h a t  such  e f f o r t s may r e d u c e t h e o u t p u t power t o t h e e x t e n t t h a t i t i s . i n d i s t i n g u i s h a b l e from n o i s e .  I n s u c h a c a s e , t h e r e i s no s i m p l e  a l t e r n a t i v e b u t t o p e r m i t more t h a n one a x i a l mode t o be e x c i t e d . When t h e s e o t h e r h i g h e r l o s s modes a r e a t l i n e c e n t e r , h o w e v e r , t h e peak o u t p u t power s h o u l d b e s m a l l e r t h a n i f t h e d o m i n a n t mode were t h e r e . . it  Thus, by m e a s u r i n g  t h e s e p a r a t i o n between these  peaks,  i s p o s s i b l e t o d e t e r m i n e t h e d i s t a n c e t h e m i r r o r moves b e t w e e n  a x i a l resonances.  Prom e q u a t i o n ( 3 - 5 ) , A. i s d e t e r m i n e d  A = 4_d KA(m+n) K = 1 - 4 tan" it  (4.12) 1  b-d b+d  where d = d i s t a n c e t h e m i r r o r moves b e t w e e n a x i a l resonances.  from  80 4.3.3  Water Vapor L i n e s I n s e c t i o n 4.3.1 i t was s t a t e d t h a t  calibration  s h o u l d be p e r f o r m e d u s i n g a g a s w i t h known t r a n s i t i o n s .  Laser  a c t i o n h a s s u c c e s s f u l l y b e e n o b t a i n e d i n w a t e r v a p o r and i t s t r a n s i t i o n l i n e s a c c u r a t e l y measured b y s e v e r a l a u t h o r s . T a b l e 4-3 l i s t s l i n e s  i n w a t e r v a p o r t h a t have been o b t a i n e d  and t h e i r r e l a t i v e o u t p u t  power. Table  4-3  Water Vapor T r a n s i t i o n  Lines  (n)  (w)  (cm )  (W)  16.931  0.02  45.523  0.007  23.365 '  0.1  47.251  0.08  26.666  0.5  47.469  0.06  27.974  3  47.693  0.04  - 1  28.054  -  48.677  0.07  28.273  0.6  53.906  0.0008  28.356  0.01  55.077  0.06  32.929  0.4-  57.660  0.02  33.033  7  67.177  0.01  35.000  -  73.402  0.002  35.841  0.1  78.455  0.007  36.619  0.009  79.106  0.006  37.859  0.003  89.775  0.0007  38.094  -  115.42  39.698  0,1  118.65  40.629  0.01  120.08 220.34  Table  4-3 c o n t i n u e d  on t o p o f page 8 1 .  0.001  -  81 A. i s t h e w a v e l e n g t h i n vacuum, and p i s t h e peak output  power f r o m t h e t u b e .  a) The p o s s i b l e e r r o r i s - 0,05 and  - 0.1 p e r c e n t  b) The power l i e s figure  percent  f o r A,<80|i,  f o r A>80|-i.  b e t w e e n 1/3  and 3 t i m e s t h e  quoted.  c) The 220.34p l i n e was o b t a i n e d by E l e s h e r and Muller  4 4  , and t h e r e s t by M a t h i a s  and  Crocker ''. 4  The l i n e s and t h e i r power w e r e o b t a i n e d b y M a t h i a s Crocker..and  were d e t e c t e d u s i n g c o o l e d p h o t o d e t e c t o r s .  and  Since  the present system uses l e s s e f f i c i e n t d e t e c t i o n methods,not a l l t h e t r a n s i t i o n s i n t h e a b o v e l i s t w i l l be o b s e r v e d . p o s s i b l e t o p r e d i c t whether the r e l a t i v e amplitudes  A l s o , . i t i s not at the v a r i o u s  t r a n s i t i o n w a v e l e n g t h s w i l l be e f f e c t e d b y u s i n g t h e l o w e r  dis-  charge c u r r e n t d e n s i t i e s t h a t a r e used i n the present p r o j e c t . E v e n i f e v e r y t h i n g i s assumed l i n e a r , t h e s h o r t e r w a v e l e n g t h w i l l appear a t t h e output  slit  i n such a h i g h order t h a t  lines  their  c o n t r i b u t i o n t o t h e t o t a l power r e a c h i n g t h e G-olay C e l l may be v e r y small, i f not n e g l i g i b l e .  