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Integrated optical devices in lithium niobate Jaeger, Nicolas August Fleming 1985

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INTEGRATED OPTICAL DEVICES IN LITHIUM NIOBATE by NICOLAS AUGUST FLEMING JAEGER B.S c , E l e c t r i c a l Engineering, The University of the P a c i f i c , 1981 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE 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 thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA October 1985 Nicolas August Fleming Jaeger, 1985 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. The University of British Columbia 1956 Main Mall Vancouver, Canada Department V6T 1Y3 r»F.fin/ftii i i Abstract A class of integrated o p t i c a l devices i s based on l i g h t propagation i n o p t i c a l channel waveguides. It includes o p t i c a l modulators such as the integrated Mach-Zehnder (IMZ). Many applications have been proposed for such integrated o p t i c a l devices. The present work was motivated by a proposed a p p l i c a t i o n to voltage determination on high voltage l i n e s , for example, SF 6 bus ducts i n Hydro substations. For the voltage measurement a p p l i c a t i o n two device types were proposed. The f i r s t includes devices using capacitive voltage d i v i d e r s . A novel d i v i d e r f or the SF 6 bus duct a p p l i c a t i o n was proposed using a LiNb0 3 wafer into which an IMZ could be b u i l t to give an integrated u n i t . Time permitted the d i v i d e r to be tested only using a separate IMZ. The second type of device includes Immersion devices. Two novel immersion devices are proposed and t h e i r theory i s developed. IMZs were made for the demonstrated, high voltage sensor, by d i f f u s i n g T i into LiNb0 3. Much e f f o r t was put into s o l v i n g a sequence of experimental obstacles including the e l i m i n a t i o n of L i 2 0 o u t - d i f f u s i o n (which causes a waveguide to be produced on the whole surface), the p o l i s h i n g of the LiNb0 3 c r y s t a l s and o p t i c a l f i b e r s , and the butt coupling of the f i b e r s to the c r y s t a l s . In the end IMZs were fabricated with state-of-the-art e x t i n c t i o n r a t i o s . A t h i r d device, employing voltage induced waveguides, was proposed and was demonstrated. A mathematical treatment of the theory of the IMZ i s provided. i i i TABLE OF CONTENTS Page ABSTRACT i i TABLE OF CONTENTS i i i LIST OF TABLES v i LIST OF FIGURES v i i ACKNOWLEDGEMENTS xiv 1. INTRODUCTION 1 2. HIGH VOLTAGE SENSORS 5 2.1 Introduction 5 2.2 High Voltage Sensing Using a Capacitive Divider and an IMZ 5 2.3 The Immersion Device 9 2.3.1 The Asymmetric Waveguide Immersion Device 12 2.3.2 The Strip-Loaded Diffused Waveguide Immersion Device 19 3. FABRICATION OF THE DEVICES 27 3.1 Introduction 27 3.2 Mask Design 27 3.3 Fabr i c a t i o n of Ti:LINb0 3 Devices 32 3.3.1 The Crystals 34 3.3.2 The Cleaning Process 34 3.3.3 The Evaporation of Titanium 37 3.3.4 Patterning the Titanium 40 3.3.6 The D i f f u s i o n Process 43 3.3.6 Depositing the Buffer Layer 50 3.3.7 Depositing the Electrode Metal and 52 Patterning the Electrodes i v TABLE OF CONTENTS (CONT'd) Page 3.4 Polishing the Crystals 54 3.4.1 Preparing the Samples f or Po l i s h i n g 59 3.4.2 Grinding and Pol i s h i n g the LiNb0 3 60 3.5 Testing the Devices 73 3.6 Separating the Dies Containing the Devices from the Sample 79 3.7 Preparing O p t i c a l Fibers for Butt Coupling 81 3.8 Attaching the Fibers to the Device 90 4. RESULTS 98 4.1 Introduction 98 4.2 Device Parameters 98 4.3 The Capacitive Divider 102 4.4 Waveguide E f f e c t i v e Mode Refractive Index Measurements 115 4.5 High Voltage Test 120 4.6 The Voltage Induced Waveguide 122 5. SUMMARY AND CONCLUSIONS 131 APPENDIX 1 Waveguide Analysis 133 A l . l Introduction 133 A1.2 Planar Waveguides 133 Al.2.1 The Asymmetric Slab Waveguide 141 Al.2.2 The Exponential Waveguide 144 A1.3 Channel Waveguides 1 4 9 APPENDIX 2 The Integrated Mach-Zehnder Modulator 159 A2.1 Introduction 1 5 9 A2.2 The Integrated Mach-Zehnder Modulator 159 A2.3 Design Considerations I 6 9 V TABLE OF CONTENTS (CONT'd) Page APPENDIX 3 186 A3.1 Introduction 186 A3.2 The Asymmetric Slab Waveguide With an Anisotropic Substrate 186 A3.3 The Strip-Loaded Diffused Waveguide With an Anisotropic 192 Substrate REFERENCES 192 vi LIST OF TABLES Table P a S e 3.1 Photolithographic parameters. 42 4.1 Device parameters. 105 v i i LIST OF FIGURES Figure Page 2.1 A high voltage monitoring system i n which the source 7 and detector are e l e c t r i c a l l y i s o l a t e d from the high voltage environment. 2.2 An IMZ with I n t e r d i g i t a l electrodes. 8 2.3 A monolithic high voltage sensor with a capacitive 10 voltage d i v i d e r and an IMZ on the same substrate z-cut LiNb0 3 substrate. 2.4 An IMZ with a section of length L of each of the 13 branches with a structure d i f f e r e n t from that of the other branch. 2.5 The cross section of a waveguide with a z-cut LiNb0 3 14 substrate, a ZnS slab, and eit h e r an a i r or la2% superstrate. 2.6 P i i s plotted vs. n m for three d i f f e r e n t values of n g 16 and n Q for both TEg and TM Q modes. For the T M Q modes n e and n Q are 2.2007 and 2.2881 for curve A, 2.2017 and 2.2884 f o r curve B, and 2.2027 and 2.2887 for curve C. For the T E Q modes n Q i s 2.2881, 2.2884 and 2.2887. 2.7 p i i s plotted vs. n e for the T M Q mode at the operating 18 points I (curve D) and II (curve E ) shown i n f i g u r e 2.6. 2.8 A st r i p - l o a d e d d i f f u s e d waveguide made with ZnS f i l m on 21 a y-cut Ti:LiNb0 3 d i f f u s e d region. 2.9 P i i s plotted vs. t for the T E Q mode for three 23 d i f f e r e n t values of n e . n i s 2.2007 for curve A, 2.2017 for curve B, and 2.2027 for curve C 2.10 P i i s plotted vs. n e for the T E Q mode for the operating 24 points I (curve D) and II (curve E ) shown i n f i g u r e 2.9. 2.11 p i i s pl o t t e d vs. n Q for the T M Q mode for loading f i l m 25 thicknesses of 0 (curve F) and 200 nm (curve G) which correspond to the f i l m thicknesses of operating points I and II shown i n fi g u r e 2.9. v i i i LIST OF FIGURES (CONT'D) Figure Page 3.1 The design of the IMZs used i n this work. 28 3.2 The design of the electrodes used i n t h i s work. 30 3.3 The electrodes mask. 31 3.4 The wafer a f t e r being cut by M i c r o t e l P a c i f i c 35 Research. 3.5 An Alpha Step 200 pl o t of a device well d e l i n i a t i o n 39 mark made a f t e r the deposition and patterning of the T i l a y e r . 3.6 A Y-branch for an IMZ with w = 4Lim and 6 = 2.005°, 44 at (a) 56x and (b) at 560x. 3.7 A sample placed on an alumina wafer surrounded by 51 stoichiometric LiNb0 3 powder. 3.8 The E x p o l a r i z a t i o n of the output of an IMZ. 51 3.9 An Alpha Step 200 pl o t of the height of the S i 0 2 53 buffer l a y e r . 3.10 An Alpha Step 200 plot made a f t e r the deposition and 55 patterning of the electrode metal. 3.11 The electrode pattern of a 1mm device at 56x. 56 3.12 The connection between the outer electrodes of an IMZ 56 modulator at 140x. 3.13 A cross s e c t i o n a l view of a d i f f u s e d waveguide, the 57 buffer layer and the metal electrodes on e i t h e r side of the waveguide. 3.14 The f a b r i c a t i o n process steps for manufacturing IMZ 58 modulators. 3.15 How the sample was cut i n preparation for p o l i s h i n g . 61 The broken l i n e s i n d i c a t e the cut l i n e s . 3.16 A sample prepared for p o l i s h i n g . 63 3.17 The j i g used to p o l i s h the edges of our samples. 63 ix LIST OF FIGURES (CONT'D) Figure Page 3.18 The crystal's edge after grinding at (a) 140 and (b) 67 560x. 3.19 The crystal's edge after polishing with a 9um paste 68 at (a) 140 and (b) 560x. 3.20 The crystal's edge after polishing with a lum slurry 69 at (a) 140 and (b) 560x. 3.21 The crystal's edge after polishing with a .lum slurry 70 at (a) 140 and (b) 560x. 3.22 The crystal's edge after polishing with a .05um 71 slurry at (a) 140 and (b) at 560x. 3.23 A scale for measuring distances on the pictures taken 72 at 560x magnification. The distance between two neighbouring arrows i s lOum. 3.24 A finished sample with the cover pieces s t i l l attached. 74 3.25 The test setup used to test the devices. The laser 74 can be seen on the l e f t of the picture. 3.26 End-fire coupling light into the Ti:LiNb0 3 77 waveguides, (a) The "bushy" pattern is seen leaning to the right of the picture, (b) The "bushy" pattern i s erect in the center of the picture. 3.26(cont.)End-fire coupling light Into the Ti:LiNb0 3 78 waveguides, (c) The light i s confined to the Ti:LiNb0 3 and the surface waveguides. 3.27 The modulating voltage and the output signal of an 80 IMZ modulator. 3.28 Final die containing a useful device. 82 3.29 The j i g used to polish the ends of our 85 capillaries/fibers. 3.30 The end of the fiber at 560x after (a) grinding and 87 (b) polishing with the 9um paste. 3.30(cont.)The end of the fiber at 560x after (c) polishing with 88 the lum slurry and (d) polishing with the .05um slurry. 3.31 The finished capillary/fiber at 56x. 89 X LIST OF FIGURES (CONT'D) Figure Page 3.32 The nominal dimensions and the s p e c t r a l attenuation 91 of the ITT T-1601 f i b e r used i n t h i s work as supplied by ITT. 3.33 The l a s e r , the input objective, the f i b e r , and the 92 output of the f i b e r projected onto a screen. 3.34 The setup used to a l i g n the c a p i l l a r i e s / f i b e r s with 95 the device (a) with the l i g h t s on and (b) i n the dark. 3.35 The microprobe s t a t i o n with both f i b e r s attached and 97 mounted on the c a p a c i t i v e d i v i d e r port. 4.1 The modulating signals and (a) E x and (b) E y 100 output signals for a 4um IMZ with L • 5mm. 4.2 The modulating s i g n a l and E p o l a r i z a t i o n output 101 s i g n a l for a 4um IMZ with L • 10mm. 4.3 The modulating s i g n a l and E x p o l a r i z a t i o n output 101 s i g n a l for a fym IMZ with L * 1mm. 4.4 The Ey p o l a r i z a t i o n of an IMZ for (a) the case i n 103 which the l i g h t i s confined to the output waveguide and (b) the case i n which the l i g h t i s radiated into the bulk of the c r y s t a l . 4.5 The port and c a p a c i t i v e d i v i d e r . 104 4.6 The capacitance and d i s s i p a t i o n factor of the 107 c a p a c i t i v e d i v i d e r measured at ten d i s c r e t e points between 10kHz and 10MHz. 4.7 The impedence, (a) phase and (b) magnitude, of the 108 c a p a c i t i v e d i v i d e r (plus a connecting wire) measured 1000 d i s c r e t e points between 1MHz and 10MHz. 4.8 The input and output signals from the capacitive 110 d i v i d e r for a 50kV applied s i g n a l . 4.9 C e versus applied voltage. I l l 4.10 The input and output signals from the capacitive 112 d i v i d e r for a 6000Hz applied s i g n a l . 4.11 The (a) slow and (b) f a s t r i s e time impulse 113 measurements. 4.12 The capacitance and d i s s i p a t i o n f a c t o r of a device H 4 with (a) L • 5mm. x i LIST OF FIGURES (CONT'D) Figure Page 4.13 Drawing of the prism coupler used to measure the 116 waveguide e f f e c t i v e mode r e f r a c t i v e i n d i c e s . 4.14 Picture of the prism coupler used to measure the 118 waveguide e f f e c t i v e mode r e f r a c t i v e i n d i c e s . 4.15 Arrangement used for measuring the base angle of the 119 prism, c. 4.16 The modulating and output signals of the deviced used 121 i n our high voltage sensor. 4.17 Plot of P Q u t / P p p . 123 4.18 The predicted values of the output s i g n a l based on 124 the measured ca p a c i t i v e d i v i d e r r a t i o s . 4.19 The measured outputs of our high voltage sensor. 125 4.20 The applied and output signals f o r an applied voltage 126 of (a) 20 and (b) 50kVrms. 4.21 The test setup used to make the high voltage 127 measurements. 4.22 The cross section of a voltage induced waveguide. 129 4.23 The output power of the voltage induced waveguide as 130 a function of the voltage applied across the electrodes. 4.24 The output 6pot of the voltage induced waveguide with 130 35V applied across the electrodes. A l . l (a) The cross section of a symmetric slab waveguide, (b) 134 The r e f r a c t i v e index d i s t r i b u t i o n , n(y), f o r the symmetric slab waveguide. A1.2 A wave-vector diagram used to determine the change i n 139 phase i n the t h i n slabs of Hocker and Burns method. A1.3 A piecewise l i n e a r approximation to an a r b i t r a r y 139 r e f r a c t i v e index d i s t r i b u t i o n . A1.4 A constant r e f r a c t i v e index slab approximation to an 140 a r b i t r a r y r e f r a c t i v e index d i s t r i b u t i o n . A1.5 (a) The cross section of an asymmetric slab waveguide. 142 (b) The r e f r a c t i v e index d i s t r i b u t i o n . x i i LIST OF FIGURES (CONT'D) Figure Page A1.6 (a) The r e f r a c t i v e index d i s t r i b u t i o n of an asymmetric 145 slab waveguide. The f i e l d d i s t r i b u t i o n s of (b) the 0 t h order mode and (c) the 4 C order mode. A1.7 The r e f r a c t i v e index d i s t r i b u t i o n of an exponentially 146 tapered waveguide covered by a medium with a constant r e f r a c t i v e index. A1.8 (a) The r e f r a c t i v e index d i s t r i b u t i o n and (b) the 0 t h 150 and (c) 4 order modes of an exponential waveguide. A1.9 A rectangular rod embedded i n a substrate and covered 151 by a i r . A L I O The cross section of the waveguide used by M a r c a t i l i . 153 A l . l l The equivalent structures for f i n d i n g (a) Py^ and (b) 156 Pxl* A1.12 The f i e l d d i s t r i b u t i o n of an E y 0 0 mode. 158 A2.1 The Integrated Mach-Zehnder modulator (IMZ). The 160 input power, Pi n» i s divided between the two branches of the device and i s recombined at the output. A2.2 IMZs with electrodes (a) beside, (b) above and 161 beside, and (c) above the waveguides of an IMZ. A2.3 E(x) and n(x) along a l i n e perpendicular to the 165 d i r e c t i o n of propagation i n the recombining Y-branch of an IMZ at a f i x e d moment i n time. An a r b i t r a r y r e l a t i v e phase d i f f e r e n c e , between the two branches, has been assumed. A2.4 The x dependence of e t ( x , y ) , e t l ( x , y ) , and e t 2 ( x , y ) , 167 f o r A«> • Orad. A2.5 The output s i g n a l of an IMZ with a t r i a n g l e wave 170 applied to i t s electrodes, (a) The E x p o l a r i z a t i o n and (b) the E y p o l a r i z a t i o n . A2.5(cont.) (c) The output s i g n a l of E x + E y . 