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Integrated optical devices in lithium niobate Ahmed, Mohammad Jamil 1981

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INTEGRATED OPTICAL DEVICES IN LITHIUM NIOBATE by Muhammad Jam i l Ahmed B.Sc. (E.E.), W. P a k i s t a n Univ. of Eng. & Tech., 1966 M.Sc. (E.E.), U n i v e r s i t y of A l b e r t a 1970 M.B.A., Simon Fraser U n i v e r s i t y , 1979 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY i n THE FACULTY OF GRADUATE STUDIES Department of E l e c t r i c a l Engineering We accept t h i s t h e s i s as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA December 1981 ® Muhammad J a m i l Ahmed In presenting t h i s thesis i n p a r t i a l f u l f i l m e n t of the requirements f o r an advanced degree at the University of B r i t i s h Columbia, I agree that the Library s h a l l make i t f r e e l y a v a i l a b l e f o r reference and study. I further agree that permission for extensive copying of t h i s thesis for s c h o l a r l y purposes may be granted by the head of my department or by his or her representatives. I t i s understood that copying or pu b l i c a t i o n of t h i s thesis for f i n a n c i a l gain s h a l l not be allowed without my written permission. Department of The University of B r i t i s h Columbia 2075 Wesbrook Place Vancouver, Canada V6T 1W5 Date DF-fi (2/79) ABSTRACT Integrated o p t i c a l devices use l i g h t to perform c i r c u i t f u n c t i o n s . One c l a s s of devices using T i i n d i f f u s e d waveguides i n Li N b 0 3 are i n v e s t i g a t e d i n t h i s t h e s i s . The a p p l i c a t i o n s s t u d i e d i n c l u d e s e r i e s and multibranch i n t e r f e r o m e t e r s , a comparatorless A/D converter, and a high voltage sensor. An Impedance transformation equation f o r an exponential l i n e i s derived and used to o b t a i n r e l a t i o n s f o r the propagation constant of an o p t i c a l waveguide w i t h l i n e a r l y graded index. The r e s u l t s are used to study the e f f e c t of a T a 2 0 j f i l m on the propagation constant of a T i d i f f u s e d waveguide. Heating i n 0 2 of the T a 2 0 5 f i l m , l o a d i n g one arm of the Mach-Zehnder modulator, i s shown to tune the modulator. The f a b r i c a t i o n of devices i n Y-cut L i N b 0 3 by T i d i f f u s i o n i s described. Microscope o b j e c t i v e s are used to couple 0.6328 urn l i g h t i n t o 4 um wide waveguides through p o l i s h e d edges. An a p p l i c a t i o n of the Mach-Zehnder modulator and a two mode BOA ( B i f u r c a t i o n optique a c t i v e ) modulator to high voltage measurement i s d i s c u s s e d . The output I n t e n s i t y of the s e r i e s i n t e r f e r o m e t r i c f i l t e r i s c a l c u l a t e d . Measured r e s u l t s on a two s e c t i o n f i l t e r are presented. A l s o , the output i n t e n s i t y of a multibranch i n t e r f e r o m e t r i c f i l t e r i s determined. Experimental r e s u l t s on a three branch f i l t e r are i n c l u d e d . i i An e l i m i n a t i o n of comparators from the e l e c t r o o p t i c A/D converters (ADCs) u t i l i z i n g Mach-Zehnder modulators i s proposed. Design parameters of a 4 - b i t p r e c i s i o n comparatorless ADC are obtained. The measured r e s u l t s on such an ADC to produce a s i n g l e b i t are encouraging. i i i TABLE OF CONTENTS Page ABSTRACT i i TABLE OF CONTENTS i v LIST OF TABLES i x LIST OF FIGURES . x ACKNOWLEDGEMENTS x v i i I . INTRODUCTION 1 I I . A REVIEW OF INTEGRATED OPTICS 5 2.1 I n t r o d u c t i o n 5 2.2 O p t i c a l waveguides 5 2.2.1 O p t i c a l damage 8 2.2.2 D r i f t phenomenon 8 2.3 Waveguide a n a l y s i s 9 2.3.1 WKB and the e f f e c t i v e index method 10 2.3.2 Linear segment approximation a n a l y s i s 13 2.4 Modulators 17 2.4.1 Parameters of a phase modulator 17 2.4.2 Strip-waveguide modulator 18 2.4.3 D i r e c t i o n a l coupler modulator 20 2.4.4 Integrated o p t i c a l Mach-Zehnder modulator . . . 22 2.5 Switches 22 2.5.1 D i r e c t i o n a l coupler switch 23 i v 2.6.1 Corrugated/grating f i l t e r . . . 28 2.6.2 Mode converter f i l t e r 29 2.6.3 D i r e c t i o n a l coupler f i l t e r 32 I I I . TAPERED LINE AND LINEARLY GRADED WAVEGUIDES 33 3.1 I n t r o d u c t i o n 33 3.3 E x p o n e n t i a l l y tapered l i n e 3.2 D i f f e r e n t i a l equation f o r input impedance 37 3.4 Di s p e r s i o n equation f o r a l i n e a r l y graded index guide . 39 . . . 39 3.4.2 TM mode 43 IV. PHASE COMPENSATION BY FILM LOADING 45 4.1 I n t r o d u c t i o n 45 4.2 Phase compensation 45 4.3 C r i t e r i a f o r the l o a d i n g f i l m 48 4.3.1 A review of the m a t e r i a l s 48 4.4 Modelling of the loa d i n g f i l m 48 4.4.1 TE modes, n £ ( x ) > n 51 f s 4.4.2 TE modes, n f ( x ) < n g . 53 4.4.3 TM modes, n £ ( x ) > n 54 f s 4.4.4 TM modes, n,(x) < n 55 I S 4.5 Propagation constant of f i l m loaded guide of width w . . 56 v Page 4.6 Computations 58 4.6.1 D e s c r i p t i o n of computed r e s u l t s 59 4.7 Experimental r e s u l t s 72 V. FABRICATION AND TESTING OF DEVICES 72 5.1 I n t r o d u c t i o n 72 5.2 Mask 72 5.3 C r y s t a l 75 5.4 Cleaning 76 5.5 Evaporation of T i 78 5.6 Exposing, developing, and etching 79 5.7 D i f f u s i o n 81 5.8 Sputtering of S i 0 2 85 5.9 Forming Ta 20 5 p a t t e r n 86 5.10 Forming the electrode p a t t e r n 88 5.11 C u t t i n g , g r i n d i n g , and p o l i s h i n g 90 5.11.1 Preparation of the c r y s t a l f o r c u t t i n g 90 5.11.2 Grinding and p o l i s h i n g of the c r y s t a l 93 5.12 F a b r i c a t i o n tolerances 101 5.13 E n d - f i r e coupling procedure 103 V I . INTEGRATED OPTICAL MACH-ZEHNDER MODULATOR 109 6.1 Y-branch modulator . . . . . . . . . 109 6.2 Design and f a b r i c a t i o n I l l 6.3 Measurement r e s u l t s 112 v i Page V I I . HIGH VOLTAGE SENSOR .' . . . 117 7.1 I n t r o d u c t i o n 117 7.2 Y-branch modulator 118 7.3 BOA modulator 124 7.4 P a r a l l e l l i n e modulator 128 V I I I . SERIES AND MULTIBRANCH INTERFEROMETERS/FILTERS 130 8.1 I n t r o d u c t i o n 130 8.2 Series i n t e r f e r o m e t e r / f i l t e r 130 8.2.1 N interferometers i n s e r i e s 132 8.2.2 Series interferometers w i t h l i n e a r l y i n c r e a s i n g phase r e t a r d a t i o n 135 8.2.3 Experimental r e s u l t s 139 8.2.4 E f f e c t of the i n t r i n s i c phase 144 8.3 Multibranch i n t e r f e r o m e t e r / f i l t e r . . . . 144 8.3.1 N branch interferometer 147 8.3.2 Three branch interferometer w i t h g e o m e t r i c a l l y i n c r e a s i n g electrode lengths 151 8.3.3 Four branch interferometer w i t h g e o m e t r i c a l l y i n c r e a s i n g electrode lengths 153 8.3.4 Experimental r e s u l t s 154 IX. ELECTROOPTIC ANALOG-TO-DIGITAL CONVERTER 160 9.1 I n t r o d u c t i o n 160 9.1.1 E l e c t r o o p t i c d i f f r a c t i o n ADC 161 v i i Page 9.1.2 E l e c t r o o p t i c phased-array d e f l e c t o r ADC . . . . 161 9.1.3 O p t i c a l ADC with Mach-Zehnder modulators . . . . 161 9.2 Comparatorless A/D converter 166 9.3 Design parameters of a 4-bit ADC 170 9.3.1 Electrode l e n g t h 170 9.3.2 Electrode capacitance 172 9.3.3 Sign a l sampling er r o r s 173 9.3.4 J i t t e r 173 9.3.5 E l e c t r o o p t i c i n t e r a c t i o n d u r a t i o n e r r o r . . . . 173 9.3.6 O p t i c a l power 174 9.3.7 Measurement r e s u l t s 176 9.4 Branching network 181 9.4.1 Bending and branching l o s s e s 182 X SUMMARY AND CONCLUSIONS 188 REFERENCES 192 APPENDIX A 202 APPENDIX B 207 v i i i LIST OF TABLES Table Page 4.1 Comparison of the p r o p e r t i e s of f i l m s at X = 0.6328 urn f o r TE modes 49 9.1 ADC parameters 175 9.2 Performance of the ADC 181 9.3 The branching network output power r a t i o 185 9.4 Comparatorless ADC output power r a t i o 185 LIST OF FIGURES Figure Page 2.1 Index p r o f i l e perpendicular to the surface (Noda 1980). . . 11 2.2 Index p r o f i l e p a r a l l e l to the surface (Noda 1980) 11 2.3 Li n e a r segment approximation of the index p r o f i l e (Noda 1980) .' 11 2.4 Planar o p t i c a l waveguide 15 2.5 Propagation constants and e l e c t r i c f i e l d d i s t r i b u t i o n s of TE modes (Taylor and Y a r i v 1974) 15 2.6 T y p i c a l org diagram of a d i e l e c t r i c waveguide (Tamir 1979). 15 2.7 TE mode e l e c t r i c f i e l d d i s t r i b u t i o n (Conwell 1973) 16 2.8 O p t i c a l i n t e n s i t y d i s t r i b u t i o n s i n a 3-D waveguide (Noda and Fukuma 1980) 16 2.9 Schematic diagram of a strip-waveguide phase modulator (Kaminow et a l . 1975) 19 2.10 T r a v e l l i n g wave L i N b 0 3 modulator using asymmetric e l e c -trodes ( I z u t s u et a l . 1978) 19 2.11 A d i r e c t i o n a l coupler modulator with t r a v e l l i n g wave electrodes (Kubota et a l . 1980) 21 2.12 Integrated o p t i c a l Mach-Zehnder modulator 21 2.13 Schematic of an e l e c t r o o p t i c d i r e c t i o n a l coupler s w i t c h . . 24 2.14 V a r i a t i o n of power i n the i n i t i a l l y e x c i t e d guide with the propagation length (Papuchon et a l . 1975) 24 2.15 A reversed Ag d i r e c t i o n a l coupler switch (Schmidt and Kogelnik 1976) 26 2.16 (a) Corrugated waveguide f i l t e r , and i t s response (Flanders et a l . 1974) 26 2.17 (a) Phase-matched e l e c t r o o p t i c TE++TM c o n v e r t e r / f i l t e r ; and (b) measured conversion e f f i c i e n c y (Alferness 1981). . . . 30 x Figure Page 2 . 1 8 The d i r e c t i o n a l coupler f i l t e r : (a) schematic r e p r e s e n t a t i o n ; waveguide d i s p e r s i o n ; and f i l t e r response ( A l f e r n e s s 1 9 8 1 ) 3 2 3 . 1 Schematic r e p r e s e n t a t i o n of a generalised tapered transmission l i n e 3 5 3 . 2 Schematic r e p r e s e n t a t i o n of an e x p o n e n t i a l l y tapered l i n e . 3 5 3 . 3 Cross-section of a planar waveguide and i t s equivalent transmission l i n e r e p r e s e n t a t i o n 4 1 4 . 1 Location of the loading f i l m on the Mach-Zehnder modulator 4 6 4 . 2 (a) Equivalent transverse network, and (b) c o n f i g u r a t i o n of an o p t i c a l waveguide loaded by a f i l m 46 4 . 3 A p p l i c a t i o n of the e f f e c t i v e index method; (a) representa-t i o n of the waveguide under c o n s i d e r a t i o n , ( b ) , (c) planar waveguide and e f f e c t i v e i n d i c e s : w i t h f i l m ( t i j j ) and without f i l m ("in), ( d ) , (e) i n c l u s i o n of the width c o n s t r a i n t ; e f f e c t i v e i n d i c e s : w i t h f i l m n z f and without f i l m n z a 5 7 4 . 4 Roots of ( 4 . 2 7 ) , which correspond to e f f e c t i v e i n d i c e s of planar waveguide modes; with f i l m F^ and without f i l m F J - J - . 6 0 4 . 5 E f f e c t i v e index n 2 vs. d, f o r planar ( n ^ ^ ) and f i n i t e width waveguide ( n z > < ) ; w i t h and without f i l m 6 1 4 . 6 Mode c u t - o f f curves f o r waveguides 3 and 4 ym wide . . . . 6 3 4 . 7 E f f e c t i v e index n z v s . d, w i t h w as parameter; f o r T E Q 0 and TE n modes 6 4 4 . 8 Change i n the propagation constant as a f u n c t i o n of l o a d i n g f i l m t h i c k n e s s , w i t h An as parameter 65 4 . 9 Change i n e f f e c t i v e index 6n z due to loading f i l m thickness t , w i t h the f i l m index n j as parameter 66 4 . 1 0 Change i n e f f e c t i v e index due to loading f i l m ; 6n z v s . An, w i t h f i l m thickness as parameter 6 7 4 . 1 1 Change i n the e f f e c t i v e index due to a loading f i l m ; An z v s . d, w i t h An as parameter 6 8 4 . 1 2 Applied t r i a n g u l a r voltage and the modulator response before treatment i n oxygen 7 0 x i Figure Page 4.13 Applied t r i a n g u l a r voltage and the modulator response a f t e r 11 minutes of treatment i n oxygen; i|;=dll 0 70 4.14 Applied t r i a n g u l a r voltage and the modulator response a f t e r 52 minutes of treatment i n oxygen; ^=400° 71 5.1 A flow chart f o r the f a b r i c a t i o n process 73 5.2 Line drawings of (a) s t r a i g h t waveguide and the Mach-Zehnder modulator 74 5.3 F a b r i c a t i o n steps; developing, e t c h i n g , d i f f u s i n g s p u t t e r i n g , and m e t a l l i z i n g 77 5.4 J i g to hold the wafer; (a) s t a t i o n a r y and (b) spinning . . 80 5.5 Arrangement f o r c a r r y i n g out the d i f f u s i o n 80 5.6 The d i f f u s i o n c y c l e 82 5.7 Arrangement f o r L i 2 0 compensation during d i f f u s i o n . . . . 84 5.8 Computed curves of S i 0 2 on S i 87 5.9 Sputtered Ta over the T i i n d i f f u s e d waveguide and between A l , p r i o r to A l l i f t - o f f 87 5.10 Photograph of the d i f f u s e d waveguides and the electrode p a t t e r n ; m a g n i f i c a t i o n : (a) 14X; and (b) 280X 89 5.11 Mounting of the c r y s t a l i n pr e p a r a t i o n f o r c u t t i n g . . . . 91 5.12 Mounting of a c r y s t a l piece before p o l i s h i n g 94 5.13 Arrangement to view the c r y s t a l edge 94 5.14 The c r y s t a l a f t e r g r i n d i n g ; m a g n i f i c a t i o n : 140X 95 5.15 The c r y s t a l a f t e r p o l i s h i n g w i t h 9 pm diamond paste f o r 90 minutes; m a g n i f i c a t i o n : 140X 95 5.16 The c r y s t a l edge a f t e r p o l i s h i n g w i t h 9 ym diamond paste f o r 3 1/2 hours; m a g n i f i c a t i o n : (a) 14X; and (b) 140X. . . 97 5.17 The c r y s t a l edge a f t e r p o l i s h i n g w i t h 6 pm diamond paste m a g n i f i c a t i o n : (a) 140X; and (b) 280X 99 5.18 The c r y s t a l edge a f t e r p o l i s h i n g w i t h (a) 1 ym paste, 560X; and (b) 1/4 ym paste, 560X 100 x i i Figure Page 5.19 Measurement set-up 104 5.20 Photograph of the experimental set-up. 105 5.21 Output l i g h t p a t t e r n as the microscope o b j e c t i v e and the c r y s t a l are adjusted to d i s p l a y the guided l i g h t 107 6.1 Applied t r i a n g u l a r voltage (8 V p ) and the output l i g h t i n t e n s i t y of the Mach-Zehnder modulator; V.,=4 V, ^=180°. . 113 6.2 Applied t r i a n g u l a r voltage (20 V ) and the output l i g h t i n t e n s i t y of the Mach-Zehnder modulator. 113 6.3 Applied t r i a n g u l a r voltage (24 V p p ) and the output l i g h t i n t e n s i t y of the Mach-Zehnder modulator 114 6.4 Applied s i n u s o i d a l voltage (20 V ) and the output l i g h t i n t e n s i t y of the Mach-Zehnder modulator . . . . . 114 6.5 V a r i a t i o n of the e x t i n c t i o n r a t i o R, with i n c r e a s i n g s i g n a l xE^ i n one arm of the modulator 116 7.1 Schematic of an o p t i c a l E - f i e l d detector (Erickson 1979) . 119 7.2 Scheme f o r o p t i c a l measurement of high voltage 120 7.3 Y-branch modulator as a hgh voltage sensor 120 7.4 Y-branch modulators w i t h various arm separ a t i o n s : (a) 88 um; (b) 98 um; and (c) 108 um 122 7.5 Performance of the Y-branch modulator with 88 um separation; w i t h a p p l i e d t r i a n g u l a r voltage (5 V p p ) . . . . 123 7.6 Applied t r i a n g u l a r voltage (20 V p p ) and the output l i g h t i n t e n s i t y of the Y-branch modulator with 88 um arm separation 123 7.7 BOA modulator w i t h e l e c t r o d e s 125 7.8 BOA modulator as a high voltage sensor 125 7.9 Applied t r i a n g u l a r voltage (30 V ) and the output l i g h t i n t e n s i t y of the BOA modulator out of one arm only . . . . 127 7.10 Applied t r i a n g u l a r voltage (15 V ) and the output l i g h t i n t e n s i t y of the BOA modulator out of one arm onl y , i n (a) 10 kV f i e l d , and (b) no f i e l d 127 x i i i Figure Page 7.11 P a r a l l e l l i n e modulator: (a) i s o m e t r i c view; and (b) top view 129 8.1 (a) Interferometer composed of N e l e c t r o o p t i c modulators i n s e r i e s 131 8.1 (b) I n t e r f e r o m e t r i c f i l t e r composed of N Mach-Zehnder interferometers i n s e r i e s 131 8.2 P l o t of s e r i e s f i l t e r response w i t h N=l and N=3 134 8.3 R e l a t i v e i n t e n s i t y of s e r i e s i n t e r f e r o m e t e r / f i l t e r ; 9 i s change i n angle from the p r i n c i p a l maxima 136 8.4 ( a ) , (b) and ( c ) : Modulator c o n f i g u r a t i o n s ; and (d) r e l a t i v e output i n t e n s i t y f o r the three c o n f i g u r a t i o n s . . 138 8.5 Two inte r f e r o m e t e r s In s e r i e s 140 8.6 Applied t r i a n g u l a r voltage (20 V p p ) and the output l i g h t i n t e n s i t y of two interferometers In s e r i e s 141 8.7 Applied t r i a n g u l a r voltage (30 V p ) and the output l i g h t i n t e n s i t y of two interferometers In s e r i e s 141 8.8 Applied t r i a n g u l a r voltage (40 V p p ) and the output l i g h t i n t e n s i t y of two interferometers i n s e r i e s 142 8.9 Applied s i n u s o i d a l voltage (40 V p ) and the output l i g h t i n t e n s i t y of two interferometers In s e r i e s 143 8.10 R e l a t i v e i n t e n s i t y I Q / I ± as a f u n c t i o n of v o l t a g e , w i t h A\p as parameter 145 8.11 E l e c t r o o p t i c multibranch i n t e r f e r o m e t e r 146 ' 8.12 V a r i a b l e length multibranch i n t e r f e r o m e t r i c f i l t e r . . . . 146 8.13 R e l a t i v e i n t e n s i t y of multibranch interferometer or a f i l t e r ; 6 i s change i n angle from the p r i n c i p a l maxima . . 149 8.14 A comparison of the FWHM bandwidth of the s e r i e s (m=N) and the multibranch (m=N-l) interferometers 150 8.15 A three branch interferometer w i t h g e o m e t r i c a l l y i n c r e a s i n g e l e c t r o d e lengths 152 8.16 A four branch interferometer w i t h g e o m e t r i c a l l y i n c r e a s i n g e l e c t r o d e lengths 152 x i v Figure Page 8.17 Comparison of N=2, 3 and 4 branch interferometers w i t h 2 NL e l e c t r o d e lengths 155 8.18 A three branch Interferometer 156 8.19 A p p l i e d t r i a n g u l a r voltage on the short electrode of the three branch i n t e r f e r o m e t e r and the output l i g h t i n t e n s i t y 157 8.20 A p p l i e d t r i a n g u l a r voltage on the long electrode of the three branch modulator and the output l i g h t i n t e n s i t y . . . 157 8.21 Applied t r i a n g u l a r voltage on both electrodes of the three branch interferometer and the output l i g h t i n t e n s i t y . . . 158 9.1 (a) E l e c t r o o p t i c d i f f r a c t i o n modulator; (b) Sequential t r a n s f e r c h a r a c t e r i s t i c s and threshold l e v e l s (c) Experimental arrangement (Wright et a l . 1974) . . . . 162 9.2 (a) L i g h t d e f l e c t o r w i t h apodized e l e c t r o d e s ; (b) P o s i t i o n of the d e f l e c t e d spot w i t h d r i v e voltage as a parameter (Saunier et a l . 1977) . 163 9.3 (a) Schematic diagram of a 4-bit A/D converter; (b) I n t e n s i t y vs. voltage w i t h Gray sc a l e output (Taylor et a l . 1978) 165 9.4 (a) Output l i g h t i n t e n s i t y v a r i a t i o n of a s i n g l e modulator; (b) output of the comparator; and (c) approximation of the rectangular wave by three s i n u s o i d s 168 9.5 S i n g l e c e l l of an A/D converter i n c o r p o r a t i n g three ^ modulators 171 9.6 Schematic diagram of a 4 - b i t A/D converter 9.7 Equivalent c i r c u i t f o r the modulator c i r c u i t r y 171 9.8 Waveguide s t r u c t u r e and the electrode p a t t e r n of the comparatorless A/D converter 177 9.9 Applied t r i a n g u l a r voltage and the output l i g h t i n t e n s i t y of the comaratorless A/D converter; (a) f i r s t harmonic, (b) t h i r d harmonic, (c) f i f t h harmonic, and (d) composite I Q . 178 9.10 (a) The branching network and (b) the A/D converter waveguide s t r u c t u r e 183 9.11 Two p a r a l l e l waveguides j o i n e d by a s t r a i g h t segment . . . 183 xv Figure Page 9.12 The branching network 187 B . l Flow chart of FORTRAN IV program to compute change i n the propagation constant of waveguide when loaded w i t h f i l m . . 207 i xv I ACKNOWLEDGEMENT I thank my s u p e r v i s o r Dr. L. Young, f o r s u p p o r t , guidance and encouragement during the course of t h i s work. I am obl i g e d to Dr. D.J. Smith f o r e l l i p s o m e t r y , and f o r many i n t e r e s t i n g and productive d i s c u s s i o n s . I thank Drs. T.R. Ranganath, R.V. Schmidt, G. Raimier, S. Jensen and G.L. Tangonan f o r a tour of Hughes Research L a b o r a t o r i e s , M a l i b u , and poin t e r s on making o p t i c a l waveguides. I am g r a t e f u l to Mr. B. Cranston f o r suggestions on p o l i s h i n g , and to Mr. A. L a c i s f o r doing the e l e c t r o n microprobe a n a l y s i s . The experimental set-up was made by Mr. J . Stuber. Mr. K.S. Lowe prepared the r u b y l i t h and Mr. L. Jones the devices f o r the HV Sensor. I thank Dr. D. P u l f r e y f o r the platinum f o i l , and Mr. T. Lester f o r l o a n of the wafer f i x t u r e . I w i s h t o e x p r e s s my a p p r e c i a t i o n to Mrs. Kathy Brindamour and Mrs. G a i l Schmidt f o r typing the t h e s i s . Moral support by my f r i e n d s , mother, f a t h e r and wife made the work e a s i e r . F i n a n c i a l support by NSERC and the B.C. Science Council i s g r a t e f u l l y acknowledged. x v i i 1 CHAPTER I INTRODUCTION The term i n t e g r a t e d o p t i c s [ M i l l e r 1969] r e f e r s to devices i n which c i r c u i t f u n c t i o n s are achieved using l i g h t i n s t e a d of electrons and holes of conventional i n t e g r a t e d c i r c u i t s . Various r e a l i z a t i o n s of t h i s concept have been proposed. One c l a s s of c i r c u i t s i s based on using semiconductors such as GaAs. In the present work T i i n d i f f u s e d waveguides i n LiNbQj are used to form the devices. Semiconductors GaAs and InP are used to make l a s e r s and o p t i c a l waveguides, but L i N b 0 3 and LiTaOg to make more e f f i c i e n t modulators and switches. One method of making waveguides i s by d i f f u s i n g T i i n t o LiNbOg. A t y p i c a l T i : L i N b 0 3 s i n g l e mode waveguide i s 3 ym wide and 2 ym deep. L i g h t can be coupled i n t o and out of the waveguide by the use of prisms, g r a t i n g s , lenses and f i b r e s . In the f u t u r e , the emphasis w i l l be on coupling l i g h t by the butt j o i n i n g of l a s e r diodes or s i n g l e mode f i b r e s to i n t e g r a t e d o p t i c a l devices {Hsu et a l . 1977; Boyd and Sriram 1978; Campbell 1979; Saruwatari and Nawata 1979]. With the development of low l o s s (0.5 dB at 1300 nm) o p t i c a l f i b r e s and s o l i d s t a t e l a s e r s , the need f o r integrated o p t i c a l devices to perform modulation, switching and f i l t e r i n g e t c . i s i n c r e a s i n g . The main advantages i n t e g r a t e d o p t i c a l devices would o f f e r are very high speed (GHz), m i n i a t u r i z a t i o n , low power consumption, and l e s s weight. Losses and o p t i c a l damage In i n t e g r a t e d o p t i c a l devices are two problem areas. The f i b r e to 2 waveguide coupling l o s s i s > 1 dB, and the waveguide propagation l o s s i s 1 dB/cm. Bends, d i r e c t i o n a l changes, and f u r c a t i o n s i n the waveguide network produce s c a t t e r i n g l o s s e s . Branching angles of 1-2° that are required to keep the l o s s below 3 dB, make the devices long and l i m i t the number of components that can be accommodated on a s u b s t r a t e . The waveguides are s u s c e p t i b l e to o p t i c a l damage even at a power l e v e l of 0.1 mW due to large power d e n s i t y , > 1 kW/cm2. Although I n t e g r a t i o n of the l i g h t source and s e v e r a l i n t e g r a t e d o p t i c a l devices on a common substrate has not been r e a l i z e d so f a r , i n the i n t e g r a t e d o p t i c a l spectrum analyzer [Anderson 1978], and the multichannel data processor [Vahey et a l . 1978], s e v e r a l components have been s u c c e s s f u l l y i n t e g r a t e d . A l a r g e number of i n t e g r a t e d o p t i c a l devices l i k e couplers [ M a r c a t i l i 1969; Somekh et a l . 1973], switches [Schmidt and Kogelnik 1976; Kogelnik and Schmidt 1976], modulators [Kaminow 1975; M a r t i n 1975; Kubota et a l . 1980], d e f l e c t o r s [Tsai and Saunier 1975; Bulmer et a l . 1979], and f i l t e r s [Flanders et a l . 1974] have been developed. In t h i s t h e s i s i n t e g r a t e d o p t i c a l devices i n v e s t i g a t e d are; a high voltage sensor, i n t e r f e r o m e t r i c f i l t e r s / m o d u l a t o r s , and a comparatorless A/D converter. In a d d i t i o n , adjustment of the propagation constant of a waveguide by f i l m l o a d i n g i s achieved. A review of o p t i c a l waveguides and i n t e g r a t e d o p t i c a l devices i s given In Chapter I I . Progress i n switches, c o u p l e r s , modulators and f i l t e r s i s covered. An input impedance equation, f o r a complex impedance transformed through an e x p o n e n t i a l l y tapered transmission l i n e Is derived i n Chapter I I I . I t i s used to o b t a i n a c h a r a c t e r i s t i c equation f o r the propagation constant of a 3 l i n e a r l y graded o p t i c a l waveguide. The "transverse resonance" method i s used. Some i n t e g r a t e d o p t i c a l modulators and couplers depend on the path length to perform p r o p e r l y , c o n t r o l l i n g i t to f r a c t i o n of guide wavelength i s i m p r a c t i c a l . So there i s a need f o r a means to adjust the propagation constant or the e f f e c t i v e length of the waveguide, [Mikami et a l . 1977; Mikami and Zembutsu 1979 ]. For example, when the two arm lengths i n the i n t e g r a t e d o p t i c a l Mach-Zehnder modulator (Chapter VI) are not equal, then i n the absence of a p p l i e d voltage the output i n t e n s i t y i s not maximum and the i n t r i n s i c phase d i f f e r e n c e T\>*0. Phase tuning, that i s , adjustment of the propagation constant i s needed to s h i f t \p or the operating p o i n t . In order to e s t a b l i s h the propagation constant requirements to solve the phase tuning problem, r e s u l t s of Chapter I I I are used to model a d i f f u s e d waveguide loaded w i t h a f i l m . In Chapter IV, numerical r e s u l t s on a T a 2 0 5 f i l m l oading a T i : L i N b 0 3 d i f f u s e d waveguide at 0.6328 ym are given. Heating i n 0 2 of a T a 2 0 5 f i l m , which loads one arm of the Mach-Zehnder modulator i s used to modify the e f f e c t i v e arm length and hence the i n t r i n s i c phase of the modulator. The f a b r i c a t i o n procedure f o r T i d i f f u s e d waveguides i n L i N b 0 3 i s described i n Chapter V. A p o l i s h i n g technique to obt a i n defect free edge to f a c i l i t a t e end f i r e coupling i s presented. An A l l i f t - o f f procedure, to form a sputtered Ta loading f i l m on a d i f f u s e d guide, i s described. A d e s c r i p t i o n of the measurement set-up, and the alignment procedure f o r the l a s e r , l e n s , c r y s t a l and the detector i s i n c l u d e d . Design and performance of the i n t e g r a t e d o p t i c a l Mach-Zehnder modulator i s reviewed i n Chapter V I . 