Only a c t u a l experimentation can d e t e r -  mine how s m a l l t h i s c o n t r i b u t i o n i s . tatively,  w i t h t h e 130|i b l a z e d g r a t i n g , t h e 118u- l i n e  a p p e a r t o be t h e most p o w e r f u l . to  A l l things considered  f i n d A9 i n e q u a t i o n  This r e a l i z e d ,  quali-  should  i t i s possible  (4.7) and t h u s c a l i b r a t e t h e m o n o c h r o m a t o r .  82 5. 5.1  Tests  on  TESTS ON LASER-  Laser  The l a s e r s y s t e m , a s d e s i g n e d ,  i s meant t o e n c o u r a g e  l a s e r a c t i o n i n the f a r i n f r a - r e d r e g i o n of the frequency To t h i s e n d , t h e l o s s e s due t o t h e v a r i o u s s o u r c e s a minimum i n t h e c a v i t y .  system.  were k e p t t o  Any m a t e r i a l w i t h s u h m i l l i m e t e r t r a n - •  s i t i o n s which can o b t a i n s u f f i c i e n t overcome t h e s e  i n v e r s i o n of population t o  l o s s e s w i l l y i e l d a n o u t p u t power t o t h e d e t e c t i o n  I n most g a s e s t h e e x i s t e n c e o f s u c h t r a n s i t i o n s  be p r e d i c t e d a n d c a n o n l y be d e t e r m i n e d b y a c t u a l Aside  from keeping  cannot  experimentation.  l o s s e s down, l a s e r a c t i o n c a n be  e n c o u r a g e d b y u s i n g t h e a p p r o p r i a t e gas p r e s s u r e sities.  spectrum.  For a given t r a n s i t i o n , these  c a n o n l y be d e t e r m i n e d by p e r f o r m i n g may h a v e more t h a n one t r a n s i t i o n ,  and c u r r e n t  den-  c a n n o t be p r e d i c t e d , and  tests.  Also, a given material  within or without  the f a r i n f r a -  r e d r e g i o n , e a c h o f w h i c h h a v e t h e i r own optimum c o n d i t i o n s o f pressure  and c u r r e n t d e n s i t y .  f i n d these  Therefore,  i t i s interesting to  conditions f o r transitions within the region of interest. Once.'it h a s b e e n d e t e r m i n e d t h a t l a s e r a c t i o n i s i n d e e d  obtainable, the t r a n s i t i o n frequencies o r b o t h o f t h e methods d e s c r i b e d 5.1.1  Tests  c a n be d e t e r m i n e d b y one  i n section 4.3.  t o be P e r f o r m e d  P o u r m a t e r i a l s and d i f f e r e n t c o m b i n a t i o n s o f them a r e u s e d i n t h e l a s e r t o see i f l a s e r a c t i o n i s o b t a i n a b l e . are: water  vapor, helium,  These  a c e t o n e and r e a g e n t m e t h y l a l c o h o l .  Of t h e s e , w a t e r v a p o r i s known t o have t r a n s i t i o n s t h a t c a n y i e l d  o u t p u t power u n d e r t h e c o n d i t i o n s on t h e p r e s e n t  laser.  The  o t h e r s a r e t e s t e d r e a l i s i n g t h a t t h e l a s e r d e s i g n may n o t he able t o e x c i t e l a s e r a c t i o n i n suhmillimeter t r a n s i t i o n s , t h o u g h t h e y may  even  exist.  