171 A2.6 The Y-branch of an IMZ. The three regions of the 173 Y-branch are the input/output waveguide, the horn, and the output/input waveguides. A2.7 The mode converting behaviour of the beam s p l i t t i n g 177 Y-branch of an IMZ for (a) the 1 ^ - 0 and (b) the n± • 1 modes. x i i i LIST OF FIGURES (CONT'D) Figure Page A2.7(ccmt.) The mode converting behaviour of the beam s p l i t t i n g 178 Y-branch of an IMZ for (c) the ta^ = 2 and (d) the m^  = 3 modes. A2.8 The mode converting behaviour of the recombining 179 Y-branch of an IMZ for the n i a r m • 0 modes of the input waveguides with phase differences between the modes i n the two arms of (a) 0 and (b) it radians. A2.9 The output s i g n a l of the E x p o l a r i z a t i o n for (a) a 181 multi-mode and (b) a mono-mode IMZ modulator. A2.10 One step of the small step approximation of the fork 182 of a recombining Y-branch. A 2 . l l The E y p o l a r i z a t i o n of the output of an IMZ for 184 (a) the case i n 185 which the l i g h t i s confined to the output waveguide and (b) the case i n which the l i g h t i s radiated into the bulk of the c r y s t a l . A2.12 The output s i g n a l of the E y p o l a r i z a t i o n of an IMZ 185 made during t h i s work. The device has an e x t i n c t i o n r a t i o of ~98%, an i n t r i n s i c phase of ~65°, and a V u of 24V. A3.1 An asymmetric slab waveguide with an anisotropic 190 substrate. A3.2 A strip-loaded waveguide with an exponential r e f r a c t i v e index p r o f i l e . 190 x i v ACKNOWLEDGEMENTS My deepest appreciation goes to my parents for t h e i r support throughout the course of this work. I also thank Dr. L. Young for suggesting the topic. His support and guidance were invaluable to me during t h i s program. My gratitude goes to the Science Council of B r i t i s h Columbia whose f i n a n c i a l support was e s s e n t i a l to t h i s work. I thank a l l of the l o c a l companies and t h e i r employees whose cooperation and expertise helped make my l i f e that much e a s i e r . My s p e c i a l thanks go to Dr. J . Ahmed, Mr. W. Grunmann, and Mr. D. Wellborn of M i c r o t e l P a c i f i c Research, Dr. L. Snider, Mr. G. Frank, and Dr. B. Nielsen of B.C. Hydro, Mr. G. Cheng of P a c i f i c Micro C i r c u i t s , and Dr. D. Smith of B a l l a r d Research. I thank a l l of the professors and students of the Department of E l e c t r i c a l Engineering who have discussed my project with me, a few of whom stand out for t h e i r help; Mr. I. Abdel-Motaleb, Dr. H. Dommel, Dr. M. Beddoes, Mr. R. Jankowski, and Mr. N. Beaulieu. Mr. C. Sudhakar's help i n the high voltage lab Is most g r a t e f u l l y acknowledged and deserves s p e c i a l mention. Nearly a l l of the members of the s t a f f of the Department were involved with my work to some degree and I thank them a l l accordingly. F i n a l l y I would l i k e to posthumously thank Mr. P. Stephenson for his help during the f i r s t months of the p r o j e c t . 1 Chapter 1 Introduction An o p t i c a l technique for monitoring the current i n a high voltage l i n e , using a material e x h i b i t i n g the magnetooptic e f f e c t , was proposed and demonstrated i n 1973 [Rogers 1973]. Later methods used e l e c t r o o p t i c or el e c t r o g y r a t i o n e f f e c t materials to measure the voltages as well [Massey, Erlckson, and Kadlec 1975; Rogers 1976]. These i n i t i a l systems used a free space o p t i c a l l i n k to interrogate the sensor material which was placed i n the f i e l d to be measured. Later the use of o p t i c a l f i b e r s replaced the free space l i n k s [Erickson 1980; Smith, Dommel, and Young 1983], U n t i l the end of the 1970's work concentrated on the development of bulk sensors. These are large devices that use o p t i c a l l y polished c r y s t a l s , lenses, p o l a r i z e r s , prisms, e t c . In 1980 work began at the University of B r i t i s h Columbia to apply the advances i n integrated o p t i c a l devices to the f i e l d of high voltage measurements. Three devices were proposed i n 1981 [Ahmed 1981]. They were an integrated Mach-Zehnder modulator (IMZ) with one of i t s branches shielded from the applied f i e l d , a Bifurcate Optique Active (BOA) modulator, and a p a r a l l e l l i n e modulator. A l l three devices were passive i n that they required no e l e c t r i c a l power supplies, conducting leads, or electrodes. They were a l l immersion type devices. In t h i s t hesis the use of IMZs as high voltage sensors i s Investigated. Two new types of devices are proposed, one of which i s demonstrated. IMZs have, of course, many ap p l i c a t i o n s other than voltage measurement. As a 2 waveguide modulator the IMZ has taken, many forms. Its most basic form i s as a broad-band (> 1GHz) modulator [Leonberger 1980; Becker 1984a] with large e x t i n c t i o n r a t i o s (98%-99%). Modulators with wide bandwidths of 11.2GHz have been reported [Alferness 1982] using phase matched traveling-wave electrodes. A p o l a r i z a t i o n independent version has also been developed [Burns et a l . 1978]. The IMZ has been used as an A/D converter [Taylor, Taylor, and Bander 1978; Leonberger, Woodward, and Spears 1979], an integrated b i s t a b l e o p t i c a l device [Ito, Ogawa, and Inaba 1979], an integrated o p t i c a l temperature sensor [Johnson, Leonberger, and Pratt 1982], an u l t r a f a s t a l l o p t i c a l gate [Lattes et a l . 1983], an o p t i c a l - o p t i c a l modulator [Yajima et a l . 1984], and an integrated 1x4 high-speed o p t i c a l switch and time demultiplexer [Haga, Izutsu, and Sueta 1985]. The new device types are described i n Chapter 2. One type consists of a capaci t i v e voltage d i v i d e r used i n conjunction with an IMZ. An integrated u n i t , c o n s i s t i n g of an IMZ and capacitive d i v i d e r on a sing l e substrate of z-cut LiNb0 3, i s proposed and an example i s given. The other type consists of new immersion devices. One immersion device consists of an IMZ made by depositing a f i l m with a large r e f r a c t i v e index on an e l e c t r o o p t i c substrate. The f i l m i s then appropriately patterned. Each of the branches i s covered with a superstrate with a d i f f e r e n t r e f r a c t i v e index. The other immersion device consists of an IMZ made by the i n d i f f u s i o n of an appropriately patterned Impurity into an e l e c t r o o p t i c substrate. One of the branches of the IMZ i s covered with a t h i n f i l m of material with a large r e f r a c t i v e index. The theory governing the operation of both immersion devices i s presented and t h e i r behavior, as high voltage sensors, using designs based on 3 e x i s t i n g materials, i s predicted. The main problem encountered i n t h i s research was the f a b r i c a t i o n of the device that was demonstrated. Chapter 3 discusses the layout of the masks used, the f a b r i c a t i o n of Ti:LiNb0 3 waveguides, the p o l i s h i n g of c r y s t a l edges and f i b e r ends, the bench t e s t i n g of the devices, and the method of attaching the f i b e r s to the c r y s t a l . In Chapter 4 the r e s u l t s of measurements of the parameters describing the operation of some of the IMZs fabricated during t h i s work are given. The f a b r i c a t i o n and t e s t i n g of the c a p a c i t i v e voltage d i v i d e r are then described. The method of measuring waveguide e f f e c t i v e mode r e f r a c t i v e indices i s explained. The r e s u l t s of a 60Hz high voltage test on a sensor, employing a capacitive d i v i d e r and a separate IMZ, are given. F i n a l l y , the f a b r i c a t i o n of and tests on a new device, employing voltage induced waveguides, are presented. Chapter 5 contains a summary of the work, conclusions and suggestions for further work. Appendix 1 i s a review of electromagnetic wave propagation i n the d i e l e c t r i c waveguide structures relevant to this work. It i s based on material from various papers and monographs. Appendix 2 i s a treatment of the theory of the IMZ. A new mathematical approach for a r r i v i n g at the v o l t a g e - i n / o p t i c a l - i n t e n s i t y - o u t transfer function i s presented. Design considerations are also presented. Experimental and t h e o r e t i c a l j u s t i f i c a t i o n s for the assumptions made i n the mathematical development are discussed. 4 In Appendix 3 the eigenvalue equations for TE and TM modes used i n Chapter 2 are developed, and the choice of some of the design parameters are discussed. 5 Chaptjer 2 High Voltage Sensors 2.1 Introduction In t h i s chapter two types of devices are proposed. The f i r s t type includes devices using capacitive voltage dividers i n conjunction with an IMZs. In these devices the capacitive d i v i d e r supplies a modulating voltage to the electrodes of an IMZ. The second type includes immersion type devices. In these devices the design of the waveguide, of each of the branches of an IMZ, controls the r e l a t i o n s h i p between the change i n the propagation constants of the l i g h t i n the waveguide and the change i n the r e f r a c t i v e index of i t s e l e c t r o o p t i c substrate. Devices of these types would have several advantages over conventional methods of measuring voltage on high voltage l i n e s . F i r s t , these sensors would be interrogated by l i g h t c a r r i e d i n o p t i c a l f i b e r s . Since the o p t i c a l f i b e r s are themselves i n s u l a t o r s a l l of the e l e c t r o n i c equipment that i s part of the monitoring system could be i s o l a t e d from the high voltage environment. Also signals transmitted by the o p t i c a l f i b e r s would not be corrupted by electromagnetic i n t e r f e r e n c e . Second, no e l e c t r i c a l power supplies would be required to operate the sensor. Third, they would have large bandwidths > 1MHz. Fourth, these sensors promise to be r e l a t i v e l y inexpensive. 2.2 High Voltage Sensing Using a Capacitive Divider and an IMZ When a cap a c i t i v e voltage d i v i d e r i s used i n conjunction with an IMZ to form a high voltage sensor, the output voltage, V , of the divider i s 6 changed into an o p t i c a l s i g n a l by the IMZ and i s transmitted, v i a o p t i c a l f i b e r , to a detector (see figure 2.1). This allows the detector to be e l e c t r i c a l l y i s o l a t e d from the high voltage environment. The sensor's capacitance, C £, i s designed to be much larger than that between the electrodes of the IMZ. The output voltage i s thus related to the applied voltage, ^ a p p n e ^ » by C V = — V 2.1 out C £ applied where C g i s the capacitance from the sensor to the high voltage electrode which i s several orders of magnitude smaller than C . V i s applied across ° c out r r the electrodes of the IMZ and thus supplies a modulating s i g n a l . The v o l t a g e - i n / o p t i c a l - i n t e n s i t y - o u t transfer function of an IMZ i s given by equation A2.13 as I - ( I /2)[1 + cos(nV/V +$,)] 2.2 out i n 1 n i J where V i s the half-wave voltage and o>. i s the i n t r i n s i c phase diffe r e n c e Tt I Tt (see Section A2.2). For a device with <t> £ = - equation 2.1 becomes I = (I /2)[1 + sin (T tV/V ) ] . 2.3 out i n 1 n For an IMZ designed to e x p l o i t the 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 Ti:LiNb0 3 waveguides and which uses an i n t e r d i g i t a l electrode arrangement (see figure 2.2) the half-wave voltage i s given by (see equation A2.5) V - X g/(2n 3roL) 2.4 Tl O where X i s the free space wavelength of the l i g h t used, g i s the o i n t e r e l e c t r o d e gap, n i s the r e f r a c t i v e index at X q , r Is the relevant e l e c t r o o p t i c c o e f f i c i e n t , o i s the overlap f a c t o r , and L i s the length of the propagation constant modulation region. 7 HIGH VOLTAGE ENV1ROMENT • I E-field I ! ! I SENSOR Figure 2.1 A high voltage monitoring system in which the source and detector are e l e c t r i c a l l y isolated from the high voltage environment. Figure 2.2 An IMZ with I n t e r d i g i t a l electrodes 9 For a di v i d e r r a t i o of 4*10"* and an operating voltage of 440kV rms a device with > 50V would be necessary to monitor the voltage under normal operating conditions. An IMZ with V^ = 50V, g = 20um, o = .5 (see Chapter 4) would have value of L, of .77mm for operation at X q = 632.8nm. If z-cut LiNb0 3 were used as the sensor d i e l e c t r i c i t would be possible to integrate the capacitive d i v i d e r with the IMZ mo n o l i t h i c a l l y while s t i l l taking advantage of the large r^-j e l e c t r o o p t i c c o e f f i c i e n t . Figure 2.3 depicts a monolithic high voltage sensor. Theoretical work [Ramer 1982; Marcuse 1982] has shown that i f d/g i s ~3, where d Is the separation between the waveguides, the f i e l d modulating the r e f r a c t i v e index i n the region of the waveguide i s ~.12V/g and o i s ~1. For an interelectrode gap of lOum i t i s possible to b u i l d a device that would have a branch separation of 30um which i s smaller than that of the devices b u i l t i n this work (see Chapter 3). For the same d i v i d e r r a t i o and operating voltage as i n the preceding example a device with L * I.6mm could be used for operation at X = 632.8nm. o 2.3 The Immersion Devices As has already been stated various immersion devices have been proposed [Ahmed 1981]. In t h i s s ection two new devices of t h i s type are submitted, t h e i r theories of operation are presented, and examples are given. One device has an asymmetric slab waveguide structure and the other has a str i p - l o a d e d d i f f u s e d waveguide s t r u c t u r e . The new feature of these devices i s that the r e l a t i o n s h i p between the change i n the propagation constant of a confined mode of a waveguide and the change i n the r e f r a c t i v e index of a section of the waveguide can be affected by c o n t r o l l i n g the extent of the o p t i c a l f i e l d s i n that section. For a Figure 2.3 A monolithic high voltage sensor with a capacitive voltag divider and an IMZ on the same z-cut LiNb03 substrate. 