4 An a p p l i c a t i o n of the i n t e g r a t e d o p t i c a l devices to high voltage (HV) measurement i s discussed i n Chapter V I I . In p a r t i c u l a r , a use of the Mach-Zehnder modulator w i t h 88-108 um arm separation i s considered. A l s o , the performance of a two-mode (BOA) modulator, i s described. An int e r f e r o m e t e r composed of two p a r a l l e l , contiguous, but uncoupled waveguides, only one of which i s e l e c t r o o p t i c , i s proposed f o r the HV sensing. A compression of the passband of an i n t e r f e r o m e t r i c modulator, i s p r o p o s e d by use of t h e s e r i e s and m u l t i b r a n c h i n t e r f e r o m e t r i c f i l t e r s / m o d u l a t o r s ; Chapter V I I I . An expression f o r the output i n t e n s i t y of N N s e r i e s i n t e r f e r o m e t e r s , w i t h 2 L length f o r the Nth electrode i s d e r i v e d . The measured f u l l width h a l f maximum (FWHM) bandwidth of a two s e c t i o n i n t e r f e r o m e t e r agrees w e l l w i t h the theory. S i m i l a r l y , an equation f o r the output i n t e n s i t y of a multibranch f i l t e r / m o d u l a t o r , w i t h NL length f o r the Nth el e c t r o d e Is obtained. The measured performance compares f a v o r a b l y w i t h the computed ones. Such f i l t e r s are voltage tunable. An e l i m i n a t i o n of e x t e r n a l comparators, from the e l e c t r o o p t i c A/D converter (ADC) u t i l i z i n g the Mach-Zehnder modulators Is proposed i n Chapter IX. The comparators (maximum bandwidth 300 MHz) l i m i t the p o t e n t i a l speed, 1-2 GHz, of the above ADCs. Each comparator i s replaced by three modulators. A design of a 4-bit comparatorless ADC i s given. The measured performance of a c i r c u i t to produce 1 b i t i s encouraging. The design and performance of a three branch network used i n conjunction w i t h the three modulators i s disc u s s e d . 5 CHAPTER I I A REVIEW OF INTEGRATED OPTICS 2.1 I n t r o d u c t i o n The previous work on o p t i c a l waveguides, i n t e g r a t e d e l e c t r o o p t i c modulators, switches, and f i l t e r s i s reviewed. These components are l i k e l y to be used i n o p t i c a l communication systems to perform modulation, m u l t i p l e x i n g , d e m u l t i p l e x i n g and f i l t e r i n g of s i g n a l s . Various f a c t o r s a f f e c t i n g the f a b r i c a t i o n of T i : L i N b 0 3 waveguides are discussed. Sin g l e mode waveguides are needed f o r e f f i c i e n t modulation. The e f f e c t i v e index method to estimate the parameters of a s i n g l e mode waveguide i s reviewed. E x t e r n a l modulators w i t h up to 10 GHz bandwidth have been demonstrated [ I z u t s u et a l . 1978], Such modulators are l i k e l y to replace d i r e c t modulation of l a s e r diodes, since the d i r e c t modulation r a t e i s l i m i t e d to < 1 GHz. The modulation r a t e could be extended to 2 GHz, i f the s e l f - p u l s a t i o n s and the r e l a x a t i o n o s c i l l a t i o n s i n the l a s e r diode could be suppressed [Arnold et a l . 1980]. The subject of i n t e g r a t e d o p t i c s has been reviewed f r e q u e n t l y ; [Tien 1971; Marcuse 1973a; Taylor and Y a r i v 1977; Tamir 1977; Y a r i v 1979; Botez and Herskowitz 1980; A l f e r n e s s 1981; Noda 1981]. 2.2 O p t i c a l waveguides Schmidt and Kaminow (197A) reported metal ( T i , N i and V) i n d i f f u s e d o p t i c a l waveguides i n L i N b 0 3 . With t h i s technique, the waveguide depth and width can be c o n t r o l l e d to form s i n g l e mode waveguides. Planar and three 6 dimensional waveguides have been demonstrated using f i l m s on substrates [ G o e l l 1969; Tien et a l . 1969; Tien 1971; U l r i c h and Weber 1972]. Planar waveguides, formed by o u t d i f f u s i o n of L i 2 0 from L i N b 0 3 produce only a small change i n index (An = 0.003) between the guide and the substrate Index. Due to the lar g e d i f f u s i o n depth (500 ym), as many as 198 modes can be supported [Kaminow and Carruthers 1973]. The T i d i f f u s i o n i n t o L i N b 0 3 produces a An as much as 0.04, and i t can be c o n t r o l l e d by the metal t h i c k n e s s . The depth of the waveguide can be c o n t r o l l e d by the d i f f u s i o n time and temperature. I t has been found that [Noda 1980] 2 + valence s t a t e ions increase the e x t r a o r d i n a r y i n d e x n g ; NiO and ZnO i n c r e a s e the o r d i n a r y index n Q , but MgO [Noda et a l . 1978a] d e c r e a s e s i t . However, > 2 + v a l e n c e s t a t e ions increase n and n . ' e o Fe*1" and Cr3"*" replace L i , but T i * * + replaces Nb 5* or T a ^ [Noda 1980]. T y p i c a l propagation l o s s i n a T i d i f f u s e d waveguide i s 1 dB/cm and 0.5 dB/cm at 0.6328 ym and 1.153 um r e s p e c t i v e l y . There i s no increase i n abso r p t i o n , 0.1 dB/cm at 1.15 ym, of bulk L i N b 0 3 due to the presence of T i . So, a low propagation l o s s should a l s o be p o s s i b l e f o r a T i d i f f u s e d waveguide [Alfe r n e s s 1980]. Use of t h i n (<300 A) T i l a y e r s , and removal of the undif f u s e d T i 0 2 from the c r y s t a l surface have been found to reduce s c a t t e r i n g [Vahey 1980]. A s i n g l e mode waveguide can be formed by the d i f f u s i o n of 300 A t h i c k and 3 ym wide T i s t r i p , i n t o L i N b 0 3 f o r 6 hours, at 1020°C, i n 0 2. Some problems i n forming T i : L i N b 0 3 waveguides, are: 1. L i , 0 o u t d i f f u s i o n [Miyazawa 1977; Burns et a l . 1978; Ranganath and - 2 * -Wang 1979] 7 2. Phase transformation [Vahey 1980] 3. Domain i n v e r s i o n [Miyazawa 1979] 4. Microdefects [Ramaswamy and Standley 1975] During metal d i f f u s i o n i n t o L i N b 0 3 around 1000°C, L i escapes as L i 2 0 . The l o s s of L i i n c r e a s e s n g . As a r e s u l t , a g u i d i n g l a y e r c a p a b l e of supporting a la r g e number of unwanted modes i s formed. This problem can be solved by d i f f u s i n g T i i n the presence of L i N b 0 3 powder [Burns et a l . 1978a; Ranganath and Wang 1979], Although L i C 0 3 has been used s u c c e s s f u l l y , i t requires longer compensation time [Miyazawa et a l . 1977]. Recently, i n an attempt to h e a l the o p t i c a l damage, i t was discovered that by exposing a hot c r y s t a l to moisture laden 0 2, o u t d i f f u s i o n was suppressed [Ja c k e l et a l 1981a; 1981b]. In the devices made f o r t h i s work, L i 2 0 d e f i c i e n c y was compensated by c a r r y i n g out d i f f u s i o n f o r 4.5 hours without the L i N b 0 3 powder, and 1.5 hour w i t h the powder. Phase transformation to L i N b 3 0 g can occur near 850° f o l l o w i n g d i f f u s i o n at ~ 1000°C [Vahey 1980], This can produce surface c r a t e r s and scratches and c o n t r i b u t e to s c a t t e r i n g l o s s e s . The damage can be minimized by a r a p i d passage through 850°C during heating and c o o l i n g . Domain i n v e r s i o n can occur i n T i d i f f u s e d i n the +c plane, at temperatures exceeding 1020°C. T h i s , and the degradation of the e l e c t r o o p t i c c o e f f i c i e n t i s ascribed to a lowering of the Curie temperature [Miyazawa 1979], Thus, T i - d i f f u s e d waveguides i n Z-cut L i N b 0 3 should be formed i n the -c plane. The problem of m i s f i t - d i s l o c a t i o n s , and microcracks running p a r a l l e l and perpendicular to the c-axis are due to the s t r e s s created by the T i d i f f u s i o n [Ramaswamy and Standley 1975]. 8 2.2.1 O p t i c a l damage When v i s i b l e l i g h t at power d e n s i t i e s of 1-10 kW/cm2 i s fed i n t o a waveguide, the near f i e l d l i g h t p a t t e r n changes [Tangonan et a l . 1977]. This phenomenon i s known as o p t i c a l damage or the p h o t o r e f r a c t i v e e f f e c t . While i t has been u t i l i z e d f o r w r i t i n g holograms [Young et a l . 1974; Vahey et a l . 1978], i t has d e l e t e r i o u s e f f e c t on other i n t e g r a t e d o p t i c a l devices w i t h narrow waveguides. For example, i t degrades the c r o s s - t a l k of the coupler-switch [Schmidt et a l . 1980], and i t produces d r i f t i n the output of Mach-Zehnder modulator [Sasaki 1977], L i N b 0 3 has the same value f o r the r 3 3 e l e c t r o o p t i c c o e f f i c i e n t as L i T a 0 3 , but i t s o p t i c a l t h r e s h o l d , ~ 100 W/cm2, i s only 0.01 of L i T a 0 3 . The Curie temperature of L i N b 0 3 i s 1125°C, but that of LiTaOg i s only 600°, so t h a t , r e p o l i n g of L i T a 0 3 i s necessary a f t e r the d i f f u s i o n at ~ 1000°C. Recent work on the formation of 0.5 dB/cm l o s s o p t i c a l waveguides by Ag and L i exchange at 250°C would e l i m i n a t e L i 2 0 o u t d i f f u s i o n and r e p o l i n g problems [ J a c k e l 1980]. One l i m i t a t i o n of t h i s method i s that waveguides can be formed only i n X-cut L i N b 0 3 and L i T a 0 3 c r y s t a l s . This would s t i l l permit u t i l i z a t i o n of r 3 3 . 2.2.2 D r i f t phenomenon The output of an i n t e g r a t e d o p t i c a l device, such as a Mach-Zehnder modulator, can d r i f t at constant dc bia s [Sasaki 1977]. One p o s s i b l e source of the short term d r i f t i s an incomplete o x i d a t i o n of the SiO^ or A 1 2 0 3 b u f f e r l a y e r between the c r y s t a l and the electrodes [Tangonan et a l . 1978]. The b u f f e r l a y e r i s required to reduce l o s s , p a r t i c u l a r l y to the TM mode. The d r i f t can be h a l t e d by an anneal i n 0 2, or by removal of the b u f f e r l a y e r from 9 the area between the electrode edges and on top of the waveguide. S i 0 2 l a y e r formed by chemical vapour d e p o s i t i o n (CVD) works b e t t e r than a sputtered l a y e r . The long term d r i f t i s due to the o p t i c a l damage, and i t i s v i r t u a l l y absent at wavelengths exceeding 1 um. 2.3 Waveguide a n a l y s i s An a n a l y s i s of waveguides i s necessary to estimate the parameters of a s i n g l e mode waveguide, and to compute modulation e f f i c i e n c y . The modulation e f f i c i e n c y i s determined by overlap of the o p t i c a l and the a p p l i e d e l e c t r i c f i e l d s . The number of modes a waveguide can support and the c u t - o f f c o n d i t i o n s , are determined by the waveguide depth and width, and r e f r a c t i v e i n d i c e s of the s u b s t r a t e (n ) and the waveguide ( n f ) . In g e n e r a l , the r e f r a c t i v e index of S J -the guide v a r i e s i n the transverse d i r e c t i o n . Waveguides w i t h various p r o f i l e s have been analyzed; l i n e a r [Chen et a l . 1974], p a r a b o l i c [Tamir 1979], exponential [Conwell 1973], e t c . Exact s o l u t i o n f o r the propagation constant, i s p o s s i b l e only f o r two p r o f i l e s , namely, the exponential, and the Morse. For other index p r o f i l e s , approximate methods l i k e the WKB [Marcuse 1973b; Hocker and Burns 1977], transverse F-matrix method [Suematsu and Furuya 1972], and the v a r i a t i o n a l method [Geshiro et a l . 1978] must be used. The WKB approximation y i e l d s r e s u l t s w i t h a 1 0 - 5 accuracy r e l a t i v e to the exact method f o r the exponential p r o f i l e . 10 2.3.1 WKB and the e f f e c t i v e Index method [Noda 1980] The WKB approximation i n conjunction with the e f f e c t i v e index method [Hocker and Burns 1977] i s a p p l i e d to a waveguide loaded w i t h a f i l m of r e f r a c t i v e i n d e x n^ and t h i c k n e s s t . The r e f r a c t i v e i n d e x p r o f i l e f o r a waveguide confined i n both of the transverse dimensions i s , n(x,y) = n + An f ( x / d ) g(y/d ) (2.1) where, n i s the i s o t r o p i c s u b s t r a t e r e f r a c t i v e i n d e x , An (=n -n ) i s the ' s O S maximum change i n r e f r a c t i v e index at the surface, f ( x / d x ) i s the r e f r a c t i v e index p r o f i l e f u n c t i o n perpendicular to the surface, and g(y/dy) p a r a l l e l to i t . Terms d and d are the d i f f u s i o n l e n g t h s . The index p r o f i l e during x y d i f f u s i o n i s i n i t i a l l y e r f c , and Gaussian l a t e r on. Representative index p r o f i l e s are shown i n F i g . 2.1 and 2.2. With the WKB approximation and the e f f e c t i v e index method, the x - a x i a l mode di s p e r s i o n equation i s , k / X t [ n 2 ( x ) - n 2 ] 1 / 2 d x = (p + 1/4) T T + $ (2.2) o n(x) = n + An f ( x / d ) = n(x»o) (2.3) S X <), = t a n _ 1 [ n ( P /P,:)R] (2.4) a t £P a/P f - t a n * ( P f t ) R = 1 + £(Pa/Pf)tan*(Pft) ( 2' 5> P ± = k ( | n j - *X\V'> i = a,f For TE modes; n = £ = 1 2,,1/2 , = a f (2.6) (2.7) F i g . 2.3. L i n e a r segment approximation of the index p r o f i l e (Noda 1980). 12 2 2 For TM modes; n = (n /nf) , E, = n (2.8) a x a Here, k = 2TT/X i s the free space wavenumber, x^ i s the turning p o i n t , n and o t a n^ are r e f r a c t i v e i n d i c e s of a i r and the l o a d i n g f i l m , and p i s the mode number. And tan* = tan f o r n^ > n ( o ) , but tan* = tanh f o r n^ < n ( o ) . I n the absence of a loading f i l m , t = 0, An/n i s s m a l l , and n(o) » n , s a 2 2 1/2 so that <f> = n/2. Then (2.2) w i t h k[n (x) - n ] = b ^ x ) becomes, J S j C x ) dx = (p + 0 . 7 5 ) T T , p = 0,1,2,... (2.9) b 2 ( x ) + 32 = k 2 n 2 ( x ) (2.10) and b l ( x t ) = 0 (2.11) For a g i v e n index p r o f i l e n ( x ) , b^(x) can be computed from (2.10) and x t from (2.11). Then the I n t e g r a l i n (2.9) can be c a l c u l a t e d f o r any value of 6 [Tien et a l . 1971]. Values of $ are d i s t i n c t f o r d i f f e r e n t modes. For an e x p o n e n t i a l p r o f i l e [Conwell 1973], An = 0.043, n = 2.177, and d = 0.931 pm, s f o r the two p o s s i b l e modes, B= 2.1899 and 2.1790. For a waveguide with uniform r e f r a c t i v e index b ^ = (q + -J-)* + <t> (2.12) When the waveguide i s not planar but has a width 2w, the y - a x i a l mode d i s p e r s i o n equation, assuming step r e f r a c t i v e index i s , [Noda 1980], k J Y t [ n 2 ( y ) - n 2 ] 1 / 2 d y = (q + n/2) - wS (2.13) 13 S = k [ n 2 ( o ) - n 2 ] 1 / 2 (2.14) n y - n ( x t , y) (2.15) Where, x t i s the t u r n i n g p o i n t , and q the mode number. At the waveguide surface n(o) i s replaced by n^. 2.3.2 Linear segment approximation a n a l y s i s [Noda 1980] The wave equation f o r the e l e c t r i c or magnetic f i e l d G of a planar waveguide along x i s given by, 2 ^ - f + k 2 [ n 2 ( x ) - n 2 ] G = o (2.16) d x 2 X The d e r i v a t i v e of the d i e l e c t r i c constant has been neglected, as the r e f r a c t i v e index v a r i a t i o n i s very gradual w i t h wavelength. By co n s i d e r i n g the index p r o f i l e to be made up of s e v e r a l l i n e a r segments, as shown In F i g . 2.3, the s o l u t i o n s of (2.16) are [Noda and Fukuma 1980]; G = C exp[P (x+t)] -oo < x < - t 3 = A f c o s ( P f x ) + B f s i n ( P f x ) , n f > n ( o ) , - t < x < o = A^ c o s h ( P f x ) + B^ s i n h ( P f x ) , n^ < n ( o ) , - t < x < o = Jwi[Ai J 1 / 3 ( u i ) + B ± J_ 1/ 3( u 1)]» x < x t , x ± < x < x ± + 1 W i " " i " a i ( x " X i } " n x 14 2 2 w, = n - n. + a.(x - x.) j x J J J a i , j = 2 n i , j ( n i , 1 " n i + l , j + l ) / A x u, , = (2k/3a. .) w. . 3 / 2 (2.17) Where, Ax = ( x . ., - x.) i s the l a y e r t h i c k n e s s , and J are the B e s s e l f u n c t i o n s . A, B and C are the amplitude components e s t a b l i s h e d by matching e l e c t r i c or magnetic f i e l d s , and t h e i r d e r i v a t i v e s at l a y e r boundaries. The above r e l a t i o n s are u s e f u l i n estimating the overlap of the o p t i c a l and the a p p l i e d e l e c t r i c a l f i e l d s , and the overlap i n t e g r a l of f i b r e and guide f i e l d s f o r c o upling e s t i m a t i o n . A planar waveguide i s shown i n F i g . 2.4. Various regimes of the propagation constant B, and the corresponding f i e l d d i s t r i b u t i o n s are shown i n F i g . 2.5 and 2.6. When 3 < kn , o n l y the a i r r a d i a t i o n modes are e x c i t e d . W i t h kn < 8 < kn , the s u b s t r a t e r a d i a t i o n modes are supported. For the 3 . S r a d i a t i o n modes, B i s continuous. However, f o r d i s c r e t e 0 i n the range k n g < 6 < k ( n + An), guided modes p r o p a g a t e . In the case of guided modes, the s f i e l d i s n e a r l y s i n u s o i d a l i n the n r e g i o n . I t decays e x p o n e n t i a l l y i n the a i r and substrate regions. The t r a n s i t i o n from s i n u s o i d a l to exponential occurs at the t u r n i n g p o i n t [Conwell 1973]. The smaller the value of 3 the higher the mode, and the l a r g e r i s the distance at which o s c i l l a t o r y behaviour e x i s t s . The number of nodes correspond to the mode order, see F i g . 2.7. A l s o , the wave amplitude increases as the t u r n i n g point i s approached, as shown i n F i g . 2.7. The propagation l o s s i s greater f o r the higher order DISCRETE CONTINUUM *\*~*\< CONTINUUM e d c b a 0 ^ " 'knVlkn'/l /kn^ B x=o X=d X AIR t G GUIDE SUBSTRATE GUIDED FORBIDDEN MODE AIR SUBSTRATE (RADIATION)(RADIATION) MODE MODE F i g . 2.5". Propagation constants and e l e c t r i c f i e l d d i s t r i b u t i o n s of TE modes (Taylor and Y a r i v 1974), m=0 m = l F i g . 2.6. T y p i c a l to-B diagram of a d i e l e c t r i c waveguide (Tamir 1979). 16 DEPTH BELOW SURFACE (ym) F i g . 2.7. TE mode e l e c t r i c f i e l d d i s t r i b u t i o n (Conwell 1973). -4 0 4 x ( p m ) F i g . 2.8. O p t i c a l i n t e n s i t y d i s t r i b u t i o n s i n a 3-D waveguide (Noda and Fukuma 1980) . 17 modes, as i l l u s t r a t e d by the ray model [ T i e n 1971] i n F i g . 2.6. The higher order modes undergo a large number of r e f l e c t i o n s accompanied by s c a t t e r i n g , at the guide boundaries. 2.4 Modulators Modulators are needed i n o p t i c a l communication systems. The informa t i o n i s impressed on the o p t i c a l wave as phase modulation using the l i n e a r e l e c t r o o p t i c e f f e c t . The phase modulation can be converted to i n t e n s i t y modulation through i n t e r f e r e n c e , mode conversion or d i f f r a c t i o n . Two other types of modulators are the waveguide c u t - o f f and the d i r e c t i o n a l coupler modulators. In t h i s s e c t i o n , the strip-waveguide modulator, the coupled guide m o d u l a t o r and t h e Y - b r a n c h i n t e n s i t y m o d u l a t o r a r e r e v i e w e d . 2.4.1 Parameters of a phase modulator Change i n the r e f r a c t i v e index i s given by An = - n r j (2.18) where n i s the r e f r a c t i v e index, r the appropriate e l e c t r o o p t i c c o e f f i c i e n t , V the ap p l i e d voltage and d the electrode gap. The change i n phase <(> due to An, wi t h e l e c t r o d e length L , at free space wavelength X q i s , <(, = n ( y - ) n 3 r J ^ (2.19) o where n i s determined by the o p t i c a l and the e l e c t r i c f i e l d o verlap. The power to d r i v e the capacitance C over bandwidth Af * (irRC) * i s , 18 p = IR = i M cy2 (2,20) Then the power required per bandwidth f o r phase s h i f t $ i s , 2 _ ! _ « 2 C V 2 U _ L . J L l 2 = A . f J _ l f C d 2 l (2 21) — 2 ~ 2 ^ "IT ~ LV' . 2 U 2 ^ T 2 J U ' Z 1 ) Af <j> n n r 2nn n r L This i s a measure of the performance of the modulator, and i t i s u s u a l l y quoted i n mW/MHz r a d 2 . The term l / C n ^ 2 ) i s determined by the m a t e r i a l p r o p e r t i e s , but the term C d 2/L 2 depends on the electrode geometry. 2.4.2 Strip-waveguide modulator The modulator e l e c t r o d e s t r u c t u r e can be a lumped element network or a t r a v e l l i n g wave s t r u c t u r e . In the case of the lumped element v e r s i o n , the bandwidth i s l i m i t e d by the RC product, where R i s the impedance of the system, and C the electrode capacitance. For the phase modulator shown i n F i g . 2.9, the e l e c t r o d e capacitance i s given by [Kaminow et a l . 1975], C = — L (1 + K ) to (42) F (2.22) where L, d and W are the electrode length, gap, and ' outer edge distance r e s p e c t i v e l y , and K i s r e l a t e d to the p r i n c i p a l d i e l e c t r i c constants. The m bandwidth can be increased by using shorter e l e c t r o d e s , but at the expense of higher modulating voltage to achieve the same phase change. The phase modulator shown i n F i g . 2.9 re q u i r e s only 0.3 V/rad and 1.7 uW/MHz r a d 2 at 0.6328 pm. The bandwidth of a lumped element modulator can be t r i p l e d by using a t r a v e l l i n g wave modulator [ I z u t s u et a l . 1977;.1978']. The bandwidth i s l i m i t e d 19 F i g . 2.9. Schematic diagram of a strip-waveguide phase modulator (Kaminow et a l . 1975) . MODULATING SIGNAL F i g . 2.10. T r a v e l l i n g wave LiNb0 3 modulator using asymmetric electrodes ( I z u t s u et a l . 1978) . 20 by the o p t i c a l and the e l e c t r i c f i e l d t r a n s i t time d i f f e r e n c e [ I z u t s u et a l . 1977]; Af = 1.4c/(irL|n r f - n|) (2.23) For L i N b O a n c = Ynn . = 4.3 and n = 2.2, but f o r GaAs n c 2 n so that i r f s a i r ' r f electrode l e n g t h can be increased without s a c r i f i c i n g the bandwidth [Alf e r n e s s 1981]. A t r a v e l l i n g wave phase modulator w i t h a s i n g l e guide i s shown i n F i g . 2.10. The electr o d e s form a microwave coplanar transmission l i n e terminated i n 50ft. For a T i d i f f u s e d modulator i n Y-cut LiNb 0 3 at 0.6328 um, a bandwidth of 10 GHz was achieved [Izutsu et a l . 1977; 1978]. The electrode parameters were; le n g t h = 9.1 mm, width = 35 \im, gap = 55 um, and thickness = 2 um. The e l e c t r o d e l o s s was 3 dB at 10 GHz. The on/off r a t i o was 4.5 dB at 11V. 2.4.3 D i r e c t i o n a l coupler modulator A d i r e c t i o n a l coupler modulator with t r a v e l l i n g wave electrodes i s shown i n F i g . 2.11, [Kubota et a l . 1980]. In order to reduce the electrode l o s s e s , asymmetric 3-um t h i c k A l electrodes were used. The o p t i c a l i n s e r t i o n l o s s was 5.4 dB, the 3 dB bandwidth was 3.6 GHz, the e x t i n c t i o n r a t i o was 17 dB at 1.317 um, and 100% modulation at 4V was obtained. A d i r e c t i o n a l coupler modulator w i t h a l t e r n a t i n g AB with a bandwidth of 1 GHz and r i s e time of 590 ps has been reported [Cross and Schmidt 1979]. SEMIRIGID RF INPUT LIGHT 2.11. A d i r e c t i o n a l coupler modulator w i t h t r a v e l l i n g wave e l e c t r o d e s (Kubota et a l . 1980). F i g . 2.12. Integrated o p t i c a l Mach-Zehnder modulator. 22 2.4.4 Integrated o p t i c a l Mach-Zehnder modulator A Y-branch i n t e n s i t y modulator i s an i n t e g r a t e d o p t i c v e r s i o n of a Mach-Zehnder modulator [Martin 1975]. The two Y's serve as a 3 dB s p l i t t e r and a combiner as shown i n F i g . 2.12. I f the phase of the l i g h t i n one arm of the modulator i s retarded by 180°, then the output i n t e n s i t y i s minimum upon recombination. The output i s maximum with no phase r e t a r d a t i o n . For an e l e c t r o d e gap and l e n g t h of 4 um and 3 mm r e s p e c t i v e l y , a of 4.5 was required at 0.6328 pm, i n Y-cut LiNbOg. The e x t i n c t i o n r a t i o was 98% [Leonberger et a l . 1979], Push-pull c o n f i g u r a t i o n of electrodes i s u s u a l l y employed. A p o l a r i z a t i o n i n s e n s i t i v e modulator has been demonstrated [Burns et a l . 1978b], Use of the modulators as A/D converters [Taylor 1975] and as l o g i c elements [Taylor 1977] has been proposed. The Y-branch modulator i s covered i n greater d e t a i l i n Chapter V I . 2.5 Switches [ A l f e r n e s s 1981] Switches change the s p a t i a l l o c a t i o n of l i g h t i n response to an a p p l i e d v o l t a g e . A p p l i c a t i o n s of switches includ e time d i v i s i o n m u l t i p l e x i n g and d e m u l t i p l e x i n g , i n order to b e t t e r u t i l i z e the bandwidth c a p a b i l i t y of o p t i c a l systems by combining s e v e r a l low b i t ra t e s i g n a l s . Switches have a l s o been used as ADCs and modulators. A 2 x 2 switch has two output and two input p o r t s . The performance c r i t e r i a of a good switch are; low i n s e r t i o n l o s s , small s w i t c h i n g v o l t a g e , i s o l a t i o n or low c r o s s t a l k , and high speed. Two types of switches a r e , the d i r e c t i o n a l coupler switch and the balanced modulator s w i t c h . 23 2.5.1 D i r e c t i o n a l coupler switch A coupler switch c o n s i s t s of two p a r a l l e l waveguides, separated by a gap g, over a l e n g t h L, along which two c o d i r e c t i o n a l coupled waves propagate. A schematic diagram of a t y p i c a l device i s shown i n F i g . 2.13, i t has been analyzed e x t e n s i v e l y [ M a r c a t i l i 1969; Somekh et a l . 1973; Taylor 1973; Tamir 1979]. In a coupler, the two guides are such that t h e i r propagation constants Bj and 8 2 are equal, the gap g i s small so that the evanescent f i e l d s o v e r l a p , and L i s l o n g . The l i g h t R q that i s i n i t i a l l y i n guide 1 gets t r a n s f e r r e d to guide 2 a f t e r t r a v e l l i n g d i s t ance L, and back to guide 1 a f t e r a d d i t i o n a l distance L, and so on. Here, L the c r i t i c a l l e ngth i s given by L = H / 2 K (2.24) Where K i s the co u p l i n g / u n i t l e n g t h , determined by the waveguide parameters, gap g, and the wavelength. When the two guides are not phase-matched, Ag = 3 2 - 6X = k ( N 2 - Nj) = 25 where N j , N 2 are the e f f e c t i v e guide i n d i c e s . The coupling i s obtained by s o l v i n g the coupled wave equations, R * - j 6R = - j ic S (2.25) S' - j 6S = - j K R The crossover i n t e n s i t y n = I 1 / I 2 i s given by, < _,_2 t ./J- j. * 2 (2.26) n = _ s i n L •< + 6 < + 6 For i d e n t i c a l waveguides, Nj = N 2 and 6 - 0, so V 24 F i g . 2.14. V a r i a t i o n of power i n the i n i t i a l l y e x c i t e d guide w i t h the propagation l e n g t h (Papuchon et a l . 1975). 2 5 n = s i n 2 K L (2.27) and complete crossover occurs at K L = n = 1,3,5,... (2.28) When 6 t 0, complete t r a n s f e r i s impossible. This i s i l l u s t r a t e d i n F i g . 2.14. Phase mismatch, A3, can be introduced by applying voltage to the e l e c t r o d e s . For example, with electrodes on top of the waveguides i n Z-cut L i N b 0 3 to u t i l i z e r 3 3 , * * m ¥ n l r 3 3 l r ( 2 ' 2 9 ) where T i s the overlap between the o p t i c a l and e l e c t r i c f i e l d s , V i s the a p p l i e d voltage and d the electrode gap. The coupling length i s 200 ym-1 cm. The two coupling s t a t e s are the cross s t a t e , and the through or bar s t a t e . The bar s t a t e i s r e a l i z e d by applying voltage to produce A3» so that n = 0 f o r K L = -j» then ABL = / ? I T . The voltage required to switch from one s t a t e to the other, can be reduced by i n c r e a s i n g £ or reducing d. The crossover n can be modified through A3 or K . In order to have a cross s t a t e w i t h low c r o s s t a l k , the value of K L has to be c o n t r o l l e d a c c u r a t e l y . The d i f f i c u l t y of c o n t r o l l i n g L to w i t h i n ± 3.5% f o r -25 dB c r o s s t a l k [Papuchon 1975], can be overcome by using a stepped A3 r e v e r s a l i n the coupler [Schmidt and Kogelnik 1976]. A switched d i r e c t i o n a l coupler w i t h a l t e r n a t i n g A0 over two sections i s shown i n F i g . 2.15. A phase mismatch A3 = 31 - 32» between the propagation constants of the two coupled waveguides i s induced by the a p p l i e d v o l t a g e . F i g . 2.15. A reversed Ag d i r e c t i o n a l coupler switch (Schmidt and Kogelnik 1976). 