U s i n g w a t e r v a p o r , t h e f o l l o w i n g t e s t s were p e r f o r m e d : ( i ) V a r i a t i o n o f t o t a l o u t p u t power w i t h d e n s i t y and  current  pressure. ( i i ) S c a n n i n g w i t h t h e monochromator t o d e t e r m i n e  transition  frequencies. ( i i i ) V a r i a t i o n o f o u t p u t power i n 118u- l i n e  c u r r e n t and  with  pressure. ( i v ) V a r y i n g m i r r o r s e p a r a t i o n f o r a g i v e n mono-  chromator  setting. • ' (v) A l t e r i n g l a s e r c a v i t y c o n f i g u r a t i o n hy r e p l a c i n g  one m i r r o r w i t h f l a t m i r r o r s h a v i n g d i f f e r e n t and 5.2  repeating Test  s i z e output  holes  ( i ) and ( i v ) .  Data This  performed.  s e c t i o n c o n t a i n s graphs: r e s u l t i n g f r o m t h e t e s t s  These a r e : ( i ) T o t a l o u t p u t power o f w a t e r v a p o r u s i n g t h e  near-confocal  l a s e r ( f i g u r e 5.1)( i i ) Power o u t p u t i n t h e 118u l i n e o f w a t e r v a p o r  using the near-confocal  c a v i t y l a s e r ( f i g u r e 5.2).  ( i i i ) T o t a l o u t p u t power o f w a t e r v a p o r u s i n g a p l a n o - c o n c a v e c a v i t y l a s e r , w i t h a 1mm (figure  5-3).  hole  i n t h e plane  mirror  84 ( i v ) T o t a l o u t p u t power o f w a t e r v a p o r u s i n g a p i a n o - , concave  c a v i t y l a s e r , w i t h a 2mm h o l e i n t h e p l a n e m i r r o r (v) T y p i c a l monochromator scans  ( f i g u r e s 5.5  (figure and  5.6).  I n i t e m ( v ) , t h e t w o g r a t i n g s w e r e p l a c e d i n t h e monochromator  i n s u c h a way t h a t t h e A© o f e q u a t i o n (4.5)  same f o r b o t h .  i s the  T h i s was c h e c k e d u s i n g a He-Ne L a s e r beam, a  f l a t m i r r o r and a d i s t a n t  wall.  No l a s e r a c t i o n was o b t a i n e d u s i n g a c e t o n e , r e a g e n t m e t h y l a l c o h o l o r V a t 69 S c o t c h W h i s k e y .  I t was f o u n d t h a t t h e  a l c o h o l a s w e l l a s h e l i u m e a c h d e c r e a s e d t h e power o u t p u t when added t o w a t e r v a p o r . No power v a r i a t i o n s i n d i c a t i n g r e s o n a n c e were o b s e r v e d when t h e m i r r o r s e p a r a t i o n was s t e a d i l y a l t e r e d three cavity configurations  0,(J> 8  10  P i g u r e 5.1  i n each o f t h e  used.  . . . . _ 14 16 18 20 22 C u r r e n t (ma) T o t a l O u t p u t Power, N e a r - C o n f o c a l C a v i t j r 2 mm C o u p l i n g A p e r t u r e 12  5.4).  •  .  8  10  12  Figure  5.2  o.d  Figure  •  .  .  .—  14 16 18 20 22 C u r r e n t (ma) O u t p u t Power i n 118(1 L i n e , N e a r Conf o c a l C a v i t y -  5.3  C u r r e n t (ma) T o t a l O u t p u t Power, P i a n o - C o n c a v e lmm C o u p l i n g A p e r t u r e  Cavity  £!  8  10  H  d>  12  F i g u r e 5.4 5.3  14 Current  16 (ma)  18  T o t a l Output Power, Piano-Concave C a v i t y 2mm C o u p l i n g A p e r a t u r e  O u t p u t Power F i g u r e s 5.1  and  5.2  show t h a t t h e r e i s no  r e l a t i o n s h i p b e t w e e n t o t a l o u t p u t power and  and  line. current.  