11 waveguide i n which only a portion of 'the o p t i c a l f i e l d s are i n an e l e c t r o o p t i c region the change In the propagation constant can be expressed as a function of a small change i n the r e f r a c t i v e index of the region by the expression Ap J = C,An 2.5 i i s where p, i s the propagation constant of the i * * 1 mode, n g i s the r e f r a c t i v e index of the e l e c t r o o p t i c region, and i s the constant of p r o p o r t i o n a l i t y l i n k i n g the change i n p. to the change i n n . Thus by having d i f f e r e n t X s waveguide structures for each of the branches of an IMZ i t i s possible to obtain d i f f e r e n t constants of p r o p o r t i o n a l i t y . The phase difference induced between two waves propagating i n two separate waveguides i s given as the difference of the induced phase change i n each. If both waveguides are of length L then the phase difference can be expressed i n terms of the change i n the propagation constants as A0 = ( A p n - A p i 2 ) L 2.6 where the subscripts 1 and 2 r e f e r to the waveguide. An expression for the half-wave voltage of such a device can be obtained from i t s d e f i n i t i o n (see equation A2.3) using equation 2.6 = n V / ( A P i l - A p i 2 ) L . 2.7 S i m i l a r l y , an expression for the half-wave e l e c t r i c f i e l d , , can be derived. This i s the e x t e r n a l l y applied f i e l d that w i l l produce a change of phase of T t r a d between the outputs of an immersion IMZ. If an IMZ i s fa b r i c a t e d on an e l e c t r o o p t i c substrate and If a section of length L of each of the branches has a structure d i f f e r e n t from that of the other branch (see 12 fi g u r e 2.4) then each branch w i l l have i t s own value of . Using the two values of C^, say for branch 1 and f ° r branch 2, equation 2.6 can be rewritten as A0 - (C, 0 - C,.)n 3rE.L/2 2.8 1/ 11 s 1 where i s the Internal e l e c t r i c f i e l d (assumed uniform i n the region of the two waveguides) and r i s the relevant e l e c t r o o p t i c c o e f f i c i e n t . Since many el e c t r o o p t i c materials, such as LiNb0 3, have large r e l a t i v e p e r m i t t i v i t i e s w i l l be equal to the e x t e r n a l l y applied f i e l d , E , times a reduction factor £t p, i . e . E = pE . Substituting pE i n equation 2.8 and using the r e l a t i o n A0 = nE /E the expression for E becomes a n n E = 2n/(C - C )n 3 rip . 2.9 i i 12 i l s Using t h i s d e f i n i t i o n the output power i s given by P o u t = ( ^ j / 2 ) * 1 + m c o s [ ( C i 2 - C 1 1 ) n s 3 r L E a p / 2 + ^ J ) 2.10 where P i s the input power, and the constants y and m are r e l a t e d to the i n i n s e r t i o n loss and the depth of modulation r e s p e c t i v e l y [Johnson, Leonberger, and Pratt 1982]. 2.3.1 The Asymmetric Waveguide Immersion Device In t h i s device the waveguide has an asymmetric waveguide structure. A high r e f r a c t i v e index f i l m i s deposited on an e l e c t r o o p t i c substrate and i s covered by a lower r e f r a c t i v e index superstrate. The extent of the o p t i c a l f i e l d s i n the e l e c t r o o p t i c substrate i s c o n t r o l l e d by the choice of the r e f r a c t i v e index of the superstrate. In t h i s section the behavior of such a device i s predicted. Figure 2.5 depicts the cross section of a waveguide with a z-cut LiNb0 3 substrate, a ZnS slab, and e i t h e r an a i r or Ta 20 5 superstrate. For the following example the applied e l e c t r i c f i e l d i s assumed 13 Figure 2.4 An IMZ with a section of length L of each of the branches with a structure different from that of the other branch. 14 15 to be a n t i p a r a l l e l to the p o s i t i v e z 'axis of the substrate thus causing a p o s i t i v e change i n n g . The eigenvalue equations for TE and TM modes of an asymmetric slab waveguide with an anisotropic substrate i n which the main o p t i c a l f i e l d component i s p a r a l l e l to a p r i n c i p a l axis are given i n Appendix 3. For z-cut LiNbOj with the wave's d i r e c t i o n of propagation p a r a l l e l to the y axis of the c r y s t a l they are tan(ht) = h ( p + ^  2.11 h 2 - pq for TE modes and , t N h(p' + q') tan(ht) = — ^ h 2 - p'q' 2.12 for TM modes, where h •= (n 2 k 2 - p 2 ) 1 / 2 , g o *! « = <P!2 - n m 2 k o 2 ) 1 / 2 « p - (p 2 - n 2 k 2)1/2. l o o q' = (n 2 / n 2 ) q , g m and p' - (n 2 / n n )(p 2 - n 2 k 2 ) 1 / 2 g e o i e o where n and n are the f i l m and superstrate r e f r a c t i v e indices and n and n g m e o are the extraordinary and ordinary r e f r a c t i v e indices of LiNbOg r e s p e c t i v e l y . t i s the f i l m thickness and k Q i s the free space propagation constant (k - 2rtA )• o o Figure 2.6 i s a plot of p^ ^ vs. n m for the TE Q and T M Q modes of the waveguide structure i n fi g u r e 2.5 for t • 200nm, X » 632.8nm, n «= 2.342, o ^ and for three d i f f e r e n t values of n^ and n . n i s the r e f r a c t i v e index of e o g 16 Figure 2.6 P A is plotted vs. n m for three different values of n e and n for both T E 0 and T M Q modes. For the T M Q mode n g and n Q are 2.2007 and 2.2881 for curve A, 2.2017 and 2.2884 for curve B, and 2.2027 and 2.2887 for curve C . For the T E Q mode nQ i s 2.2881, 2.2884, and 2.2887. 17 sputtered ZnS given by Tien [Tien 1971]. The values of n g and n Q are 2.2007 and 2.2881 for curve A, 2.2017 and 2.2884 for curve B, and 2.2027 and 2.2887 for curve C. n g and n Q for curve B are the extraordinary and the ordinary r e f r a c t i v e indices of LiNb0 3 with no applied f i e l d , at 20°C, and for \ = 632.8nm [CRC Handbook 1971]. Curves A, B, and C i l l u s t a t e that C, i s a function of An as well as of n for the TM_ mode of the structure. The s m 0 onset of the T E Q mode e x h i b i t i n g the same e f f e c t Is also shown i n figure 2.6 fo r n Q equal to 2.2881, 2.2884, and 2.2887, however, the spreading i n the curves i s not resolvable. On curve B of figu r e 2.6 there are two operating points l a b e l l e d I and I I . They correspond to values of n m of 1.000 ( a i r ) and 2.2136 (Ta 20 5 [Tien 1971]). Figure 2.7 i s a plot of p, vs. n g for the T M Q mode at operating points I (curve D ) and II (curve E ) . C^ and are the slopes of curves D and E re s p e c t i v e l y (where the subscript I has been dropped since only the e f f e c t on the T M Q mode w i l l be considered). [Although the T E Q mode i s supported i n the region with • 2.2136 i t i s not supported In the region with n = 1.000, therefore, the induced change i n phase due the change i n i t s m propagation constant i n that region w i l l have no e f f e c t on the output power of the IMZ.] TM For t h i s example E for the TM n mode, E , i s given by T t U Tt \ ™ m 2 % n C 2 - C l ) n e 3 r 3 3 ^ ' 2 - 1 3 The c a l c u l a t e d value of ( C 2 - CJ i s -7.6* 106rad/m. p w i l l depend on the p e r m i t t i v i t i e s of the LiNb0 3 and of the surrounding medium as well as the geometry of the substrate and the geometry of the high voltage l i n e . We w i l l Figure 2.7 P. i s plotted vs. n e for the TM 0 node at the operating points (curve D) and I I (curve E) shown in figure 2.6. 19 assume a reduction factor of .05 which l i e s between that of a z-cut thin disk (~.035) and a long z-cut c y l i n d e r (~.07) of LiNb0 3 i n a uniform external f i e l d i n a i r . Thus i f L = 10mm and r 3 3 = 30.8*10~12m/V [Yariv 1976] the TM device described i n th i s example would have an E of ~5000V/mm. TC The intended a p p l i c a t i o n of these devices i s the determination of voltages on high voltage l i n e s , for instance, i n gas insulated bus ducts where e l e c t r i c f i e l d s of several thousand v o l t s per millimeter are encountered under normal operating conditions. Gas insulated systems with operating f i e l d stresses of 6.6kV/mm-7.1kV/mm are being designed [Cooke et a l . 1982; Kobayashi et a l . 1984]. In order to be able to measure these large external f i e l d s i t would be necessary to scale the device described above. With proper tuning [Ahmed and Young 1983] and a large value of E^ the sensor could be used i n a l i n e a r region. A sensor with fl>^ = -n/2 and a peak phase change of .lrad corresponding to a peak applied f i e l d of 7.1kV/mm would have an E^ of 220kV/mm. Using the parameters from above a value of L = .23mm for such a device i s obtained. [A discussion of the propagation of o p t i c a l waves i n planar d i e l e c t r i c waveguides i s provided i n Appendix 1. The asymmetric slab waveguide i s discussed i n p a r t i c u l a r and the eigenvalue equations for i t are presented. In Appendix 3 the eigenvalue equations 2.5 and 2.6 are derived and a disc u s s i o n of the choice of the f i l m thickness, t , i s provided]. 2.3.2 The Strip-Loaded Diffused Waveguide Immersion Device This device would have waveguides formed by d i f f u s i n g appropriately patterned impurities into an e l e c t r o o p t i c substrate (e.g. T i into LiNb0 3) with t h i n f i l m s , with large r e f r a c t i v e i n d i c e s , deposited onto the diffused 20 regions. The extent of the o p t i c a l f i e l d s i n the e l e c t r o o p t i c portion of the waveguide would be co n t r o l l e d by the thickness of the f i l m . Figure 2.8 depicts a strip-loaded d i f f u s e d waveguide made with a ZnS f i l m on a y-cut Ti:LiNb0 3 d i f f u s e d region. For the following example the applied e l e c t r i c f i e l d i s assumed to be a n t i p a r a l l e l to the p o s i t i v e z axis of the substrate thus causing a p o s i t i v e change i n n g . The eigenvalue equations for TE and TM modes of a strip-loaded diffused waveguide with an anisotropic substrate are shown to be equivalent to those f o r an i s o t r o p i c substrate i f the substrate i s u n i a x i a l and the main f i e l d component i s p a r a l l e l to the optic axis i n Appendix 3. For an i s o t r o p i c substrate with an exponential d i f f u s i o n p r o f i l e the eigenvalue equations are [Noda et a l . 1978] Jq - l t g < ° » - Vll8< ° > 1 _ „ 2h r S - tan(ht) J q[g(0)] r & - c .nt; i 0 . , ^ k ( 2 n K A n ) ! ^ L l + Stan(ht)J 2 , 1 4 4 o b where g(0) = 2 d k o ( 2 n b A n ) 1 / 2 , q = 2d( P l2 - 1 ^ ) 1 / 2 , h = (n f2k o2 - p 1 2 ) l / 2 i (p 2 - n 2 k 2 ) l / 2 / ( n 2 k 2 _ 2)1/2 F O R TE M O D E S v t l a o f o i S = (n 2/ n 2 ) ( p 2 - n 2 k 2 ) 1 / 2 / ( n , 2k 2 - p . 2 ) 1 / 2 for TM modes and 1 for TE modes T) = ( n b + A n ) 2 / n f 2 f o r TM modes where n^, n f , and n& are the bulk, f i l m , and a i r r e f r a c t i v e i n d i c e s . An i s 21 a l r . Z n S T i : Li NbO 3 y « J — x Figure 2.8 A strip-loaded diffused .a»egulde made with a Z«S film on a , rc»t Ti:LiNb0 3 diffused region. 22 the difference between the surface and the bulk r e f r a c t i v e indices and d i s the d i f f u s i o n depth. Figure 2.9 i s a plo t of vs. t for the TE Q mode for three d i f f e r e n t values of the substrate r e f r a c t i v e index. Curve B i s plotted using the parameters n^ = n g = 2.2017, n f - 2.342, n f l = 1.000, An = .001, d = 2.0Lim, and \ = 632.8nm. Curves A and C i l l u s t a t e that Ap^ i s a function of the o r i change i n n^ as well as of t. For curve A n^ i s set equal to 2.2007 and for curve C to 2.2027. On curve B of figu r e 2.9 there are two operating points l a b e l l e d I and I I . They correspond to f i l m thicknesses of 0 and 200nm r e s p e c t i v e l y . Figure 2.10 i s a plot of p^ vs. n g for the TE^ mode i n the unloaded (curve D) and i n the strip-loaded (curve E) regions. Figure 2.11 i s a plot of p^ vs. n Q for the T M Q mode, which i s also supported i n both branches (see Appendix 3), i n the unloaded (curve F) and In the strip-loaded (curve G) regions. The calculated values of C 2 - ^ for the T E Q mode, ( C 2 - O.^ , a n d f o r t h e ™ 0 mo de, ( C 2 - C j ) ^ , are -4.3*106rad/m and -lxlO^rad/m r e s p e c t i v e l y . From the r e l a t i v e magnitudes of E ^ f o r the T E Q mode T E E - 2TC/(C 0 - O n 3 r , , l 4 0 - -8300V/mm 2.15 ii / l It e J J and for the T M Q mode T M it E_""' - 2n/(C 2 - C x > T Mn 3 r ^ I p « -12.2x 10 6 V/mm, 2.16 using L • 10mm and p • .05, we can treat the power contribution of the TMQ mode as being constant and write for the output power TF i TM P o u t - ( P i n * / 2 > { 1 + m C O S l ( C 2 " C l > T E n e r 3 3 L E a P / 2 + * J + P ' 2 ' 1 ? If such an immersion device were designed to operate i n a li n e a r region 23 2 2 . 2 n Figure 2.9 p 4 i s plotted vs. t for the T E Q mode for three different values of n e . n e is 2.2007 for curve A, 2.2017 for curve B, and 2.2027 for curve C . Figure 2.10 p 4 is plotted vs. n e for the TX 0 .ode for the o p e n i n g points (curve D) and I I (curve E) shown i n figure 2.9. 25 22.724 -\ p . 22.722H ( « 1 0 6 ) 22.720 H 22.718 2.2887 Figure 2.11 p± is plotted vs. n Q for the T M Q mode for loading film thicknesses of 0 (curve F) and 200nm (curve G) which correspond to the film thicknesses of operating points I and II in figure 2.9. 26 (see Section 2.3.1) using the value E = 220kV/mm and using the parameters TC from above, a value of L = .38mm for the device i s obtained. [The exponential r e f r a c t i v e index p r o f i l e i s discussed i n Appendix 1. The strip-loaded exponential r e f r a c t i v e index p r o f i l e waveguide i s discussed In Appendix 3. The choice of substrate o r i e n t a t i o n , the d i f f u s i o n depth and An, and the choice of t are discussed In d e t a i l . ] 27 Chapter 3 Fabri c a t i o n of the Devices 3.1 Introduction In t h i s chapter the design of the photolithographic masks, the process for f a b r i c a t i n g waveguides i n LiNb0 3, and the methods of polishin g the edges of the c r y s t a l s and the ends of the o p t i c a l f i b e r s are outlined, the device t e s t i n g procedure i s described, and the method of attaching the f i b e r s to the c r y s t a l i s given. 