27 When the phase mismatch i s equal but opposite i n the two sec t i o n s , i n c i d e n t e n e r g y R q f r o m t h e t o p guide i s t r a n s f e r r e d to the bottom g u i d e , i . e . crossover s t a t e e x i s t s . On the other hand, when there i s wniform mismatch, any energy that i s t r a n s f e r r e d from the top guide to the bottom guide i n the f i r s t h a l f , i s returned to the top guide i n the second h a l f ; then bar s t a t e e x i s t s . For s u f f i c i e n t l y l a r ge a voltage always e x i s t s to achieve complete cross s t a t e . To s w i t c h , from one s t a t e to the other, a change i n ABL of l e s s than 2 T T i s r e q u i r e d . A two s e c t i o n reversed Ag coupler [Schmidt and Kogelnik 1976], had a c r o s s t a l k of -27 dB, and a switching voltage of 27 V. Recently, a s i x s e c t i o n a l t e r n a t i n g Ag coupler, w i t h an i n t e r a c t i o n length of ~ 1 cm, required a d r i v e voltage of ~ 3 V, and has a 10 dB e x t i n c t i o n r a t i o . I t had bandwidth of 1 GHz, and a r i s e time of 590 ps, [Cross and Schmidt 1979]. The device was i n Z-cut LiNbOg. A p o l a r i z a t i o n i n s e n s i t i v e stepped AB switch has been formed w i t h a v a r i a b l e gap coupler [ A l f e r n e s s 1979]. The p o l a r i z a t i o n independent cross s t a t e i s achieved w i t h reversed Ag, and at an operating point i n s e n s i t i v e to Ag v a r i a t i o n s . Shaped t r a n s f e r c h a r a c t e r i s t i c w i t h weighted coupling i s used to obt a i n p o l a r i z a t i o n independent bar s t a t e . Although An^^^An^, the c o u p l i n g s t r e n g t h i s e q u a l i z e d by s u i t a b l e c h o i c e of the TE TM waveguide and coupler parameters, that i s , < and L e t c . are chosen so that S T E = S ™ a t A W A * I M , : 1 3 / r 3 3 - 1 ' 3 i 28 2.6 F i l t e r s [ A l f e r n e s s 1981] The i n f o r m a t i o n - c a r r y i n g c a p a c i t y of an o p t i c a l f i b r e communication system can be b e t t e r u t i l i z e d by combining s e v e r a l channels. Wavelength s e l e c t i v e f i l t e r s are required to m u l t i p l e x and demultiplex the channels. The f i l t e r s are c h a r a c t e r i z e d by wavelength, bandwidth, i n s e r t i o n l o s s , and e l e c t r i c a l t u n a b i l i t y . Narrow-band (5-15 A) f i l t e r s are needed to accommodate s e v e r a l narrow channels w i t h small i n t e r c h a n n e l spacing. But broad-band (200-300 A) f i l t e r s are r equired because of source d r i f t w i t h temperature, and f a b r i c a t i o n u n c e r t a i n t i e s . Thus, f i l t e r s w i t h a wide range of bandwidths are needed Three types of f i l t e r s that have been demonstrated are; the corrugated or g r a t i n g f i l t e r , TE«--»TM mode converter f i l t e r , and the d i r e c t i o n a l coupler f i l t e r . 2.6.1 Corrugated/grating f i l t e r [Tamir 1979] The corrugated f i l t e r has a p e r i o d i c p e r t u r b a t i o n , which produces a p e r i o d i c index change f o r phase matching. For a p e r t u r b a t i o n period A, at an e f f e c t i v e i n d e x N, a backward r e f l e c t i o n a t wavelength X q meets the Bragg c o n d i t i o n , X q = 2NA. T y p i c a l l y A < 0.5 ym f o r X Q = 0.5-1.5 ym. The AX 2 A f r a c t i o n a l bandwidth i s — = -—. The coupling constant K i s a f u n c t i o n of the c o r r u g a t i o n depth and the waveguide parameters. T y p i c a l f i l t e r l e ngth i s 1 cm. A f i l t e r and i t s response i s shown i n F i g . 2.16. A f i l t e r w i t h as l i t t l e bandwidth as 0.1 A has been reported [Schmidt et a l . 1974]. 29 2.6.2 Mode converter f i l t e r [ A lferness 1981] In L i N b O a because of l a r g e b i r e f r i n g e n c e , (n -n =0.09 at X=0.6328 um), 3 o e t h e e f f e c t i v e i n d i c e s N m „ and N w a r e q u i t e d i f f e r e n t . S i n c e t h e TE TM M b i r e f r i n g e n c e changes with wavelength, the TE++TM mode conversion v a r i e s w i t h wavelength. However, i f phase matching c o n d i t i o n , (2.30) at X Q i s met, then there i s strong coupling between the asynchronous modes TE and TM. Here, A i s the e l e c t r o d e p e r i o d . The mismatch at X = X +AX i s ' o A 6 = - 2 T T A X / A X . The conversion e f f i c i e n c y n i s given by (2.26) , and the coupling constant K by (2.27). The f u l l width h a l f maximum (FWHM) bandwidth i s AX/X=A/L. I n the case of L i N b 0 3 , n Q - n e = 0.086 at X = 0.6328 um, and the ele c t r o d e period A = 7 urn. For L i T a 0 3 , the b i r e f r i n g e n c e i s smaller and the bandwidth wider f o r the same A. A f i l t e r w i t h d i r e c t e d f i e l d u t i l i z e s the r 5 1 = 28 x 1 0 ~ 1 2 m/V c o e f f i c i e n t , and a bandwidth 50 A - 5 A can be obtained at X = 0.6328 um f o r A = 0.5 - 6 mm. The bandwidth i s four times as much at 1.3 um» a l l e l s e being the same. Performance of a three channel converter i s shown i n F i g . 2.17 [Al f e r n e s s 1981]. The electr o d e s were t i l t e d to obtain small period d i f f e r e n c e s . The bandwidth at 50% conversion e f f i c i e n c y i s 15 A , and the channel separation 80 A, at a c r o s s t a l k of 20 dB. TITANIUM DIFFUSED WAVEGUIDE 30 +V / A / / zzz E Z Z Z Z 3 E Z Z / / -V H — A —>i LITHIUM NIOBATE (a) ELECTRODES s g 100 M 3 > M O fa _ O H 0 -JWV /I -5964 6045 6120 WAVELENGTH (%) (b) F i g . 2.17. (a) Phase-matched e l e c t r o o p t i c TE«-*TM c o n v e r t e r / f i l t e r ; and (b) measured conversion e f f i c i e n c y (Alferness 1981). 31 2.6.3 D i r e c t i o n a l coupler f i l t e r [ A l f e r n e s s 1981] This type of f i l t e r i s made up of two coupled waveguides of unequal dimensions and r e f r a c t i v e i n d i c e s , F i g . 2.18. As a r e s u l t , the modal c h a r a c t e r i s t i c s of the two guides are d i s t i n c t . I f width W 2 then index N 1<N 2. At a wavelength X q , where phase matching e x i s t s , there i s complete t r a n s f e r of power from one guide to the other. At a d i f f e r e n t wavelength X=X+AX, the mismatch i s -; r~» a n d the f r a c t i o n a l bandwidth i s ; ef f ^ 1 ! l x < W ' = 1 T > 1 0 0 A ( 2 ' 3 1 ) The f i l t e r i s tuned to a d i f f e r e n t wavelength by s h i f t i n g the d i s p e r s i o n c h a r a c t e r i s t i c s with an applied v o l t a g e . Complete crossover can be a f f e c t e d by reversed AB coupler [Alf e r n e s s and Schmidt 1978]. For a T i : L i N b 0 3 d i r e c t i o n a l coupler f i l t e r , w i t h L = 1.5 cm, the 3 dB bandwidth i s 200 A at X=6.33 urn, at a peak crossover e f f i c i e n c y n = 100%. The tuning range i s 600 A, with a t u n a b i l i t y of 100 A/V. The -3 dB bandwidth i s , AX AN L (2.32) AXBW X where a change i n wavelength A X v > c o r r e s p o n d s to a change i n e l e c t r i c a l l y Induced AN which i s equal to (N—.-N™.) or (N 0-N,). The e l e c t r i c a l t u n a b i l i t y v TE TM z. 1 of a f i l t e r i s given by AX = A AN (2.33) v v F i g . 2.18. The d i r e c t i o n a l coupler f i l t e r : (a) schematic r e p r e s e n t a t i o n ; waveguide d i s p e r s i o n ; and f i l t e r response ( A l f e r n e s s 1981) . 33 CHAPTER I I I TAPERED LINE AND LINEARLY GRADED WAVEGUIDES 3.1 I n t r o d u c t i o n A new and simple set of c h a r a c t e r i s t i c equations f o r the propagation constant of an o p t i c a l waveguide with l i n e a r l y graded r e f r a c t i v e index are obtained. To t h i s end, tapered transmission l i n e theory, and the method of "transverse resonance" are used. A planar o p t i c a l waveguide i s made up of three d i e l e c t r i c l a y e r s ; the s u b s t r a t e , f i l m and cover, F i g . 2.4. In general, the r e f r a c t i v e index n^ of the guiding l a y e r v a r i e s i n the transverse d i r e c t i o n x. The c h a r a c t e r i s t i c e q u a t i o n s f o r k z a r e obtained by s o l v i n g Maxwell's equations. The s o l u t i o n s i n v o l v e Bessel f u n c t i o n s , Hermite polynomials, e t c . Computations using such complicated f u n c t i o n s are expensive. So, an a l t e r n a t i v e approach using the method of "transverse resonance" [Tamir 1973] i s followed here f o r the case when n^(x) I s a l i n e a r f u n c t i o n . F i r s t the s u b s t r a t e , f i l m and cover that make up the o p t i c a l waveguide are represented by an equivalent t r a n s m i s s i o n network i n the transverse x - d i r e c t i o n . Then the propagation constants are determined by s o l v i n g the eigenvalue equation. The r e f r a c t i v e index of the f i l m i s v a r i a b l e i n the transverse d i r e c t i o n , consequently the c h a r a c t e r i s t i c impedance by which i t i s represented i s v a r i a b l e too. A f t e r l a y i n g the ground-work i n Section 3.2, an impedance transformation equation f o r a non-uniform transmission l i n e i s derived i n Sectio n 3.3. F i n a l l y , the 34 c h a r a c t e r i s t i c equations f o r the propagation constant corresponding to the TE and the TM modes are obtained i n Sections 3, 4 and 5 r e s p e c t i v e l y . In Chapter IV t h i s work i s a p p l i e d to the study of non-uniform f i l m s deposited on a d i f f u s e d waveguide s t r u c t u r e . Such f i l m and waveguide combinations have the p o t e n t i a l f o r the phase tuning of the i n t e g r a t e d o p t i c a l d e v i c e s . 3.2 D i f f e r e n t i a l equation f o r input impedance In t h i s s e c t i o n , a second order nonlinear d i f f e r e n t i a l equation f o r the input impedance of a tapered transmission l i n e i s d e r i v e d . This equation i s then solved f o r e x p o n e n t i a l l y tapered l i n e s [Ahmed 1981], For a u n i f o r m - t r a n s m i s s i o n l i n e of c h a r a c t e r i s t i c impedance Z q , a load impedance Z when t r a n s f o r m e d a d i s t a n c e I towards the g e n e r a t o r i s Z. v a i n [Ragan 1948], Z. Z + j Z tan g£ i n _ a J o M n Z Z + j Z tan 8£ v-"w o o J a The c h a r a c t e r i s t i c impedance of a non-uniform transmission l i n e i s v a r i a b l e ; i t i s a f u n c t i o n of d i s t a n c e 2,, thus Z q becomes Z( Z) = Z ( f o r b r e v i t y ) . To determine an expression f o r the input impedance consider F i g . 3.1, and l e t Z^be input impedance at £, and ( Z£ n +dZ^ n) at (H + d&). I f i t i s assumed that the l i n e i s of uniform c h a r a c t e r i s t i c impedance Z ( i ) = Z, over the incremental distance di, then using (3.1), Z. + dZ. Z. + j Z tan ( Bdfc) i n i n _ i n . . Z Z + j Z ± tan (fcU) K } 35 F i g . 3.2. Schematic r e p r e s e n t a t i o n of an e x p o n e n t i a l l y tapered l i n e . 36 For small Bd£, tan (Bd£) = Bd£, using t h i s i n (3.2) Z., + dZ. Z. + jZgdJl i n i n i n J ( . z " Jz<„e<H v ; Z [ l + — | ^ ] The denominator of (3.3) can be expressed a s , j Z 6d£ -1 j Z Bd£ Using t h i s i n (3.3) j Z Bdfc Z i n + d Z i n 5 ( Z i n + j Z 6 d £ ) ( 1 " " i M Ignoring the products of d i f f e r e n t i a l terms [ C o l l i n 1966]; dZ. -J3Z 2 _ i E = _ i E + j 3 Z (3.5) L e t t i n g Z l n = y (3.6) R - jB/Z (3.7) S u b s t i t u t i n g (3.6) and (3.7) i n (3.5) H - V - | 2 (3.8) Equation (3.8) i s the w e l l known R i c c a t i equation, which can be transformed i n t o a homogeneous l i n e a r d i f f e r e n t i a l equation of second order and then solved [Davis 1962]. Making the transformation y = ('^j) (3.9) h ( a ! ) ( 3 - 1 0 ) 37 D i f f e r e n t i a t i n g (3.10) w i t h respect to £, *L = J L ^ I £ u _ z piuf + _ z _ [ a 2 u ] ( 3 > n ) d£ j 3 d£ u d£ j Bu d£ j Bu d£ S u b s t i t u t i n g (3.9) i n t o (3.8), M u l t i p l y i n g (3.11) and (3.12) by -uR 2 and then equating the r i g h t hand sides and using (3.7), -uR 2 dZ _du uR 2Z rdu -,2 uR 2Z d 2u j g d£ ud£ j Bu j Bu d£ S u b s t i t u t i n g value of R from (3.7), 2 2 - u3 P dZ 1 du _ uj g d u _ uj 38 Z 2 d£ u d£ Z u d£ 2 Z 2 d u . r l dZ "i du , 2 . ,„ , or — j + L J — + 3 u = 0 (3.13) d£ Z d£ d£ Equation (3.13) w i l l serve as the springboard f o r d e r i v i n g expressions f o r the input impedances of the e x p o n e n t i a l l y tapered transmission l i n e . 3.3 E x p o n e n t i a l l y tapered l i n e Along an exponential taper, F i g . 3.2, £n Z( £) v a r i e s l i n e a r l y w i t h £ [Burrow 1938; J a s i k 1961; Womack 1962; Berquist 1972]; 38 D i f f e r e n t i a t i n g w i t h respect to £, i S ' r * " < 3- 1 5 ) S u b s t i t u t i n g (3.15) i n (3.13), + 2 k ^ + g^u = 0 * J i  9V ±1 + R 2 = 0 (3.16) d£ 2 d£ S o l u t i o n of (3.16) i s given i n (A14), which a f t e r appropriate s u b s t i t u t i o n y i e l d s , Z 1/2 1/2 1/2 z {( g -k ) - k tan£(g - k z ) } + j g tan£(g -k z) * - , 1/2 1/2 JeT 1/2 ( 3 , 1 7 ) Z ( B - k ) + k t a n £ ( B - k ) + t a n £ ( g - I t ) where k = I (I |^) Z(£) = Z x {exp £ £n (^ £)} (3.18) Although exponential transmission l i n e s have been studied [Ghose 1957; Das and Rustogi 1968; Arnold and B a i l e y 1974; Arnold et a l . 1974], an input impedance expression i n a convenient form l i k e (3.17) i s not a v a i l a b l e . 39 3.4 D i s p e r s i o n equation f o r a l i n e a r l y graded Index guide The method of transverse resonance [Tamir 1973] i s used to o b t a i n the d i s p e r s i o n equation f o r a planar o p t i c a l waveguide w i t h l i n e a r l y graded r e f r a c t i v e index. The three media s t r u c t u r e i s represented by an equivalent tra n s m i s s i o n network corresponding to the transverse x d i r e c t i o n , as i n d i c a t e d i n F i g . 3.3. The propagation constants i n the l o n g i t u d i n a l d i r e c t i o n f o r the guided modes are determined by s o l v i n g the eigenvalue equation, Z" + i = 0 (3.19) or Z, + Z = 0 (3.20) i n r F o r t h e waveguide s t r u c t u r e of F i g . 3.3 where n , n ( x ) , and n are the r e f r a c t i v e i n d i c e s of the s u b s t r a t e , f i l m and cover r e s p e c t i v e l y , and Z , Z(x) and Z^ are the corresponding impedances. 3.4.1 TE mode The impedance equation f o r the TE mode i s [Tamir 1979: 109], Z l = " V ^ c i ( 3 , 2 1 ) where Z^ i s the c h a r a c t e r i s t i c impedance and k ^ i s the propagation f a c t o r i n the transverse x d i r e c t i o n . The d i s p e r s i o n r e l a t i o n Is . 2 , * 2 .2 2 k j + k = k n. x i z i Dro p p i n g the s u f f i x i , and using k = kn., where n. i s the e f f e c t i v e index i n the l o n g i t u d i n a l propagation z d i r e c t i o n . R e f r a c t i v e index n i s a f u n c t i o n of x 40 1/2 k = k ( n 2 - n 2 ) (3-22) x 1 Z = °vo 1 k /2 2 vn - n j dZ _ _ a ) y o n dn ~ 7~2 27372 , dx k (n - t i j ) dx 1 dZ n dn 2 2~ Z dx (n - n ) dx I f the v a r i a t i o n i n n i s s m a l l n=n c [Heibei and Voges 1978], that i s , k x=k. then -n r l dZ^ c dn (3.23) L * ~ , 2 2, -Z dx (n - n.) dx c 1 When the r e f r a c t i v e index changes l i n e a r l y w i t h distance as shown i n F i g , 3.3, and n = ( n c + 6n) + 6n dn 6n dx t I dZ = 2 " " c 2 . i E = 2A (say) (3.24) Z dx (n - n ) t c 1 Comparing (3.24) w i t h (3.13) F i g . 3.3. C r o s s - s e c t i o n of a planar waveguide and i t s equivalent t r a n s m i s s i o n l i n e r e p r e s e n t a t i o n . 42 £ 4 + 2 A ^ + k 2 u = 0 (3.25) d x 2 dx C Comparing (3.25), w i t h (3.16) and i t s s o l u t i o n (3.17), f o r the c o n f i g u r a t i o n of F i g . 3.3, Z a ,,v2 2 . 1 / 2 2 . 2 , 1 / 2 , , „ 2 _ A 2 , 1 / 2 { ( k 2 - A 2 ) +A tan t ( k ^ - A Z ) }-jk ctan t ( k £ - A ) Z i n = Z f 2 ^ , , 1/2 1/2 k Z 1/2 ( 3 ' 2 6 ) (k -A Z) -A tan t ( k -A Z) - j - ^ - * - tan t ( k -A^) C C c Since Z, = -Z from (3.20), i n r tan mt (Z Z r i + Z Z,„) = r f l a f2 fo ? 7 N m " A ( Z r Z f l - Z a Z f 2 ) + j k c ( Z a Z r + Z f l Z f 2 ) where m . ( k 2 _ A 2 } 1 / 2 (3.28) c 2 2 1 / 2  k c = k ( n c " n l > Here k = 2n/X , and X i s the f r e e space wavelength, o o Since, f o r the TE modes, Z^ = tot^/k^, tan mt ( k a k f 2 + k r k f l ^ = A ( k a kf2 " V W + j V k f l k f 2 + k . V F i n a l l y , the d i s p e r s i o n r e l a t i o n f o r the TE modes i n a f i l m w i t h l i n e a r l y graded index i s given by, tan mt ( k ' k f 2 + k r k f l ^ -V- = A ( k ; k f 2 - k ; k f l > + k c ( k f l k f 2 - K K ) ( 3 ' 2 9 ) 43 Where the va r i o u s decay and propagation constant are, 2 2 1 / 2 2 2 1 / 2 k = k ( n j - n,) = j k ( n , - n) = j k ' (3.30) si SL L J. a a 1/2 1/2 k r = k ( n ^ - n p = j k ( n ^ - n * ) = j k r (3.31) ? o 1 / 2 k f l = k(n ^ - n j ) - k c (3.32) 2 2 1 / 2 k, 0 = k{(n + 6n) Z - n, } (3.33) xl L c 1' m - ( k 2 - A 2 ) ' 7 ' (3.28) c -n 6 A C ^ (3.24) 2 ( n Z - n f ) t c 1 3.4.2 TM mode The p r o p a g a t i o n c o n s t a n t k ^ and the c h a r a c t e r i s t i c impedance f o r the i - t h medium f o r the TM modes are r e l a t e d by [Tamir 1979: 109], k Z ± = SSij (3.34) me n. o i 2 2 2 where k . + k = k n.. x i z i Dropping the s u f f i x i , an expression f o r B analogous to A, (3.24), f o r the TE modes i s , -6n(n 2 - 2n 2) B \ ± - (3.35) n c ( n c - n x ) t 44 The d i s p e r s i o n equation from (3.27), (3.34) and (3.35) i s , , _ r _ f l _ a _ f 2 1 1 2 2 2 2 > tan m, L n n.., n n._ 1 r f l a f2 f . m. k k,.. k k. 0 k k k c . k,_ V J . J O ; 1 „ ( r f l a f2 > , ,, f a r , f 1 f2 •> n n_. n n_„ n n n_, n,_ r f l a f2 a r f l f2 tan nijL (k£k f l + k f l k f 2 ) = B ( k r k f l " k ? f 2 ) + k c ( k f l kf2 - k a V Where, ( 3 . 3 7 ) B = -6n(n 2 - 2 n J ) / [ ( n 3 - n . i i j ) t ] „ = ( k 2 _ B 2 ) l / 2 (3.38) 1 c 1/2 k" = ( n 2 - n 2) / n 2 (3-39) a 1 a a k r - ( n l " n r ) 1 / 2 / n r ( 3 , 4 0 ) k = ( n 2 _ n 2 ) / n 2 (3.41) k f l ^ f l r ' f l 1/2 k 2 = ( n 2 - n 2) / n 2 (3.42) k f 2 ^ f2 V ' f2 The above d i s p e r s i o n r e l a t i o n s are applied to a study of a f i l m loaded d i f f u s e d waveguide i n Chapter IV. 45 CHAPTER IV PHASE COMPENSATION BY FILM LOADING 4.1 I n t r o d u c t i o n The i n t r i n s i c phase d i f f e r e n c e of an i n t e g r a t e d o p t i c a l Mach-Zehnder modulator can be adjusted by means of a loading f i l m as shown i n F i g . 4.1. F i r s t , a review of various m a t e r i a l s which may be s u i t a b l e f o r t h i s purpose i s c a r r i e d out. Next, a transmission l i n e model and the theory f o r a f i l m l o a d i n g a T i i n d i f f u s e d o p t i c a l waveguide are described. Then, a d e s c r i p t i o n of the computer program and the computational r e s u l t s on the e f f e c t of a high index f i l m l oading a d i f f u s e d waveguide are given. F i n a l l y , the experimental r e s u l t s are presented. 4.2 Phase compensation Several devices depend on the path length to perform as intended. Examples of these are f i l t e r s , d i r e c t i o n a l c o u p l e r s , and i n t e r f e r o m e t e r s . The p a r a l l e l guide d i r e c t i o n a l coupler performance i s c r i t i c a l l y dependent upon the c o u p l i n g l e n g t h . In case of the Mach-Zehnder Interferometer, the i n t r i n s i c phase d i f f e r e n c e i s determined by d i f f e r e n c e i n the len g t h of the two arms. In order to e i t h e r operate the interferometer i n the l i n e a r p o r t i o n (e.g. f o r HV measurement) or to combine the output of se v e r a l i n t e r f e r o m e t e r s , i t i s necessary to have p r e c i s e design lengths. But, c o n t r o l of the path l e n g t h to a f r a c t i o n of the guide wavelength (= X/n) i s i m p r a c t i c a l . So, an a l t e r n a t i v e i s to tune the devices by ad j u s t i n g the propagation constant. This had been done [Mikami et a l . 1977; 1979] by lo a d i n g a high r e f r a c t i v e F i g . 4.2. (a) Equivalent transverse network and (b) c o n f i g u r a t i o n of an o p t i c a l waveguide loaded by a f i l m . 47 index Se-S based chalcogenide glass on top of one of the d i r e c t i o n a l coupler arms, and then i r r a d i a t i n g the g lass f i l m w i t h 0.5 ym halogen l i g h t . This i n c r e a s e d the r e f r a c t i v e index n^ by as much as 0.03, and the change i n index was reversed by heating at 190°C. By a l t e r i n g the r e f r a c t i v e index and hence the propagation constant, the t r a n s f e r of power was adjusted from minimum to maximum. Unfor t u n a t e l y , the chalcogenide glass f i l m has high absorption i n the v i s i b l e spectrum, consequently i t i s not s u i t a b l e f o r use at the He-Ne wavelength. Many d i f f e r e n t m a t e r i a l s have been used to f a b r i c a t e planar o p t i c a l waveguides i n the form of m u l t i l a y e r d i e l e c t r i c f i l m s . Some of these f i l m s are amenable to a change i n the r e f r a c t i v e index when subjected to heat, l i g h t or o x i d a t i o n . P r o p e r t i e s of s e v e r a l such m a t e r i a l s are compared, with an a p p l i c a t i o n to the phase compensation of the i n t e r f e r o m e t e r , and ease of f a b r i c a t i o n i n mind. A d d i t i o n a l phase r e t a r d a t i o n introduced by a f i l m of length on an arm of the interferometer i n F i g . 4.1, i s given by • = ( Bp - P A ) L j • * T ( n z " V L 1 <4-J> where Bp and B^ are the e f f e c t i v e propagation constants f o r the waveguide with and without the loading f i l m r e s p e c t i v e l y . The change induced i n the propagation constant with a change i n f i l m Index can be c o n s i d e r a b l e . For example, by changing the f i l m r e f r a c t i v e i n d e x from 2.2134 to 2.2084, changes: 2.225230 to 2.225156. For a f i l m l ength = 1 mm, the phase r e t a r d a t i o n induced i s 42°. 48 4.3 C r i t e r i a f o r the l o a d i n g f i l m C h a r a c t e r i s t i c s of a f i l m s u i t a b l e f o r the phase compensation are : 1. The f i l m be transparent at 0.6328 um with low o p t i c a l l o s s (< 2 dB/cm) 2. The f i l m i n d e x n^ be g r e a t e r than the e x t r a o r d i n a r y i n d e x n =2.203 of a T i d i f f u s e d waveguide e 3. The f i l m i n d e x n^ be amenable to change by heat t r e a t m e n t , o x i d a t i o n , e t c h i n g e t c . 4. P r e f e r a b l y , the f i l m index n^ be r e v e r s i b l e by a simple chemical or p h y s i c a l a c t i o n 5. The change i n f i l m index be s u f f i c i e n t l y large to induce a phase change of up to 360° 6. The f a c i l i t i e s f o r processing the f i l m be r e a d i l y a v a i l a b l e . 7. I t would be very d e s i r a b l e i f the f i l m index could be modified w h i l e the device i s operating 4.3.1 A review of the m a t e r i a l s Some of the candidate m a t e r i a l s and t h e i r p r o p e r t i e s f o r the loading f i l m are compared i n Table 4.1. I t appears that T a 2 0 5 may be a p p r o p r i a t e . However, Ta i s d i f f i c u l t to e t c h . The r e f r a c t i v e index of T a 2 0 5 f i l m depends on the d u r a t i o n f o r which i t Is kept i n 0 2 at 500°C. 4.4 Modelling of the l o a d i n g f i l m [Uchida et a l . 1976;Uchida 1976;Noda 1978b] An o p t i c a l waveguide formed by d i f f u s i o n and loaded by a f i l m i s shown In F i g . 4.2(a). A l s o , a r e p r e s e n t a t i o n of the f i l m loaded guide by an equivalent TABLE 4.1 COMPARISON OF THE PROPERTIES OF FILMS AT X = 0.6328 \sa FOR TE MODES M a t e r i a l s Reference n Loss dB/cm Change i n n a f t e r d e p o s i t i o n Process Coming 7059 [Goell et a l . 1969] 1.62 1 - Sputtered i n 0 2 V i n y l t r i m e t h y s i l a n e [Tien et a l . 1972] 1.531 0.04 Yes, i n 0 2 at 140°C Rf po l y m e r i z a t i o n Polyurethane P o l y e s t e r epoxy Organic polymer N b 20 5 [ U l r i c h and Weber 1972] [McGraw and Zernike 1974] 2.276 0.3 Yes, w i t h UV i f dye i n f i l m Dipping Sputtered Nb i n Ar, 0 2 ZnO [Tien et a l . 1969] 1.973 20 — Sputtered ZnS [Tien 1971] 2.342 5 - •i Ion exchange with X-cut HNb0 3 [Jackel 1980] 2.23-2.26 1.5 Probably AgNO3+LINb0 3 at -300°C T a 2 0 5 [Hensler et a l . 1971 and Fujumori et a l . 1972] 2.2136 0.9 Yes, i n 0 2 at 500°C Sputtered Ta followed by o x i d a t i o n 50 transmission l i n e network, i n the transverse x d i r e c t i o n , i s shown i n F i g . 4.2(b). The r e f r a c t i v e index v a r i a t i o n s In the x d i r e c t i o n a r e , n(x) = n -<*> < x < - t a = n-(x) - n - 6n x/t - t < x < 0 (4.2) r c = n + An exp(-x/d) 0 < x < <*> s Where n , n £ and n are the r e f r a c t i v e i n d i c e s of the a i r , f i l m and substrate a' f s r e s p e c t i v e l y , and An i s maximum change i n index due to d i f f u s i o n . The f i l m thickness i s t , and d i s the d i f f u s i o n depth at which An decreases to An/e, i . e . an exponential d i f f u s i o n p r o f i l e i s assumed. The c h a r a c t e r i s t i c equation f o r the TE mode propagation i n a planar waveguide w i t h an exponential d i f f u s i o n p r o f i l e i s [Conwell 1973]; ^ »(2n A n ) 1 ^ s where g = 2 dk (2n A n ) 1 / 2 exp(-x/d) (4.4) s 2 2 , 1 / 2 V = 2 dk (n? - n Z) (4.5) 1 s 9 9 M 2 1 / 2 P i = ^ " l " £ i V (4*6) C and n^ i s the e f f e c t i v e mode index i n the propagation d i r e c t i o n z. In order to a p p l y (4.3) to a waveguide loaded w i t h a f i l m , an appropriate value of p.^  has t o be u s e d . So p^ c o r r e s p o n d i n g to a f i l m of i n d e x n^(x) i s used. 51 Equation s i m i l a r to (4.3) corresponding to a f i l m w i t h l i n e a r l y graded Index was derived i n the previous chapter. S p e c i a l cases, when the f i l m index i s constant are determined and compared with [Noda et a l . 1978b], The eigenvalues using (4.3) are determined at the x = 0 plane, so g(x) = g(0) = g f o r b r e v i t y . 4.4.1 TE modes, n r ( x ) > n r s The i n p u t impedance Z f n at x = 0, f o r a f i l m w i t h l i n e a r l y graded index of thickness t , covering a d i f f u s e d waveguide, of c o n f i g u r a t i o n i n F i g . 4.2 f o r the TE modes (3.26) i s , k f l -= (m + A tan mt) - j k tan mt toy k J c Z, = T - ° - - a . (4.7) i n k.„ k k... f2 , _ , c f l ^  vi - A tan mt -1—s tan mt J k a where, 2 2 1 / 2 k f l = k ( n 2 - n 2) - k c 2 2 1 / 2 k f 2 = k { ( n c + 6n) - nj} 2 2 1 / 2  k a = k ( n a " n l } 2 2 1 / 2 m = ( k Z - AT) c 52 A = -n 6n c 2 ( n 2 - n 2 ) t c 1 R e c a l l i n g (4.6) w 2 2 , 1 / 2 + .., 2 2 , 1 / 2 P i - * J ^ 0 / Z i = ± J a ) V Z i n U s i n g the v a l u e of i n p^ the c h a r a c t e r i s t i c e q u a t i o n (4.3) becomes, J V - l ( e ) - W g ) -2 ^""o s s For the c a s e , when n f ( x ) = n f ( c o n s t a n t ) , k £ = k f l = k f 2 = k r > 6n = 0 and hence A = 0 and m = k , so that Z. reduces to c i n toy (k^/k ) - j tan t k r 7 _ o f a f _ i n k f 1 - j ( k f / k a ) tan t k f toyQ - j / S - j tan t k f Z = 1 7 T 7 2 1 - (tan t k f ) / S ( 4 ' 9 ) In ,, I Zv k ( n f - n j ) Thus from (4.8) and (4.9) , 9 9 1/2 ? ? 1 / 2 S - tan t (n^ - np k J V ( g ) (2n A n ) 1 / 2 1 + S tan t ( n 2 - n 2 ) 1 / 2 k s t l J v _ i ( g ) ~ J v + i ( g ) _ 2 ( nf " V " - f "1 where, q , 2 2 , 1 / 2 / r 2 2 . 1 / 2 S = (n - n ) /(n - n ) l a r 1 53 Which agrees w i t h (7) of [Noda et a l . 1978b], 4.4.2 TE modes, n r ( x ) < n r s F o r t h i s case which i s of p r a c t i c a l importance a l s o , (4.7) f o r Z^ n becomes, 4 TT-lfim'+jA tanh m ' t l + j k tanh m't OJU k' V J J > J c z m = 3 k f ~ k^kj 2 jm' - j A tanh m't + j 1 tanh m't a where j k i = k i • f o r I = a , c , f 1 , f 2 jm' = m Thus f o r the TE modes, when n^ < n g , the c h a r a c t e r i s t i c equation i s given by (4.11) and (4.8) — V A .11) J v ( g ) (2n gAn) ' l Z^ When the f i l m i n d e x n f ( x ) i s a constant, 6n = 0 and hence A=0, m' = k , with S' = k'/k' (4.12) reduces t o , J ^ C g ) - J v + l ( g ) - 2 ( n ? - n | ) 1 / 2 S' + t a n h t ( n ^ - n | ) 1 / 2 k = TTT~ 9 — ? " i /'9 (4.13) J (g) (2n gAn) ' 1 + S' tanh t (n*-n* ) ' Tc which i s anologous to (7) of [Noda et a l . 