Each have independent  t h e 118u- l i n e t h e p = 0.7  definite  o u t p u t power i n t h e  o p t i m a l c o n d i t i o n s of p r e s s u r e  There i s a g e n e r a l tendency  the c u r v e s t o have n a r r o w e r  may  22  D i s c u s s i o n of R e s u l t s  5.3.1  118u  20  i n b o t h , however, f o r  p e a k s a t h i g h e r gas p r e s s u r e s .  curve b e l i e s  this  be b e c a u s e t h e l a s e r has n o t y e t r e a c h e d  o b s e r v a t i o n but a proper  In this  oscillation  level. F i g u r e s 5.3 coupling hole size.  and  5.4  demonstrate the e f f e c t of  The  1mm  h o l e system  outputs n e a r l y  the double  Figure 5.6  Monochromator Scan, 262|x Blazed Orating  00 00  89 the amount o f power o f the 2mm h o l e system.  This i s probably  because of t h e mode d i s t o r t i o n s caused by the l a r g e r h o l e , as d i s c u s s e d i n s e c t i o n 4.2.1.  No e x p l a n a t i o n can be o f f e r e d  here f o r the change i n the c h a r a c t e r i s t i c curve shapes. I t i s i n t e r e s t i n g t o note t h a t t h e plano-concave system w i t h the 1mm c o u p l i n g h o l e outputs more power than the  near-  c o n f o c a l system, even though i t s d i f f r a c t i o n l o s s e s a r e l a r g e r . While the a p e r t u r e s i z e s may have c o n t r i b u t e d a l a r g e p a r t t o t h i s f a c t , t h e mode volumes p r o b a b l y a r e t h e important f a c t o r s i n v o l v e d , the mode volume of t h e plano-concave c a v i t y b e i n g much l a r g e r than t h a t >.of ,the n e a r - c o n f o c a l . c a v i t y . 5.3.2  T r a n s i t i o n Lines F i g u r e s 5-5 and 5.6 can be used to determine t h e t r a n -  s i t i o n l i n e s w i t h h e l p o f equations  (4.6) and ( 4 . 7 ) .  I n the  131u b l a z e d g r a t i n g scan, f i g u r e 5-5, the h i g h e s t peak i s assumed I f t h e c a l i b r a t i o n e q u a t i o n (4.4) i s used,  t o be t h e 118u l i n e .  t o A. = 114u-, s i n c e X  t h i s l i n e corresponds t o be 3800 A . 0  i s read from f i g u r e 5-5  The e r r o r , A9 can be c a l c u l a t e d f o r the f i r s t  g r a t i n g t o be: A9  =  s s 2d co~Sj0cos9 . s ^  =  (118.65 - 114)u 0.254x0.99x0.974xl0 u  n  A X  '  l:  5  = 0.0095 Cos9 was determined u s i n g e q u a t i o n (4.3).  Within the  range o f 9 t h a t the monochromator i s r o t a t e d , t h e denominator  90 can be assumed t o be 0.5xl0^p. Vs  =  300  \)  +  A  '  7 5  The E q u a t i o n  (4.6 ) becomes  ^  ( 5 , 1 )  The v a l u e s of n s A.s are t a b u l a t e d i n Table  5-1.  When the 26lp b l a z e d g r a t i n g i s used, the maximum Assuming AO = 0.0095 i s the same f o r  peak occurs at 3820 A . 0  t h i s g r a t i n g , e q u a t i o n (4.7)  i n d i c a t e s t h a t A, = 238.7p. s  l o o k s l i k e the 118.65p l i n e i n second order. amplitude  This  The f a c t t h a t the  of the l i n e i s g r e a t e r than the f i r s t order l i n e  cause concern.  I t may  may-  be e x p l a i n e d away.by the f a c t t h a t the  2 6 l p g r a t i n g has a l o w e r r e f l e c t i o n l o s s t h a n the 131p s i n c e the number of l i n e s per i n c h i s s m a l l e r .  