3.2 Mask Design The masks incorporated several v a r i a t i o n s of the IMZ modulator. Two masks were necessary to fa b r i c a t e our IMZ modulators: they were the waveguide and the electrode masks. The waveguide mask included the patterns for IMZ modulators with waveguide widths, w, of 4, 6, 8, and lO^im. Devices with Y-branch angles, 6, of 2.005°, .8913°, .5730°, and .4456° and corresponding propagation constant modulation lengths, L, of 15, 10, 5, and 1mm were included for each value of w. Also Included on the waveguide mask were st r a i g h t through waveguides and long (19mm) Y-branches with 8 • 2.000° for each waveguide width. Figure 3.1 shows the design of an IMZ. The electrode mask had d r i v i n g electrodes f o r each of the IMZ modulators. The electrodes were the same length as the en t i r e propagation constant modulation region. Each electrode had a 20um int e r e l e c t r o d e gap. The c e n t r a l electrode was 50um wide and the outer electrodes were 70um wide. Also included were 20um wide s t r i p s that would cover the propagation constant 28 Figure 3.1 The design of the IMZs used in this work 29 modulation regions of one of the branches of the devices with L = 5 and 1mm. Figure 3.2 shows the design of an electrode. The masks were designed using the CMOS Design System of M i c r o t e l P a c i f i c Research of Burnaby, B.C. This program was run on the Hewlett-Packard 9836 microcomputer. It created CIF f i l e s that were stored on floppy-disk. The floppy-disk was taken to M i c r o t e l P a c i f i c Research and translated into a modified CIF format c a l l e d BIF. The BIF f i l e s were copied onto a magnetic tape which was taken to P a c i f i c Micro C i r c u i t s of White Rock, B.C., and were converted into CALMA format. At t h i s stage a l l the f i l e s were v i s u a l l y v e r i f i e d on the CAD stations at P a c i f i c Micro C i r c u i t s . VERSATEC plots were made of each of the masks at t h i s stage. The CALMA tape was then taken to UBC's computer center and two back-up copies were made. F i n a l l y , a copy of the tape was sent to S i e r r a c i n of Santa Clara, C a l i f o r n i a , where the masks were generated. The waveguide mask was E-beam written at f i n a l s i z e , with a .25um beam, and the electrode mask was photo generated. Figure 3.3 i s a picture of the electrode mask. The E-beam generated mask was guaranteed to have l i n e widths within .25|im of the s p e c i f i c a t i o n s and an o v e r a l l dimensional tolerance of 1%. The Y-branches of the IMZ modulators and the long Y-branches were approximated by a s t a i r c a s e structure with a step height of .25um which was 1/4 of the step height of the s t a i r c a s e approximation used s u c c e s s f u l l y here at UBC i n the past (Ahmed 1981; Smith, Dommel, and Young 1983) and was expected to s i g n i f i c a n t l y reduce the i n s e r t i o n losses of the devices. The electrode mask l i n e widths were guaranteed within . 5um and o v e r a l l dimensional tolerances of 2%. T 70/jm 4 ~T 50/im / -— 275 /im —> _ i 90/im Figure 3.2 The design of the electrodes used in this work. 31 Figure 3.3 The electrodes mask. 32 3.3 Fabrication of Ti;LiNbO ? Devices The formation of waveguides i n LiNbC^ by the i n d i f f u s i o n of T i , commonly referred to as Ti:LiNb0 3 waveguides, i s one of the oldest [Schmidt and Kaminow 1974], best understood, and most commonly used methods of making channel waveguides. While experiencing i t s own set of problems this process has been used to create low loss mono-mode waveguides with stable r e f r a c t i v e Index p r o f i l e s . An added feature i s that while both the ordinary and the extraordinary r e f r a c t i v e indices of these waveguides increase with increasing T i concentration [Minakata et a l . 1978] there i s no s i g n i f i c a n t change i n the properties of the waveguides from those of the undoped substrate. Increases i n the extraordinary r e f r a c t i v e index of .04 have been reported [Schmidt and Kaminow 1974] and losses of ldB/cm for the ordinary p o l a r i z a t i o n and 1.5dB/cm for the extraordinary p o l a r i z a t i o n have been reported [Kaminow and Stulz 1978]. Channel waveguides are fabricated by patterning the T i ( p r i o r to d i f f u s i o n ) using photolithographic techniques [Stulz 1979]. Other methods of creating o p t i c a l waveguides i n LiNb0 3 include the voltage-induced waveguide [Channin 1971], the L i 2 0 o u t - d i f f u s i o n technique [Kaminow and Carruthers 1973], ion implantation [Wei, Lee, and Bloom 1974; Destefanis, Townsend, and G a i l l i a r d 1978], l i q u i d phase e p i t a x i a l growth of LiNb0 3 on a LiTa0 3 substrate [Miyazawa, Fushimi, and Rondo 1975], and the proton-exchange techniques [Jackel, Rice, and Vaselka 1982]. The voltage-induced waveguide disappears once the applied voltage i s reduced below a c e r t a i n value. The L i 2 0 o u t - d i f f u s i o n technique can be used to make high q u a l i t y low loss waveguides (<ldB/cm), however, the process i s not 33 suited to making channel waveguides since a method of c o n t r o l l i n g the out-diffused region's width has not been developed. LiNb0 3 films grown by l i q u i d phase epitaxy on LiTa0 3 had high losses i n the 5 to lldB/cm range for low order modes. The implantation of ions i n LiNb0 3 has been reported to decrease the r e f r a c t i v e index i n the bombarded region by ~10% but t h i s decrease i s incurred by damaging the c r y s t a l l a t t i c e and thus destroying the u s e f u l properties of the c r y s t a l . The proton-exchange ( L i i s replaced by H) technique also r e s u l t s i n a large change i n the extraordinary r e f r a c t i v e index (no change i s seen i n n Q) of ~.12, however, the value of n g has been found to o s c i l l a t e with time [Yi-Yan 1983]. A problem that i s encountered during the i n d i f f u s i o n of the T i i s the simultaneous o u t - d i f f u s i o n of L i 2 0 . There are two commonly used methods of counteracting the o u t - d i f f u s i o n of L i 2 0 ; one i s the i n c l u s i o n of LiNb0 3 powder In the furnace with the sample [Burns, Bulmer, and West 1978; Esdiale 1978] and the other i s the bubbling of gas through HgO [Jackel, Ramaswamy, and Lyman 1981; Forouhar, Betts, and Chang 1984]. Our devices were fa b r i c a t e d by T i i n d i f f u s i o n of LiNb0 3. 400A of T i was thermally evaporated onto the surface of the sample and was then patterned using the photolithographic and wet etching techniques described below. The d i f f u s i o n was done at 980°C i n a continuous flow of 0 2 bubbled through an 8-inch column of deionized (D.I.) water while being surrounded by sto i c h i o m e t r i c LiNb0 3 powder. Af t e r the d i f f u s i o n a buffer layer of SiC^ was sputtered onto the sample. This was followed by the evaporation of A l which was also patterned 34 as described below. The sample was then cut using a slow-speed diamond saw. F i n a l l y , the edges of the devices were polished. 3.3.1 The Crystals The c r y s t a l s (from C r y s t a l Technology Inc., Palo A l t o , C a l i f o r n i a ) were y-cut wafers with the y axis X-ray oriented to within 30 arc minutes of being perpendicular to the polished face of the c r y s t a l . The z-axis of the c r y s t a l was X-ray oriented to be perpendicular to the reference f l a t to within 6 arc minutes. One surface was polished to C r y s t a l Technology Inc.'s "Optical P o l i s h " which i s designed to be s u i t a b l e for the f a b r i c a t i o n of integrated o p t i c a l devices. The wafers were then cut into 6 pieces using a diamond saw at M i c r o t e l P a c i f i c Research ( f i g u r e 3.4). 30 samples were obtained from 5 wafers (cost: US$120/wafer). Each sample held > 16 devices. 3.3.2 The Cleaning Process I t i s extremely important to have a d i r t and dust free substrate p r i o r to the deposition of the T i on the sample because each waveguide that i s going to be useful a f t e r the d i f f u s i o n process must run uninterrupted the e n t i r e length of the device (23mm). A si n g l e dust p a r t i c l e can render a device useless. It i s also desirable to remove materials from the sample that could d i f f u s e i n t o the substrate and a l t e r i t s o p t i c a l properties. The samples were cleaned as follows [Ahmed 1981]: 1. Boiled i n acetone for 10 minutes (56°C). 2. U l t r a s o n i c a l l y agitated i n acetone for 10 minutes (new acetone). 3. Rinsed i n D.I. water for 10-15 minutes (2-5 minutes downstream and 8-10 minutes upstream). 35 p i g u r e 3.4 The . . f e r . f t e r b e i n g c u t by M i c r o t e l P . c i f l c R e s e a r c h 36 4. Etched i n 5% H.F. ( h y d r o f l o r i c acid) for 2 minutes. 5. Rinsed again i n deionized water. 6. Boiled i n methanol for 5-10 minutes (65°C). Whenever the samples were heated to b o i l i n g they were heated with the acetone or methanol so as to avoid t h e i r cracking due to thermal shock. After they were removed from the b o i l i n g acetone they were transferred to a second beaker of b o i l i n g acetone and allowed to cool during the u l t r a s o n i c a g i t a t i o n . They were then transported to the D.I. water cascade i n the acetone (now at room temperature). Af t e r the rinse i n D.I. water they were placed i n a beaker of fresh D.I. water and transported to the chemical room fo r t h e i r soak i n H.F. following which they were retransported to the D.I. water cascade i n more fresh D.I. water. After t h i s f i n a l rinse they were placed d i r e c t l y i n a beaker containing methanol and brought to a b o i l . After b o i l i n g i n the methanol they were transferred to another beaker of b o i l i n g methanol i n which they were allowed to cool to room temperature. They were kept and transported In t h i s beaker of methanol u n t i l they reached t h e i r d e s t i n a t i o n , for example, the Vacuum E l e c t r o n i c s Co. VE 400 (Veeco) thermal/E-beam deposition system. Each step i n the process had i t s own dedicated beaker (with the exception of the D.I. water transf e r beaker). A l l glass and p l a s t i c ware was cleaned r e g u l a r l y using a 1:1 mixture of 30% hydrogen peroxide and 98% s u l f u r i c a c i d , f o r 3-5min per beaker, followed by a rinse i n D.I. water. The masks also had to be cleaned o c c a s i o n a l l y . This was done by soaking them In a 1:1 s o l u t i o n of D.I. water and 98% s u l f u r i c acid for about lOmin and then they were rinsed i n D.I. water. A l l glass and p l a s t i c ware (including the 37 masks) was handled with new disposable gloves. If anything was accidentally touched by hand i t was cleaned before reuse. 3.3.3 The Evaporation of Titanium During the cleaning process the Veeco was turned on and allowed to warm up. A tungsten filament wrapped with a 0.045" diameter T i wire was used as a source (generally these filaments could be used for 3-5 depositions). The sources had been obtained from Vacuum Atmospherics several years e a r l i e r at which time the primary contaminants of the T i wire had been quoted as: carbon 0.009ppm, i r o n 0.034ppm, oxygen 0.126ppm, hydrogen 0.004ppm, and nitrogen 0.007ppm. Immediately p r i o r to lowering the b e l l - j a r on the Veeco the samples were brought into the room i n methanol and were loaded into the Veeco. Once the b e l l - j a r was lowered the pump down process began. The pressure i n the evaporation chamber was lowered to between 1 and 2*10~ 6Torr, as measured by a Consolidated Vacuum Corporation GIC-100A i o n i z a t i o n vacuum gauge. Then the evaporation process began. F i r s t the carousel i n the Veeco was started so that the samples were rotated about the filament at approximately 30rpm. The filament current was gradually increased (with a shutter placed between the source and the samples) u n t i l the ammeter on the Veeco read 70 amps. At t h i s point the T i wire was aglow but not quite ready to melt. This current was maintained for a few minutes i n order to drive out impurities absorbed by the T i wire's surface during the time i t was on the s h e l f . The current was then slowly increased to 80 amps while monitoring the i o n i z a t i o n vacuum pressure gauge f o r a sudden increase i n pressure which would i n d i c a t e that T i was now being evaporated. Once the 38 evaporation process had begun the source current was reduced to about 65 amps which maintained the evaporation but at a reduced rate. The shutter between the source and the samples was then opened. The thickness of the f i l m was monitored on the Inficon 321 quartz c r y s t a l f i l m thickness monitor. This was c a l i b r a t e d , f i r s t using a Sloan M-100 angstrometer and l a t e r by using a Tencor Instruments Alpha Step 200, a f t e r each deposition and was found to give a reading co n s i s t e n t l y between 70-72% of the actual f i l m thickness ( i . e . desired thickness = ~1.4* monitor reading). The c a l i b r a t i o n was done a f t e r the patterning of the T i by measuring the step height of the device well del i n e a t i o n marks. Figure 3.5 shows a t y p i c a l output from the Alpha Step 200 a f t e r a T i deposition. Once the desired f i l m thickness was obtained (40QA) the shutter between the source and samples was closed. The source current was reduced to 0 amps and the carousel was turned o f f . The samples were l e f t i n the chamber, under vacuum, f or 30-40min to c o o l . F i l t e r e d a i r was then l e t into the chamber through the vent on the Veeco. The f i l t e r was a M i l l i p o r e FGLP04700 .2um a i r f i l t e r . 20-30min were needed to bring the pressure i n the b e l l - j a r into equilibrium with the pressure i n the room. Two people removed the samples from the b e l l - j a r . One person raised the b e l l - j a r u n t i l i t s base plate was approximately p a r a l l e l with the base of the car o u s e l . The second person then reached i n and l i f t e d the hood, covering the samples, up into the b e l l - j a r . The f i r s t person would immediately remove the samples, s t i l l i n t h e i r holders, from the Veeco and place them i n some s p e c i a l l y prepared sample trays with covers. The samples were then taken to the photoresist spinner and covered with photoresist. 