1978b], 54 4.4.3 TM modes, n,(x) > n In case of the TM mode propagation, the c h a r a c t e r i s t i c equation d i f f e r s from the one f o r the TE modes, i t i s [Conwell 1973); J (g) - J (g) (2n M ) 1 / 2 n 2 2p 2An JLi Yli + ! = -(-£) i _ (1+ ) (4.14) J v ( g ) d k n 2 n± k(2n sAn) When the f i l m index i s l i n e a r l y graded, then t,^ i s given by (3.26) w i t h B i n s t e a d of A, f o r the TM modes i t i s , k hr) K+B t a n V h ^ c t a n V f 2 a f l Z (4.15) ° f 2 m r B tan n^t " j - ^ [~^] tan m^ Where, B = - t o ( n | - 2 n f ) / [ ( n | - n c i i i ) t ] (4.16) The term p^ i n (4.6) i n t h i s case i s , P t = k ( n f n ; ) 1 / 2 = ± J k ( n 2 - n ? ) 1 / 2 p i = « V i Z i = ± j U > e o n f 2 Z i n (4.17) Thus the c h a r a c t e r i s t i c equation f o r mode propagation using (4.15) and (4.17) i n (4.14) i s , 55 W ' - W ^ ^ . ^ ' j ^ ^ ( , 1 8 ) V * 5 d k n 2 V , k(2n A n ) 1 / 2 s "f2 For the case when the f i l m index n^ i s constant, n^ = n^ = n f = n c > <5n = 0 and hence B = 0, s i m p l i f i e s , and (4.18) reduces t o , , + = - I — J (4.19) J V ( g ) d k n 2 n f ( 2 n s A n ] 1 / 2 1+£S tan t k f where, 5 = (n f/nj* k f = k ( n 2 - n | ) 1 / 2 4.4.4 TM modes, n^(x)-<-n g When the r e f r a c t i v e i n d e x of the f i l m n^(x) i s l e s s than that of the substrate n g , then Z^ given by (4-15) modifies t o , n f 2 2 k' 1 t , ( — ) vT- O ' + JB tanh m t ) + j k ' tanh m't J 1 C f 2 n a K f l 1 1 C 1 Z i n = (4.20) coe n 2 k'k' f , „ ° jm* - j B tanh m\t + i-^A ( ) t a n h m ^ 1 fcfl n a Where j k | = k ( n 2 - n 2 ) 1 / 2 , f o r i = a , c , f l , f 2 jm\ = m x (4.21) 56 The c h a r a c t e r i s t i c equation f o r the mode propagation constants i s given by (4.18) and (4.21). I f the f i l m r e f r a c t i v e index i s uniform so that n f ( x ) = n f = n f l = n f 2 = n . 6n = 0 and hence B = 0. The expression f o r Z. s i m p l i f i e s and the charac-c In t e r i s t i c equation reduces to J v - 1 ( g ) - J m ( g ) + ( 2 n g A n ) 1 / 2 _ - n 2 2(nf - n | ) 1 / 2 gS' + tanh tk« J V ( g ) dk n 2 " f (2n A n ) 1 / 2 1 + £S' tank t k l s s x where S' = ( n 2 - n 2 ) 1 7 2 / ( n 2 - n 2 ) 1 / 2 (4.23) 4.5 Propagation constant of f i l m loaded guide of width w The e f f e c t i v e index method [Hocker and Burns 1977; Ramaswamy 1973; Furuta et a l . 1974] i s used to determine the propagation constant B = k n z of a f i l m l o a d e d g u i d e of f i n i t e w i d t h . The e f f e c t i v e index n i s determined i n two steps. F i r s t , the width of the f i l m i s considered to be i n f i n i t e , F i g . 4.3(b) or ( c ) , and the e f f e c t i v e index n x i s obtained by s o l v i n g one of the a p p l i c a b l e r e l a t i o n s ; ( 4 . 7 ) , (4.10), (4.11), (4.14), e t c . Second, the e f f e c t i v e index n 2 of the s t r u c t u r e formed by a channel of width w sandwiched by the s u b s t r a t e , F i g . 4.3(d) or ( e ) , i s computed from; b 2w = 2 t a n - 1 ( ? V g / b 2 ) + qu (4.24) where, I« w >l n a YM n s n s • ' • • • " n — x=-t — x=0 — x=d (a) t x 57 n — x=-t _ x=d .n,(x) (b) n 1 = n n n n I I (d) n 2 = n z f (c) n i = n n i n l l l I n s (e) n =n 2 za F i g . 4.3. A p p l i c a t i o n of the e f f e c t i v e index method; (a) r e p r e s e n t a t i o n of the waveguide under c o n s i d e r a t i o n . (b) , (c) Planar waveguide and e f f e c t i v e i n d i c e s : w i t h f i l m ( n ^ ) and without f i l m (n ) . (d), (e) I n c l u s i o n of the width c o n s t r a i n t ; e f f e c t i v e i n d i c e s : w i t h f i l m n z f and without f i l m n za 58 and b, = k ( n 2 _ n g ) V g = k ( n 2 - n 2 ) 1/2 1/2 (4.25) (4.26) C = (n x/n ) 2 , f o r TE modes . f o r TM modes q (4.27) Therefrom, B=kn 2=kn z i s the d e s i r e d propagation constant of the f i l m loaded guide of width w, i n the l o n g i t u d i n a l d i r e c t i o n z. 4.6 Computations Computations were done f o r a uniform T a 2 0 5 f i l m on a T i d i f f u s e d waveguide i n Y-cut L i N b 0 3 . Exponential r e f r a c t i v e index p r o f i l e was assumed. The c a l c u l a t i o n s were c a r r i e d out f o r the TE and TM modes using (4.10) and (4.19) r e s p e c t i v e l y . The computer program was checked by confirming the r e s u l t s published i n [Noda et a l . 1978b] and [Mikami et a l . 1979], For the TE modes, the c h a r a c t e r i s t i c equation (4.10) was used. The roots of t h i s e q u a t i o n l i e close to where Jy(g) = 0. In order to avoid a d i v i s i o n by zero, (4.10) was rearranged as, 2 ( n | - n 2 ) 1 / 2 S _ tan t ( n 2 - n f ) 1 / 2 k V i ( g ) " Jv+i ( g ) = _ J v ( g ) ( 0 A a/2 T~7~—~7~2 2~7T7\ (2n AnJ 1 + S tan t [nir - nf J k (4.27) In the computer program FT i s d i f f e r e n c e between the LHS and RHS (LHS = l e f t hand s i d e ) of (4.27). The propagation constant w i t h the f i l m thickness t and 59 z e r o , a r e = and n^ = "J-J-J r e s p e c t i v e l y . The data used were; Y-cut L i N b O a ; X = 0.6328 ym; n = n = 2.203 f o r TE modes, n = n = 2.2868 f o r the a' ' s e s o TM modes [Nelson and Mikulyak 1974]; n f = 2.2134 f o r the TE modes, n f = 2.2038 f o r the TM modes [Hensler et a l . 1971); 0 < t < 0.6 ym; 0.5 < d < 6 ym; and 0.01 < An < 0.04. P l o t s of and F ^ , which correspond to (4.10) w i t h and without the f i l m r e s p e c t i v e l y are shown i n F i g . 4.4. Values of range from ( n g + An) to n g . Roots f o r the lowest order mode correspond to the l a r g e s t value of the propagation constant n^. The propagation constants w i t h and without the f i l m are n ^ and n ^ j j r e s p e c t i v e l y . To study the e f f e c t of the f i l m w i t h various parameters, the roots n^ were computed and tab u l a t e d . The roots were found by using the h a l f i n t e r v a l search method [Ley 1970]. The program given i n [Ley 1970] has f l a w s , so i t was modified. A flow chart and l i s t i n g f o r the computer program are included i n Appendix B. The search i n t e r v a l was kept s m a l l , so as not to include more than one r o o t ; i t s t a r t e d at (n g+An) and extended downwards. I f no root was d i s c o v e r e d In the i n t e r v a l , i t was s h i f t e d towards n ; and the p r o c e s s ' s» r repeated u n t i l a root was found. F i r s t , n, corresponding to zero t h i c k n e s s , and then c o r r e s p o n d i n g to f i n i t e f i l m thickness were l o c a t e d . When n^ > n , n,,. was searched w i t h the c o n d i t i o n n,_ > n,__. s' I I I I I I I 4.6.1 D e s c r i p t i o n of computed r e s u l t s The e f f e c t i v e index, n z , as a f u n c t i o n of the d i f f u s i o n depth d, i s shown i n F i g . 4.5. The p l o t s compare n^ f o r planar and f i n i t e width (w) waveguides, w i t h ( n , ) and w i t h o u t (n ) f i l m . For f i x e d f i l m t h i c k n e s s and An, the f z za 2.218 2.214 2.210 2.206 2 .202 Y-CUT LITHIUM NIOBATE; TE oo ; X=0.6328 m; n =2.203; W •*• oo n f=2.2134; An= " w=4 ym nn ; t = o . i n ; t=0 za _L 2 4 WAVEGUIDE DEPTH d (ym) 4.5, E f f e c t i v e index n^ vs. d, f o r planar (^ ) and f i n i t e widt waveguide (n ) ; w i t h and without f i l m . z • s 62 e f f e c t i v e index increases w i t h the d i f f u s i o n depth. Everything e l s e being the same, the e f f e c t i v e index of a f i n i t e width guide i s l e s s than that of a planar guide, and the e f f e c t i v e index i s increased by the loading f i l m . For the T E Q Q and T E ^ modes the c u t - o f f curves are shown i n F i g . 4.6, and n z v s . d w i t h w = 2.5, 3 and 4 un i n F i g . 4.7. R e l a t i v e change produced i n the propagation constant of 4 i n wide guide increases w i t h the l o a d i n g f i l m t h i c k n e s s , as shown i n F i g . 4.8. For f i x e d d, the change produced i s greater f o r l a r g e r An. In the case of TM, the change l e v e l s o f f a f t e r a sharp increase at t < 0.1 ym. The e f f e c t of a s m a l l change i n the f i l m index (An^ = 0.005), on n z i s depicted i n F i g . 4.9. Here, a change i n the e f f e c t i v e index &»z (= n ^ - n z g ) f o r n f = 2.2134 and 2.2084, i s shown as a f u n c t i o n of t . The e f f e c t of l o a d i n g f i l m i s l a r g e s t , at l a r g e s t t and An. Change In the e f f e c t i v e index w i t h An as the v a r i a b l e i s p l o t t e d i n F i g . 4.10, w i t h f i l m thickness t as the parameter. F i n a l l y , 6 n z vs. d, w i t h An as a parameter i s shown i n F i g . 4.11. From these r e s u l t s i t i s concluded, that f o r the TE mode, the change 6n z increases w i t h t and An, but decreases w i t h d. An a p p l i c a t i o n of the above r e s u l t s i s i l l u s t r a t e d by an example. In Y-cut L i N b 0 3 , f o r T E Q 0 mode, at A = 0.633 ym, n g = 2.203, An = 0.04, t = 0.2 ym, and d = 2 ym; i t i s computed that n ^ = 2.225230 and 2.225156 corresponding to n^ = 2.2134 and 2.2084 r e s p e c t i v e l y . Thus, change i n phase produced by a l o a d i n g f i l m of l e n g t h L, 6q = c58 L = f- 2^ 6n .) L = 42°/mm A ZX But, f o r t = 0.5 ym; 6iJ> = 160°/mm. 0.04 0.03 An 0.02 0.01 0.00 Y-CUT LITHIUM NIOBATE; TE AND TE,, CUT-OFF CURVES: oo 11 A=0.6328 um ; n =2.203; t=0; w=4 ym TE 11 w=3,4 ym X X 2 4 WAVEGUIDE DEPTH d (ym) 63 F i g . 4.6. Mode c u t - o f f curves f o r waveguides 3 and 4 ym wide. X w o > M H w W 2.218 2.213 2.208 2.203 TE oo Y-CUT LINbO ; n e=2.203; 3 t=0 TE 11 w=4 ym / An=0.02 w=4 ym w=3 ym w=2*2ym An=0.01 w=4 ym, w=3 ym w=2^ym An= 0.0051 w=4 ym w=3 ym 64 2 3 WAVEGUIDE DEPTH d (ym) F i g . 4.8. Change i n the propagation constant as a f u n c t i o n of " . ' l o a d i n g f i l m t h i c k n e s s , w i t h An as parameter. 66 FILM THICKNESS t (um) F i g . 4.9. Change i n e f f e c t i v e index 6n due to loading f i l m thickness t , w i t h the f i l m index n as parameter. 4.10. Change i n e f f e c t i v e index due to loading f i l m - 6n vs. An z ' w i t h f i l m t h i c k n e s s as parameter. 40 XI0 -4 30 20 10 1 1 Y - C U T L I T H I U M N I O B A T E ; T E q o ; X=0.6328 pm; n e=2.203; nf=2.2134; w=4 pm t=0.3 pm \ \ \ \ \ t=0.3 pm ' \ \ s. \ - t=0.2 pmv > VAn=0.04 An=0.02 t=0.1 pm 1 1 0 2 4 6 W A V E G U I D E D E P T H d (pm) g. 4.11. Change i n the e f f e c t i v e index due to a loading f i l m ; 6n z vs. wi t h An as parameter. 69 4.7 Experimental Results I n t r i n s i c phase of a Mach-Zehnder madulator was changed with a T a 2 0 5 f i l m . To t h i s end, a Ta f i l m was formed on one arm of a Y-branch i n t e r f e r o m e t e r . An A l l i f t - o f f procedure described i n Chapter V was fo l l o w e d . The Ta f i l m was o x i d i z e d f o r 75 minutes at 500° C, before the ele c t r o d e formation. The waveguide and the T a 2 0 5 f i l m turned out to be wider than intended; 6 and 8 ym r e s p e c t i v e l y . Length of f i l m loaded waveguide was ~ 3.2mm, and i t s thickness was estimated to be 0.1 - 0.2 ym. Output l i g h t i n t e n s i t y of the modulator was measured with an ap p l i e d v o l t a g e . The r e s u l t s w i t h no o x i d a t i o n a f t e r the electrode formation are shown i n F i g . 4.12. The top t r a c e , a p o s i t i v e and negative t r i a n g u l a r waveform corresponds to the a p p l i e d v o l t a g e , and the bottom trace i s the output l i g h t I n t e n s i t y . The e x t i n c t i o n r a t i o i s poor because of surface g u i d i n g . The i n t r i n s i c phase d i f f e r e n c e 1(1 = 56°. The Ta 20 5 was treated w i t h 0 2 at 500°C f o r 11 min. The measured r e s u l t s a f t e r the 0 2 treatment are given i n F i g . 4.13; and i|>2 = 111°. Thus, 11 min. of o x i d a t i o n produced a change i n phase of 55°. The T a 2 0 5 f i l m was tre a t e d i n 0 2 f o r an a d d i t i o n a l 41 min., a f t e r which \p3 = 400°, F i g . 4.14. The second 0 2 treatment (41 min.) produced a change i n phase of 289°. The average change i n phase was ~ 6.6°/min. of o x i d a t i o n . This technique of phase tuning may be used to adjust the i n t r i n s i c phase of the BOA modulators (Chapter V I I ) , and the coupling length of d i r e c t i o n a l couplers. 0 10 ms/DIV. F i g . 4.12. Applied t r i a n g u l a r v o l t a g e and the modulator response before treatment i n oxygen. 10 V/DIV. 0.5 V/DIV. 10 ms/DIV. F i g . 4.13. Applied t r i a n g u l a r v o l t a g e and the modulator response a f t e r 11 minutes of treatment i n oxygen; i j ; = l l l 0 . F i g . 4.14. Applied t r i a n g u l a r voltage and the modulator respon a f t e r 52 minutes of treatment i n oxygen; ^=400°. 72 CHAPTER V FABRICATION AND TESTING OF DEVICES 5.1 I n t r o d u c t i o n The f a b r i c a t i o n procedure that was used to make T i d i f f u s e d waveguides i n Y-cut L i N b 0 3 and the technique to p o l i s h the c r y s t a l edges i s described below. A d e s c r i p t i o n of the measurement apparatus and steps to l i n e i t up are given. A flow chart f o r the f a b r i c a t i o n process i s shown i n F i g . 5.1 5.2 Mask Line drawings of the devices were made, and the data f o r the coordinates were entered on the AMDAHL 470 UBC computer. The data were then t r a n s f e r r e d , v i a a data l i n k to the PDP8/E computer i n the E l e c t r i c a l Engineering Department, and stored on a d i s k . A 16"x38" r u b y l i t h mask was cut on a computer c o n t r o l l e d coordinatograph using a k n i f e blade. The k n i f e blade i s p r i m a r i l y meant f o r s t r a i g h t c u t s , however, i t was t r i e d i n t h i s a p p l i c a t i o n where non-orthogonal cuts are required because of the minute f o r k angle of 1°. An o m n i d i r e c t i o n a l point c u t t e r was t r i e d and was abandoned, since i t tended to tear the p l a s t i c and produced ragged edges. The software that c o n t r o l l e d the c u t t e r motor d r i v e was modified to incorporate gradual a c c e l e r a t i o n i n the c u t t e r speed. A drawing of a Mach-Zehnder interferometer w i t h t y p i c a l dimensions i s shown i n F i g . 5.2. The c u t t e r followed the path ABCDEF, GHJKLM, PQR, TSR, PN, and TN. When c u t t i n g sections s i m i l a r to PNR, the c u t t e r d i r e c t i o n was P to N, and T to N as i n d i c a t e d i n the diagram. This s t r a t e g y 73 APPLY RESIST :PREBAKE| EXPOSE AND EOSTBAKE DEVELOP BAKE STRIP RESIST YES ETCH SPUTTER METALLIZE ALUMIN, EXPOSE: DEVELOP: ETCH CUT AND POLISH YES — NO OK? TEST - > ~ < [ o K ^ ^ > ^STOP ^ F i g . 5.1. A flow chart f o r the f a b r i c a t i o n process. (a) T i GUIDE M X 3600 H- 7200 -ELECTRODES 5.2. Li n e drawing of (a) s t r a i g h t waveguide and the Mach-Zehnder modulator. 75 of c u t t i n g avoided l i f t i n g of the r u b y l i t h adjacent to the coordinate N. Photograph masks were prepared from the r u b y l i t h masters by P r e c i s i o n Photomask L t d . , Montreal. The r u b y l i t h pattern was reduced 50 times, conse-quently the 4 micron wide waveguides were 0.008" wide on the r u b y l i t h . The p a t t e r n was stepped and repeated on the mask; 2 times i n the long d i r e c t i o n and 4 times i n the narrow d i r e c t i o n , with 1 mm i n t e r - p a t t e r n spacing. Two negative g l a s s masks were obtained, one f o r the waveguide c i r c u i t r y and another f o r the electrode network. By negatives I t i s meant that areas that were transparent on the r u b y l i t h were dark on the mask. 5.3 C r y s t a l O p t i c a l waveguide devices were f a b r i c a t e d on L i N b 0 3 c r y s t a l s obtained from C r y s t a l Technology Inc., Palo A l t o . These were 2" diameter, 0.020" t h i c k YZ wafers w i t h the Y-axis (X-ray oriented) perpendicular to the major face w i t h i n ±30 arc minutes, and the Z-axis (X-ray oriented) perpendicular to a 1" wide reference f l a t w i t h i n ±6 arc minutes. The f r o n t surface had "SAW p o l i s h " , i . e . , a p o l i s h s u i t a b l e f o r p h o t o f a b r i c a t i o n of i n t e r d i g i t a l transducers, and the back surface had been f i n e ground to 9 microns lapped f i n i s h . The c r y s t a l surface on which waveguides are to be formed has to be s c r a t c h - f r e e ; at the same time, the substrate has to be d e f e c t - f r e e since evanescent modes propagate through i t . This p a r t i c u l a r cut of c r y s t a l was s e l e c t e d to u t i l i z e the highest e l e c t r o o p t i c c o e f f i c i e n t r 3 3 (30.8 x 10~ 8 m/V) to modulate the TE mode propagating i n the X - d i r e c t i o n w i t h planar e l e c t r o d e s . 76 5.4 Cleaning Care i s required i n cleaning and handling of the substrates because of the small dimensions i n v o l v e d . Freedom from dust during photolithography i s c r u c i a l , as a s i n g l e dust p a r t i c l e would I n t e r r u p t the wave path and render the device u s e l e s s . The L i N b 0 3 c r y s t a l s r e q u i r e s p e c i a l care because they are b r i t t l e , very s e n s i t i v e to mechanical and thermal shock, and a t t r a c t dust. The waveguides are narrow (4 microns) and very long (18 mm). Because of the la r g e aspect r a t i o (4500), unusual f o r an i n t e g r a t e d c i r c u i t , the mask and the c r y s t a l have to be s c r a t c h and dust f r e e . A l s o , as only four to s i x devices can be accommodated per wafer, the y i e l d has to be h i g h . The glassware, fluoroware, baskets and tweezers were cleaned f o r three minutes with 30% hydrogen peroxide and 98% s u l p h u r i c a c i d (1:1). Polyethylene disposable gloves and l a t e x f i n g e r cots were used to handle the glassware, masks, e t c . Beakers were dedicated to various chemicals and not interchanged. Most of the work was c a r r i e d out i n a clean area w i t h p o s i t i v e a i r pressure. The f a b r i c a t i o n steps are i l l u s t r a t e d i n F i g s . 5.3. P r i o r to the d e p o s i t i o n of T i , the c r y s t a l s were cleaned as f o l l o w s : 1. B o i l e d i n acetone f o r 10 minutes 2. Put i n u l t r a s o n i c bath of acetone f o r 10 minutes 3. Rinsed i n deionized (DI) water cascade f o r 10 minutes; 2 and 8 minutes i n the downstream and upstream baths r e s p e c t i v e l y 4. Etched i n 5% h y d r o f l u o r i c a c i d f o r 2 minutes 5. Rinsed i n DI water cascade f o r 10 minutes, as above T i (a) R u b y l i t h ( f ) Etching T i (b) Mask LITHI u C Z Z Z Z Z Z Z Z Z Z Z Z 3 NIOBATE (g) D i f f u s i n g \ N N •SILICON DIOXIDE (c) T i m e t a l l i z a t i o n (h) Sputtering I I I MASK >c PHOTORESIST! (d) Exposing s s s s ALUMINUM (e) Developing ( i ) Contact m e t a l l i z a t i o n F i g . 5.3. F a b r i c a t i o n steps; developing, et c h i n g , d i f f u s i n g , s p u t t e r i n g , and m e t a l l i z i n g . 78 6. B o i l e d i n methanol f o r 5 minutes As L i N b 0 3 tends to a t t r a c t dust, the c r y s t a l was transported i n warm methanol. The c r y s t a l was then allowed to dry near i t s d e s t i n a t i o n , such as vacuum evaporation chamber, furnace, e t c . A l t e r n a t i v e procedures are the so c a l l e d RCA Clean [Kern and Puotinen 1970], and t r i c h l o r o e t h y l e n e , hydrogen peroxide, and ammonium hydroxide treatment [ S t u l z 1979]. 5.5 Evaporation of T i About 450 A t h i c k l a y e r of 99.99% T i was evaporated onto the clean c r y s t a l s , using the Veeco (VE400) system. The pressure p r i o r to evaporation was < 5x10" 6 Torr as measured at the base p l a t e w i t h an I o n i z a t i o n Vacuum Gauge. A 0.045" diameter T i wire wrapped around a tungsten filament was used as a source. A f i l a m e n t current of 80 A was r e q u i r e d , and the evaporation r a t e was about 10 A/s. The T i wrapped tungsten f i l a m e n t was obtained from Vacuum Atmospherics, Hawthorne, C a l i f o r n i a . The main contaminants i n the T i , as quoted by the s u p p l i e r were: carbon (0.009 ppm); i r o n (0.034 ppm); oxygen (0.126 ppm); hydrogen (0.004 ppm); and n i t r o g e n (0.007 ppm). The quartz c r y s t a l f i l m thickness monitor ( I n f i c o n ; Model 321) used to determine the thickness of the evaporated metal had to be c a l i b r a t e d . The c a l i b r a t i o n was done by two methods. In the f i r s t method, a clean dry c r y s t a l was weighed before and a f t e r evaporation of the T i . The f i l m thickness was c a l c u l a t e d to be 761 A, w i t h d e n s i t y = 4.54 gm/cc, diameter = 2", and weight = 0.7 gm. Thus, the a c t u a l thickness i s about 57% of the monitor reading. In the second method, T i was evaporated over part of a clean s i l i c o n wafer to 79 form a step. Then a 10 k A t h i c k l a y e r of aluminium was evaporated over the T i step. The Sloan Angstrometer (M100) was used to determine thickness of the T i , and i t was estimated to be 618 A . Thus, the thickness i s 47% of the moni-t o r reading. 5.6 Exposing, developing, and etching The c r y s t a l w i t h the evaporated metal was taken from the vacuum system d i r e c t l y to the p h o t o r e s i s t spinner, i n order to e l i m i n a t e baking to d r i v e out moisture. The L i N b 0 3 c r y s t a l was placed i n a t e f l o n f i x t u r e and spun at 2500 rpm f o r 15 seconds to dislodge any dust p a r t i c l e s . The use of the f i x t u r e , F i g . 5.A, was necessary to hold the c r y s t a l , otherwise I t tended to warp, f l y o f f , and break. P o s i t i v e p h o t o r e s i s t (Waycoat P o s i t i v e LSI 295 R e s i s t ) was spun on the m e t a l l i z e d c r y s t a l at 2500 rpm f o r 15 seconds tc o b t a i n a r e s i s t thickness of about 2 microns. Pre-bake of the p h o t o r e s i s t was c a r r i e d out at 90°C f o r 30 minutes. The c r y s t a l temperature was r a i s e d and lowered at a r a t e not exceeding 20°C/ minute. The p h o t o r e s i s t was exposed to u l t r a v i o l e t l i g h t f o r 18 seconds through the waveguide mask. The mask a l i g n e r (Kasper Instruments), which i s normally used f o r i n t e g r a t e d c i r c u i t s , was employed. The exposed c r y s t a l was loaded i n t o a s i n g l e substrate fluoroware clamped h o l d e r . The p a t t e r n was then developed u n t i l the p h o t o r e s i s t came o f f , i . e . , when the clouds and r i n g s formed on the surface disappeared completely. The development was h a l t e d by soaking i n deionized water f o r 10 minutes. The c r y s t a l was blown dry and then examined under the microscope. I f the c o n t r a s t i n the r e s i s t p a t t e r n was not s u f f i c i e n t , f u r t h e r development was done. I f , f o r some reason the r e s i s t WAFER s \ !s"!s s s v ST s yfl a u 3 fail D8 VACUUM (a) WAFER VACUUM (b) F i g . 5.4. J i g to hold the wafer; ( a ) s t a t i o n a r y and (b) spinning, HEATER REGULATOR AND PRESSURE REDUCER PRESSURE GAUGE O - o H OXYGEN CYLINDER COOLER CONTROLS DIFFUSION TUBE -•-EXHAUST F i g . 5.5. Arrangement f o r c a r r y i n g out the d i f f u s i o n . 81 p a t t e r n was unacceptable, i t was necessary to d i s s o l v e the r e s i s t i n b o i l i n g acetone, and bake the c r y s t a l at 200° C f o r 30 minutes to d r i v e out the moisture before repeating the whole procedure. I f the r e s i s t pattern was s a t i s f a c t o r y , post-bake (pre-etch) was done at 120°C f o r 30 minutes, again w i t h gradual heating and c o o l i n g of the c r y s t a l . The exposed T i was etched i n 5% HF f o r 6 seconds, and c o n t r o l of t h i s d u r a t i o n i s c r i t i c a l to avoid u n d e r c u t t i n g . E t c hing was ha l t e d w i t h a 10 minute soak i n f r e s h deionized water. The c r y s t a l was d r i e d and examined under the microscope. I f necessary, the etching processing was repeated only one second at a time u n t i l s a t i s f a c t o r y r e s u l t s were obtained. I f the etching was acceptable, the r e s i s t was s t r i p p e d i n b o i l i n g acetone. The pa t t e r n was then examined under the microscope, device by device. Of course, i f the patter n was unacceptable, i t was n e c e s s a r y to s t a r t a l l over a g a i n , i . e . , r e p e a t the c l e a n i n g , m e t a l l i z a t i o n and e t c h i n g . 5.7 D i f f u s i o n The c r y s t a l w i t h T i patter n was cleaned (acetone; DI water; methanol) and loaded i n t o the centre of a 2.5" diameter M i n i Brute furnace. The furnace had been turned o f f 12 hours e a r l i e r f o r i t to co o l to room temperature. The flow of oxygen (medical grade) through the furnace was adjusted to be 1 l i t r e / minute, F i g . 5.5. The complete d i f f u s i o n c y c l e i s shown i n F i g . 5.6. When the furnace was turned on, the rate of increase of temperature was 20°C/minute. A f t e r the temperature reached 400°C, i t was f u r t h e r increased to 500°C at 20°C/minute. The temperature was maintained at 500°C f o r two hours to o x i d i z e the T i , a f t e r DIFFUSION 4% HOURS (WITHOUT POWDER) DIFFUSION IU HOURS (WITH POWDER) TIME (MINUTES) Fig . 5.6. The d i f f u s i o n c y c l e . 83 which i t was r a i s e d to 780° C at 20°C/minute. When the temperature reached 780°C the c o n t r o l s were adjusted to 950°C, to force as quick a passage through 850°C as p o s s i b l e . This i s necessary to avoid the formation of surface c r a t e r s due to the phase transformation of L i N b 0 3 to L i N b 3 0 g . This occurs i f the temperature i s maintained near 850°C f o r more than 10 minutes[Vahey 1980]. Once the temperature reached 950°C, i t was increased to 1020°C at 20°C/minute. The temperature of 1020°C and the oxygen f l o w of 1 l i t r e / m i n u t e were held constant f o r 4.5 hours. During t h i s period the o x i d i z e d T i d i f f u s e d i n t o L i N b 0 3 . A f t e r 4.5 hours, the furnace was turned o f f and allowed to cool to room temperature. I n i t i a l l y , the temperature decreased at 20°C/minute, but the r a t e diminished w i t h time. During the d i f f u s i o n c y c l e L i 2 0 escapes from the L i N b 0 3 c r y s t a l , forming a l a y e r of o u t d i f f u s e d waveguide a l l over the surface [Miyazawa et a l . 1977; Burns et a l . 1978; E s d a i l e 1978; Ranganath and Wang 1979]. The L i 2 0 d e f i c i e n c y i n c r e a s e s the e x t r a o r d i n a r y r e f r a c t i v e index, n e« This a f f e c t s propagation only of the TE but not the TM modes i n Y-cut c r y s t a l s . O u t d i f f u s i o n was compensated by continu i n g the d i f f u s i o n c y c l e i n the presence of LiNbOj powder. The c r y s t a l was removed from the cooled furnace, and placed face down on top of a platinum box (2"x2"x0.25") c o n t a i n i n g 1 gm of f r e s h L i N b 0 3 powder, F i g . 5.7. The c r y s t a l and the platinum box were r e p o s i t i o n e d i n the centre of the furnace. The above d i f f u s i o n c y c l e was repeated, except that the temperature was maintained at 1020° C f o r 90 minutes before the furnace was turned o f f . Once the furnace cooled to room temperature, the oxygen f l o w was terminated, the c r y s t a l withdrawn from the furnace, and examined under the microscope. F i g . 5.7. Arrangement f o r Li„0 compensation during d i f f u s i o n . 