grating,  The l a r g e r the  number of l i n e s t o be drawn on the g r a t i n g , the more t h e wear on the c u t t i n g t o o l and hence t h e more i r r e g u l a r the  lines.  Furthermore, the o n l y known t r a n s i t i o n l i n e i n t h i s r e g i o n i s the 220p l i n e . corresponds  Under the assumption that the A, =3820 A  to t h i s l i n e , A9 of the second g r a t i n g would then  -0.019 r a d i a n s .  be  Such a A9 would have d i r e c t e d the r e f l e c t e d  beam 0 . 0 0 9 5 - ( - 0 . 0 1 9 ) x 5 f t . =1.7  inches away from the  spot i f a w a l l o n l y 5 f e e t away i s used i n the simple d e s c r i b e d i n s e c t i o n 5.2. than 0.25  reading  0  q  original test  The beam w i d t h i s c o n s i d e r a b l y l e s s  inches i n the d i s t a n c e t r a v e l l e d and hence the  c o i n c i d e n c e would have appeared i n t h a t t e s t . n o t , i t i s s a f e t o assume t h a t the 3820 A  0  non-  Since i t d i d  r e a d i n g o f f i g u r e 5.6  i s not the 220p water vapor l i n e . U s i n g these arguments, e q u a t i o n (4.7) n A s  s  = 600X  Q  + 9.5P  becomes (5-2)  The r e a d i n g s f r o m f i g u r e s 5.5 equations  and 5.6,  along with  (5.1) and (5.2) l e a d t o T a b l e 5-1. Table  5-1  Monochromator Scans Grating  Reading  n\*  Error  (|i, b l a z e d )  (A°)  (u)  131  3030  95.65  3080 3670  97.15 114.85  3800  118.65  1.65  4300  133.65  1.65  4700  145.75  1.65  3580  218.3  2.30  3820  . 238.7  . 2.30  4290  266.9  ...2.3-0  4700  291.5  2.30  262  1.65 ...  1.65 1.65  * U s i n g e q u a t i o n s ( 5 . 1 ) and ( 5 . 2 ) The r e s o l u t i o n o f t h e m o n o c h r o m a t o r i s 2|i.  Also,  due t o n o i s e e t c . , t h e p e a k s c a n o n l y be d e t e r m i n e d t o - 1mm o f t h e c h a r t s c a l e , w h i c h c o r r e s p o n d s t o - 100 A . 0  The d i r e c t  6 r e a d i n g s a r e a l s o r o u n d e d o f f t o t h e n e a r e s t 10 A , s o t h a t t h e o v e r - a l l e r r o r i n A.  i s (- 100 -• 5) A . 0  Converted t o X , t h e  r e a d i n g e r r o r i s - 0.65u f o r t h e 131U- b l a z e d g r a t i n g and - 1.3H f o r t h e 262u b l a z e d g r a t i n g . i n T a b l e 5-1 i s - 1.65H  a n d  Thus t h e t o t a l e r r o r , a s shown  - - 2.30u f o r t h e two g r a t i n g s .  The t r a n s i t i o n w a v e l e n g t h s , X, a t a b u l a t e d form.  c a n be d e t e r m i n e d i n  T a b l e 5-2 shows how some o f t h e s e c a n c o r -  respond t o c e r t a i n l i n e s i n t h e i n f r a - r e d r e g i o n , as read i n T a b l e 4-3.  92 A c c o r d i n g t o Table 5-2, most o f the l i n e s have been i d e n t i f i e d w i t h r e s p e c t t o Table 4 - 3 . however, about t h e A.=33.033a l i n e .  There i s some doubt, I n the 131a b l a z e d g r a t i n g  scan i t appears i n f o u r t h o r d e r as 4 A. =133.65a.  I n the 262p.  b l a z e d g r a t i n g scan i t should appear a t 6A. = 198,198a  ?  7A. = 231.231a  I  and 8A, = 264.3a.  While t h e l a s t o f these t h r e e i s observed,  the o t h e r two are n o t .  I n view of t h i s , i t i s concluded t h a t  the 33.033a l i n e does not appear i n the two scans. Table' 5-2 T r a n s i t i o n Wavelength A n a l y s i s nA* (a)  Identified  1. 