39 K R . 0 6 !:. i! 0.4!:. 0 2i: 0.0 : ^ . c -0.21: 100 "260" i i i " Figure 3.5 An Alpha Step 200 plot of a device well deliniation mark made after the deposition and patterning of the Ti layer. AO The sample trays that were used to transport the samples were cleaned by wiping them down thoroughly with acetone, r i n s i n g them with D.I. water, and blow drying them with nitrogen under a hood with p o s i t i v e a i r pressure. 3.3.4 Patterning the Titanium The samples with the newly evaporated T i were taken to the photoresist spinner immediately a f t e r being removed from the Veeco. The area i n and around the photoresist spinner was prepared beforehand. The photoresist spinner was situated In a p o s i t i v e pressure environment. The en t i r e surrounding area was wiped down with damp cloths to remove dust. Clean p l a s t i c sheets were hung around the photoresist spinner with about a 1-foot square hole cut i n them to allow one to reach into the spinner area and to work through. There was quite a hefty breeze blowing out of the hole making i t extremely u n l i k e l y that any dust would work Its way upstream to the clean area. A l l of the necessary glass and p l a s t i c ware had been placed i n the clean area. A 50ml beaker was f i l l e d with photoresist to the necessary l e v e l for the number of samples to be coated. Each sample was removed from i t s sample tray and placed on the photoresist spinner with the metalized surface upward. It was spun for 20 seconds at 4000rpm to remove any loose p a r t i c l e s . Photoresist was then poured onto the sample from the beaker and spun again for 20 seconds at 4500-5000rpm. This l a v i s h use of photoresist always gave us a uniform coat whereas photoresist a p p l i c a t i o n from an eye dropper or syringe did not. The photolithographic parameters f o r achieving a good photoresist pattern were a l l dependent on the type of photoresist used. The parameters are; spin speed, prebake temperature, prebake time, exposure time, 41 development time, postbake temperature, and postbake time. Table 3.1 l i s t s these parameters for Shipley 1450J and 1350B p o s i t i v e photoresists and Waycoat HR200 negative photoresist. The K a r l Suess mask align e r was set to d e l i v e r llmW/cm2 of 40Cvim r a d i a t i o n to the imaging area. This was determined using a Mirmir Model 100 o p t i c a l power meter. Using t h i s information plus exposure time charts supplied by the manufacturer we were able to approximate the i n i t i a l exposure times. These were then adjusted by experimenting on metalized microscope s l i d e cover pieces. During the patterning of the T i four samples were usually processed at the same time i n the hope that one would make It through the process with an acceptable pattern. Exposure and developing were c r i t i c a l steps i n t h i s process. Each sample was exposed and developed i n d i v i d u a l l y . After exposure the sample was immediately developed. The sample was immersed i n a beaker of developer for the necessary period of time a f t e r which developing was arrested by t r a n s f e r r i n g the sample to a beaker of D.I. water. After l-2min i n the D.I. water the sample was blown dry and inspected for r e s i d u a l films ( f i r s t by eye and then under the microscope). If a sample had acquired a r e s i d u a l f i l m the developer was changed for the remaining samples. When a l l the samples had been developed they were postbaked. Following postbaking they were cooled to room temperature i n the a i r (~10-20min), taken i n t o the chemical room, and etched, one by one. When the sample was immersed i n 5% H.F. nothing appeared to happen f o r 5-10 seconds then suddenly minute bubbles would appear across the en t i r e surface of the sample. These were removed by a quick s t i r r i n g motion and the Waycoat HR200 Shipley 1450J Shipley 1350J Spin Speed 5000rpm 4500rpm 4500rpm Prebake Temp. 65° C 65°C 65°C Prebake Time 15min. 30rain. 15min. Exposure Time 20sec. 1.5min. 1.5min. Developer Time 90sec. (xylenes) 15sec. (alcohol) 25sec. lOsec . Postbake Temp. 135°C 135°C 125°C Postbake Time 15min. 20min. 15min. Table 3.1 Photolithographic parameters. A3 sample was transferred to a beaker of D.I. water to arrest the etching process. The sample was blown dry and Inspected by eye to see i f a l l of the T i was removed from the appropriate areas. If not, the sample was reimmersed i n the HF for one second at a time, and i f so, i t was inspected under the microscope. Once a l l of the samples had been etched the photoresist was removed. The Shipley r e s i s t s were removed i n acetone and the Waycoat r e s i s t i n Indust-Ri-Chem Laboratory Resist S t r i p J-100. F i n a l l y , a l l the samples were Inspected under the microscope and the best one or two were chosen for the d i f f u s i o n process. Figures 3.6a and b show a Y-branch p r i o r to d i f f u s i o n , for an IMZ with w - 4um and 6 <= 2.005°, at 56x and 560x r e s p e c t i v e l y . This process was usually successful i n y i e l d i n g at least one whole wafer of useable devices per run. 3.3.5 The D i f f u s i o n Process The e f f e c t of L i 2 0 o u t - d i f f u s i o n on the extraordinary r e f r a c t i v e index, n g , of LiNbOg was studied by Kaminow and Carruthers [Kaminow and Carruthers 1973]. The change i n the extraordinary r e f r a c t i v e index with changing mole f r a c t i o n of L i 2 0 , i n the LiNb0 3 phase of the ( L i 2 0 ) x - ( N b 2 0 5 ) ^ system (x = .480 to .500), i s given by [Carruthers, Kaminow, and Stulz 1974] dn /dx - -1.6. 3.1 e The problem of surface waveguiding, caused by the increase i n n g due to L i 2 0 o u t - d i f f u s i o n , led researchers to try to f i n d a method of compensating the substrate for L i 2 0 o u t - d i f f u s i o n . Successful methods of suppressing the surface waveguide using the concept of L i 2 0 compensation of the surface layer have been reported. These Include treatment with a L i 2 0 source included In F i g u r e (b ) 5 6 0 * . 45 the furnace upstream from the sample'[Ranganath and Wang 1977b], vapor from LiNb0 3 powder [Chen and Pastor 1977; Burns, Bulmer, and West 1978; Esdaile 1978], and vapor from L1 2C0 3 powder [Miyazawa, Gugllelml, and Carenco 1977]. Other methods of eliminating surface waveguiding are the method of simultan-eous magnesium I n - d i f f u s i o n [Noda, Fukuma, and Saito 1978] and water vapor "soaking" [Jackel, Ramaswamy, and Lyman 1981]. A method of recompensating the LiNb0 3 substrate for l o s t L i 2 0 was reported here at U.B.C. [Ahmed 1981] i n which the sample was placed above lgm of LiNb0 3 powder, following a 4.5hr d i f f u s i o n c y c l e , f o r 1.5hr at 1020°C. However, attempts to reproduce t h i s technique were not always successful [Smith, Dommel, and Young 1983]. Recently the method of water vapor "soaking" has been the most used method of impeding L I 2 0 o u t - d i f f u s i o n reported i n the l i t e r a t u r e . It has been found that i n an uncompensated sample that along with the L i 2 0 concentration decrease there i s a simultaneous decrease i n the hydrogen concentration i n the c r y s t a l . Water vapor "soaking" increases the H concentration i n the c r y s t a l and simultaneously suppresses waveguide formation. Hydrogen i n the c r y s t a l i s believed to reduce the L i mobility i n the c r y s t a l as i t can suppress waveguide formation but i t cannot eliminate (or even a f f e c t ) previously created waveguides. E l e c t r o n microprobe [Mlnakata, Saito, and Shibata 1979], X-ray Photo-ele c t r o n Spectroscopy (XPS), and Secondary Ion Mass Spectrometry (SIMS) [Burns et a l . 1979] have been used to determine the T i d i s t r i b u t i o n i n Ti:LiNb0 3 waveguides. Both studies found that there was extensive l a t e r a l d i f f u s i o n at the surface of samples. Minkata et a l . examined a sample made of Y-cut LiNb0 3 with a lOum wide, 500A thick, T i s t r i p d iffused at 1000°C for 46 lOhr. They found that the l a t e r a l d i f f u s i o n was ~11 times the depth d i f f u s i o n (calculated as the r a t i o of 0% to 0% T i concentration width to the 0% T i concentration depth). Burns et a l . also studied the l a t e r a l T i concentration d i s t r i b u t i o n of various samples using XPS and observed extensive l a t e r a l d i f f u s i o n . Using SIMS they found that there was an increase i n the T i and L i concentrations within a few thousand angstroms of the samples' surfaces (where the i n i t i a l T i pattern had been found) whereas further Into the bulk of the samples the T i concentration d i s t r i b u t i o n was Gaussian. Their measurements of the L i concentration d i s t r i b u t i o n showed that there was a decrease i n the LI o u t - d i f f u s i o n i n the regions with higher T i and L i surface concentrations. They accounted for these e f f e c t s by suggesting the formation of stable L i - T i - 0 compounds (probably L i 2 T i 0 3 and L i j T ^ O j , ) at the surface. They a t t r i b u t e d the large l a t e r a l d i f f u s i o n to anisotropic d i f f u s i o n i n LiNb0 3. However, more recent work [Holmes and Smyth 1984] has studied T i d i f f u s i o n i n t o LiNbOg as a function of stoichiometry. Holmes and Smyth found that there was no difference i n the d i f f u s i v i t i e s with c r y s t a l o r i e n t a t i o n but rather that they were a strong function of L i 2 0 content. Other work has shown the I n i t i a l c r eation of T i Nb, 0_ compounds on the x 1-x 2 surface of the LINb0 3 [Armenise et a l . 1982]. It has been proposed that these compounds act as the source of T i to the c r y s t a l . Holmes and Smyth suggest that i n actual f a c t a Li-Ti-Nb-0 compound i s formed at the surface. Both studies have found that r e s i d u a l source compound remains on the surface f o r 6 t r i p thicknesses of ~400A even f o r d i f f u s i o n times of > lOhr at 950°C. 47 Now a summary of the r e s u l t s that have been discussed thus far i s given and an examination of t h e i r e f f e c t on the d i f f u s i o n process i s made. L i 2 0 o u t - d i f f u s i o n i s a serious problem as i t a f f e c t s the extraordinary r e f r a c t i v e index of LiNb0 3, leading to surface waveguiding of l i g h t polarized p a r a l l e l to the c-axis of the substrate, and i t a f f e c t s the d i f f u s i v i t y of the T i which increases with decreasing mole f r a c t i o n of L i 2 0 ( D ^ = 2.6 * 10 - 1 2cm 2/s, 1.06 x 10 - 1 2cm 2/s, and 0.4 x 10 _ 1 2cm 2/s for x = .481, .486, and .500 r e s p e c t i v e l y [Holmes and Smyth 1984] for a d i f f u s i o n temperature of 1050°C). The other r e s u l t i s the formation of unknown surface compounds. The main concern with these i s the f a c t that t h e i r properties are unknown and t h e i r e f f e c t on the performance of the devices i s uncertain. However, at the present time we must assume that they do not severely a f f e c t the waveguiding properties of the waveguides since numerous reports of working devices made with T i s t r i p thicknesses of > 40QA e x i s t i n the l i t e r a t u r e although the d i f f u s i o n times are generally i n the 4-6hr range and the d i f f u s i o n temperatures vary. In l i g h t of the need for a s i n g l e l a t e r a l mode i n the output waveguide (see Appendix 2) i t seemed necessary to f i n d a method of c o n t r o l l i n g the l a t e r a l d i f f u s i o n of T i i n Ti:LiNb0 3 waveguide f a b r i c a t i o n . Also the surface waveguides, induced by L i 2 0 d e f i c i e n c y , tend to degrade the output of integrated o p t i c a l devices due to leakage of l i g h t from/into the channel waveguide. Following the procedures described below TirLiNbOj waveguides could be repeatedly created. Less success was obtained i n suppressing the creation of surface waveguides. 48 A l l d i f f u s i o n s were c a r r i e d out at 980°C, i n lA/min of flowing 0 2, i n a Thermco Products Corporation Minibrute furnace. The temperature was c a l i b r a t e d using a thermocouple and was found to agree with the setting on the Minibrute's controls rather than with the reading on the b u i l t - i n thermocouple. This temperature was chosen as i t has frequently been used to create Ti:LiNb0 3 waveguides both for studying the properties of the waveguides [Holmes and Smyth 1984] as well as to create integrated o p t i c a l devices [Schmidt, Cross, and Glass 1980; Leonberger 1980]. Presumably i t has been chosen so frequently as a d i f f u s i o n temperature because i t i s well below the Curie temperature (~1120°C [Raeuber 1978]) f or LiNb0 3 with .486 mole f r a c t i o n L i 2 0 . The f i r s t d i f f u s i o n was c a r r i e d out with no compensation technique and n a t u r a l l y yielded the worst r e s u l t s . In t h i s method the sample was placed, patterned face up, on a fused s i l i c a boat i n the center of a fused s i l i c a tube i n the furnace. An attempt was made to duplicate Ahmed's compensation technique. For t h i s we employed a boat, made from platinum f o i l , p a r t i a l l y f i l l e d with l-2gm of stoichiometric LiNb0 3 powder which was evenly d i s t r i b u t e d over i t s bottom. The wafer was placed on the boat with the patterned side face down above the powder. The large area of the wafer provided a p a r t i a l seal for the wafer/platinum boat system. The two were placed on a fused s i l i c a boat i n the center of the fused s i l i c a tube i n the furnace. Ahmed recompensated his wafers with a 1.5hr recompensation d i f f u s i o n following a 4.5hr i n i t i a l d i f f u s i o n . However, due to Smith, Dommel, and Young's lack of success i n du p l i c a t i n g t h i s process as we l l as the recent work i n d i c a t i n g that the 49 d i f f u s i v i t y of T i into LiNb0 3 i s a function of the L i 2 0 content we decided to carry out the e n t i r e d i f f u s i o n i n the presence of the LiNb0 3 powder. We too were unable to suppress