85 The d i f f u s i o n of T i atoms i n t o L i N b 0 3 produced bulging e a s i l y seen with a microscope. In a d d i t i o n to the transverse d i f f u s i o n there was some l a t e r a l d i f f u s i o n which widened the l i n e s s l i g h t l y . I t a l s o straightened the waveguide edges, and thus e l i m i n a t e d some of the i r r e g u l a r i t i e s of the mask and e t c h i n g . A s c r u t i n y of the c r y s t a l surface a f t e r d i f f u s i o n revealed some worm-like s t r i a t i o n s about 0.2" l o n g . These were probably induced by the heating and c o o l i n g of the c r y s t a l . 5.8 S p u t t e r i n g of S i 0 2 Metal e l e c t r o d e s In d i r e c t contact w i t h d i f f u s e d waveguides cause loading and produce l o s s e s , since decaying mode f i e l d s extend beyond the waveguide. A low-index d i e l e c t r i c b u f f e r l a y e r interposed between the waveguides and the e l e c t r o d e s reduces the l o s s due to metal l o a d i n g . Subsequent to the T i d i f f u s i o n and the L i 2 0 compensation, the c r y s t a l surface was scrubbed c l e a n w i t h deionized water to remove any traces of L i N b 0 3 powder. Then the substrate was cleaned, and a 2000 A l a y e r of S10 2 was sputtered on i t using the Perkin-Elmer Vacuum System, which had a 6" diameter and 1/8" t h i c k water cooled S i 0 2 target of 99.95% p u r i t y . The s p u t t e r i n g was done i n an argon atmosphere at a 35 mTorr pressure, at a forward power of 150 W, and a r e f l e c t e d power of < 5 W. The separation between the target and the c r y s t a l was about 2". Adjustments were made to the gas pressure and the r f power every 10 minutes or so, to keep the s p u t t e r i n g c o n d i t i o n s constant and to maintain a uniform and s t a b l e plasma. The s p u t t e r i n g r a t e was approximately 36 A/minute. The d e p o s i t i o n r a t e can be increased by boosting the gas 86 pressure [ M a i s s e l and Glang 1970], but at pressures exceeding 45 mTorr secondary plasmas were e x c i t e d . The s p u t t e r i n g r a t e was determined p r i o r to de p o s i t i n g the S i 0 2 l a y e r on the L i N b 0 3 c r y s t a l . Three pieces of S i (n-type, 1-2 ohm-cm, [100] o r i e n t a t i o n ) were cleaned and S i 0 2 was sputtered on these f o r 15, 32 and 37 minutes. Using e l l i p s o m e t e r y , the corresponding oxide thickness was determined to be 600, 1200 and 1350 A. Measured data are i n d i c a t e d on the f i l m thickness and r e f r a c t i v e index curves i n F i g . 5.8. The average s p u t t e r i n g r a t e was c a l c u l a t e d to be 36 A/minute. The sputtered l a y e r growth i s assumed to be l i n e a r w i t h time, t h i s i s u s u a l l y the case i f the gas pressure and r f power con d i t i o n s are s t a b l e . An estimation of the oxide thickness was made by c o n s u l t i n g the IBM colour c h a r t . When the sputtered f i l m was viewed i n d a y l i g h t , the oxide l a y e r on LINbOg c r y s t a l was not as p e r c e p t i b l e as i t was on the s i l i c o n c r y s t a l . Nevertheless, i t could be detected by observing the r e f l e c t i o n of f l u o r e s c e n t l i g h t s from the c r y s t a l s u r f a c e . The 2000 A l a y e r of S i 0 2 was of yellow-green hue. 5.9 Forming T a 2 0 5 P a t t e r n A T a 2 0 5 f i l m was formed on an arm of the Y-branch modulator to be able to change i t s i n t r i n s i c phase l a t e r on. The f i l m was formed a f t e r the T i d i f f u s i o n , and without an S i 0 2 l a y e r . An A l l i f t - o f f technique was used to form a Ta pa t t e r n ; F i g . 5.9. F i r s t , a ~ 3 kA A l f i l m was deposited on the wafer by evaporation. Then, a ~ 4 ym window was etched i n the A l f i l m on one arm of the modulator. A f t e r s t r i p p i n g the negative p h o t o r e s i s t , a ~ 400 A Ta f i l m was sputtered i n Ar at 25 mTorr. The s p u t t e r i n g rate was 62 A/min at a SPUTTERED TANTALUM ZZZZZZZZ3 LITHIUM NIOBATE SUBSTRATE •ALUMINUM .TITANIUM VI AVE GUIDE F i g . 5 . 9 . Sputtered Ta over the T i md i f fused waveguide and between A l , p r i o r to A l l i f t - o f f . 88 forward power of 100 W. Unwanted Ta was l i f t e d o f f by d i s s o l v i n g A l i n phosphoric a c i d . The Ta pa t t e r n thus obtained was o x i d i z e d (02:l£/m) at 500°C, f o r 90 minutes. The r e s u l t i n g oxide f i l m was about 1100 A t h i c k . E l e c t r o d e s were then formed, and the c r y s t a l cut and p o l i s h e d . The i n t r i n s i c phase of the modulator was measured. The T a 2 0 5 was o x i d i z e d at 500°C f o r 10 minutes, and the i n t r i n s i c phase remeasured. The r e s u l t s are discussed i n Chapter V I I . 5.10 Forming the Electrode P a t t e r n A f t e r s p u t t e r i n g the S i 0 2 b u f f e r l a y e r , the c r y s t a l was cleaned i n acetone, deionized water, and methanol, and then a 10 kA l a y e r of aluminium was deposited by e l e c t r o n beam evaporation, using the Veeco. The evaporation r a t e was about 30 A/second at a current of 280 mA. Next, the electrode p a t t e r n was etched using the procedure o u t l i n e d e a r l i e r . A s p l i t f i e l d microscope on the mask a l i g n e r was used to a l i g n the electrodes w i t h the waveguides. A s o l u t i o n of phosphoric a c i d (85%) and deionized water (1:1) at 50° C was used to etch the aluminium p a t t e r n ; the etch time was about 7 minutes. I f the ele c t r o d e p a t t e r n was not s a t i s f a c t o r y , i t was necessary to s t r i p the r e s i s t , remove the aluminium, and s t a r t a l l over again. A photograph of a t y p i c a l d i f f u s e d waveguide and the electrode p a t t e r n Is i n F i g . 5.10. F i g . 5.10. Photograph of the d i f f u s e d waveguides and the e l e c t r o d e p a t t e r n ; m a g n i f i c a t i o n : (a) 14X; and (b) 280X. 90 5.11 C u t t i n g , g r i n d i n g , and p o l i s h i n g To launch l i g h t i n t o the waveguide by " e n d - f i r i n g " , a p o l i s h e d c r y s t a l edge i s r e q u i r e d . For e f f i c i e n t coupling the edge has to be square, since the waveguide i s only a couple of microns deep. Furthermore, the edge has to be d e f e c t - f r e e and po l i s h e d to a surface f i n i s h approaching a f r a c t i o n of the guide wavelength. Edge p o l i s h i n g o f f e r s s e v e r a l advantages over c l e a v i n g [ S t u l z 1979]. The cleavage i s accompanied by chi p p i n g , a l s o i t tends to wander f o r substrates wider than 2 mm [ S t u l z 1979]. An i r r e g u l a r edge causes l i g h t to r e f l e c t and s c a t t e r at the entrance and the e x i t to the guide. The u l t i m a t e operation of the device and i t s e f f i c i e n c y , depend on how w e l l the l i g h t i s coupled i n t o and out of the waveguide. So, the p o l i s h i n g procedure e s t a b l i s h e d a f t e r much t r i a l and e r r o r i s o u t l i n e d i n some d e t a i l . This procedure, however, i s s u i t e d to the p o l i s h i n g of only one c r y s t a l at a time. 5.11.1 Pr e p a r a t i o n of the c r y s t a l f o r c u t t i n g A f t e r the waveguide p a t t e r n had been d i f f u s e d , a S i 0 2 l a y e r sputtered, and the aluminium contact electrodes etched, the c r y s t a l was ready f o r c u t t i n g and p o l i s h i n g . The c r y s t a l was temporarily cemented to a s t e e l p l a t e using Canada balsam. I t was then cut w i t h a diamond saw. The s t e e l p l a t e had surfaces f l a t to w i t h i n ± 0.001", and the dimensions are shown i n F i g . 5.11. The s t e e l p l a t e was placed on a hot p l a t e and heated to about 110°C, j u s t warm enough to form a molten l a y e r of the canada balsam. Ju s t enough balsam to form a strong bond was a p p l i e d . Any balsam that flowed to the top surface of the wafer i n t e r f e r e d w i t h the cover pieces and smeared the e l e c t r o d e s , and i t was very d i f f i c u l t to remove. During t h i s p eriod the c r y s t a l was placed on an _ CANADA BALSAM STEEL PLATE F i g . 5.11. Mounting of the c r y s t a l i n preparation f o r c u t t i n g . 92 adjacent s t e e l p l a t e to warm up g r a d u a l l y . The warm LiNb0 3 c r y s t a l was very c a r e f u l l y placed on the molten balsam, and i t s f l a t 1" reference edge was a l i g n e d a c c u r a t e l y w i t h the s t e e l p l a t e edge. The assembly was then allowed to c o o l . As mentioned e a r l i e r , the waveguide edges were protected from chipping and rounding by permanently bonding L i N b 0 3 cover pieces, about 1/10" wide and 2" l o n g , on the c r y s t a l where i t had to be cut t r a n v e r s e l y . I t was necessary to use L i N b 0 3 cover p i e c e s , since any other m a t e r i a l would have worn o f f at a d i f f e r e n t r a t e during p o l i s h i n g , and produced scratches. The cover pieces were bonded w i t h a two p a r t , 5 minute epoxy (Devcon, Danvers, Mass.). To ensure a strong bond, 24 hours were allowed f o r the epoxy to s e t . Once the epoxy s e t , i t had the hardness to withstand c u t t i n g and p o l i s h i n g . A small bead of epoxy was formed where the cover piece was to be bonded. Then a cover piece w i t h the rough side towards the c r y s t a l was pressed i n t o p l a c e , to form as t h i n an epoxy l a y e r as p o s s i b l e to f a c i l i t a t e p o l i s h i n g . The epoxy was used s p a r i n g l y to avoid smearing the aluminium electrodes. A f t e r the epoxy was d e f i n i t e l y s e t , the assembly was placed on a hot p l a t e and heated to 70°C, the me l t i n g point of Pyseal wax ( F i s h e r S c i e n t i f i c , Fairlawn, N.J.). The wax was a p p l i e d to form a puddle over the exposed areas of the c r y s t a l . I t was a p p l i e d to protect the waveguides and the electrode pattern during c u t t i n g and p o l i s h i n g . A f t e r the wax hardened, the c r y s t a l was ready f o r c u t t i n g and d i v i d i n g . C u t t i n g was done with a diamond saw which has a v e r t i c a l blade 8" In diameter, 0.02" t h i c k and 180 g r i t . The c u t t i n g r a t e was 2"/hour. Of course, the slower the c u t , the b e t t e r the f i n i s h . A f t e r a l l the cuts were made, the 93 assembly was removed, cleaned i n deionized water, and d r i e d . The assembly was warmed on a hot p l a t e to melt the Canada balsam, and the cut pieces were removed and s t o r e d . 5.11.2 Grinding and p o l i s h i n g of the c r y s t a l In order to o b t a i n a d e f e c t - f r e e p o l i s h e d edge, g r i n d i n g and p o l i s h i n g was done. The g r i n d i n g was done on an emery paper. A f t e r which the p o l i s h i n g was c a r r i e d out using 9 , 6 , 1 and 1/4 micron diamond paste compound (Metadi I I and I; Buehler L t d . , Evanston, 111.). In p r e p a r a t i o n f o r g r i n d i n g and p o l i s h i n g , a piece of c r y s t a l was centred and bonded to a s t r i p of glass or metal, F i g . 5.12. The s t r i p was cut wide enough to provide adequate support to the c r y s t a l , yet narrow enough to give s u f f i c i e n t overhang so as not to i n t e r f e r e w i t h the p o l i s h i n g . I f necessary, another coat of the Pyseal wax was applied to p r o t e c t the waveguides and the e l e c t r o d e p a t t e r n . The edge of the c r y s t a l was examined m i c r o s c o p i c a l l y . To view the edge, one end of the glass s t r i p was held i n a lump of modelling c l a y seated on a glass s l i d e . The c r y s t a l edge was l e v e l l e d and viewed, F i g . 5.13. I f the c r y s t a l edge was not smooth, or i f i t had epoxy on i t , the edge was ground on an emery p o l i s h i n g paper (4/0 Z948, Closekote, Norton). A f i g u r e of e i g h t or a c i r c u l a r motion was executed to o b t a i n uniform g r i n d i n g . U s u a l l y 15 to 30 minutes of g r i n d i n g per edge was required to smooth the i r r e g u l a r i t i e s and scratches r e s u l t i n g from c u t t i n g . Grinding was done one minute at a time followed by a pause, to avoid heating the c r y s t a l and weakening the epoxy bond. A view of the ground edge i s shown i n F i g . 5.14. The g r i n d i n g was terminated when there was no f u r t h e r improvement. 94 EDGE TO BE POLISHED EDGE TO BE POLISHED GLASS STRIP F i g . 5.12. Mounting of a c r y s t a l piece before p o l i s h i n g . .5.15. The c r y s t a l a f t e r p o l i s h i n g w i t h 9 ym diamond paste f o r 90 minutes; m a g n i f i c a t i o n : 14 OX. 96 The c r y s t a l was cleaned i n deionized water and then put i n u l t r a s o n i c bath f o r 10 minutes; t h i s prevented the transmission of ground p a r t i c l e s from one stage to the next. Cotton swabs ( 0 - t i p s ) , soaked i n DI water were used to wipe the edge. The wiping was c a r r i e d out i n a s i n g l e s t r o k e , and no p o r t i o n of the swab was reused. The next step was p o l i s h i n g w i t h a 9 micron diamond paste. A p o l i s h i n g c l o t h w i t h adhesive backing (Buehler L t d . , 111.) was applied to a g l a s s p l a t e 9"x9". The diamond paste, which comes i n a s y r i n g e , was dispensed to form 3 or 4 dabs, 1/4" long, spaced at equal distances over 2 square inches. The diamond compound was spread l i g h t l y w i t h a clean f i n g e r t i p . Three or four drops of extender o i l were a p p l i e d w i t h a dropper, over the area charged w i t h paste. An atomizer should be used f o r a c o n t r o l l e d and uniform a p p l i c a t i o n of the o i l . The o i l was used parsimoniously, since too much o i l produced sc r a t c h e s . The c r y s t a l edge was then rubbed l i g h t l y on the o i l e d diamond compound with s t r a i g h t s t r o k e s , to wear down large p a r t i c l e s . The charge was "broken-in", and the c r y s t a l edge was p o l i s h e d t r a c i n g a figure of eight to prevent r o l l i n g . The p o l i s h i n g w i t h the paste was continued, u n t i l the gouges and scratches disappeared. This can be seen by comparing F i g s . 5.15 and 5.16. A f t e r about 90 minutes of p o l i s h i n g , the edges on e i t h e r side of the epoxy l i n e became v i s i b l e . These were u s u a l l y jagged and chipped. With subsequent p o l i s h i n g small chips of L i N b 0 3 broke o f f the c r y s t a l . These can be seen embedded i n the epoxy. The p o l i s h i n g was continued u n t i l the edges became c h i p - f r e e , and formed two smooth p a r a l l e l l i n e s on e i t h e r side of the epoxy l i n e . This required about 60 to 90 minutes of p o l i s h i n g . (a) \ 14 OX (b) Fig. 5.16. The crystal edge after polishing with 9 pm diamond paste for 3h hours; magnification: (a) 14X; and (b) 140X. 98 Once the surface was smooth, i t was a matter of co n t i n u i n g w i t h f i n e r grades of diamond paste u n t i l the d e s i r e d f i n i s h was obtained. The c r y s t a l edge was cleaned w i t h cotton swab soaked i n DI water before proceeding w i t h f i n e p o l i s h i n g . The use of s o l v e n t s , t r i c h l o r o e t h y l e n e , xylene, e t c . , was avoided, to prevent weakening the epoxy bond. The unused area on the p o l i s h i n g c l o t h was charged w i t h a 6 microns diamond paste. The diamonds were broken-in, and the p o l i s h i n g resumed w i t h s t r a i g h t and f i g u r e of e i g h t motions. The diamond compound was used s p a r i n g l y , as excessive diamonds can-not f i n d niches and skate on the s u r f a c e , causing edge damage by s c r a t c h i n g . A f t e r the edge acquired an appearance s i m i l a r to F i g . 5.17, the c r y s t a l was cleaned, and the whole process of charging, b r e a k i n g - i n , and p o l i s h i n g repeat-ed w i t h 1 micron and 1/4 micron diamond paste f o r 30 minutes i n each case. U l t i m a t e l y , the surface was h i g h l y p o l i s h e d and the edge roughness l e s s than one micron; i t had the appearance of F i g . 5.18. The epoxy l i n e was about 6 microns wide at the end of p o l i s h i n g . I f the epoxy j o i n t i s wider, more p o l i s h i n g i s required r e s u l t i n g i n rounding of the edges. An a l t e r n a t i v e method of g r i n d i n g and p o l i s h i n g i s to use an e l e c t r i c a l l y d r i v e n p o l i s h i n g wheel. The p o l i s h i n g time i s reduced c o n s i d e r a b l y , but t h i s method i s r i s k y without the use of appropriate f i x t u r e s : on two d i f f e r e n t occasions the c r y s t a l caught i n the r o t a t i n g wheel and broke. A f t e r both c r y s t a l edges had been p o l i s h e d and cleaned, the Pyseal wax was removed w i t h b o i l i n g t r i c h l o r o e t h y l e n e . The edges were wiped cl e a n w i t h acetone and methanol, the c r y s t a l was ready f o r t e s t i n g by e n d - f i r e d c o u p l i n g . In order to remove unwanted Canada balsam, warm xylene was used w i t h p a r t i a l F i g . 5.17. The c r y s t a l edge a f t e r p o l i s h i n g w i t h 6 ym diamond paste m a g n i f i c a t i o n : (a) 1A0X; and (b) 280X. F i g . 5.18. The c r y s t a l edge a f t e r p o l i s h i n g w i t h (a) 1 um paste; 560X; and (b) 1/4 ym paste; 560X. 101 success. To d i s s o l v e epoxy (Devcon), a 24-hour soak i n t r i c h l o r o e t h y l e n e was e f f e c t i v e . A l t e r n a t i v e l y , the epoxy was burnt o f f at 500°C i n 0. 5.12 F a b r i c a t i o n tolerances During the f a b r i c a t i o n of the i n t e g r a t e d o p t i c a l c i r c u i t s , s e v e r a l f a c t o r s a f f e c t the device dimensions. A t y p i c a l device i s shown i n F i g . 5.2. A small branching angle of 0.5° at the waveguide j u n c t i o n s i s needed to f a c i l i t a t e equal d i v i s i o n of the l i g h t . Narrow gaps (6 microns) between the e l e c t r o d e s , and long waveguides (18000 microns), are required f o r e f f i c i e n t modulation. Tolerances i n the processing steps that contribute to d e v i a t i o n s from the above o b j e c t i v e s are: 1. C u t t i n g and p e e l i n g 2. Mask 3. Exposing, developing, and etching 4. D i f f u s i o n I r r e g u l a r i t i e s i n the r u b y l i t h a f f e c t d e f i n i t i o n of the p a t t e r n on the mask and q u a l i t y of the d e v i c e s . A r u b y l i t h p a t t e r n only 50 times the a c t u a l device s i z e (18 mm long) could be c u t , as the coordinatograph bed i s only 40" lon g . Therefore, any e r r o r s i n c u t t i n g were reduced by a f a c t o r of 50 o n l y . A k n i f e blade designed f o r making s t r a i g h t c u t s , was used f o r the skew l i n e s , which as a r e s u l t had ragged edges. Skew l i n e s w i t h opposite slopes had unequal widths due to the asymmetric k n i f e blade. A l s o , the width of the skew l i n e s was narrower than the design, due to t r i a n g u l a r motion of the c u t t e r . As the c u t t e r could move only i n 0°, 90° or 45° d i r e c t i o n s , a skew l i n e could be approximated e i t h e r by a s t a i r c a s e , or by a concatenation of 45° l i n e 102 ±0 on On me segments. The l a t t e r s t r a t e g y minimizes d e v i a t i o n s from the design, so i t had been incorporated i n the c u t t e r d r i v e program. The c u t t e r was d r i v e n by stepping motors w i t h a minimum step of 0.001", thus the e r r o r i n each cut was .001". A d e s i r e d waveguide width of 4 microns which corresponds to 0.008" the r u b y l i t h , was cut as 0.008 ± .002". Consequently, the waveguide width on the mask was 4±1 micron. Masks from the r u b y l i t h s were prepared e x t e r n a l l y : some had a b e r r a t i o n s , one mask, an L-shaped l i n e w i t h a uniform design width of 20 microns, asured 24 and 28 microns on the two arms. The l i n e widths were d i f f i c u l t to measure, because at very high m a g n i f i c a t i o n (560X) the pattern on the mask appeared granu l a r w i t h d i f f u s e d edges. A l s o , repeated use and handling s u l l i e d the mask. The exposure, development, and etch times were e s t a b l i s h e d by t r i a l and e r r o r . By j u g g l i n g these times, the width of the l i n e s could be adjusted by a micron or two. Thickness of the p h o t o r e s i s t was a f f e c t e d by the s p i n speed and time. Exposure and development times depend on the r e s i s t thickness and a f f e c t the c o n t r a s t . Etching i s u s u a l l y accompanied by undercutting. In the case of the p o s i t i v e r e s i s t photolithography, the e r r o r s due to overexposure and overetch are a d d i t i v e . As a r e s u l t , the etched p a t t e r n i s narrower than the design. In c o n t r a s t , w i t h the negative r e s i s t photolithography, overexposure and overetch have opposite e f f e c t s and tend to cancel each other. In a d d i t i o n to the transverse d i f f u s i o n , there i s l a t e r a l d i f f u s i o n which increases the l i n e width, but reduces the i r r e g u l a r i t i e s due to the mask and the e t c h . 103 5.13 E n d - f i r e coupling procedure The f o l l o w i n g procedure was used to a l i g n the l a s e r , the input and output microscope o b j e c t i v e s , and the c r y s t a l . The measurement set-up of F i g . 5.19 was used. L i g h t was focussed w i t h an input o b j e c t i v e at the p o l i s h e d end of the guide, and c o l l e c t e d at the output by another o b j e c t i v e . This method of coupling l i g h t i s c a l l e d " e n d - f i r e " c o u p l i n g , i t i s s u i t a b l e f o r use w i t h o p t i c a l f i b r e s . Other methods of coupling l i g h t require the use of prisms, g r a t i n g s , e t c . 1. The l a s e r L and the input o b j e c t i v e J l (100X), F i g . 5.19, were al i g n e d to obt a i n maximum output. This was done by p l a c i n g a paper beyond the o b j e c t i v e J l , and obtai n i n g a c i r c u l a r patch of uniform b r i g h t l i g h t . 2. The second o b j e c t i v e J2 (AOX), placed at a distance of 2 cm from J l . Then J2 was adjusted to obt a i n a uniform c i r c u l a r p a t t e r n of d i f f u s e d l i g h t . 3. The t e s t c r y s t a l was mounted on a platform; adjustable i n X, Y and Z d i r e c t i o n s , and r o t a t a b l e around the Y - a x i s . A photograph of the set-up i s shown i n F i g . 5.20. A piece of masking tape was used to secure the c r y s t a l - c a r r y i n g glass s l i d e to the p l a t -form. 4. The two o b j e c t i v e s were lined-up using the electrode p a t t e r n as a guide. Next, the o b j e c t i v e s were adjusted to be 1 mm from the c r y s t a l edges. 5. The c r y s t a l was then moved downwards to Intercept the beam of l i g h t . Next, the o b j e c t i v e s and the c r y s t a l were adjusted to LASER POLARIZER POWER SUPPLY V CRD ATT J l PROBES (lOOX) SIGNAL GENERATOR * ADJUSTABLE IN X, Y AND Z DIRECTIONS ATT ATTENUATOR AMP AMPLIFIER J MICROSCOPE OBJECTIVE DET DETECTOR GRD GROUND AMP OSCILLOSCOPE PLATFORM (4 OX) F i g . 5.19. Measurement set-up. o F i g . 5.20. Photograph of the experimental set-up. 106 o b t a i n a focussed set of p a r a l l e l l i n e s , see F i g . 5.21(a). Then the c r y s t a l was moved downwards u n t i l the l i n e s moved f u r t h e r a part, as shown i n F i g . 5.21(b). 6. The c r y s t a l was moved back and f o r t h ( Y - d i r e c t i o n ) u n t i l a bushy Int e r f e r e n c e p a t t e r n of F i g . 5.21(c) was seen. Such a bushy p a t t e r n i n d i c a t e d the presence of an o p t i c a l waveguide. The pa t t e r n was bigger and more complex when there was more than one waveguide. 7. Once the bushy patte r n was obtained, i t was simply a matter of a d j u s t i n g the pl a t f o r m height and the input o b j e c t i v e J l , to ob t a i n a b r i g h t focussed spot of l i g h t ; see F i g . 5.21(d). 8. The TE p o l a r i z a t i o n of the l i g h t was se l e c t e d by p l a c i n g the p o l a r i z e r at the l a s e r ; moving the p o l a r i z e r adjacent to the detector made n e g l i g i b l e d i f f e r e n c e . 9. The screen was removed, and the output l i g h t allowed to impinge the d e t e c t o r . To el i m i n a t e extraneous l i g h t from the s u b s t r a t e , room l i g h t s , e t c . , a paper w i t h 0.5 mm diameter pinhole was placed at the detector Input. 10. The output i n t e n s i t y a f t e r d e t e c t i o n and a m p l i f i c a t i o n was di s p l a y e d on an o s c i l l o s c o p e . 11. The modulating voltage was a p l i e d through s t e e l probes. While viewing the probe and i t s r e f l e c t i o n through a microscope, the probe was lowered to the contact pad. The p o s i t i o n of the probe was adjusted, i f necessary, before the contact was made. Once the probe t i p and i t s r e f l e c t i o n coalesced, the probe movement (d) F i g . 5.21. Output l i g h t p a t t e r n as the microscope o b j e c t i v e and the c r y s t a l are adjusted to d i s p l a y the guided l i g h t . 108 was h a l t e d . When the probe t i p made contact w i t h the pad, the speckle p a t t e r n on the c r y s t a l surface s h i f t e d . P r e s s i n g the probe on the pad i n v a r i a b l y decreased the output l i g h t l e v e l , but the l e v e l was regained by lowering the input o b j e c t i v e . Excessive probe pressure was avoided to prevent s c r a t c h i n g of the ele c t r o d e p a t t e r n . Of course, once a l l the probes were i n pl a c e , the platform was not moved. The modulating s i g n a l was then turned on and dis p l a y e d on the o s c i l l o s c o p e . The system was tweaked; that i s , the input coupling and the detector p o s i t i o n s were adjusted to ob t a i n a symmetrical output waveform w i t h as small a dc component as p o s s i b l e . 109 CHAPTER VI INTEGRATED OPTICAL MACH-ZEHNDER MODULATOR The design, measured performance and a p p l i c a t i o n s of the i n t e g r a t e d e l e c t r o o p t i c Mach-Zehnder modulator are reviewed below. The modulator i s a component of the HV sensor, s e r i e s and multibranch i n t e r f e r o m e t e r , and the A/D converter i n v e s t i g a t e d i n t h i s work. 6.1 Y-branch modulator The e l e c t r o o p t i c Y-branch modulator shown i n F i g . 5.2 i s an i n t e g r a t e d o p t i c a l v e r s i o n of the bulk Mach-Zehnder type interferometer [Martin 1975; Ohmachi and Noda 1975; Ranganath and Wang 1979]. The output ( I q ) and input (1^) l i g h t i n t e n s i t i e s are r e l a t e d by, I = -i [1 + cos(KLV + i|»)] + I , (6.1) o 2 dc where I , and I , are the input and unmodulated l i g h t i n t e n s i t i e s r e s p e c t i v e l y , i dc L i s the ele c t r o d e l e n g t h , V i s the ap p l i e d v o l t a g e , and ip i s the i n t r i n s i c phase d i f f e r e n c e due to unequal path lengths. Here, $ = KLV and K i s given by, * = IT (1*^1 ( 6 * 2 ) Where, X i s the wavelength, n and r are the r e f r a c t i v e index and e l e c t r o o p t i c c o e f f i c i e n t of the waveguide r e s p e c t i v e l y , d i s the gap between e l e c t r o d e s , and n i s overlap between o p t i c a l and e l e c t r i c a l f i e l d s . For TE modulation e l e c t r o d e s are on e i t h e r side of the waveguide, n = 0.6. For Z-cut L i N b 0 3 , TM 110 p o l a r i z a t i o n u t i l i z e s , r 3 3 , and one electrode r e s i d e s on top of the waveguide, and i n t h i s case n = 0.4 i s s m a l l e r . Various v e r s i o n s of t h i s type of modulator have been reported [Martin 1975; Minakata 1979]. In one v e r s i o n [Ramaswamy et a l . 