65 97.15 + 1. 65 114.85 + 1. 65  47.251a t o 47.693a l i n e s i n second order 47.693a t o 48,677a l i n e s i n second. o r d e r 115.42a l i n e i n f i r s t , o r d e r , and 57.66a l i n e i n second order 118.65a l i n e i n f i r s t order 33.033a l i n e i n f o u r t h order  95.65  118.65 133.65 145.75 218.3 238.7 266.9 291.5 * **  + + + + + +  1. 65  1. 65 1. 65 2. 30 2. 30 2. 30 + 2, 30  w i t h **  -  220.34a l i n e i n f i r s t order 118.65a l i n e i n second order  —  As read from Table 5-1 As i d e n t i f i e d w i t h l i n e s l i s t e d i n Table 4-3 Thus, t h e r e a r e f o u r u n i d e n t i f i e d v a l u e s o f n.\; 133.65a,  145.75a', 266.9a, and 291.5a.  Of t h e s e , t h e 29-1.5a r e a d i n g may  be the 145.75a l i n e i n second o r d e r and the 266.9a may be t h e 133.65a l i n e i n second o r d e r . new t r a n s i t i o n  I t appears, t h e r e f o r e , t h a t two  l i n e s i n the f a r i n f r a - r e d  r e g i o n have been d i s -  93  covered i n water vapor. 145.75 -  These a r e : 133.65p-  - 1 . 6 5 m and  1.65P.  A c e r t a i n amount o f s k e p t i c i s m fairly justified.  o f t h e above r e s u l t i s  Water vapor has been i n t e n s i v e l y studied i n  the past w i t h t h e s p e c i f i c o b j e c t i v e  of f i n d i n g a l l of i t s ex-  citable transitions.  methods used were more  sophisticated  The d e t e c t i o n  than t h e simple scheme adopted i n t h i s t h e s i s .  However, t h e two l i n e s , p a r t i c u l a r l y t h e 1 4 5 ^ l i n e , a r e so pronounced i n f i g u r e s 5»5 and 5 . 6 t h a t f u r t h e r i n v e s t i g a t i o n worthwhile. use  seems  More p o s i t i v e i d e n t i f i c a t i o n c o u l d be made w i t h the  of f i l t e r s and i n t e r f e r o m e t e r s which were n o t a v a i l a b l e i n  the p r e s e n t stage o f t h i s work. . The d e t e c t i o n  arrangement  should a l s o be evacuated so as t o m i n i m i z e a t m o s p h e r i c a b s o r p t i o n . One check of t h e r e s u l t s t h a t could, be made i s by scanning w i t h the mirrors. configurations  T h i s was done u s i n g the v a r i o u s  cavity  d e s c r i b e d i n s e c t i o n 3 . 5 . but i t was found t h a t a  s u f f i c i e n t number o f modes were e x c i t e d were d i s c e r n i b l e from n o i s e .  so t h a t no power v a r i a t i o n s  Other mode s e l e c t i o n t e c h n i q u e s  would have t o be employed. 5.3-4  Hypotheses This project  quantum l e v e l s i n v o l v e d  i s i n no way geared t o determine t h e i n the laser action.  of the d i s c h a r g e i n d i c a t e s s o c i a t e t o form OH  -  The p i n k c o l o u r  t h a t t h e water v a p o r m o l e c u l e s d i s -  r a d i c a l s and 0  +  ions.  I n such a case the  l a s e r t r a n s i t i o n s can be i n one o r b o t h o f these and they a r e stimulated 3.2.4  p r i m a r i l y by e i t h e r o f t h e methods d e s c r i b e d  and 3 . 2 . 5 .  in:section  Witteman and B l e e k r o d e ^ a t t r i b u t e t h e a c t i o n 4  94  to t r a n s i t i o n s between r o t a t i o n s t a t e s i n the OH"" r a d i c a l s . A l c o h o l and h e l i u m may have l e v e l s near the upper t r a n s i t i o n l e v e l s of water vapor so as t o d e p l e t e them by n o n - s u b m i l l i meter t r a n s i t i o n s .  