the creation of a surface waveguide. In addition to the problem of surface waveguiding we found that grains of LiNb0 3 had sint e r e d to the wafer. We are not sure how they managed to get onto the wafer but we believe that they were thrown up while the boat was being moved to the center of the furnace. The "soaking" technique of Jackel et a l . ( i . e . bubbling gas through a column of water) was more su c c e s s f u l . However, the surface waveguiding s t i l l p e r s i s t e d . In t h i s technique a f l a s k of D.I. water was placed i n the gas flow path immediately before the gas entered the furnace. Jackel et a l . used argon during the d i f f u s i o n cycle followed by . We used 0 2 throughout. The f l a s k was f i l l e d with new D.I. water for each d i f f u s i o n to a depth of ~8 inches. A proximity anneal was also attempted. In t h i s technique the sample was placed face down on a precharged z-cut LiNb0 3 wafer. The z-cut wafer had been precharged by a 2hr anneal i n stoichiometric LiNb0 3 powder at 1000°C i n Ut/min of flowing 0 2. This method of precharging has been shown to cause a decrease i n the surface extraordinary r e f r a c t i v e index of z and y-cut wafers (measured a f t e r 5-6.5hr d i f f u s i o n s at temperatures of 950-1000°C) [Burns, Bulmer, and West 1978]. The r e s u l t s of t h i s method were not s a t i s f a c t o r y . The method f i n a l l y used consisted of a combination of the water "soaking" method and a modified version of Ahmed's compensation technique. The sample was placed patterned face up on a A1 20 3 wafer measuring 2 * 2 " . A mound of stoichiometric LiNbCs powder was placed around the entire rim of 50 the alumina wafer (fig u r e 3.7). A second alumina wafer was placed on top of the mound to provide a s e a l . This setup was then placed on a boat i n the center of the furnace and the d i f f u s i o n was performed. Throughout the d i f f u s i o n the 0 2 was bubbled through an 8-inch column of water. Figure 3.8 i s a picture of the E p o l a r i z a t i o n of the output of an IMZ that was created i n t h i s manner. As can be seen the surface waveguiding on either side of the output spot i s not very severe. 3.3.6 Depositing the Buffer Layer Since the presence of metal electrodes, when i n contact with the guiding region, can s c a t t e r the guided wave and s i g n i f i c a n t l y perturb the f i e l d d i s t r i b u t i o n i t i s necessary to Include a buffer layer between the electrodes and the Ti:LiNb0 3 region. In order for the f i e l d to be well confined the buffer layer should have a low r e f r a c t i v e index ( r e l a t i v e to the LiNb0 3). This w i l l allow the buffer layer to be t h i n and the electrodes w i l l remain i n close proximity to the c r y s t a l surface. S i 0 2 was used as the buffer layer d i e l e c t r i c . It has a r e f r a c t i v e index of about 1.46. It was sputtered onto the sample using a Perkin-Elmer Sputtering System Model 3140 vacuum system with a S i 0 2 target of 99.95% p u r i t y . The sputtering was done i n an argon + oxygen atmosphere. The oxygen was included i n order to reoxidize any Si or SiO that was created during sputtering as both are highly absorbent i n the o p t i c a l range. The argon pressure was adjusted to 32-33mTorr and then oxygen was added u n t i l the combined pressure was 37-38mTorr. The sputtering was done at a forward power of 100W (±10W) and a r e f l e c t e d power as low as was obtainable ~5W. 51 Figure 3 . 7 A sample placed on an alumina wafer surrounded by stoichiometric LiNbO, powder. Figure 3 . 8 The E* p o l a r i z a t i o n of the output of an IMZ. 52 C a l i b r a t i o n of the deposition rate was done using glass microscope s l i d e s arranged so that one p a r t i a l l y covered the other. The r e s u l t i n g step height was measured on the Alpha Step 200. Figure 3.9 shows a t y p i c a l step height for a S i 0 2 deposition. The deposition rate was found to be about 75nm/hr. To deposit a 300nm layer took. 4.5hr since each deposition was preceded by a .5hr etch of the target, to remove contaminants, with a shutter placed between the target and the sample. 3.3.7 Depositing the Electrode Metal and Patterning the Electrodes P r i o r to depositing the electrode metal the wafer was cleaned ( b o i l i n g acetone, u l t r a s o n i c a g i t a t i o n i n acetone, rinse i n D.I. water, and b o i l i n g methanol). It was transported to the C a r l Herrmann Associates high vacuum deposition system (CHA) In methanol and loaded. The CHA was used i n preference to the Veeco because i t can hold three filaments loaded with the electrode metal whereas the Veeco can hold only one. The system was pumped down to l x l O ^ T o r r before the metal was deposited. The electrode metal (Al) was evaporated onto the wafer at a source current of ~65 amps. Enough A l wire was hung on a tungsten filament to allow Turn of A l to be deposited on the wafer. A f t e r the A l was deposited i t was allowed to cool for 30min and then the b e l l - j a r was f i l l e d with f i l t e r e d a i r and the sample was removed from the CHA and coated with photoresist with the same care as when the T i was deposited. The photoresist was prebaked, exposed, and developed as per table 3.1. Once the photoresist pattern had been made the sample was blown dry and inspected under the Zeiss microscope. If the pattern was not s a t i s f a c t o r y the 53 Kfl 6 4 I t r. . : U y i •; 0 - r ' f . ; ; :l .1: : : : i ; : .. .. . : . a o ~ B O O ™ — .ooo "-"I'sbo •*•"•;£,• Figure 3.9 An Alpha Step 200 plot of the height of the S i 0 2 buffer layer. 5A photoresist was stripped o f f and a new coat was applied. It was sometimes necessary to s t r i p the Al and apply a new f i l m i f the sample had become too s o i l e d during repeated photoresist applications ( r e a p p l i c a t i o n of photoresist on the waveguide T i was never s u c c e s s f u l ) . Once a s a t i s f a c t o r y photoresist pattern had been obtained the sample was postbaked. After the sample had cooled to room temperature the A l was etched i n a 1:1 s o l u t i o n of 85% phosphoric acid and D.I. water at ~50°C. The sample was heated i n the mixture. The etch rate was pretty slow (5-10min) so the sample was removed from the etchant and transferred to a beaker of warm D.I. water (~50°C) at regular i n t e r v a l s (to stop the r e a c t i o n ) . It was then inspected to see i f the A l was completely removed. If not, i t was reimmersed i n the acid s o l u t i o n and etching was allowed to continue. Once the A l etch was deemed successful the sample was cooled and inspected under the microscope. If at t h i s point the pattern seemed to be acceptable the photoresist was stripped and the actual aluminum pattern was inspected. If the actual aluminum pattern was unacceptable the remaining A l was etched away and a new layer was applied. Figure 3.10 shows a t y p i c a l scan of the A l layer of a device well d e l i n e a t i o n mark taken on the Alpha Step 200. Figure 3.11 shows the electrode pattern of a 1mm device at 56* and f i g u r e 3.12 6hows the connection between the two outer electrodes of an IMZ modulator at 140*. Figure 3.13 shows a cross s e c t i o n a l view of a diffused waveguide, the buffer l a y e r , and the metal electrodes on e i t h e r side of the waveguide. F i n a l l y , f i g u r e 3.14 shows a l l the process steps to this point. 3.4 P o l i s h i n g the Crystals In order to butt couple l i g h t into or out of a waveguide e f f i c i e n t l y i t 55 KR L.:-1 ' J. • > • ^ i •i :| l i i: 1 i :i : l ] I 4r, i 1 '1 Ii c i : 2 I 1 "1 1 1 !: 'Ii i Figure 3.10 An Alpha Step 200 plot made after the deposition and patterning of the electrode metal. 56 Figure 3.12 The connection between the outer electrodes of an IMZ modulato at 140* . 57 Figure 3.13 A cross sectional view of a diffused waveguide, the buffer layer and the metal electrodes on either side of the waveguide. (a) Cutting the wafers (e) The d i f f u s i o n process I I T i J Substrate ( c ) The T i deposition Mask \ \ \ \ \ \ \ \ \ v \ v\ \ \ \ \ \ Photo-r e s i s t ".Ti T777\ / / / f ? / / <• J / / (g) A l deposition Mask Photo-ns \ \\\ v \ \ v \ \ \ v \ \ l r e s i s t / / / / / / / / / / / / / / / ' A l L (d) Patterning the T i ( h ) Patterning the A l Figure 3.14 The fabrication process steps for manufacturing IMZ modulators. 59 i s necessary to have a f l a t and defect free edge at the waveguide's input or output. The c r y s t a l edge needs to be as square as possible since butt coupling i s s e n s i t i v e to angular v a r i a t i o n s but can t o l e r a t e small deviations [Hunsperger, Yariv, and Lee 1977]. P r i o r to p o l i s h i n g the excess LiNb0 3 was removed from the sample and edge cover pieces were prepared and attached to the c r y s t a l . 3.4.1 Preparing the Samples f o r P o l i s h i n g Once the f a b r i c a t i o n of the devices had been completed the samples were prepared for p o l i s h i n g . This was done by c u t t i n g excess LiNb0 3 o f f of the wafer on a Buehler Isomet 11-1180 low-speed diamond saw at UBC's Department of Geology. To prepare the c r y s t a l for c u t t i n g i t was mounted on a 2><2" glass microscope s l i d e . This was done by covering the microscope s l i d e with Fisher S c i e n t i f i c Company Pyseal Wax shavings, heating the s l i d e i n a Thermolyne Hot Plate Oven OV-10600 to ~80°C, and allowing the wax to melt and form a uniform layer on the s l i d e . The wax coated s l i d e was then cooled to room temperature at which time the sample was placed, d i f f u s e d side up, on the wax coated surface. The sample's reference edge was aligned with an edge of the s l i d e . Both the s l i d e and sample were reheated u n t i l the wax melted and was seen to uniformly coat the bottom surface of the sample. The s l i d e and sample were then allowed to cool to room temperature. While cooling, the sample was coated with a generous layer of beeswax to protect i t from being scratched by small p a r t i c l e s In the diamond saw's cooling f l u i d during the cutti n g process. 60 Three pieces were cut from each sample for use in the remaining process steps. F i r s t , there was the diffused area of the crystal. This was entirely circumscribed by the cut. Second, two pieces the same width as the diffused region were cut from the crystal. These would be used as cover pieces during the polishing process. They were about 2mm long and were cut immediately adjacent to the crystal edge to be polished (figure 3.15). The sample's edges would thus have the same orientation as the cover pieces and would be ground and polished at the same rate. Once the sample and cover pieces had been removed from the rest of the crystal they were separated from the glass pieces upon which they were mounted. This was done by heating them in a bottom of trichloroethylene to boiling (87°C) under a fume hood. After the trichlorethylene started to b o i l the heat was removed and the bottom was agitated by hand to create a slow circular swirling motion. This was usually enough to remove a l l the beeswax and to completely undercut the Pyseal wax from the crystal. If necessary, a bit more trichloroethylene was added and the process was repeated. Once a piece of LiNb03 had been removed from it s glass mount i t was put in a clean bottom with new trichloroethylene and the process was repeated (this was done to remove the f i n a l visible traces of wax). Finally, the pieces were rinsed in a beaker of D.I. water. 3.4.2 Grinding and Polishing the LiNbOq The sample was prepared for polishing by fixing LiNbOg cover pieces over the edge to be polished using DEVCON 5 Minute Epoxy. The epoxy layer between the sample edge and the cover piece should be thin to minimize the rel i e f at the crystal edge. Relief i s the term used to describe the rounding of a hard 61 Figure 3.15 How the sample was cut i n preparation for p o l i s h i n g . The broken l i n e s i n d i c a t e the cut l i n e s . 62 material's (the c r y s t a l ' s ) edge caused by the d i f f e r e n t p o l i s h i n g rates of a hard (LiNb0 3) and a soft (epoxy) material at an i n t e r f a c e . The sample was then placed on a glass microscope s l i d e and a second s l i d e was placed on top of the cover pieces. Even pressure was then applied to the upper microscope s l i d e by placing one finger above each of the cover pieces (excessive pressure was avoided as the sample could crack, i f the bottom s l i d e was d i r t y or uneven). Using t h i s method we were con s i s t e n t l y able to achieve epoxy thicknesses of < lOum. It i s important to achieve the thinnest epoxy layer possible for two reasons; f i r s t , p a r t i c l e s may become embedded i n It and thus be transferred to the pol i s h i n g mats with smaller s i z e p a r t i c l e s and second, i t i s nearly impossible to get the edge of the c r y s t a l to a roughness of < 5um during the grinding process i f the epoxy layer i s wider than the grinding paper's p a r t i c l e s . A f t e r both cover pieces had been mounted the epoxy was allowed to set for 10-20min. Pyseal wax shavings were then put onto the sample's d i f f u s e d surface i n a large mound. The c r y s t a l was then slowly heated on a hot plate u n t i l the wax formed an even coat over the surface. Figure 3.16 shows a sample prepared for p o l i s h i n g . P r i o r to grinding and pol i s h i n g the sample i t was mounted i n a po l i s h i n g j i g . The j i g i s shown In figu r e 3.17. Its p o l i s h i n g surfaces are 24*26mm and i t i s 22.5mm long. It i s made of two parts that can be aligned on a f l a t surface using two s t e e l plates on either s i d e that are held to the base by two screws per side and a dowel through the plates and the l i d . When a l i g n i n g the faces the dowel i s inserted through the s t e e l plates and the l i d , the screws to the base are l e f t loose, and the assembly i s placed on a clean, f l a t surface. The assembly i s then pressed Figure 3.17 The j i g used to polish the edges of our 64 down onto the surface and the screws.are tightened. The l i d can then be