1978], the Y-sections were replaced by two tunable 3 dB couplers. In another case [Ranganath and Wang 1977], the s p l i t t i n g of l i g h t was adjusted by p l a c i n g e l e c t r o d e s at the input Y. In order to e l i m i n a t e losses due to branching, two p a r a l l e l l i n e 3 dB couplers were used i n l i e u of the Y's, and an i o n etched s l o t was used to decouple the p a r a l l e l arms over the modulating p a r t , [Minakata 1979]. The i n t e g r a t e d Mach-Zehnder modulator, has found a p p l i c a t i o n s as an A/D converter [Taylor 1975], a D/A converter [Papuchon et a l . 1980], a s t a b l e m u l t i v i b r a t o r [ I t o et a l . 1980], b i s t a b l e device [ I t o et a l . 1979], o p t i c a l l o g i c [Taylor 1977] and an electromagnetic f i e l d sensor [Bulmer et a l . 1980]. A p o l a r i z a t i o n independent modulator to modulate the TE and TM mode has been demonstrated a l s o [Burns et a l . 1978]. In order to u t i l i z e the highest e l e c t r o o p t i c c o e f f i c i e n t r 3 3 i n L i N b 0 3 , i t i s necessary to use Y-cut f o r the TE mode. The problems of the branching angle, suppression of o u t d i f f u s e d waveguide due to L i 2 0 escape, and r a d i a t i o n modes were addressed i n [Miyazawa et a l . 1977; Burns et a l . 1978; Ranganath and Wang 1979], Considerable progress has been made towards understanding the problems caused by L i 2 0 escape and the s o l u t i o n s . Loss at the Y-sections remains a problem. An e x t i n c t i o n r a t i o as high as 97% has been reported [Leonberger et a l . 1979]. I l l 6.2 Design and f a b r i c a t i o n Several Y-branch modulator designs were t r i e d . The f i r s t one had 6 ym wide guides, and a t o t a l branching angle 29 = 2°. There was very l i t t l e output l i g h t compared to a s t r a i g h t waveguide. In order to diagnose the problem, the device was d i s s e c t e d , and l i g h t coming out of the two arms measured. The l i g h t from the two arms was very weak as compared to that from a s t r a i g h t waveguide. The poor performance was a t t r i b u t e d to the branching angle (29 = 2°). In the next design, the waveguide width was reduced to 4 ym, and the branching angle decreased to 29 = 1°. Because of the small angle, the i n c l i n e d waveguide sec t i o n s span 2520 ym f o r a guide separation of 22 ym, as shown In F i g . 5.2. Two important parameters are the guide width W, and the branching angle 2 9, i n the design of Y-branch modulators. A W = 2.7 ym i s required f o r s i n g l e mode propagation at 0.6328 ym [Ranganath and Wang 1977]. Since, the r u b y l i t h could be cut only a maximum of 50X the a c t u a l s i z e , the patter n width f o r W = 2.7 ym would have been 0.005 ± .002", taki n g i n t o account the c u t t e r t o l e r a n c e s . A minimum width 0.003" (= W =1.6 ym) would have been d i f f i c u l t to maintain over 18000 ym l e n g t h . So, W = 4 ym was se l e c t e d as a compromise. A la r g e branching angle conserves the device l e n g t h , but at the expense of higher s c a t t e r i n g l o s s . The angle a l s o a f f e c t s mode separating and recombining. The branching l o s s f o r 26 = 1 ° and 2° i s 1 dB and 2 dB r e s p e c t i v e l y [Ranganath and Wang 1977], 112 6.3 Measurement r e s u l t s The Y-branch modulator of F i g . 5.2 was f a b r i c a t e d i n Y-cut LiNbOg. E v a l u a t i o n was done at 0.6328 um, where n g = 2.203. For r 3 3 = 30.8 x 1 0 ~ 1 2 m/V [Turner 1966], d = 6 ym, and L = 7200 ym, i s given by, v = f* ( 2 j d j 1 = 1^6 v Q l t s ( 6 > 3 ) IT l2 3 ' n J L n n r__ e 33 A p o s i t i v e and negative going t r i a n g u l a r modulating voltage was a p p l i e d to the e l e c t r o d e s . T h i s , along w i t h the modulated output l i g h t i n t e n s i t y Is shown i n F i g . 6.1. An a p p l i e d v o l t a g e , = 4 v o l t s produces a phase change of 180°, thus n = ~ 0.4. When the applied voltage Is zero, the output has a minimum, so ij> * 180°. The e x t i n c t i o n r a t i o i s 3.8/4.4 = 86%. Measured r e s u l t s f o r l a r g e r magnitudes of a p p l i e d voltage are shown i n F i g . 6.2-6.4. The e x t i n c t i o n r a t i o i s degraded by: 1. Unequal s p l i t t i n g of l i g h t 2. Unequal recombination of l i g h t 3. Unsymmetrical Y-junctions 4. S c a t t e r i n g of rough edges of Y's 5. Presence of more than one mode 6. R a d i a t i o n of a i r and substrate modes 7. Unsymmetrical placement of the e l e c t r o d e s 8. Surface guiding due to L i 2 0 d e f f i c i e n c y When more than one mode i s present, the phase s h i f t n f o r a l l the modes i s not achieved simultaneously, and there Is only p a r t i a l e x t i n c t i o n . The substrate and a i r r a d i a t i o n modes s c a t t e r to combine with the guided wave to c o n t r i b u t e 113 5 V/DIV. 0.5 V/DIV. 10 ms/DIV. F i g . 6.1. Applied t r i a n g u l a r v o l t a g e (8 V ) and the output l i g h t pp i n t e n s i t y of the Mach-Zehnder modulator; V =4 V, ip=180 . 5 V/DIV. 0.5 V/DIV. 10 ms/DIV. F i g . 6.2. Applied t r i a n g u l a r v o l t a g e (20 V ) and the output l i g h t PP i n t e n s i t y of the Mach-Zehnder modulator. 114 10 V/DIV. 0.5 V/DIV, i!PMnit!iiiftiiif i w i n m i u i i . mam 10 ms/DIV. F i g . 6.3. Applied t r i a n g u l a r voltage (24 V ) and the output l i g h t PP i n t e n s i t y of the Mach-Zehnder modulator. 10 V/DIV. lilSSEIBIi 0.5 V/DIV. 10 ms/DIV. F i g . 6.4. Applied s i n u s o i d a l voltage (20 V ) and the output l i g h t PP i n t e n s i t y of the Mach-Zehnder modulator. 115 a dc component and mar the e x t i n c t i o n . E f f e c t of unequal s p l i t t i n g or 2 r e c o m b i n a t i o n of l i g h t i s considered below. The output l i g h t I n t e n s i t y 1 0 = E 0 i s , E 2 = ( x E j 2 + ( l - x ) 2 E 2 + 2 x ( l - x ) E 2 cos9 (6.4) o I l l I / I . = 2x 2 - 2x + 1 + 2 x ( l - x ) cose (6.5) o I 2 where, I i=E i i s the input l i g h t i n t e n s i t y , and x E A and ( l - x ) E i are the s i g n a l s i n the two modulator arms. E x t i n c t i o n r a t i o R i s given by (6.6), and i t i s p l o t t e d i n F i g . 6.5 R = -—= 4 x ( l z x ) A x ( l - x ) (6.6) 2x - 2x + 1 + 2 x ( l - x ) 116 F i g . 6.5. V a r i a t i o n of the e x t i n c t i o n r a t i o R, w i t h i n c r e a s i n g s i g n a l xE. i n one a m of the modulator. 117 CHAPTER VII HIGH VOLTAGE SENSOR 7.1 I n t r o d u c t i o n The conventional methods to measure the current and voltage i n high voltage l i n e s (> 400 kV) use transformers. The transformers l a c k the t r a n s i e n t accuracy to take advantage of the high speed s o l i d s t a t e p r o t e c t i v e r e l a y s that have been developed [Mouton et a l . 1978]. The cost of i n s u l a t i o n at > 400 kV i s h i g h . The m e t a l l i c components are s u s c e p t i b l e to electromagnetic and rad i o frequency i n t e r f e r e n c e . Passive o p t i c a l systems to measure and c o n t r o l HV generation and transmission may be f e a s i b l e . The p o s s i b l e advantages would be; 1. E l e c t r i c a l I s o l a t i o n 2. Immunity from e l e c t r i c a l noise 3. No power required - passive device 4. Absence of s a t u r a t i o n e f f e c t s 5. High s e n s i t i v i t y 6. Low cost - only s l i g h t l y a f f e c t e d by voltage l e v e l 7. Easy i n t e r f a c i n g w i t h o p t i c a l communication l i n k 8. Wide bandwidth The o p t i c a l systems would be p a r t i c u l a r l y s u i t a b l e f o r ; (1) sensing over-voltage and overcurrent t r a n s i e n t s i n p r o t e c t i v e r e l a y i n g , where a bandwidth > 10 kHz but an accuracy of only 10% i s required; and (2) f a u l t sensing, where a bandwidth > 1 MHz i s needed but an accuracy of 50% i s adequate. For 118 metering purposes, only 10 Hz bandwidth i s needed, but an accuracy of 0.1% i s necessary [Rogers 1977; Erickson 1979]. Bulk o p t i c a l measuring systems u t i l i z i n g magnetooptic, e l e c t r o o p t i c , and gy r o o p t i c e f f e c t have been demonstrated. A t y p i c a l arrangement, shown i n F i g . 7.1, c o n s i s t s of a l i g h t source, p o l a r i z e r , glass/quartz rod, m i r r o r , analyzer and a d e t e c t o r . Such systems are s e n s i t i v e to mechanical v i b r a t i o n s , misalignment, and i n t e r r u p t i o n of the o p t i c a l beams. These problems, could be a l l e v i a t e d by use of an in t e g r a t e d o p t i c a l device with o p t i c a l f i b r e s at the input and output, F i g . 7.2. The advantages of such a device would be compact s i z e , weight and cost. The b a s i c i d e a , as i l l u s t r a t e d i n F i g . 7.2, i s to immerse the e l e c t r o o p t i c modulator i n the HV f i e l d to be measured. The f i e l d modulates the phase of the l i g h t through the e l e c t r o o p t i c e f f e c t . Input and output l i g h t propagates through f i b r e s . The l i g h t source and the d e t e c t i o n system can be remote, to ensure e l e c t r i c a l - o p t i c a l i s o l a t i o n . Three types of modulators are considered f o r HV sensing: (1) The Y-branch modulator; (2) The BOA modulator; and (3) A p a r a l l e l l i n e modulator. 7.2 The Y-branch modulator This type of modulator, which was discussed i n Chapter VI i s w e l l proven; and i t i s s u i t a b l e f o r HV sensing. I t i s necessary to s h i e l d one arm of the modulator, but expose the other to the HV f i e l d , F i g . 7.3. To s h i e l d the arm the t h i c k metal i s r e q u i r e d . R e l a t i v e output i n t e n s i t y of the modulator i s given by, 119 Q HJ W M fa I a fa^ o Z O M 1 H ' U g A AMPLIFIER M MIRROR S BEAM SPLITTER W WAVEPLATE D PHOTODETECTOR r ELECTROOPTIC CRYSTAL GLASS COLUMN W LASER OUTPUT F i g . 7.1. Schematic of an o p t i c a l E - f i e l d detector (Erickson 1979). HIGH VOLTAGE COAXIAL LINE MODULATOR LASER INPUT OPTICAL FIBRE DETECTION SYSTEM 7.2. Scheme f o r o p t i c a l measurement of high voltage. MODULATOR OPTICAL FIBRE LASER INPUT OPTICAL FIBRE DETECTION SYSTEM 7.3. Y-branch modulator as a high v o l t a g e sensor. 121 I c / I i - (1 + cos6)/2 ( 7 . 1 ) where 6 = ( <|> + \(0 . When the i n t r i n s i c phase d i f f e r e n c e \|J = TT/2; lQf~L^ = (1 - sin<|>)/2. In a d d i t i o n , when ty, the e l e c t r o o p t i c a l l y induced change i n phase i s s m a l l , v i z . <}> « ir/2, the output changes l i n e a r l y w i t h the f i e l d ; I o / I ± = 0.5 (1 - <(,) = 0.5 {1 - | I (1 n 3 r ) L( ° ) n} ( 7 . 2 ) r Here, E i s the HV f i e l d s t r e n g t h , and e i s the r e l a t i v e d i e l e c t r i c constant ' o r of the c r y s t a l . F or Y-cut L i N b 0 3 , at X = 0.6328 pm, n g = 2.203, r 3 3 = 30.8 x 1 0 " 1 2 m/V, e r = 28, assuming n = 0.4, L = 1 mm, at E q = 10 6 V/m, f o r the TE p o l a r i z a t i o n , <t> = 3.785°. Thus, i n order to o b t a i n A<j> = ± 10°, an arm length of L = 5.3 mm i s needed. In order to s h i e l d one arm of the modulator from the HV f i e l d , wide arm separation i s required because of mechanical t o l e r a n c e s . Extent of the arm separation i s l i m i t e d , however, due to the small branching angle (2 9 = 1°) and the need to conserve s i z e . Modulators shown i n F i g . 7.4 w i t h arm separations of 88, 98 and 108 pm were designed and f a b r i c a t e d . The measured r e s u l t s are shown i n F i g . 7.5 and 7.6. The measured half-wave voltage V =5.5 v o l t s , as compared w i t h a t h e o r e t i c a l value of 3.6 v o l t s . Thus the o p t i c a l and e l e c t r i c a l overlap f a c t o r n = 0.65. A l s o , i|/ = 99°, and the e x t i n c t i o n r a t i o i s ~ 90%. The i n t r i n s i c phase ij> or operating p o i n t , was adjusted by heating F i g . 7.A. Y-branch modulators w i t h v a r i o u s arm separations: (a) 88 ym; (b) 98 ym; and (c) 108 ym. 10 ms/DIV. .5. Performance of the Y-branch modulator w i t h 88 ym separation-w i t h a p p l i e d t r i a n g u l a r v o l t a g e (5 V ) PP 10 V/DIV. 0.5 V/DIV. 10 ms/DIV. 6. Applied t r i a n g u l a r v o l t a g e (20 V p p ) and the output l i g h t I n t e n s i t y of the Y-branch modulator w i t h 88 ym arm sep a r a t i o n . 124 i n 0, a T a ? 0 5 l o a d i n g f i l m on one arm of the modulator, as discussed i n >2 a l a 2 u 5 Chapter IV 7.3 The BOA modulator I t may be p o s s i b l e to use the BOA ( B i f u r c a t e Optique A c t i v e ) switch [Papuchon et a l . 1977] f o r HV measurement. I t has only a s i n g l e s t r a i g h t waveguide, where the modulating f i e l d i s a p p l i e d . I f such a switch were to be placed i n HV e l e c t r i c f i e l d , the output l i g h t i n t e n s i t y would be amplitude modulated. The BOA modulator, shown i n F i g s . 7.7 and 7.8, nay be considered as zero gap p a r a l l e l l i n e coupler. The narrow (4 um) waveguides are monomode. But, the wide (8 um) waveguide can support two modes; a symmetric and an antisymmetric mode. The input s i g n a l upon entering the two mode guide, d i v i d e s i n t o the symmetric and the antisymmetric modes. As the s i g n a l t r a v e l s i n the two mode guide, the energy s h i f t s from the "top" h a l f to the "bottom" h a l f , back to the "top" h a l f , and so on. The distance over which complete energy s h i f t o c curs, i s [Papuchon and Roy 1977], mit mir (7.3) s "as J L o = (3 -B >' AB where B and B a r e the p r o p a g a t i o n c o n s t a n t of the symmetric and the s as antisymmetric modes r e s p e c t i v e l y , and m i s a p o s i t i v e odd i n t e g e r . Thus, the energy can be s h i f t e d from one branch to the other by changing Ag. I t has been shown [Papuchon et a l . 1977], that the voltage required to switch energy from one coupler arm to the other, i s reduced by an order of magnitude as the gap between coupler arms approaches zero. As the applied voltage changes, i t t C-AXIS i T -3—r: • t • • • MONOMODE GUIDE 2225 — > f ELECTRODES 125 20 um TWO MODE GUIDE 12 9004 17 960 um 4 ym _ J _ T 100 ± 4 ym >|- 5 7 2 9 > l • H F i g . 7.7. BOA modulator w i t h e l e c t r o d e s . F i g . 7.8. BOA modulator as a high v o l t a g e sensor. 1 2 6 a l t e r s the i n t e r a c t i o n l e n g t h . That i s , the voltage changes the distance required to go from a node at the bottom s e c t i o n at the output. Of course, as the a p p l i e d voltage v a r i e s , the output i n t e n s i t y i s amplitude modulated at any one output branch. A BOA modulator, w i t h the dimensions i n d i c a t e d i n F i g . 7.7, was f a b r i c a t e d i n Y-cut X-propagating LiNbOg. For TE modes, with L = 9004 ym an e l e c t r o d e separation d = 12 um, and waveguide widths of 4 and 8 ym, a = 9V was measured, see F i g . 7.9. The e x t i n c t i o n r a t i o was ~ 74%, and the i n t r i n s i c phase if) = 260°. The o r i g i n a l BOA modulator [Papuchon et a l . 1977], had 2 and 4 ym guides, an e l e c t r o d e separation of 5 ym, and electrode length of 5 mm, and = 28V. By comparison, the V^ = 9V measured ( F i g . 7.9) was only 1/3, considering that wider electrode separation (2.5X) was approximately o f f s e t by l o n g e r e l e c t r o d e s (1.8X). The measured r e s u l t s i n d i c a t e , that a HV f i e l d of 1 0 6 V/m would produce a change i n the phase of the output of ~2.7°/mm modulator l e n g t h . The BOA modulator In z-cut l i N b 0 3 was placed between HV electrodes 16 cm apart. The output l i g h t from one branch of the modulator i s shown i n F i g . 7.10. The output amplitude changed l i n e a r l y w i t h HV. The l a s e r and the d e t e c t i o n system were placed away from the HV electrodes to prevent unwanted modulation. The measurement r e s u l t i n d i c a t e that the BOA device can be used as a HV sensor. 10 ms/DIV. F i g . 7.9. Applied t r i a n g u l a r v o l t a g e (15 V ) and the output l i g h t i n t e n s i t y of the BOA modulator out of one arm o n l y . OUTPUT AT 0.9 kV/cm 10 mV/DIV. i n i i mwA OUTPUT AT 0.0 V 5 ms/DIV. F i g . 7.10. Output l i g h t i n t e n s i t y of the BOA modulator out of one arm only i n (a) 10 kV f i e l d , and (b) no f i e l d . 128 7.4 P a r a l l e l l i n e modulator This proposed device c o n s i s t s of two contiguous, s t r a i g h t , p a r a l l e l , uncoupled waveguides. One of the waveguides Is e l e c t r o o p t i c and the other one i s not. I f such a device were to be placed i n an e x t e r n a l e l e c t r i c f i e l d , o n l y the phase of the s i g n a l propagating through the e l e c t r o o p t i c guide would be a l t e r e d . At the output, where the phase modulated and the unmodulated s i g n a l s combine, a s i n u s o i d a l v a r i a t i o n i n i n t e n s i t y would r e s u l t . A c o n f i g u r a t i o n f o r the above device i s shown i n F i g . 7.11. One branch of the modulator c o n s i s t s of a T i d i f f u s e d waveguide, and the other of a su p e r s t r a t e T a 2 0 5 waveguide. The e f f e c t of 1 0 6 V/m HV f i e l d on the l i g h t propagation through the T a 2 0 5 waveguide i s n e g l i g i b l e , because the l i n e a r e l e c t r o o p t i c c o e f f i c i e n t of T a 2 0 5 i s small [Yee and Young 1975]. The coupling between the guides i s assumed to be n e g l i g i b l e , as the contiguous area between the two waveguides i s s m a l l . The output i n t e n s i t y I of t h i s modulator i s , . 3 I o / I ± = \ {1 + cos [(ilLE E) + ( B l - B 2 ) ] L } (7.4) where, E i s the f i e l d i n t e n s i t y , L the device l e n g t h , and 3 X and 3 2 the propagation constants of the d i f f u s e d and superstrate guides r e s p e c t i v e l y . This proposed p a r a l l e l l i n e modulator o f f e r s the advantages of complete u t i l i z a t i o n of the substrate l e n g t h , an absence of bends or f u r c a t i o n s i n the network, and amenability to TE mode (Y-cut LiNbOg) or to TM mode (Z-cut LiNbOg) modulation. Furthermore, the r e f r a c t i v e index of the su p e r s t r a t e T a 2 0 5 waveguide may be changed g r a d u a l l y u n t i l a ir/2 i n t r i n s i c phase d i f f e r e n c e i s obtained. 129 LIGHT INPUT TANTALUM PENTOXIDE WAVEGUIDE ELECTRODES ->- x W //////////// OUTPUT LITHIUM NIOBATE TITANIUM DIFFUSED WAVEGUIDE (a) F i g . 7.11. P a r a l l e l l i n e modulator: (a) i s o m e t r i c view; and (b) top view. 130 CHAPTER V I I I SERIES AND MULTIBRANCH INTERFEROMETERS/FILTERS 8.1 I n t r o d u c t i o n Series and multibranch i n t e r f e r o m e t e r s / f i l t e r s are proposed, analyzed and demonstrated. I n i t i a l l y , the bandwidth of s e r i e s interferometers f o r various e l e c t r o d e sequences i s estimated, and then that f o r the multibranch. Measured r e s u l t s are compared w i t h the t h e o r e t i c a l ones. 8.2 Series i n t e r f e r o m e t e r / f i l t e r [Ahmed and Young 1980a] The o u t p u t i n t e n s i t y I of a s i n g l e i n t e r f e r o m e t r i c modulator (Mach-Zehnder) v a r i e s s i n u s o i d a l l y (8.1); where 9 = (KLV + from (6.1). I f a sharper response i s d e s i r e d , s e v e r a l modulators may be connected i n s e r i e s . One arrangement of e l e c t r o o p t i c modulators to r e a l i z e a narrow passband i s shown i n F i g . 8.1. The output i n t e r f e r o m e t e r . Such a device could be r e a l i z e d on a s i n g l e substrate capable of supporting o p t i c a l waveguides. In conventional o p t i c s , an analogue of such a device i s the Lyot p o l a r i z a t i o n i n t e r f e r e n c e f i l t e r [Tolansky 1973], i t i s i 2 9 I = —^ (1 + cos 9) = I . s i n (-») (8.1) o 2 ° e 2*6 2N"1e 2"L INPUT LIGHT < •OUTPUT Fi g . 8.1(a). Interferometer composed of N electrooptic modulators i n series. Xg x+2 x+2' x+2 N X8 INPUT LIGHT • OUTPUT Fig . 8.1(b). Interferometric f i l t e r composed of N Mach-Zehnder interferometers i n series, 132 capable of passing a band only 4 A wide. The Lyot f i l t e r i s made up of a l t e r n a t i n g sheets of p o l a r i z i n g m a t e r i a l P^, P 2 ... and p a r a l l e l quartz p l a t e s Op Q 2» the l a t t e r thicknesses 2°t, 2*t, 2 2 t ... However, there are d i f f i c u l t i e s i n r e a l i z i n g a Lyot f i l t e r : (1) the thickness of the quartz p l a t e s has to be very accurate; (2) the t h i c k good q u a l i t y quartz i s d i f f i c u l t to f i n d ; (3) the temperature has to be held constant; (4) the system has to be immersed i n o i l to discourage m u l t i p l e r e f l e c t i o n s from various surfaces; and (5) the transmission l o s s i s h i g h , even with a l l the precautions 90% of the i n c i d e n t l i g h t i s l o s t . B i l l i n g used e l e c t r o o p t i c ADP (ammonium dihydrogen phosphate) c r y s t a l s w i t h temperature compensation to o b t a i n a voltage tunable passband of 1.25 A [Tolansky 1973]. An i n t e r f e r o m e t e r / f i l t e r composed of s e v e r a l Mach-Zehnder interferometers i n s e r i e s on a s i n g l e substrate (e.g. LiNbO 3) o f f e r s the advantages of compactness, temperature s t a b i l i t y , low l o s s , low c o s t , and voltage t u n a b i l i t y . 8.2.1 N i n t e r f e r o m e t e r s i n s e r i e s The output i n t e n s i t y a f t e r the f i r s t i n terferometer shown i n F i g . 8.1 i s g i v e n by ( 8 . 1 ) . B u t , the r e s u l t a n t i n t e n s i t y I a f t e r passage of i n c i d e n t l i g h t i n t e n s i t y 1^ through N interferometers of F i g . 8.1 i s ; x l / 2 m M2 ( c Q s 6 . c o s 2 1 ^ • cos 2 2 i .... cos 2 N ^) ( 8 . 2 ) O I I I 2. Z Let x = exp(j9/2); then, 133 ( I o / l i ) 1 / 2 = i - (x+x - 1) (x 2+x~ 2) (x 4+x~ 4) ... ( x 2 N ~ 1 - H x ~ 2 N S = -=- (x+x + ... + x 1 ^ -he *+x J + . . . + X 1 z ) 2 N Summing the geometric s e r i e s : (j / T = 1- p U - ( x 2 ) 2 N X ] x ^ H ^ x " 2 ) ^ \ ° 1 " 2 N (1-x- 2) 1 2 N., „-2 N 2 N 1 ( x - x " 1 ) ^ S u b s t i t u t i n g the value of x = e x p ( j 6 / 2 ) , N N , 1 (exp -(exp ^-) ( I / i ) 1 / 2 = I_ | 2 2 } 2 exp ^ exp ~ — I s i n ( | • 2 N ) ^ = {— g — ) 2 (8.3) h 2 N s i n ( | ) 6 2 As a check, f o r N = 1,2 and 3 the above e x p r e s s i o n reduces to (cos y) , 6 2 6 2 (cos j • cos 9) and (cos - j • cos 6 • cos48) r e s p e c t i v e l y . The numerator s i n 2 ( y • 2^) undergoes r a p i d f l u c t u a t i o n s as a f u n c t i o n of 8, F i g . 8.2(a) whereas the modulating f u n c t i o n ( 2 N s i n -|) 2 changes r e l a t i v e l y s l o w l y , F i g . 8.2(b) [Hecht and Zajac 1979]. A p l o t of I n t e n s i t y f o r N=l,2,3 and 4 w i t h \J/=0, are shown i n F i g . 8.3. Applying L ' H o s p i t a l ' s r u l e at 2 N0 =2mir, to (8.3) , m 134 F i g . 8.2. P l o t of s e r i e s f i l t e r response w i t h N=l and N=3. 135 N N N 2N d ( l - cos92 ) + d(2 sin92 ) + 2 cos82N = 1 2 2 N d ( l - cos9) 2 2 N d ( sin9) 2 2 N c o s 9 The p r i n c i p a l maxima I / I . = 1, occur at values of 9 when; o i m 2 N9 = 2mir, m = 0, ± 1 , ±2, ... m N T h i s i s to be expected since a l o s s l e s s system i s assumed, and f o r 2 9= 2mn there i s proper phase-matching i f \> = 0. The FWHM ( f u l l width h a l f maximum) bandwidth decreases g e o m e t r i c a l l y as the number of s e r i e s interferometers i n c r e a s e s , t h i s i s evident from F i g . 8.3. The bandwidth i s twice the value of 9 which makes I / I . = 0.5 or where; o i s i n ( | • 2 N) - /075 2 N s i n | = 0 ( 8 . 4 ) For N = 1,2,3,4,5 and 6 the FWHM bandwidth i s 180°, 82°, 40°, 20°, 10° and 5° r e s p e c t i v e l y . 8.2.2 Series i n t e r f e r o m e t e r s w i t h l i n e a r l y i n c r e a s i n g phase r e t a r d a t i o n I f the phase r e t a r d a t i o n i n successive i n t e r f e r o m e t e r s increases l i n e a r l y , the response would be sharper; but not as much as when i t increases g e o m e t r i c a l l y . Geometrically i n c r e a s i n g phase r e t a r d a t i o n , however, requ i r e g e o m e t r i c a l l y i n c r e a s i n g electrode lengths. Consequently, f o r more than three s e c t i o n s such devices become i m p r a c t i c a l . Here, the performance of three and four i n t e r f e r o m e t e r s i n s e r i e s , w i t h the phase r e t a r d a t i o n i n c r e a s i n g l i n e a r l y from one interf e r o m e t e r to the next, are considered. 137 8.2.2.1 Three Interferometers In s e r i e s The output i n t e n s i t y of the f i r s t i nterferometer shown i n F i g . 8.4 i s g i v e n by ( 8 . 1 ) . The r e s u l t a n t i n t e n s i t y , I , a f t e r passage through the three i n t e r f e r o m e t e r s , shown i n F i g . 8.4 i s : _ 1/2 _ 1/2 , 6 D 29 39, . o c x I = 1 . (cos -s- • COS -s— • COS -s—) ( 8 . 5 ) O 1 I I I Here 1^ i s the input i n t e n s i t y , and N9 i s the phase r e t a r d a t i o n introduced i n the Nth i n t e r f e r o m e t e r . S e t t i n g x = ex p ( j 8 / 2 ) , (8.5) becomes; ( I / I . ) 1 / 2 - 4 (x + x - 1 ) ( x 2 + x " 2 ) ( x 3 + x" 3) o I o -2,., - - _-6s ( I n , i / 2 . i { 2 + Z L L O ^ ) + x ( i - x _ ) } ° 1 8 ( 1 - x 2 ) ( 1 - x l ) i 7 - 7 x - x S u b s t i t u t i n g the value of x, , s i n 2 ( I o / I i ) =-6T " T i ( 8 ' 6 ) s i n - j The response of the above device i s p l o t t e d i n F i g . 8.4, with \|> = 0. The FWHM bandwidth r e l a t i v e to a s i n g l e s e c t i o n i n t e r f e r o m e t e r i s 0.28. 8.2.2.2 Four int e r f e r o m e t e r s i n s e r i e s The output i n t e n s i t y I of four interferometers i n s e r i e s , F i g . 8.4, with l i n e a r l y i n c r e a s i n g e l e c t r o d e lengths i s , CHANGE IN 9 FROM PRINCIPAL MAXIMA F i g . 8.4. ( a ) , (b) and (c) Modulator c o n f i g u r a t i o n s ; and (d) r e l a t i v e output i n t e n s i t y f o r the three c o n f i g u r a t i o n s . 00 139 / T ._ . 1/2 6 2 6 3 6 4 6 (IQ/I^) = cos y • cos Y~ ' c o s 2~ * C O S T ~ Here 1^ I s the input i n t e n s i t y , and N6 Is the phase r e t a r d a t i o n introduced i n the Nth i n t e r f e r o m e t e r . S e t t i n g x = exp(j6 / 2 ) ,~ / T \ l / 2 1 / , — \ \ f 2 , -2\f 3 , _ 3 w 4 . - 4 N ( I /I.) = -!-r (x + x )(x + x )(x + x )(x + x ) O 1 l o , f 5 - 5 N . / 11 l l s (x - x ) S u b s t i t u t i n g x = exp(j 6/2) . se lie 0 . s i n y - + s i n - s - 2 ( I o / I l ) = 256 i ~ l -) ( 8 ' 7 ) s i n y This equation i s p l o t t e d i n F i g . 8.4 with ip = 0 . The FWHM bandwidth r e l a t i v e to s i n g l e s e c t i o n i n t e r f e r o m e t e r i s 0 . 1 9 . 8 . 2 . 3 Experimental r e s u l t s An i n t e g r a t e d o p t i c a l c i r c u i t w i t h two interferometers i n s e r i e s was f a b r i c a t e d i n Y-cut LINbOg. The waveguide and electrode pattern i s shown i n F i g . 8 . 5 . The o v e r a l l device length was 17960 ym, and the electrode lengths f o r the f i r s t and second modulators were 3712 ym and 7428 ym r e s p e c t i v e l y i n c l u d i n g the push-pull e f f e c t . The measured r e s u l t s are shown i n F i g . 8.6 -8 . 9 . The h a l f - w a v e v o l t a g e V i s ~ 8 V, and the t h e o r e t i c a l value i s given by, v = ( x ) i _ = i ^ i i v o i t s ,„ R. T T 3 ' nL n ( 8 . 8 ; n r 0 _ e 33 F i g . 8.5. Two interferometers i n s e r i e s . 141 + 10 V/DIV. 0.5 V/DIV. 10 ms/DIV. F i g . 8.6. Applied t r i a n g u l a r v o l t a g e (20 V ) and the output l i g h t i n t e n s i t y of two interferometers i n s e r i e s . + 10 V/DIV. 0.5 V/DIV. 10 ms/DIV. F i g . 