95  6. CONCLUSIONS The l a s e r c a v i t y as designed i n t h i s t h e s i s i s capable of s u s t a i n i n g l a s e r a c t i o n a t l e a s t i n t h e l o w e r wavelength r e g i o n o f t h e f a r i n f r a - r e d spectrum.  This i s substantiated  by t h e f a c t t h a t water vapor l i n e s were found i n t h e v i c i n i t y of 120u.  The l a s e r was designed t o s u s t a i n o s c i l l a t i o n s over  the e n t i r e s u h m i l l i m e t e r r e g i o n , but no t e s t s were performed u s i n g m a t e r i a l s known t o l a s e a t l o n g e r wavelengths. q u a l i t a t i v e knowledge  W i t h no d e f i n i t e  o f t h e g a i n v a l u e s o f water vapor as a  l a s e r gas, i t i s d i f f i c u l t t o s t a t e c a t e g o r i c a l l y t h a t l a s e r a c t i o n w i l l be o b t a i n e d a t wavelengths around 1mm..  I t i s pos-  s i b l e t o say, however, t h a t t r a n s i t i o n l i n e s up t o 500u w i l l o s c i l l a t e i n the l a s e r c a v i t y i f the g a i n f o r the t r a n s i t i o n i s s i m i l a r t o t h a t o f t h e 118u water vapor' l i n e .  Beyond 500'd, the  g a i n must be b e t t e r t h a n t h a t o f t h i s l i n e . With water vapor i n the l a s e r , t h e g e n e r a l v a r i a t i o n s of output power w i t h gas p r e s s u r e and c u r r e n t d e n s i t y were d e t e r mined.  I t was found t h a t as p r e s s u r e was changed between 0.7  T o r r and 1.1 T o r r , t h e maximum v a l u e o f output power was r o u g h l y the same, but t h e curves were f l a t t e r a t l o w e r p r e s s u r e s .  A  s l i g h t s h i f t i n t h e v a l u e of c u r r e n t f o r which t h e output was maximum was found as t h e p r e s s u r e was changed.  The p a t t e r n i s  not d e f i n i t e enough toi make a n y f u r t h e r comments. Two t r a n s i t i o n l i n e s were found which were not i d e n t i f i e d w i t h any found i n the l i t e r a t u r e .  These l i n e s may be new  l i n e s which were s u s t a i n e d by t h e present l a s e r . of -1.65u, t h e s e a r e : 1"5"5.65|i, and 145.75u.  Within l i m i t s  96 L a s e r a c t i o n was n o t f o u n d u s i n g a c e t o n e o r a l c o h o l . Evidence e x i s t s i n the l i t e r a t u r e , can l a s e i n t h e f a r i n f r a - r e d . would have been d e s i r a b l e cause m a t e r i a l s  h o w e v e r , t h a t "both o f t h e s e  Wo a t t e m p t was made, t h o u g h i t -  t o do s o , t o see i f t h e l a s e r w o u l d  s u c h a s L^O, HON, CH^CN t o l a s e .  These a r e  a l s o known t o h a v e s t r o n g t r a n s i t i o n s i n t h e f a r i n f r a - r e d .  97 REFERENCES  A. E i n s t e i n , " Z u r Q u a n t e n t h e o r i e v o l . 18, p. 121 ( 1 9 1 7 ) .  der S t r a h l u n g " , Phy.Zeit,  P.A.M. D i r a c , "On t h e Quantum T h e o r y o f R a d i a t i o n " , Roy. Soc. A., v o l . 114, p. 243 ( 1 9 2 7 ) .  Proc.  J . 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