removed with the knowledge that reinsertion of the dowel w i l l result in realignment of the polishing surfaces. The crystal f i t s in the I*25mm slot between the l i d and the base. The inner surfaces of the l i d and base have been milled to create a .25* .25*24mm l i p along the slot at either polishing surface. A thin line of DEVCON 5 Minute Epoxy was spread along the lips of the base and the bottom of the crystal was placed on the epoxy. The l i d of the j i g was then put on and the crystal's alignment marks were used to orient the crystal. It was important to assure that the alignment marks protruded slightly from either side of the j i g . Once the crystal had been properly aligned the epoxy was allowed to set for 20-30min. Grinding down the crystal's edge to the smoothness necessary to begin polishing was done in 2 stages. At the beginning grinding was done using a 600 grit s i l i c o n carbide paper (particle size ~17um). The grinding paper was 3M Wetordry Tri-M-ite Paper A wt. 600. A new piece of grinding paper (~4" square) was mounted on a f l a t , clean, plexiglass plate (~1' square) using masking tape. It was then made wet using a couple of drops of D.I. water. The edges of the sample were ground by hand down to the beginning of the waveguiding regions. After that each edge was ground, again by hand, on fresh pieces of 600 grit s i l i c o n carbide paper. A few drops of Buehler AB Metadi f l u i d were added to the paper and i t was then broken in with a piece of LiNb0 3. This part of the grinding process was done using slow linear motions such that the direction of motion was perpendicular to the crystal/epoxy interface; this avoided particles gouging the epoxy from between the sample and the cover piece and thus eliminated most of the edge 65 damage. The crystal was ground at this stage until i t was almost but not quite flush with the jig's f l a t polishing surface. If the crystal was ground down too far further polishing with the 9+xm diamond paste would become nearly impossible as the entire stainless steel face of the j i g would have to be ground down with the crystal. The polishing was done using diamond paste and alumina slurries on a mechanical polishing wheel. The paste was Buehler Metadi II %m diamond polishing compound. The slurries had particle sizes of lum, .1+tm, and .05um. They were made by Baikalox. The paste was applied to a Buehler Texmet mat in dabs ~ l / 4 inch long spaced about 2 inches apart. It was worked into the mat with a clean forefinger made wet with Buehler AB Metadi f l u i d . The 1 and • Lam slurries were premixed and applied to Buehler Microcloth mats from their bottles. The .05Lim slurry was mixed on the mat. F i r s t , a small mound of powder (~l/4 teaspoon) was placed on a mat, then a few drops of D.I. water were applied and the two were mixed and worked into the mat. The 9um diamond polish was done on a polishing wheel rotating at a moderate speed of ~180rpm. Each edge was polished for lOmin after which i t was inspected using a metallurgical microscope at 300x magnification. If the edge roughness was more than a few microns (the thickness of the epoxy layer was used as a standard) then polishing was continued for another 5min. The cycle of inspection and polishing was continued un t i l the sample's edge was sufficiently smooth. Usually a total of 15min of polishing at the 9um diamond paste level was enough. However, i f serious damage was done at the crystal/epoxy interface during the grinding process i t had to be removed by 66 p o l i s h i n g . In a p a r t i c u l a r l y bad case this could require p o l i s h i n g times of up to 40min on one edge. The lum s l u r r y was used for ~5min/edge on a high speed polish i n g wheel the speed of which was c o n t r o l l e d by applying pressure on the j i g and subsequently on the the p o l i s h i n g wheel. The .lp.m and the .05um s l u r r i e s were each used for ~2min/edge on the low speed wheel that had been used for the 9am p o l i s h . The sample's edge was inspected between polishi n g with successively smaller s l u r r i e s to determine whether more po l i s h i n g , at that l e v e l , was necessary. Between any two stages i n the grinding/polishing process the c r y s t a l edge and the j i g ' s p o l i s h i n g surface were wiped clean with a D.I. water soaked Kimwipe or a cotton swab. It was important to ensure that large p a r t i c l e s were not transmitted from one grinding/polishing stage to another. Not only could t h i s r e s u l t i n scratches i n the c r y s t a l edge but a well broken-In p o l i s h i n g mat would become useless. Figures 3.18a and b show the c r y s t a l edge at the end of the grinding process at 140* and 560* magnification. Figures 3.19a and b show the c r y s t a l a f t e r p o l i s h i n g with the 9um diamond compound p o l i s h , figures 3.20a and b a f t e r the lum alumina s l u r r y p o l i s h , figures 3.21a and b a f t e r the .lum alumina s l u r r y p o l i s h , and figures 3.22a and b a f t e r the .05um alumina s l u r r y p o l i s h . Figures 3.18-3.22a were taken at 140* and figures 3.18-3.22b at 560* magnification. Figure 3.23 i s included as a scale by which the distances on the 560* magnification pictures may be measured; the distance between two neighboring arrows i s lOum. Figure 3.18 The crystal's edge after grinding at (a) 140 and (b) at 560x. Figure 3.19 The c r y s t a l ' s edge a f t e r p o l i s h i n g with a *m paste at (a) and (b) 560x. 140 F i g u r e 3 . 2 0 The c r y s t a l ' s edge a f t e r p o l i s h i n g w i t h a lnm s l u r r y a t (a ) 140 and (b) 560x . (a) Figure 3.22 The crystal's edge after polishing with a .05um slurry 140 and (b) 560x. 72 Figure 3.23 10um A scale f o r measuring distances on the pictures taken at 560x Location. The l i s t a n c e between two neighboring arrows is 73 Once both the edges had been polished the sample had to be removed from the j i g . F i r s t the Pyseal wax was removed from the sample by heating the sample and j i g base i n a beaker of trichloroethylene u n t i l the t r i c h l o r o e t h y l e n e was about to b o i l ( b o i l i n g point 87°C). The beaker was removed from the heat and swirled i n a gentle c i r c u l a r motion u n t i l there was no more wax v i s i b l e on the sample. The sample was then transferred to a bottom of clean trichloroethylene and reheated and swirled. The sample was removed from the j i g base and the cover pieces were removed from the sample during a b o i l i n methanol ( ~ l h r ) . Figure 3.24 i s a photograph of a f i n i s h e d sample. 3.5 Testing the Devices Once the sample edges were polished the devices on the substrate could be tested. Figure 3.25 shows the setup used. The l i g h t was coupled into the d i f f u s e d waveguide using the technique of "end-fire" coupling. The l i g h t from the l a s e r was focussed on the c r y s t a l edge i n the region of the diffused waveguide using a microscope o b j e c t i v e . The output of the waveguide was then focussed on a screen with a 1mm2 hole d r i l l e d i n i t behind which there was a detector, again using a microscope o b j e c t i v e . The l a s e r was mounted on a s t e e l L-beam that could also accommodate two sets of 3-axis micropositioners. The l a s e r was aligned with the o p t i c a l bench by p l a c i n g a s l i d i n g target on the bench and moving i t between two p o s i t i o n s , one meter apart, on a f i x e d track while adjusting the laser so that i t s beam would intercept a 5mm diameter spot on the target at both l o c a t i o n s . This allowed the l a s e r to be aligned within 18 minutes of arc of being p a r a l l e l to the track's c e n t r a l a x i s . A 3-axis micropositioner 74 on the left of the picture. 75 designed to hold the Input microscope objective was mounted on the L-beam. A target was placed ~10cm beyond the eventual l o c a t i o n to be occupied by the microscope o b j e c t i v e . The spot where the target intercepted the laser beam was marked. A 160 microscope objective was then mounted on the micropositioner and i t s p o s i t i o n was adjusted to center the c i r c u l a r output pattern of the beam on the spot. The output microscope objective ( 4 0 ) was mounted on a micropositioner with 3 axes of t r a n s l a t i o n a l freedom and 2 planes of r o t a t i o n a l freedom. The two objectives were brought to within ~1mm of each other and the output objective's p o s i t i o n was adjusted to obtain a collimated beam that was also aligned with the c e n t r a l axis of the f i x e d track. The output objective was then moved down the track to allow room for the c r y s t a l to be placed between the two objectives. The c r y s t a l was mounted on a platform, with suction from a vacuum pump, attached to a micropositioner with 3 axes of t r a n s l a t i o n a l freedom and 3 planes of r o t a t i o n a l freedom. The platform was l e v e l l e d using a plumb l e v e l l e r . The sample was then placed between the microscope objectives and using the device well d e l i n e a t i o n marks was aligned with the microscope o b j e c t i v e s . This was done by grabbing the sides of the c r y s t a l with p l a s t i c tweezers and r o t a t i n g i t on the platform. The sample was then moved toward the input objective u n t i l i t s edge was w i t h i n .5mm. Next i t was moved up and/or down u n t i l the LiNbOj substrate was aglow with l i g h t . Then the output objective was moved toward the c r y s t a l u n t i l a c l e a r image of the c r y s t a l edge was obtained on the detector/screen. By moving the c r y s t a l downward the l i n e s of constructive interference i n the 76 edge image could be made Increasingly, d i s t i n c t . When there was no doubt that interference fringes were being observed the sample was moved h o r i z o n t a l l y between the objectives u n t i l a "bushy" interference pattern appeared i n the image (figure 3.26a). The c r y s t a l was moved h o r i z o n t a l l y u n t i l the "bushy" pattern was v e r t i c a l (figure 3.26b). By slowly moving the sample downward and by r o t a t i n g i t s l i g h t l y i n the v e r t i c a l plane ( p a r a l l e l to the track's c e n t r a l axis) and i n the h o r i z o n t a l plane the "bushy" pattern and the interference fringes would expand and dim u n t i l the l i g h t was mainly confined to the surface waveguide and the output spot of the Ti:LiNb0 3 waveguide (f i g u r e 3.26c). Figures 3.26a-c were made using a 20* output microscope o b j e c t i v e . The detector/screen was then placed so that the hole i n the screen and the image of the bright spot would coincide. The sample's p o s i t i o n was then adjusted u n t i l a maximum output i n t e n s i t y was indicated on the detector. While adjusting the c r y s t a l ' s p o s i t i o n the spot could be refocussed and realigned with the hole i n the screen by "steering" the beam with the output o b j e c t i v e . Once a s u f f i c i e n t l y bright spot was obtained probes were cautiously lowered onto the bonding pads of the device's electrodes. The probes were s l i g h t l y angled from the v e r t i c a l axis and the d i r e c t i o n of observation was also o f f the v e r t i c a l so that the bonding pad and the probe t i p could be seen as they came in t o contact. As the image of the probe t i p , caused by the r e f l e c t i o n from the bonding pad, merged with the actual probe t i p (as seen through a Bausch and Lomb 0.7x-3.9x binocular microscope at 30* magnifica-t i o n ) , the rate at which the probe was lowered was decreased u n t i l a sudden change i n the l i g h t d i s t r i b u t i o n i n the c r y s t a l was observed. After both (a) Fieure 3.26 End-fire coupling l i g h t into the Ti:LiNb0 3 waveguides, (a) the "bushy" pattern i s seen leaning to the r i g h t of the p i c t u r e , (b) The "bushy" pattern i s erect i n the center of the p i c t u r e . Figure 3.26 (cont.) End-fire coupling l i g h t into the TitLiNbC^ waveguides. (c) The l i g h t i s confined to the Ti:LiNb0 3 and the surface waveguides. 79 probes were i n p o s i t i o n i t was u s u a l l y necessary to refocus the input beam on the d i f f u s e d waveguide's input. This could be done by either of two methods; one was to c a r e f u l l y readjust the c r y s t a l ' s p o s i t i o n ; the other was done by "steering" the input beam onto the waveguide input by s l i g h t l y readjusting the input objective's p o s i t i o n . The advantage of the f i r s t method was that the input coupling was more e f f i c i e n t than with the second method and the alignment of the o p t i c a l components was unaltered. The advantage of the second method was that the aluminum electrodes were less l i k e l y to suffer any damage due to the probe t i p s c u t t i n g grooves i n them. A modulating voltage was applied to the probes. Both the modulating voltage and the output s i g n a l were displayed on an oscilloscope (fi g u r e 3.27). 3.6 Separating the Dies Containing the Devices from the Sample Once the usable devices were i d e n t i f i e d i n the t e s t i n g procedure they had to be removed from the sample. To do t h i s the sample was epoxied to a 1>«3" glass microscope s l i d e using DEVCON 5 Minute Epoxy. The epoxy was a p p l i e d to the microscope s l i d e i n an extremely th i n f i l m so that It would not r o l l up onto the polished edges of the c r y s t a l when the sample was placed on i t . A f t e r the sample had been placed on the s l i d e (with i t s device well d e l i n e a t i o n marks p a r a l l e l to the short edge), and the epoxy had set, both were heated on a hot plate u n t i l the sample and i t s edges could be coated with beeswax. The devices were then removed from the sample using the slow speed diamond saw at UBC's Department of Geology. 80 Figure 3.27 The modulating voltage and the output s i g n a l of an IMZ modulator. 