8.7. Applied t r i a n g u l a r v o l tage (30 V p p ) and the output l i g h t i n t e n s i t y of two interferometers i n s e r i e s . 10 ms/DIV. F i g . 8.8. Applied t r i a n g u l a r v o l t a g e (40 V ) and the output l i g h t PP 6 i n t e n s i t y of two interferometers i n s e r i e s . 143 + 10 V/DIV. 0.5 V/DIV. 10 ms/DIV. F i g . 8.9. Applied s i n u s o i d a l v o l t a g e (40 V p p ) and the output l i g h t i n t e n s i t y of two interferometers i n s e r i e s . 144 -12 w i t h X = 0.6328 ym, n g = 2 .203 , r 3 3 = 30.8 x 10 m/V, d = 6 ym and L = 2 x 1856 ym. Comparing the measured and the t h e o r e t i c a l values of V , the overlap i n t e g r a l n =0.4. The e x t i n c t i o n r a t i o i s moderate; 75%. The side lobes are 0.25 of the main lobes i n the output response. These are a f f e c t e d by the phase d i f f e r e n c e A\|> (= ip 1 - i|>2); where ^ and i|>2 are the i n t r i n s i c phases of the f i r s t and second modulators r e s p e c t i v e l y . This p o i n t i s elaborated below. 8.2.4 E f f e c t of the i n t r i n s i c phase The r e s u l t a n t o u t p u t i n t e n s i t y 1 a f t e r p a s s a g e t h r o u g h two interferometers In s e r i e s i s , T / T „ 2 xKLV. _ 2 , K 2 L V + AiK , R Q , I II. = cos (—=—) cos C x r) C8.9J o I I l U s i n g t h e above measured v a l u e KLV = 180°, or KL - 22.5 " / v o l t , where K = ( T M I 3 r 3 3 n)/Ad. P l o t s of I Q / I 1 using A\J> = 0°, 45° and 90° are shown i n F i g . 8.10. As value of the Aip i n c r e a s e s , the peak value of the r e l a t i v e output i n t e n s i t y decreases, the passband broadens, and the sidelobes i n c r e a s e . A comparison of F i g . 8.9 and 8.10, i n d i c a t e s A\JJ = 90°. 8.3 Multibranch i n t e r f e r o m e t e r / f i l t e r [Ahmed and Young 1980a) A response narrower than that of a Mach-Zehnder interferometer may be obtained w i t h a multibranch i n t e r f e r o m e t e r . Such an e l e c t r o o p t i c f i l t e r , w i t h voltage tunable response i s shown i n F i g . 8.11. The e l e c t r o d e lengths are L, 2L, 3L, NL on the successive branches. A l t e r n a t i v e l y , a narrowband 146 F i g . 8.12. V a r i a b l e l e n g t h multibranch i n t e r f e r o m e t r i c f i l t e r . 147 f i l t e r can be r e a l i z e d by incrementing the length of each successive branch by X ( = X/n ) , as shown i n F i g . 8.12. Here, X and X are the guide and the g z g f r e e - s p a c e wavelengths r e s p e c t i v e l y , and n i s the l o n g i t u d i n a l propagation constant. 8.3.1 N branch int e r f e r o m e t e r The r e s u l t a n t I n t e n s i t y of N overlapping waves, of the same frequency and t r a v e l l i n g i n the same p o s i t i v e d i r e c t i o n i s given by [Hecht and Zajac 1979]; E = ( ^ E d r ) (8.10) o L. or r=l E = ( E , e + E - e + . . . + E . T e ) o o l o2 oN (E . e + E _ e + ... + E . e IN) (8.11) o l o2 oN I f the amplitude E^ of the i n c i d e n t wave i s s p l i t e q u a l l y i n t o N equal p a r t s , then; E,/N = E , = E = ... - E „ (8.12) i o l o2 oN Furthermore, i f the el e c t r o d e lengths are such that the phase r e t a r d a t i o n i n the branches i s 8, 2 9, 39, N9, then = 9, a 2 = 29, ... , = N8. Using (8.12) and values of a i n (8.11); E 2 = 4 { e J 6 + e 2 J e + e 3 J 9 + . . . + e N J 9 } ° N X { e - J e + e - 2 J 9 + e - 3 J e + . . . + e " ^ 6 } 148 Summing the geometric s e r i e s ; 2 JN6 _ , f i l . -JN9 ° N 2 { 1 - e ^ H 1 - e - ^ 6 1 2 E 2 f 2 _ £ j N 6 . e-3H f l | ° = 7 S - e ^ - e - J 9 1 i l N s i n (9/2) Applying L'Hospital's r u l e to (8.13), I o d ( l - cosN6) d(NsinN9) cosN9 , , D ... —— — - + — ->• l ( , 0 . 1 4 ; i N d( 1 - cos 9) N d(sine) cos 6 at N 9 = 2miv, m = 0, ±1, ±2, ... (8.15) The p r i n c i p a l maxima occur at the above value of 9 . This i s to be expected r m s i n c e a l o s s l e s s system i s assumed, and at 9 = 9^ t h e r e i s proper phase-matching i f \(J = 0. The FWHM bandwidth i s twice the value of 9 which makes sin(N9/2) = ( 0 . 5 ) 1 / 2 N sin(6/2) (8.16) The computed response of a multibranch f i l t e r f o r N = 2,3, 6 with ip = 0 i s p l o t t e d i n F i g . 8.13, and the bandwidths 180°, 112°, 82°, 65° and 54° r e s p e c t i v e l y . A comparison of the FWHM bandwidth as a f u n c t i o n of N f o r the s e r i e s and the multibranch interferometers i s made i n F i g . 8.14, the bandwidth c o n t r a c t i o n w i t h i n c r e a s i n g N i s more r a p i d i n the former case. Although the RELATIVE INTENSITY F i g . 8.13. R e l a t i v e i n t e n s i t y of multibranch interferometer or a f i l t e r ; 6 i s change i n angle from the p r i n c i p a l maxima. 150 F i g . 8.14. A comparison of the FWHM bandwidth of the s e r i e s (m=N) and the multibranch (m=N-l) interferometers. 151 bandwidth c o n t r a c t i o n i s l e s s i n the case of the multibranch f i l t e r , i t does have the merit of r e q u i r i n g l e s s " r e a l e s t a t e " . 8.3.2 Three branch int e r f e r o m e t e r w i t h g e o m e t r i c a l l y i n c r e a s i n g  phase r e t a r d a t i o n A multibranch i n t e r f e r o m e t e r has sharp response compared to that of a s i n g l e s e c t i o n two branch i n t e r f e r o m e t e r . A scheme f o r a three branch inte r f e r o m e t e r i s depicted i n F i g . 8.15. Here, the path lengths f o r the v a r i o u s b r a n c h e s d i f f e r by X , 2 A and 4X . A l t e r n a t i v e l y , f o r an g g g e l e c t r o o p t i c m a t e r i a l , the electrode lengths are L, 2L and 4L. I f amplitude E^ of the three i n c i d e n t waves i s s p l i t e q u a l l y , then; E_,/3 = E = E = E . ( 8 . 1 7 ) i o l o2 o3 Furthermore, i f the el e c t r o d e lengths are such that the phase r e t a r d a t i o n i n the branches i s = 0, = 2 9 and = 40, then from (8.11) and (8.17), E2 = f± ( e J 8 + e J 2 9 + e ^ 6 ) ( e - J 9 + e ^ 2 9 + e"^ 6) (8.18) o 9 With x = e . E 2 2 3 -1 "2 , "3x (8.19) E2 = JL ( 3 + x + x 2 + x 3 + x" 1 + x" + x ) o 9 ( 8 . 2 0 ) E 2 3.5 _ -3.5 ( 8 . 2 1 ) 152 F i g . 8.16. A four branch interferometer w i t h g e o m e t r i c a l l y i n c r e a s i n g electrode lengths. 153 i 6 S u b s t i t u t i n g x = e J I s i n -z-^ = i {2+ 1-} ( 8 . 2 2 ) i s i n j This equation i s p l o t t e d i n F i g . 8.17 with ip = 0. The FWHM bandwidth r e l a t i v e to that of a s i n g l e s e c t i o n interferometer i s 0.42. 8.3.3 Four branch interferometer Performance of a four p a r a l l e l branch interferometer of F i g . 8.16 i s d e s c r i b e d h e r e . The successive branch length increases are X , 2X , 4X and & ft 5 8X . A l t e r n a t i v e l y , f o r an e l e c t r o o p t i c m a t e r i a l , the electrode lengths are g L, 2L, 4L and 8L, and the phase r e t a r d a t i o n introduced i s = 9, = 29, = 4 8, and = 8 9. I f i s s p l i t so t h a t , E./4 = E = E = E = E . ( 8 . 2 3 ) i o l o2 o3 o4 Then the r e s u l t a n t i n t e n s i t y using (8.11) and (8.23) i s : 2 _ f l ( e J 8 + e32 8 + e j 4 8 + e 3 8 6 ) ( e - j 6 + e"326 + ^ 4 6 + ^ 8 8, o 16 (8.24) J6 S e t t i n g x = e , 2 .. ! i ( x + x 2 + x * + x 8 ) ( x ' 1 + x " 2 + x- A + x- 8) (8.25) E = ., o 16 A U - ( x 5 + x - 5 ) + I ( x n + x - n ) } (8.26) 16 1 n-1 154 E i r , 5 A -5, + x 1 / 2 ( l - x 7 ) x - l 7 2 d - x " 7 ) 1 ( g > 2 7 ) E 2 = o J8 S i m p l i f y i n g , and using x = e : X~ 1 B l n t X l _ , « l ( 8 . 2 8 ) I T " 1 6 i 3 + ^ T T i T - 2 c o s 58> i s i n (-J This equation i s p l o t t e d i n F i g . 8.17 with i|> = 0. The FWHM bandwidth r e l a t i v e to a s i n g l e s e c t i o n two branch interferometer i s ~ 0.20. 8.3.4 Experimental r e s u l t s A three branch interferometer shown i n F i g . 8.18 was f a b r i c a t e d i n Y-cut LiNbOg. The centre arm i s the reference arm w i t h the ground e l e c t r o d e on e i t h e r s i d e . The two modulating electrodes are 4752 um and 9504 um (=2x4752) long. The measured r e s u l t s are shown i n F i g . 8.19 - 8.21, where the p o s i t i v e and negative going t r i a n g u l a r waveform i s the a p p l i e d v o l t a g e . In F i g . 8.19, 8.20 and 8.21 i s the response w i t h voltage a p p l i e d to the short e l e c t r o d e , the long e l e c t r o d e , and to both electrodes r e s p e c t i v e l y . With voltage a p p l i e d o n l y t o the s h o r t e l e c t r o d e , F i g , 8.19, the h a l f wave voltage - 7 V, the i n t r i n s i c phase d i f f e r e n c e ^ = 290°, and the e x t i n c t i o n r a t i o i s ~ 86%. The t h e o r e t i c a l V = 2.43V w i t h d = 4 jm, and L = 4752 \m, so the form f a c t o r n = 0.35. The output w i t h voltage a p p l i e d to the long e l e c t r o d e i s shown i n F i g . 8.20, from which V^ =3.5 v o l t s , i|>2 = 190°, and the e x t i n c t i o n r a t i o = 65%. The output response of the complete device i s shown i n F i g . 8.21. The C H A N G E I N 9 F R O M T H E P R I N C I P A L M A X I M A F i g . 8.17. Comparison of N=2, 3 and 4 branch interferometers w i t h 2 L e l e c t r o d e l e n g t h s . On F i g . 8. 18. A three branch int e r f e r o m e t e r . 10 V/DIV. 0.5 V/DIV. 10 ms/DIV. F i g . 8.19. Applied t r i a n g u l a r v o l t a g e on the short e l e c t r o d e of the three branch interferometer and the output l i g h t i n t e n s i t y . + 10 V/DIV. .5 V/DIV. F i g . 8.20. Applied t r i a n g u l a r v o l t a g e on the long e l e c t r o d e of the three branch modulator and the output l i g h t i n t e n s i t y . 158 F i g . 8.21. Applied t r i a n g u l a r v o l t a g e on both elec t r o d e s of the three branch int e r f e r o m e t e r and the output l i g h t i n t e n s i t y . 159 measured r a t i o , (FWHM bandwidth of complete device/FWHM bandwidth w i t h voltage on short e l e c t r o d e ) , i s 0.45: the t h e o r e t i c a l value i s 0.61. The sidelobes are about 0.16 of the main l o b e s . I f the phase d i f f e r e n c e , Ai|i (= ^ - IJ^) , could be reduced, the side lobes would be suppressed. The s e r i e s and multibranch i n t e r f e r o m e t e r s / f i l t e r s narrow the passband, are voltage tunable, and would be u s e f u l f o r pulse shaping and pulse width modulation. 160 CHAPTER IX ELECTROOPTIC ANALOGUE-TO-DIGITAL CONVERTER 9.1 I n t r o d u c t i o n The s i g n a l measured i n a p h y s i c a l system i s u s u a l l y i n an e l e c t r i c a l analogue form, but there i s oft e n a need to convert i t i n t o d i g i t a l form. An a n a l o g u e - t o - d i g i t a l converter (ADC) does t h i s by sampling the analogue s i g n a l at r e g u l a r I n t e r v a l s , and generating a s e r i e s of pulses to represent the s i g n a l l e v e l . The ADCs are used i n computing, communication and c o n t r o l systems. There i s a growing need f o r high speed (> 100 MS/s) ADCs. The a v a i l a b l e ADCs use S i ICs which have been developed to t h e i r performance l i m i t s . For higher conversion r a t e s , ADCs based on t r a n s f e r r e d e l e c t r o n d evices, Josephson j u n c t i o n s , and o p t i c a l systems are being explored. Integrated o p t i c a l ADC based on e l e c t r o o p t i c d i f f r a c t i o n [Wright et a l . 1974], e l e c t r o o p t i c d e f l e c t i o n [Saunier et a l . 1977], and e l e c t r o o p t i c modulators [Taylor 1975] have been proposed, and these are reviewed below. A l l of the above ADCs re q u i r e an array of detectors and comparators. A scheme that dispenses w i t h the e x t e r n a l comparators from the one using e l e c t r o o p t i c Mach-Zehnder modulators i s proposed. Design of a 4-bit comparatorless ADC I s done. Experimental r e s u l t s on 1-bit comparatorless ADC are presented, and a three branch network used i n i t to apportion power i s described. 161 9.1.1 E l e c t r o o p t i c d i f f r a c t i o n ABC An e l e c t r o o p t i c d i f f r a c t i o n ADC, F i g . 9.1, [Wright et a l . 1974] uses v a r i a b l e t h r e s h o l d method and re q u i r e s n comparators instead of 2 n - l c a l l e d f o r i n some schemes. While I t i s capable of f a s t synchronous o p e r a t i o n , i t does introduce an n-clock period delay. The output i s i n Gray code. The ADC i s e s s e n t i a l l y an e l e c t r i c a l l y c o n t r o l l e d d i f f r a c t i o n g r a t i n g . Voltage a p p l i e d to the p e r i o d i c s t r u c t u r e produces a p e r i o d i c v a r i a t i o n In r e f r a c t i v e index to i n t e n s i t y modulate the d i f f r a c t e d beam Into side orders, F i g . 9.1. The output i s given by, I = J2( dN) m m where J i s mth order Bessel f u n c t i o n , m 9.1.2 E l e c t r o o p t i c phased-array d e f l e c t o r ADC An EO phased-array d e f l e c t o r shown In F i g . 9.2 could work as an ADC [Saunier et a l . 1977], The l i n e a r EO e f f e c t i n conjunction with v a r i a t i o n i n apodized e l e c t r o d e s , produces d i f f e r e n t i a l o p t i c a l phase delay between adjacent l i g h t beams. The l i n e a r <|> slope i s induced across aperture of the beam. A change i n voltage induces phase slope to switch the beam. 9.1.3 O p t i c a l ADC w i t h Mach-Zehnder modulators Integrated o p t i c a l ADC using Mach-Zehnder modulators has been proposed [Taylor 1975; Taylor et a l . 1978]. Such an ADC uses the f a c t that the output i n t e n s i t y v a r i e s i n a p e r i o d i c f a s h i o n w i t h the ap p l i e d voltage V; LITHIUM NIOBATE DIFFRACTED BEAMS 162 INPUT BEAM F i g . 9.1(a). E l e c t r o o p t i c d i f f r a c t i o n modulator, W H 2 > M PQ - THRESHOLD LEVELS APPLIED VOLTAGE F i g . 9.1(b). Sequential t r a n s f e r c h a r a c t e r i s t i c s and threshold l e v e l s , THRESHOLD DETECTORS PHOTODETECTORS LASER BEAM SHIFT REGISTER r3 SAMPLE CLOCK DIGITAL WORD OUT F i g . 9.1(c) Experimental arrangement (Wright et a l . 1974). 163 50 60 70 (ARBITRARY UNITS) F i g . 9.2(b). P o s i t i o n of the d e f l e c t e d spot w i t h w i t h d r i v e voltage as a parameter (Saunier et a l . 1977) 164 I = 0.5 I ± {1 + cos(<t>+ +)} (9.2) where <(> = KLV and \J> i s the i n t r i n s i c phase d i f f e r e n c e . An ADC w i t h N=4 b i t s i s d i s c u s s e d , i t s schematic and output i s shown i n F i g . 9.3. The s i n u s o i d a l v a r i a t i o n of the output i n t e n s i t y I of the modulators can be used to represent binary b i t s , because the b i t value i n a bin a r y r e p r e s e n t a t i o n a l s o v a r i e s p e r i o d i c a l l y w i t h the analogue s i g n a l . Thus, se v e r a l modulator outputs can be combined i n p a r a l l e l to represent a d i g i t a l word, and with the Gray code only one modulator per b i t i s r e q u i r e d . V a r i a t i o n of the output i n t e n s i t y w i t h the analogue s i g n a l V i s shown i n F i g . 9.3. The bin a r y code obtained a f t e r d e t e c t i o n , a m p l i f i c a t i o n , and comparison w i t h a reference s i g n a l i s shown too. A "0" i s generated f o r I > I , and "1" otherwise. The s i g n a l sampling could be performed by a mode-locked l a s e r , which puts out a t r a i n of very narrow pulses [Taylor 1977], With the Gray code, the modulator electrode lengths are L, L, 2L and 4L. In general [Taylor 1979; Leonberger et a l . 1979]; L x = L (9.3) L N = 2 N " 2 L , N = 2, 3, 4 (9.4) and • j = KLV , = IT/2 (9.5) ^ = 2 N " 2 KLV, * N = 0 , N = 2 , 3, 4 (9.6) Where N = 1 corresponds to the MSB (most s i g n i f i c a n t b i t ) , N = 2 to the next-to-MSB, and N=4 to the LSB. Value of the i n t r i n s i c phase d i f f e r e n c e i s ipj = TT/2 f o r MSB, and ^ = 0 f o r a l l other b i t s . A phase change <|> of TI/2 f o r AMPLIFIER PULSED LASER LIGHT J _ PHOTODETECTOR DELAY COMPARATOR =0 o H M O M O •J W >J 0< STROBE F i g . 9.3(a). Schematic diagram of a 4- b i t A/D converter. 0 0 VA-A-A-/ F i g . 9.3(b). I n t e n s i t y v s . vo l t a g e w i t h Gray s c a l e output (Taylor et a l . 1978) . 166 t h e LSB c o r r e s p o n d s to a q u a n t i z a t i o n s t e p "q" i n the analogue v o l t a g e N V = V ( s i n w t ) , to produce one b i t change. There are 2 q u a n t i z a t i o n steps, et in so q = V / 2 N 1 and KL = u/V . The Gray code f o r a given applied voltage and m m e l e c t r o d e l e n g t h s , gives one more b i t of p r e c i s i o n over the binary o f f - s e t code. The Gray code a l s o minimizes e r r o r , since only a s i n g l e channel b i t changes w i t h a change i n the q u a n t i z a t i o n step q; whereas, with the o f f - s e t b i n a r y code s e v e r a l b i t s change. The above ADC, although i n theory very f a s t , would require the use of conventional e l e c t r o n i c s , such as, the sample and hold c i r c u i t s and the comparators. The u l t i m a t e speed of t h i s ADC i s l i m i t e d by the e x t e r n a l e l e c t r o n i c s . I f the output i n t e n s i t y of the modulators was a square wave in s t e a d of a s i n e wave, the comparators could be e l i m i n a t e d . In the f o l l o w i n g s e c t i o n a "Comparatorless A/D converter" i s described. Another method to o b t a i n square wave output, would be to use f o r each b i t , a modulator followed by a b i s t a b l e d e v i c e . The b i s t a b l e device could be an interferometer w i t h feedback. 9.2 Comparatorless A/D converter In order to u t i l i z e the p o s s i b l e high speed c a p a b i l i t i e s of ADCs employing waveguide modulators, the comparators would have to be elimin a t e d [Ahmed and Young 1980b]. In Taylor's scheme each modulator output i s t r a n s l a t e d i n t o a two l e v e l square wave by the comparator. I t i s proposed that the s i n u s o i d a l v a r i a t i o n of modulator output be a l t e r e d to a square 1 6 7 v a r i a t i o n by s u i t a b l y combining the outputs of two or more modulators, F i g . 9.4. A square wave i s approximated by i t s truncated F o u r i e r s e r i e s ; v(x) = 4 + — {cos x ~ 4" c o s 3x + 4- cos 5x} (9.7) Let two a d d i t i o n a l modulators f o r each b i t have outputs: 1 2 = {1 - cos (3KLV + ip 2)} (9.8) 1 3 - ^ {1 + cos (5KLV + * 3 ) } (9.9) Then summing the output l i g h t i n t e n s i t i e s (not amplitudes) I 2 and I 3 of the three modulators, and n e g l e c t i n g s t a t i c phase s h i f t s ( T|>' s ) : 3 I I = I I ± = - | { j | + cos(KLV) - y C O s ( 3 K L V ) + j cos(5KLV)} (9.10) A schematic of a s i n g l e element of the proposed Comparatorless ADC i s shown i n F i g . 9.5. The three beams must not overlap before d e t e c t i o n . The s t a t i c phase s h i f t s can be tuned, e i t h e r w i t h dc voltage on compensation electrodes or by f i l m l o a d i n g technique (Chapter I V ) . The previous schemes [Taylor 1979; Leonberger et a l . 1979] a l s o c a l l f o r a dc voltage on an a d d i t i o n a l e l e c t r o d e to o b t a i n IT/2 phase d i f f e r e n c e between the i n t e n s i t y output f o r MSB and next-to-MSB. For each b i t , i t i s necessary to apportion l i g h t i n t e n s i t y between the three modulators, so that r e l a t i v e strength of the three outputs i s 1:1/3:1/5. For t h i s purpose, e i t h e r d i r e c t i o n a l couplers or branching network can be employed. A design i n d i c a t e d 2 ym gap c o u p l e r s . Because such narrow gap was d i f f i c u l t to r e a l i z e , a branching network was used. The design and I F i g . 9.4. (a)Output l i g h t i n t e n s i t y v a r i a t i o n of a s i n g l e modulator; (b) Output of the comparator; and (c) Approximation of the rectangular wave by three s i n u s o i d s . ANALOGUE INPUT V LASER LIGHT AMPLIFIER F i g . 9.5. S i n g l e c e l l of an A/D converter i n c o r p o r a t i n g three modulators. 170 experimental r e s u l t s of a three branch network are presented, a f t e r a d i s c u s -s i o n of 4-bit comparatorless A/D c o n v e r t e r . 9.3 Design parameters of a 4 - b i t ADC [Taylor 1979; Leonberger et a l . 1979] Various design parameters f o r a 4 - b i t e l e c t r o o p t i c ADC, f o r sampling (S) r a t e s of 1 GS/s and 2 GS/s, are considered. The e l e c t r o d e l e n g t h and capacitance, the modulator d r i v i n g power, as w e l l as the o p t i c a l power requirements are c a l c u l a t e d . In a d d i t i o n , pulse j i t t e r and width, and t r a n s i t times are c a l c u l a t e d . 9.3.1 Electrode l e n g t h A comparatorless ADC of F i g . 9.6, w i t h N = 4 b i t s of p r e c i s i o n , using Gray code req u i r e s f o r the Nth b i t , an electrode l e n g t h l^, f o r the f i r s t harmonic modulator, F i g . 9.4 and 9.5; N-? A, = 2 A (9.11) where I i s the e l e c t r o d e l e n g t h to produce a phase s h i f t of n i n the output. IT For the t h i r d and f i f t h harmonic modulators, the electrode lengths are £ 3 = 3 ^ , and = 5A 1 r e s p e c t i v e l y . For a Y-cut, X propagating L i N b 0 3 , at X = 0.6328 um, r 3 3 = 3 0 . 8 x l 0 ~ 1 2 m/V, and n& = 2.203; I = 1 = 1.281 mm (9.12) n 3 r 0 0 n V e 33 m Assuming a maximum m o d u l a t i n g voltage V = 10V, w i t h the coplanar e l e c t r o d e gap d = 4 ym, and the e l e c t r i c a l and o p t i c a l f i e l d overlap f a c t o r x\ = 0.6. 171 APD PULSED LASER LIGHT o Pi o < H H O W AMPLIFIERS F i g . 9.6. Schematic diagram of a 4 - b i t A/D converter. R n : l F i g . 9.7. Equivalent c i r c u i t f o r the modulator c i r c u i t r y . 172 Thus, f o r N = 4 b i t s of p r e c i s i o n , length of the longest electrode i s , I,. - 5 ( 2 N ~ 2 I ) - 20£ = 2.562 cm (9.13) Since the modulating voltage i s a p p l i e d to both arms of the modulator, the t o t a l modulator l e n g t h i s &5/2 = 1.281 cm. A f t e r a l l o w i n g f o r compensation electrodes and the branching network, t o t a l device length i s estimated to be 3.429 cm, see F i g . 9.6. Thus, s e v e r a l such devices could be accommodated on 2" diameter wafer. 9.3.2 Electrode capacitance The e l e c t r o d e capacitance C, w i t h e l e c t r o d e width equal to the electrode gap d, i s given by [Taylor 1979], C = 0.6 e 0(l+e)L - 17.486 pF (9.14) where e = / e ^ g = 34.5 pF/cm f o r the Y-cut LiNbOg, and e Q = 8 . 9 x l 0 ~ 2 pF/cm. The e l e c t r i c a l power, P , d i s s i p a t e d i n the modulator c i r c u i t r y I s , P = n C V 2 B/2 (9.15) e m where B i s the -3 dB bandwidth. For a h i g h speed ADC, Sampling r a t e (Samples/s) = 3 3 (9 16) Max. s i g n a l f r e q . , f (Hz) The above r a t i o ranges from 2 (the Nyquist rate) to 4. For a sampling r a t e of 1 GS/s, then f = 300 MHz. Assuming the bandwidth B = 2 f = 600 MHz, the m m power d i s s i p a t i o n i s ; P_ = T T C V i B/2 s 1.65 W (9.17) 173 The power d i s s i p a t i o n determines the analogue s i g n a l a m p l i f i e r requirements, and hence the s i z e , weight and cost of the ADC. The power d i s s i p a t i o n must be l i m i t e d to prevent damage by overheating. 9.3.3 Sign a l sampling e r r o r s Use of a mode-locked l a s e r , p u t t i n g out a t r a i n of pulses, as an o p t i c a l power source has been suggested [Taylor 1977]. This i s i n l i e u of the sample-and-hold c i r c u i t s i n the conventional high speed ADC, and l i k e the sample-and-hold c i r c u i t s , pulsed l a s e r produces e r r o r s . The e r r o r s due to the f l u c t u a t i o n i n sampling time ( j i t t e r ) , width of the o p t i c a l pulse, and the o p t i c a l t r a n s i t time are c a l c u l a t e d [Taylor 1979]. 9.3.4 J i t t e r The maximum e r r o r due to a pulse a r r i v i n g at t ^ + ^ = t ^ + At + 6t ins t e a d of t J = t J + At, f o r a s i g n a l of the form V = V si n ( 2 u f t) i s , i+1 i m m I 6V I = 2mf V 6t (9.18) 1 max1 m m max The c o n d i t i o n that the e r r o r i n an ADC be l e s s than h a l f the l e v e l spacing AV/2 = V / 2 N g i v e s , m 6t < l / ( 2 W " 1 T r f ) = 33.2 ps (9.19) max v m' 9.3.5 E l e c t r o o p t i c i n t e r a c t i o n d u r a t i o n e r r o r For the above V, at time t ± , the e r r o r due to AT, the sum of the pulse width T and the o p t i c a l t r a n s i t time T [Taylor 1979] i s , r> r Opt 174 t^+O.SAT SV = -V(t ) + - j l / V ( t ) dt t ±-0.5AT = f'rf A T ) 2 V ( t , ) / 6 (9.20) m ' I Again, w i t h the c o n d i t i o n the Ifivl < 0.5 AV, ^ ' 1 'max ' AT < ( 3 / 2 N - 1 ) /nf s 650 ps (9.21) The o p t i c a l t r a n s i t time through the longest electrode I - 2.562 cm f o r the LSB i s , T = — - 188 ps (9.22) opt c where n g = 2.203 i s the guide index, and c = 29.97925 x 10 9 cm/s i s the speed of l i g h t i n free-space. Thus, the maximum allowable pulse width i s T p = AT -T t = 462 ps. opt 9.3.6 O p t i c a l Power In order to s a t i s f y a given e r r o r p r o b a b i l i t y c r i t e r i o n , s u f f i c i e n t o p t i c a l power P^ from the source i s r e q u i r e d . For in s t a n c e , to c o r r e c t l y detect MSB ( o r the b i t next-to-MSB), when there i s simultaneous zero c r o s s i n g of the output i n t e n s i t y of the LSB and the MSB (or the b i t next-to-MSB) [Leonberger et a l . 1979], i x 2 N " 1 P i > A , y G ( 9 ' 2 3 ) For S i av a l a n c h e photodiode (APD) i = /4kTAf. w i t h R = 50fl, and Af = 3 GHz; n / R 175 because thermal noise dominates the shot n o i s e . The u n i t y - g a i n r e s p o n s i v i t y Y = 0.2 uA/uW, and the gain G = 100. The t o t a l source to guide, and guide to detector coupling f a c t o r k = 0.005, f o r e n d - f i r e c o u p l i n g . The s i g n a l to rms noise l e v e l x = 6, corresponding to a 2-bit e r r o r p r o b a b i l i t y of 10" 9 assuming Gaussian s t a t i s t i c s . In [Taylor 1979] the power required by an o p t i c a l r e c e i v e r w i t h S i APD, at a SNR of 21.5 dB, f o r 10" 9 b i t e r r o r r a t e , w i t h N = 4, was estimated to be -33 dBm. This power was estimated by computer s i m u l a t i o n s , using the Monte Carlo c a l c u l a t i o n to determine the e f f e c t of the quantum e r r o r s on the ADC performance. Thus, f o r a mode-stabilized i n j e c t i o n l a s e r diode w i t h 7 dBm output, a 40 dB l o s s through the device can be t o l e r a t e d . The above design parameters are compared f o r 1 GS/s, and 2 GS/s i n t e g r a t e d o p t i c a l ADC i n Table 9.1. Table 9.1 ADC PARAMETERS B i t s Sample Rate GS/s T r a n s i t Time ps Laser Pulse Width ps Pulse J i t t e r ps Peak Opt. Power mW ^max cm C pF Mod. Power D i s s . W 4 1 188 462 33 0.16 2.56 17.5 1.65 4 2 188 137 17 0.16 2.56 17.5 3.3 176 9.3.7 Measurement r e s u l t s One b i t of the ADC was produced by the c i r c u i t shown i n F i g . 9.8. I t was b u i l t i n Y-cut, X propagating L i N b 0 3 . The waveguide width was 4 pm, and the e l e c t r o d e gap 6 um. A l l the b i f u r c a t i o n angles were 1°. The three modulators had e l e c t r o d e lengths of 2 mm, 6 mm and 10 mm, i n c l u d i n g the push-pull e f f e c t . E n d - f i r e technique was used to couple 0.6328 um l i g h t , i n t o and out of the c r y s t a l . Microscope o b j e c t i v e s 100X and 40X were used at the input and the output r e s p e c t i v e l y . The modulating voltage was a p p l i e d v i a s t e e l probes on the A l e l e c t r o d e pads. The output l i g h t was viewed on a paper screen, or e l s e fed to a d e t e c t o r - a m p l i f i e r - o s c i l l o s c o p e c h a i n . The three output beams could not be discerned separately w i t h a naked eye; the beams formed a t h i n narrow s t r i p of l i g h t . This i s to be expected, since the inter-waveguide spacing i s only 16 um. The three outputs were examined i n d i v i d u a l l y w i t h a photodiode and used f o r d i a g n o s t i c s and e v a l u a t i o n . The three outputs were from the f i r s t , t h i r d and f i f t h harmonic modulators; these are shown i n F i g . 9.9(a), (b) and (c) r e s p e c t i v e l y . These are i n response to a t r i a n g u l a r v o l t a g e . For the f i r s t harmonic, the measured value of V was 11.5V, at an ° TI e x t i n c t i o n r a t i o of 81% and the i n t r i n s i c phase d i f f e r e n c e was estimated at ~ 230°. The t h e o r e t i c a l value of V I s , X d v = • — T 11 n3 r „ n e 33 0.6328 6 = J - 7 6 5 v o l t s (9.24) (2.203) 3 30.8x10-12 n(2x1000) n „ here the e l e c t r o d e gap d - 6 the t o t a l e l e c t r o d e length L - 2,1000 p . . 5 V/DIV. FIRST HARMONIC I o 0.2 V/DIV. 10 ms/DIV. (a) THIRD 10 ms/DIV. (b) 10 ms/DIV. (d) F i g . 9.9. Applied t r i a n g u l a r v o l t a g e and the output l i g h t i n t e n s i t y of the comparatorless A/D converter; (a) f i r s t harmonic, (b) t h i r d harmonic, (c) f i f t h harmonic, and (d) composite IQ. 180 and n i s the o p t i c a l and e l e c t r i c a l f i e l d o v e r l a p f a c t o r . Thus, n=5.765/11.5=0.5. From F i g . 9.9(a) the e x t i n c t i o n r a t i o ~ 81%. These could be improved by a b e t t e r L i 2 0 compensation, use of a higher wavelength (1.15 ym) or e l s e a narrower waveguide (3 ym). A l s o , symmetrical Y b i f u r c a t i o n s w i t h uniform edges would ensure equal s i g n a l s p l i t and reduce the dc component i n the output. The three harmonic outputs and the composite square wave are compared i n Table 9.2. The harmonic beams were coalesced at the photodiode w i t h a l e n s , and the output waveform i s shown i n F i g . 9.9(d). The r e s u l t i s approximately a square wave. The d i s t o r t i o n i s due to the d i f f e r e n c e s i n the i n t r i n s i c phases i n the three modulators. The phase d i f f e r e n c e between the I and I I I harmonic i s ~ 150° i n s t e a d of 180° from F i g . 9(a) and ( b ) . Bet t e r r e s u l t s could be obtained by using a T a 2 0 5 f i l m f o r phase matching, Chapter IV. The branching network was used to apportion power In the 1:0.33:0.2 r a t i o . The measured r a t i o was ~ 1:0.5:0.1. A low frequency s i g n a l was used to t e s t the c i r c u i t , but the device could operate 1-4 GHz, by making the elect r o d e s t r a v e l l i n g wave s t r u c t u r e s made up of properly terminated m i c r o s t r i p l i n e s to the harmonics. 181 Table 9.2 PERFORMANCE OF THE ADC Harmonic Modulator F i g . 9.9 Meas. ( V o l t s ) Theor. V ( V o l t s ) $ R e l a t i v e I Harmonic 1/2 Cycles /30 V p p I (Arb. U n i t s ) E x t i n c t i o n R a t i o % I (a) 11.5 5.77 0° 2.6 .44 81 I I I (b) 4.8 1.92 ~ 150° 6.3 .24 64 V (c) 3.8 1.15 ~ 0° 8.0 .05 38 Composite (d) 10. 5.77 — 1.3 .14 50 This could be done by forming coplanar l i n e s of 4 pm width and gap, around 3 pm wide guides. A d d i t i o n a l l y , a f a s t APD i n conjunction w i t h a microwave a m p l i f i e r would be r e q u i r e d . F i n a l l y , replacement of the Y-branch modulators by the BOA devices (Chapter V) would s i m p l i f y the electrode and waveguide s t r u c t u r e s . 9.4 Branching network A power s p l i t t i n g network i s required to feed the three Mach-Zehnders i n the ADC. One option i s to use couplers to apportion power, and another i s to use a branching network. A design of the d i r e c t i o n a l couplers [ M a r c a t i l i 1969] i n d i c a t e d a gap of 2 pm between the p a r a l l e l coupler arms. Such a narrow gap was considered i m p r a c t i c a l due to l i m i t a t i o n s of the mask and equipment, so a branching network shown i n F i g . 9.10 was designed and evaluated. 182 For the ADC an i n t e n s i t y s p l i t i n the proportion I ^ l g i l ^ , : : l : l / 3 : l / 5 i s re q u i r e d . This i s approximated by the branching network of F i g . 9.10. The s i g n a l s p l i t s at the f i r s t b i f u r c a t i o n i n t o I 2 and 1^, and then 1^ d i v i d e s at the second b i f u r c a t i o n i n t o I 5 and I & . The d i v i s i o n of the s i g n a l i s ; I ^ : I 5 : I 7 : : l : l / 4 : l / 4 . A more accurate estimate of the s i g n a l s p l i t i s made by tak i n g i n t o account the branching angle [Burns and M i l t o n 1975], and the bending losses [Hutcheson et a l . 1980]. 9.4.1 Bending and branching lo s s e s The bending l o s s e s of two s t r a i g h t , p a r a l l e l , n o n c o l l i n e a r waveguides are c a l c u l a t e d . The output power, P Q, a f t e r the second bend f o r the case shown F i g . 9.11 i s given by [Hutcheson et a l . 1980], P 0 " P i I a 1 2 I 2 la231 2 e x p ( - Y 0 L 0 ) (9.25) where i s the input to the f i r s t bend, Y 0 *-s t n e attenuation constant due to Rayleigh s c a t t e r i n g and absorption, L Q i s the length of the j o i n i n g segment, and I I 2 i s t n e r e l a t i v e power coupling of the fundamental mode of the two s t r a i g h t waveguides p and q. The power coupling c o e f f i c i e n t f o r the c o n f i g u r a t i o n shown i n F i g . 9.11 are given by [Hutcheson et a l . 1980], | a 1 2 | 2 - | a 2 3 | 2 = e x p ( = B 2 X 0 2 s i n 2 6/4) (9.26) where B and X Q are the propagation constant and h a l f width of the fundamental mode r e s p e c t i v e l y . The bending angle 6 i s , 6 = t a n " 1 (X /Z ) (9.27) s s 184 where X i s the t r a n s v e r s e s e p a r a t i o n of the p a r a l l e l guides, and Z i s the s s a x i a l displacement. The absorption and the Rayleigh s c a t t e r i n g losses (1.5 dB/cm) due to the p a t h - l e n g t h d i f f e r e n c e L o ~ Z g , which i s small (0.0005 cm), f o r X g = 60 ym and 6 = 1 ° , are neglected ( y 0 = 0 ) . This i s reasonable, since f o r the branching network ( F i g . 9.13), and the ADC ( F i g . 9.8), the r e l a t i v e outputs are more important than the absolute v a l u e s . With 8 = 1 ° , and using the r e p r e s e n t a t i v e parameters i n [Hutcheson et a l . 1980], the post-bending transmission power r a t i o T £ from (9.25), f o r one c a r r i e r i s ; T £ = 0.883. The branching l o s s f o r 8 = 1 ° , from [Ranganath and Wang 1977; Burns and M i l t o n 1975] a r e about 23% ( l - 2 A 2 ; A^ = 0.62). That i s , the post-branching power r a t i o , T = 0.3844. Using the above values of post-bending power r a t i o (T = .883 ), and p o s t - b r a n c h i n g power r a t i o [T^ = 0.3844), r e l a t i v e power output f o r the branching network and the ADC ( F i g . 9.8), are given below. P i - 1; P 4 - p ± T B = 0.384; P 3 = P ± T^ T c = 0.339; P 5 = P 4 Tg = 0.148; P ? = P^ T B T c - 0.130; P A = P 3 T 2 = 0.264; P f i - P $ = 0.148; P c = P ? T 2 - 0.102 The l o s s e s corresponding to the three modulators i n F i g . 9.10(b) are ignored, because of the commonality. The c a l c u l a t e d values are compared w i t h the measured ones i n Tables 9.3 and 9.4. 185 Table 9.3 THE BRANCHING NETWORK OUTPUT POWER RATIO Output C a l c u l a t e d Absolute 0.339 0.148 0.130 P/P, 1.0 0.44 0.38 Measured Absolute P/P 3 5.0 1.0 1.8 0.36 0.5 0.10 Table 9.4 COMPARATORLESS ADC OUTPUT POWER RATIO Output Desired 1.0 0.33 0.20 Ca l c u l a t e d Absolute 0.26 0.15 0.10 P/P, 1.0 0.56 0.39 Measured Absolute 0.44 0.24 0.05 P/P, 1.0 0.5 0.1 A T t d i f f u s e d waveguide b r a n c h i n g network was made i n Y-cut LiNbOg. T y p i c a l dimensions of the branching network are shown i n F i g . 9.12. The 186 output i n t e n s i t i e s I 3 , I 5 and I 7 were measured through a 0.5 mm diameter p i n -h o l e . The measured values were: I 3 = 5, I 5 = 1.8, and l 7 = 0.5. Thus, the branching network s p l i t s l i g h t (1:0.36:0.1) f a i r l y c l o s e to the c a l c u l a t e d p r o p o r t i o n s ; (1:0.44:0.38). 188 CHAPTER X SUMMARY AND CONCLUSIONS An adjustment of the propagation constant of a d i f f u s e d waveguide by f i l m l o a d i n g has been demonstrated. An a p p l i c a t i o n of i n t e g r a t e d o p t i c a l devices to HV measurement has been d i s c u s s e d . S e r i e s and m u l t i b r a n c h i n t e r f e r o m e t e r s / f i l t e r s , and a comparatorless A/D converter (ADC) have been proposed and demonstrated. The devices were f a b r i c a t e d by d i f f u s i n g 500 A of T i at 1000°C f o r 6 hours i n t o Y-cut X-propagating LiNbOg. These were evaluated at 0.6328 ym, and the l i g h t was coupled through p o l i s h e d edges by the e n d - f i r e method. The waveguides were 4 um wide, and the electrode gap 6 ym. The b i f u r c a t i o n angle f o r the Y-branch modulators was 1°, and a l l devices were 17960 um l o n g . An A l l i f t - o f f technique was developed to p a t t e r n the sputtered Ta loa d i n g f i l m . Tests on devices w i t h TM mode modulation on Z-cut L i N b 0 3 i n d i c a t e d that L i 2 0 compensation i s required to prevent change i n n g . An input impedance equation f o r the transformation of an a r b i t r a r y complex impedance through a d i s s i p a t i o n l e s s , e x p o n e n t i a l l y t a p e r e d transmission l i n e was d e r i v e d . I t was used to obt a i n the c h a r a c t e r i s t i c equation f o r the propagation constant i n a l i n e a r l y graded o p t i c a l waveguide. The equations were used to model, and to compute numerical r e s u l t s f o r a T a 2 0 5 f i l m l o a d i n g a T i i n d i f f u s e d waveguide. An a p p l i c a t i o n of these r e s u l t s to a l t e r the i n t r i n s i c phase \ J i , of a Y-branch modulator was s u c c e s s f u l l y c a r r i e d out. A T a 2 0 5 l o a d i n g f i l m ~ 1200 A t h i c k , ~ 6400 ym long on one branch produced a change i n of about 6°/minute of heating i n 0 2. This technique 189 can a l s o be ap p l i e d to the phase tuning of other length s e n s i t i v e d e v i c e s , e.g. a d i r e c t i o n a l coupler. Three Y-branch modulators w i t h 8 8 , 9 8 and 1 0 8 ym arm sep a r a t i o n , and a two mode (BOA) modulator f o r HV measurement were b u i l t . For the former, = 5 . 5 v o l t s f o r L = 7 2 0 0 ym, and d = 8 ym was measured. For the BOA modulator, corresponding to L = 9 0 0 4 ym, and gap d = 1 2 ym, the measured V =9 v o l t s . The BOA modulator i s the simpler of the two c o n f i g u r a t i o n s . As n i t does not r e q u i r e a branching network, the s i z e i s s m a l l e r , and i t requires o n l y two e l e c t r o d e s . Because of wider e l e c t r o d e gap V i s l a r g e r . An e x p r e s s i o n f o r the output i n t e n s i t y I of a s e r i e s i n t e r f e r o m e t e r / f i l t e r i s , ] o _ r S l n 2 * }2 i . L 0 N e J i 2 s i n j where 2 N L i s t h e l e n g t h of the N*"*1 e l e c t r o d e . the FWHM bandwidth f o r N = 1 , 2 , 3 , 4 , 5 and 6 i s 1 8 0 ° , 8 2 ° , 4 0 ° , 2 0 ° , 10° and 5° r e s p e c t i v e l y . A two s e c t i o n f i l t e r w i t h L = 3 7 1 2 ym and 2 L = 7 4 2 8 ym, and an ele c t r o d e gap d = 6 ym was f a b r i c a t e d . I t has a bandwidth of ~ 1 0 8 ° , as compared to a t h e o r e t i c a l v a l u e of 8 2 ° . The o u t p u t i n t e n s i t y I of a m u l t i b r a n c h i n t e r f e r o m e t e r / f i l t e r I s g i v e n by; I / I = | S ^ N ( N 6 / 2 ) j W N E R E N L i s the ° 1 N s i n ^ e / 2 ) l e n g t h of the N T H e l e c t r o d e . The FWHM bandwidth, f o r N = 2 , 3 , 4 , 5 and 6 i s 1 8 0 ° , 1 1 2 ° , 8 2 ° , 65 ° and 54° r e s p e c t i v e l y . The bandwidth of a three branch inte r f e r o m e t e r that was f a b r i c a t e d , was 9 0 ° ; i t agrees with the t h e o r e t i c a l p r e d i c t i o n ( 1 1 2 ° ) . The s e r i e s and multibranch i n t e r f e r o m e t e r s / f i l t e r o f f e r 190 the advantage of narrow output, and voltage t u n a b i l i t y . The devices, however, are more complex, cover more area, and require a phase matching of the component modulators. An e l i m i n a t i o n of the e x t e r n a l comparators, which are the slowest component of the A/D converter (ADC) based on an int e r f e r o m e t e r , i s proposed. Each comparator, i s replaced by three modulators - the output of which i s combined i n a detector to produce a square wave. Design c a l c u l a t i o n s i n d i c a t e that such a de v i c e , f o r an analogue voltage 0-10V, with 4-bit p r e c i s i o n , using the Gray code, i s f e a s i b l e on Y—cut LiNbOg. The device would be 35 mm lo n g , w i t h 3 um wide waveguides, and an ele c t r o d e gap of 4 um. A comparatorless ADC to produce 1-bit was f a b r i c a t e d . The output i n t e n s i t y of three component mo d u l a t o r s was measured. For L = 1000 um, and d = 6 ym, a = 11.5 v o l t s , and an e x t i n c t i o n r a t i o = 81% were measured. The composite output resembled a square wave. By using e l e c t r o d e s that are e s s e n t i a l l y terminated microwave transmission l i n e s , an ADC speed 1-2 GS/s could be r e a l i z e d . The proposed ADC i s complex, covers wider area, i s longer, and requires a phase matching of the component outputs. A three branch power s p l i t t i n g network was f a b r i c a t e d and t e s t e d , i t s p l i t power i n 1:0.36:0.1 r a t i o s . When more accurate f a b r i c a t i o n t e c h n i q u e s e v o l v e , and the phase t u n i n g methods are p e r f e c t e d , the comparatorless ADC w i l l become r e a l i t y . Integrated o p t i c a l devices w i l l f i n d p r a c t i c a l a p p l i c a t i o n s , only i f the source (or f i b r e ) to waveguide l o s s , and the device attenuation are reduced. Some of the problems can be a l l e v i a t e d by operating at longer wavelengths, 1.3 -1. 5 um. The b e n e f i t s are that only one mode e x i s t s i n a 4 ym waveguide, the o p t i c a l damage threshold i n L i N b 0 3 i s two orders of magnitude higher than 191 i t i s at 0.6328 pm, and the propagation l o s s of o p t i c a l f i b r e s i s minimum, ~ 0.5 dB/km. Measured values of V f o r the BOA modulator i s lower than the one reported so f a r . As the BOA s t r u c t u r e i s simple, and i t re q u i r e s only a p a i r of e l e c t r o d e s , i t could replace Y-branch modulators i n v a r i o u s devices. I t i s p a r t i c u l a r l y s u i t e d to the HV measurement a p p l i c a t i o n , as immersion i n the HV e l e c t r i c f i e l d would modulate the l i g h t . For t h i s a p p l i c a t i o n , a BOA modulator i n Z-cut L i N b 0 3 c r y s t a l , w i t h TM mode modulation to u t i l i z e r 3 3 i s suggested. An a d d i t i o n a l b e n e f i t of t h i s c r y s t a l o r i e n t a t i o n i s a greater overlap between the f i b r e and the waveguide f i e l d s [Fukuma and Noda 1980]. An i n t e r f e r o m e t e r composed of two s t r a i g h t , p a r a l l e l , contiguous, but uncoupled waveguides, only one of which i s e l e c t r o o p t i c , i s proposed f o r HV sensing. 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QE-15, no. 4, pp. 210-216. H.F. Taylor and A. Y a r i v , 1974, "Guided wave o p t i c s " , Proc. IEEE, v o l . 62, no. 8, pp. 1044-1060. H.F. T a y l o r , M.J. Ta y l o r , and P.W. Bauer, 1977, " E l e c t r o o p t i c analog-to-d i g i t a l conversion using channel waveguide modulators", T o p i c a l Mtg. on  Integrated & Guided Wave Op t i c s , S a l t Lake C i t y , Utah, paper TuCl-1. H.R. T a y l o r , M.J. T a y l o r , and B.W. Bauer, 1978, " E l e c t r o o p t i c analog-to-d i g i t a l conversion using channel waveguide modulators", Appl. Phys. L e t t . , v o l . 32, no. 9, pp. 559-561. P.K. T i e n , 1971, "Li g h t waves i n t h i n f i l m s and i n t e g r a t e d o p t i c s " , Appl.  O p t i c s , v o l . 10, pp. 2395-2413. P.K. Ti e n , 1977, "Integrated o p t i c s and new wave phenomena i n o p t i c a l waveguides", Reviews of Modern Phys., v o l . 49, no. 2, pp. 361-420. P.K. Ti e n , R. U l r i c h , and R.J. M a r t i n , 1969, "Modes of propagating l i g h t waves i n t h i n deposited semiconductor f i l m s " , A p p l . Phys. L e t t . , v o l . 14, pp. 291. P.K. Ti e n , G. Smolinsky, and R.J. M a r t i n , 1972, "Thin o r g a n o s i l i c o n f i l m s f o r in t e g r a t e d o p t i c s " , Appl. O p t i c s , v o l . 11, no. 3, pp. 637-642. P.K. T i e n , S. Riva-Sanseverino, and R.J. M a r t i n , 1974, " O p t i c a l waveguide modes i n s i n g l e - c r y s t a l l i n e LiNbO,-LiTa0 3 s o l i d - s o l u t i o n f i l m s " , Appl. Phys.  L e t t . , v o l . 24, no. 10, pp. 503-506. S. Tolansky, 1973, An I n t r o d u c t i o n to Interferometry. N.Y.: John Wiley & Sons, pp. 204-207. 201 C.S. T s a i and P. Saunier, 1975, " U l t r a f a s t g u i d e d - l i g h t beam d e f l e c t i o n / s w itching and modulation using simulated e l e c t r o - o p t i c prism s t r u c t u r e s i n L i N b 0 3 waveguides", Appl. Phys. L e t t . , v o l . 27, no. 4, pp. 248-250. E.H. Turner, 1966, "High frequency e l e c t r o o p t i c c o e f f i c i e n t s of l i t h i u m n i o b a t e " , Appl. Phys. L e t t . , v o l . 8, pp. 303-304. N. Uchida, 1976, " O p t i c a l waveguide loaded w i t h high r e f r a c t i v e - i n d e x s t r i p f i l m " , A p p l. O p t i c s , v o l . 15, no. 1, pp. 179-182. N. Uchida, 0. Mikami, S. Uehara, and J . Noda, 1976, " O p t i c a l f i e l d d i s t r i b u t i o n i n a waveguide loaded w i t h high r e f r a c t i v e index-index f i l m ; modulation e f f i c i e n c y improvement i n a planar-type modulator", A p p l . O p t i c s , v o l . 15, no. 2, pp. 455-458. R. U l r i c h and H.P. Weber, 1972, "Solution-deposited t h i n f i l m s as passive and a c t i v e l i g h t guides", Appl. O p t i c s , v o l . 11, no. 2, pp. 428-433. D.W. Vahey, 1980, " O p t i c a l s c a t t e r i n g phenomenon i n L i N b 0 3 waveguides", Tech.  Digest Integrated and Guided Wave O p t i c s , Opt. Soc. of Amer., paper Tu D4-2. D.W. Vahey, C.M. Verber, and K.P. Kenan, 1978, "Development of an i n t e g r a t e d -o p t i c s multichannel data processor", SPIE v o l . 139, Guided Wave O p t i c a l System  and Devices ( O p t i c a l Society of America, Wash., D.C.), pp. 151-158. C.P. Womack, 1962, "The use of exponential transmission l i n e s i n microwave components", IRE Trans. Microwave Theory Tech., v o l . MTT-10, pp. 124-132. S. Wright, I.M. Mason, and M.G.F. Wilson, 1974, "High-speed e l e c t r o o p t i c analogue to d i g i t a l conversion", E l e c t r . L e t t . , v o l . 10, no. 24, pp. 508-509. A. Y a r i v , 1979, "Gulded-wave o p t i c s " , S c i . American, 240, pp. 64-72. K.K. Yee and L. Young, 1975, " E l l l p s o m e t r i c i n v e s t i g a t i o n of quadratic e l e c t r o o p t i c and e l e c t r o s t r i c t i v e e f f e c t s w i t h anodic niobium pentoxide f i l m s " , A p p l . O p t i c s , v o l . 14, no. 6, pp. 1316-1321. 202 APPENDIX A S o l u t i o n of d i f f e r e n t i a l equation f o r the input impedance  of e x p o n e n t i a l l y tapered transmission l i n e terminated i n Z^ Rewriting (3.16), l ^ i + 2k + 62u = 0 diz dl From which the d i f f e r e n t i a l operator D i s , [Murray 1958], D = -k ± / k 2 -B 2 Let p = -k and q = / k 2 -B 2 Then, s o l u t i o n of d i f f e r e n t i a l equation ( A l ) i s , u = c 1 exp(p+q)A+ c 2 exp(p-q)£ where c j and c 2 are constants of i n t e g r a t i o n . Then, = c^p+q) exp(p+q) A + c 2(p-q)exp(p-q) A S u b s t i t u t i n g (A4) and (A5) i n (3.10); Z 1 du y = j B X u X d l (A l ) (A2) (A3) (A4) (A5) (3.10) y = "c 1(p+q)exp(p+q) I••+ c2(p-q)exp(p-q)£ j l [_ c 1exp(p +q) I + c2exp(p-q)£ . Using c = c 2 / c 1 and s i m p l i f y i n g 203 Z j"~(p+q)exp(qjQ + c(p-q)exp(-q&) "1 y " j 3 I exp(qJl) + c exp(-qJl) _| From F i g s . 3.1 and 3.2, r e c a l l i n g that when, 1=0, Z(0) = Zl and y = Z l n ( 0 ) = Z& . Using t h i s i n (3.21) (p+q) + c(p-q) 1 + c (A6) or, j g Z a _ (p+d) + e(p-q) ~z7~ " 1 + c = r (say) (A7) Then, (P+q) - r  C = r - (p-q; S u b s t i t u t i n g (A8) i n (A6), (A8) Z |~rp+nUr--TPq")exp(q&) + (p-a) (p+q-r)exp(-q£) ~| Y - J g I (r-p+q)exp(qJl) + (p+q-r;exp(-q£) _| - i Z r^ r+nW-fn 2- q2)}exp(q)l) + f(p 2-a 2)-(p-q)r}exp(-q)Q = - j - (r-p+q)exp(q« + (p+q-r;exp(-qA) pr c i n h f n ^ + ar cosh(q&) - (p2-q2)sinh(q£) r sinh(qA) - p sintUqW + q cosh(q£) _| 204 j g y Z pr tanh(qft) + qr - ( p 2 - q 2 ) tanh(q&) r tanh(qfc) - p tanh(qi) + q (A9) Let J3y _ N (A10) Where N and D are numerator and denominator r e s p e c t i v e l y i n (A9) N = qr + ( p r - p ^ 2 ) tanh(qfc) ( A l l ) Using (A2), (A3) and (A7) i n ( A l l ) , N = j B - i / k 2 - B 2 + + j p) tanh l / k ^ B 2 (A12) S i m i l a r l y , D = / k ^ B 2 + (J ^ + k ) tanh £ • k 2 ^ 2 (A13) S u b s t i t u t i n g (A12) and (A13) i n (A10), j / k 2= p 2 + + j p ) t a n h t / k 2 ~ B 2 } JBy _ Z / k ^ B 2 + ( J | ^ + k) tanh i, • k 2 ^ 2 Z - _1 Z / P 2 _ k 2 _ ( M i - j g ) tan W B 2 - k 2 / g 2 _ k 2 + { S & ± + k ) tan W B 2 " k 2 205 U p2-k2 -k tan £ • 3 2-k 2) + j 3 tan I • 3 2-k 2  Z l . (A14) y = • B ^ k 2 + k tan l • B 2-k 2 + j tan £ / g 2-k 2 The propagation constant 3 = — 1 Z2 and from (15) k = yjr to — 1 Z2 2 TT From [ J a s i k 1961] k = y^ - £n j- = y-Then, 32 - k2 = K) - (—) c g c -, f 2 T T -\2 where ( B 2 ^ 2 ) i s defined to equal (_y-J X g - • i - (x/xJ 2 (A16) This expression f o r "guide" wavelength i s s i m i l a r to the one f o r waveguide propagation, where X, X£ and Xg r e s p e c t i v e l y stand f o r free-space, c u t - o f f and guide wavelength. Using (A15) i n (A14), and y = from (3.6), 2 0 6 where, 2 „ f i l „ , 2 T T J I - . > . . l ^ r 2 1 ^ z, za hr " - tan<—» + J - t a nhri i n = g c g g_ (A17) Z Z ( £ ) = Z X exp(£ Jta — ) X « 4 T T L £n ( Z . / Z . ) c 1 2' • 1 " ( A / X J 2 APPENDIX B 207 SE1 ' FILM THICKNESS=C FIND n I I I FIND n2 ; w GUIDE WIDTH SET FILM THICKNESS=t FIND n 11 1, INTERVAL SEARCH SUB h INTERVAL SEARCH SUB, FIND n 2 ; w GUIDE WIDTlJ F i g . B . l . C PROGRAM: SEP18 C PROGRAM TO CALCULATE THE EFFECT OF A FILM ON PROPAGATION C CONSTANT OF A DIFFUSED WAVEGUIDE C C NA, NF, NS ARE REFRACTIVE INDICES OF AIR, FILM AND SUBSTRATE C NE, NO ARE EXTRAORDINARY AND ORDINARY REFRACTIVE INDICES C MODE=1 FOR TE, 2 FOR TM IMPLICIT REAL*8 (A-H,0~Z) REAL*8 NA, NF, NS, K, NE, NO, NO, LHS, N1, N2, N1I, N1II REAL*8 NEFF, LEFT, NX, NY, NZ Pl=3.14159265 NA= 1 .0 QA=NA*NA NE=2.2030 NO=2.2868 C C DO 140 IF=1,1 C DO 140 IW=1,4 C W=2.5+FL0AT(IW-1)*0.5 W=3 P=0. Q=0. . WAVLEN=0.6328 K=2.0* PI/ WAVLEN C c DO 140 M0DE=1,1 NAME=0 IF (MODE-2) 130, 131, 131 130 NS=NE NF=2.2134-FLOAT(lF-1)*.005 GO TO 132 131 NS=NO NF=2.2038 -FL0AT(IF-1)*0.02 132 CONTINUE QS=NS*NS QF=NF*NF C C DO 140 ID=1,14 D=7.0-FLOAT(ID-1)*0.5 TDK=2.*D*K C C DO 140 IT=1,1 THICK= 0.1000 +FL0AT(IT-1)*0.05 C c DO 140 NAM=1,1 DN=0.001+0.002* FLOAT(NAM-1) TOP=NS+DN GX=TDK*DSQRT(2.0*NS*DN) C C DO 30 NUM=1,2 IF (NUM-2) 32, 31, 31 31 T=THICK GO TO 33 2 0 9 32 T=0.0 33 CONTINUE C C JUNE 17,1981. SOURCE: PP.164, B. J . LEY. C HALF INTERVAL SEARCH METHOD FOR FINDING ROOTS C C WRITE (6, 1) 1 FORMAT (//,' THE HALF INTERVAL METHOD IS USED TO FIND THE ROOT',/ 1////, 7X, ' T 1 ' , 13X, ' T 2 ' , 13X, ' T 3 ' , 13X, ' F ( T ) ' , 113X, ' L H S ' , 13X, 'RHS' , //) TOP= DSQRT( 2.0*NS*DN+NS*NS) IF (NUM-2) 92, 91, 91 91 T1= N1II T2=T1+0.002 ACC=0.00001 GO TO 93 92 T1=TOP T2=T1-.002 ACC=0.00001 93 CONTINUE TUP=T2 STEP=T2-T1 CALL PROP1 (MODE,DN,QA,QF,QS,TDK,GX,K,T,T1,LHS,RHS) FT1= LHS-RHS 1=0 3 1=1+1 IF (DABS(T1- T2)- ACC) 10, 10, 20 20 T3= (T1+T2)/2. CALL PROP 1 (MODE,DN,QA,QF,QS,TDK,GX,K,T,T3,LHS,RHS) FT= LHS-RHS C WRITE (6, 4) T1, T2, T3, FT ,LHS, RHS 4 FORMAT,(6D15.7) IF (FT*FT1) 5, 10, 6 5 T2= T3 GO TO 3 6 CALL PROP1 (MODE,DN,QA,QF,QS,TDK,GX,K,T,T2,LHS,RHS) FT2=LHS-RHS IF (FT*FT2) 156, 10, 150 156 T1=T3 GO TO 3 150 CONTINUE C WRITE (6, 151) T1, T2 151 FORMAT (/,_' NO ROOT IN THE RANGE', 2D15.7,/) T1=TUP T2=T1+STEP TUP=TUP+STEP GO TO 93 10 CONTINUE C WRITE (6, 7) T3, I 7 FORMAT (///, ' THE ROOT =', D15.7, ' INDEX 1 //, ' AND WAS FOUND IN ' , 115, ' ITERATIONS') IF (NUM-2) 34, 35, 35 34 N1II=T3 GO TO 30 35 N1I= T3 IF (N1I-N1II) 260,260,261 o 1 0 260 NROOT=NROOT+1 T1=N1I T2=N1I+STEP GO TO 93 261 CONTINUE C C c NAME=NAME+1 IF (NAME .GT. 1) GO TO 600 WRITE(6, 300) NS,NE,NO,NF,WAVLEN,MODE,W 300 FORMAT(////,' NS=',F8.6,5X,'NE=',F8.6,5X,'NO=', 1F8.6,5X,'NF=*,F8.6,5X,'WAVLEN=',F8.6,4X, 'MODE=* ,12, 14X,'WIDTH=',F5.2) 332 WRITE(6,41) 41 FORMAT(////,4X,'DN' ,8X,'T' ,8X,'D' ,8X,'CN' ,8X,'N11' , 18X,'N1II',8X,' NZF ',6X,'NZA ',8X,'BFILM',8X,'BAIR', 18X,'ALTER') 600 CONTINUE 30 CONTINUE DO 800 IDE=1,2 IF (IDE-1) 811,811,812 811 N0=N1I GO TO 813 812 N0=N1II 813 CONTINUE NEFF=NS C INDEX=1 C IF (INDEX.EQ.1) GO TO 140 C C JUNE 17,1981. SOURCE: PP.164, B. J. LEY. C HALF INTERVAL SEARCH METHOD FOR FINDING ROOTS C C WRITE (6,51) 51 FORMAT (//,' THE HALF INTERVAL METHOD IS USED TO FIND THE ROOT',/ 1////, 7X, 'T1', 13X, 'T2', 13X, 'T3', 13X, 'F(T)', 113X, 'LEFT', 13X, 'RIGHT', //) T1= N0-0.000001 T2= NEFF TUP=T2 STEP=T2-T1 ACC=0.1D-4 58 CONTINUE CALL PROP2 (NO,K,NEFF,W,MODE,P,Q,T1,PI,LEFT,RIGHT) FT1= LEFT-RIGHT 1=0 53 1= 1+1 IF (DABS(T1- T2)- ACC) 60, 60, 70 70 T3= (T1+T2)/2. CALL PROP2 (NO,K,NEFF,.W,MODE,P,Q,T3 ,PI ,LEFT,RIGHT) FT= LEFT-RIGHT C WRITE (6, 54) T1, T2, T3, FT, LEFT, RIGHT 54 FORMAT (6D15.7) IF (FT*FT1) 55, 60, 56 55 T2= T3 GO TO 53 56 CALL PROP2 (NO,K,NEFF,W,MODE,P,Q,T2,PI,LEFT,RIGHT) FT2=LEFT-RIGHT IF (FT*FT2) 256, 60, 250 256 T1=T3 FT1=FT GO TO 53 250 CONTINUE C WRITE(6, 251) T1, T2 251 FORMAT(/, ' NO ROOT IN THE RANGE', 2D15.7) T1=TUP T2=T1+STEP TUP=TUP+STEP GO TO 58 60 CONTINUE C WRITE (6, 57) T3, I 57 FORMAT (///, ' THE ROOT =?, D15.7, ' INDEX ', 1 //, ' AND WAS FOUND IN ', 115, ' ITERATIONS') IF (IDE-1) 801,801,802 801 ZF=T3 GO TO 804 802 ZA=T3 804 CONTINUE 800 CONTINUE CN=ZF-ZA BFILM=K*ZF BAIR=K*ZA ALTER= (BFILM-BAIR)*100./BAIR 333 WRITE(6,40)DN,THICK,D,CN,N1I,N1II,ZF,ZA, 1BFILM,BAIR,ALTER 40 FORMAT (/, F8.4,2F9.4,F10.4,F11.6,F12.6,F12.6,F11.6, 1F13.6,2X,2F11.6) C WRITE(6, 700) N0,N1, N2, NX, NY, NZ 700 FORMAT(/, 6F10.6) 90 CONTINUE 140 CONTINUE STOP END C C SUBROUTINE TO COMPUTE EFFECTIVE MODE INDICES C SUBROUTINE PROP1 (MODE,DN,QA,QF,QS,TDK,GX,K,T,N1,LHS,RHS) IMPLICIT REAL*8 (A-H,0~Z) REAL*8 NA, NF, NS, K, NE, NO, NO, LHS, N1, N2, N1I, N1II IF (MODE-2) 100, 110, 110 100 ETA=1. XI = 1 . GO TO 120 1 1 0 ETA= QS/QF _ XI= QF/QA 120 CONTINUE Q1=N1*N1 FACT=DABS(QF-Q1) VEE= TDK*DSQRT(Q1- QS) VPLUS= VEE+1. XJV= BESJ (GX, VEE) XJVP= BESJ (GX, VPLUS) XJVM= (2.0*VEE*XJV/GX)-XJVP IF (XJV) 72, 71, 72 71 WRITE (6, 73) 73 FORMAT (//, ' XJV = 0 ') 72 CONTINUE LHS=(XJVP-XJVM)-FLOAT(MODE-1)* 2.0*GX*XJV/(TDK*TDK*QS) 82 B1= K* DSQRT(FACT) S= DSQRT(DABS((Q1 - QA)/ FACT)) RHS= ETA* 2.0* DSQRT(FACT) RHS= RHS* (XJV*TDK/GX) IF (NF-N1) 85,84,84 84 RHS= RHS*(XI* S- DTAN(B1 * T))/(1.0+ XI* S* DTAN (B1*T)) GO TO 83 85 RHS=RHS*(XI* S+DTANH(B1 * T) )/( 1'. 0+XI* S*DTANH(B1*T)) 83 RHS=RHS*(1.0+(FLOAT(MODE-1)*2.*DN/DSQRT(QS))) C WRITE(6,300)GX,VEE,XJVP,XJVM,XJV,B1,S 300 FORMAT(/,'***',7D15.7) RETURN END C C SUBROUTINE TO COMPUTE N2 C c SUBROUTINE PROP2 (NO,K,NEFF,W,MODE,P,Q,N2,PI,LEFT,RIGHT) IMPLICIT REAL*8 (A-H,0~Z) REAL*8 NA, NF, NS, K, NE, NO, NO, LHS, N1, N2, N i l , N1II REAL*8 NEFF, LEFT B2= K* DSQRT( N0*N0 - N2*N2) GAMS= K* DSQRT(N2* N2 - NEFF*NEFF) IF ( MODE- 2) 210, 200, 200 200 ZETA= 1. GO TO 220 210 ZETA= (N0/NEFF)**2 220 CONTINUE LEFT= B2* W RIGHT= Q* PI RIGHT= RIGHT+2.0* DATAN (ZETA* GAMS/ B2) BAL=LEFT-RIGHT RETURN END 2 1 2 

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