81 The beeswax was removed i n trichloroethylene i n the same manner as the Pyseal wax was removed i n Section 3.4.2. The pieces of glass s t i l l attached to the dies were removed by heating each die i n a bottom of methanol u n t i l i t boile d (65°C). F i n a l l y we were l e f t with a die measuring ~.5*1*23mm (figure 3.28). One of the dies had been chosen as the candidate for our high voltage sensor during the t e s t i n g procedure and was now mounted i n a plexiglass microprobe s t a t i o n . The microprobe s t a t i o n consisted of a 5*25*25mm p l e x i g l a s s base with a .5*1* 25mm track routed i n i t b i s e c t i n g one of the square faces. At both ends of the track were 3*3*2mm deep grooves (into which the f i b e r s and c a p i l l a r i e s could be i n s e r t e d ) . The microprobes consisted of #0/80 screws with pointed ends that were mounted i n movable arms. The device to be used was mounted i n the track using DEVCON 5 Minute Epoxy to f i x i t i n place. The microprobes were then positioned over the bonding pads of the device and advanced through t h e i r arms u n t i l contact was made (as viewed through a microscope at 30*). 3.7 Preparing O p t i c a l Fibers for Butt Coupling The "end-fire" method of coupling l i g h t into a waveguide i s very useful i n a laboratory, but not for p r a c t i c a l applications i n the f i e l d since the alignment of the lenses and the sample would be too susceptible to mechanical v i b r a t i o n s . A v a r i a t i o n of the "e n d - f i r e " coupling was attempted here at by Smith, Dommel, and Young. In t h i s method multi-mode f i b e r s were stripped of th e i r p rotective coatings, cleaved, and had t h e i r ends melted to form microlenses. One f i b e r with a microlens was aligned with the device's input 82 Figure 3.28 Final die containing a useful device. 83 waveguide and another with the device '6 output waveguide. They were fixed in place with Norland NOA-61 optical adhesive. The fiber to diffused waveguide coupling loss for that work was measured in the 15-20dB range. The method of butt coupling (also referred to as end-butt and end f i r e coupling in the literature) was f i r s t proposed and demonstrated as an alternative to monolithic integration of integrated optical circuits [Hunsperger, Yariv, and Lee 1977]. In that work coupling efficiencies ranging from 24.9 to 80.6%, between GaAs laser diodes and multi-mode Ta 20 5 on glass waveguides, were reported. Estimates of the coupling efficiencies between optical fibers and diffused waveguides indicated that 50 to 80% of the optical power in the fiber could be coupled into the waveguide [Burns and Hocker 1977]. The f i r s t measurements made using butt coupling reported a total Insertion loss of lOdB for a mono-mode Ti:LiNb0 3 waveguide placed between two single-mode optical fibers [Keil and Auracher 1979]. However, more recent work has achieved coupling losses of 3dB per interface [Korotky et a l . 1985]. Following the more promising approach of butt coupling we had to devise a method of preparing the fibers for butting to the polished end faces of the devices. The output ends of the fibers were polished to a .05um finish using a series of grinding and polishing steps. In order to be able to hold the fiber during polishing i t was mounted in a glass melting point capillary (Kimble Products Kioax-51) with a 0.8mm inner diameter and a 100mm length. We also used the capillary to hold the fiber while aligning and bonding the fiber and the diffused waveguide. 84 The f i b e r was f i x e d i n the c a p i l l a r y using Norland NOA-61 o p t i c a l adhesive ( u l t r a v i o l e t s e t t i n g ) . F i r s t a couple of drops of the adhesive were placed i n the bottom of a 50ml beaker. Then using the c a p i l l a r y as a pipette the adhesive was sucked into the c a p i l l a r y f i l l i n g the f i r s t 5mm. The f i b e r was then fed into the end of the c a p i l l a r y that had served as the pipette's mouthpiece u n t i l about 3 inches of i t were protruding from the adhesive f i l l e d end. The f i b e r and the c a p i l l a r y were l a i d on a table and the f i b e r was made taut by p u l l i n g on both ends thus a l i g n i n g the f i b e r with the c a p i l l a r y . The ends were taped to the table so that the f i b e r would remain taut. The adhesive was then set by pl a c i n g a 6 watt U l t r a - V i o l e t Products Inc. Mineralight UVS-54 u l t r a - v i o l e t lamp (254nm radiation) over the c a p i l l a r y and exposing the adhesive for > l h r . Another more convenient method of f i x i n g the f i b e r s i n the c a p i l l a r y was to set the adhesive using a Norland Opticure Light Gun. This took ~1 minute. Aft e r the f i b e r was f i x e d i n the c a p i l l a r y the protruding end of the f i b e r was removed with the aid of a sharp k n i f e . The f i b e r and the c a p i l l a r y were then Inserted into the p o l i s h i n g j i g . The f i r s t couple of millimeters of the f i b e r , adhesive, and c a p i l l a r y were ground down using 600 g r i t s i l i c o n carbide paper (3M Wetordry Tri-M-ite paper). To begin with the c a p i l l a r y / f i b e r was ground on a piece of dry paper to the desired l e v e l . This was followed by grinding on a new piece of paper that had been made wet with a few drops of D.I. water. Figure 3.29 shows the p o l i s h i n g j i g . Af t e r the 600 g r i t paper 9um diamond paste was used for ~15min and then a lum paste. P o l i s h i n g with lum paste lasted ~10min. The lum paste was followed with a lum alumina s l u r r y (~5min) followed by a O.lum s l u r r y 85 86 (~5min). The f i n a l polish was done with a .05um alumina slurry for about 2min. A l l grinding was done by hand and a l l polishing was done using a slow polishing wheel (~180rpm). The j i g was hand held and pressure was applied by pushing down on the upper part of the j i g (taking care not to break the capillary). After each stage In the process the j i g and the capillary/fiber were rinsed in D.I. water (to avoid the transfer of large particles to smaller particle mats). The capillary/fiber was also inspected under a Zeiss reflection microscope. Figures 3.30a-d show the end of the fiber after grinding, the 9um paste, the ljim alumina, and the .05 urn alumina respectively at 560*. Figure 3.31 shows the finished capillary/fiber at 56*. In order to be able to couple light from a fiber into a device i t is f i r s t necessary to be able to couple light into a fiber. Both the output and the input fibers were aligned with the device by coupling light from the fiber into the device. In order to remove cladding modes at the input end of the fiber we stripped i t of i t s protective coats and imbedded i t in ~3cm of optical adhesive in a melting point capillary. Since the refractive index of the adhesive (1.56 as per the manufacturer) is higher than that of the fiber (~1.46) light coupled into the cladding w i l l be radiated into the adhesive. The input end of the fiber was then polished using a j i g designed for this purpose following the same grinding and polishing steps used previously for the other end. We used ITT T-1601 monomode fiber supplied to us by B.C. Hydro Research Center in Surrey, B.C. The fiber had a nominal core diameter of 4um and an outer diameter of 80/111. The nominal attenuation at .63um was given as lOdB/km. The fiber was surrounded with a coat of silicone rubber (outer Figure 3.30 The end of the f i b e r at 560x a f t e r (a) grinding and (b) p o l i s h i n g with the 9um paste. Figure 3.30 (cent.) The end of the f i b e r at 560x a f t e r (c) p o l i s h i n g with the Figure B i ^ r y ^ ( d ) p o l l 8 h l n g w i t h t h e .05um s l u r r y . 89 Figure 3.31 The f i n i s h e d c a p i l l a r y / f i b e r at 56x. 90 diameter 200nm) beyond which there was a jacket of Hytrel p l a s t i c (outer dimension 400um). Figure 3.32 i s a copy of the nominal dimensions of the f i b e r and the s p e c t r a l attenuation as supplied by ITT. 3.8 Attaching the Fibers to the Device The input beam was focussed onto the f i b e r using a 160* microscope o b j e c t i v e . Both the f i b e r and the objective were mounted on micropositioners, each having 3 axes of t r a n s l a t i o n a l freedom, fi x e d to the L-beam upon which the l a s e r was mounted. F i r s t the output of the microscope obje c t i v e was aligned using a target as i n section 3.5. The f i b e r was then aligned with the output of the microscope objective using the second micropositioner. To begin with the input end of the f i b e r was positioned about 3mm from the Input objective and the output end of the f i b e r was aligned with the input of an Alphametrics P1110 l i g h t probe connected to an Alphametrics DC1010 radiometer/photometer. The input end of the f i b e r was then positioned r e l a t i v e to the microscope objective u n t i l the reading on the photometer was maximized. The f i b e r was then retracted u n t i l ~ l / 2 of the maximum power was recorded. This method of defocussing the input resulted i n a more stable output. Figure 3.33 shows the l a s e r , the input objective, the f i b e r , and the output of the f i b e r projected onto a screen. The microprobe s t a t i o n holding the c r y s t a l was placed on a l e v e l platform and held i n place by a two-sided adhesive tape (3M Scotch 665). The f i b e r was held i n an attachment with a V groove that was mounted on a micropositioner with 3 axes of t r a n s l a t i o n a l freedom and two planes of r o t a t i o n a l freedom. The glass c a p i l l a r y was f i x e d i n the V groove with p l a s t i c e n e with enough of the c a p i l l a r y protruding for the f i b e r to be able 91 SINGLE MODE OPTICAL FIBER DIMENSIONS SHOWN ABE NOMINAL VALUES PROTECTIVE HYTREL^ PLASTIC JACKET MNEP. JACKET SILICA CLADDING DOPED SILICA CORE n i J I . l> COBE „ SILICA n CLADDING •OEX or REFRACTION PROFILE E t WAVELENGTH *»•» TYPICAL SPECTRAL ATTENUATION - SINGLE MODE OPTICAL FIBER Figure 3.32 The nominal dimensions and the spectral attenuation of the ITT T-1601 fiber used in this work as supplied by ITT. 92 Figure 3.33 The l a s e r , the input o b j e c t i v e , the f i b e r , and the ouput of f i b e r projected onto a screen. 93 to reach the c r y s t a l edge. The c a p i l l a r y was rotated to ensure that the f i b e r would be at the top of i t at the end where contact would be made with the c r y s t a l . The attachment holding the c a p i l l a r y was then l e v e l e d . The c a p i l l a r y / f i b e r endface was aligned with the c r y s t a l endface while viewing the two under a microscope at 30* magnification. F i r s t the two were brought nearly into contact. Then i f they were not p a r a l l e l i n the h o r i z o n t a l plane the c a p i l l a r y was retracted and the micropositioner holding the c a p i l l a r y was rotated i n the hori z o n t a l plane u n t i l the c a p i l l a r y could be brought into p h y s i c a l contact with the c r y s t a l endface without there being any noticeable gaps between the two. This was followed by an attempt to t r a n s l a t e the c a p i l l a r y i n the v e r t i c a l d i r e c t i o n while the two were nearly i n contact. If the two made contact during the t r a n s l a t i o n the c a p i l l a r y was withdrawn and rotated i n the v e r t i c a l plane u n t i l the c a p i l l a r y could be translated i n both the v e r t i c a l and h o r i z o n t a l d i r e c t i o n s while i n extremely close proximity to the c r y s t a l edge without making contact. Good alignment of the f i b e r and the input waveguide was achieved by focussing the output of the device on a screen/detector i n a manner s i m i l a r to that used i n the t e s t i n g procedure, however, now the f i b e r was moved instead of the input objective or the c r y s t a l . The output of the device was projected onto a screen/detector using a 20* microscope objective ( i t was necessary to use a lower power objective to image the output spot as the objective could not be brought any closer than 1mm from the c r y s t a l ' s edge now that i t was mounted i n the microprobe s t a t i o n ) . Finding the input of the device was a matter of successively probing with the f i b e r , butting i t right up to the c r y s t a l edge. A modulating s i g n a l was applied to the device v i a 94 the microprobes during the alignment .process. Figures 3.34a and b show the setup for attaching the f i b e r s with the l i g h t s on and i n the dark r e s p e c t i v e l y . Once a s u f f i c i e n t l y strong output s i g n a l had been achieved the c a p i l l a r y / f i b e r was withdrawn and a few drops of Norland NOA-61 o p t i c a l adhesive were placed i n the groove at the input end of the microprobe s t a t i o n . The c a p i l l a r y / f i b e r was then reinserted into the groove and again brought into contact with the c r y s t a l edge and repositioned to give the strongest output s i g n a l obtainable. The adhesive was then set using a Norland Opticure Light Gun. During the curing process the adhesive was i n c l i n e d to c o n s t r i c t s l i g h t l y and I t was necessary to make s l i g h t adjustments i n the c a p i l l a r y / f i b e r ' s p o s i t i o n during the cure. In the case that the post cure coupling was not acceptable i t was possible to remove the adhesive from both the c r y s t a l and the c a p i l l a r y with methanol but th i s was a tedious process needing a l o t of time and care. A f t e r the f i r s t f i b e r was attached to the device i t was necessary to put a f e r r u l e , that could be connected to a detector while the second f i b e r was aligned, onto i t s input end. Thus the f i r s t f i b e r to be attached was transformed into the output f i b e r . F i r s t the adhesive f i l l e d end, that had acted as a cladding mode s t r i p p i n g s e c t i o n , was removed. Then the excess c a p i l l a r y was removed from the end that was butted to the c r y s t a l . To do t h i s methanol was f i r s t i n j e c t e d i n t o the c a p i l l a r y to dissolve any adhesive that may have worked i t s way up the c a p i l l a r y and gotten under the f i b e r . This took ~20 min. The c a p i l l a r y was then scribed with the edge of a f i l e and was broken. Af t e r the excess c a p i l l a r y had been removed the f i b e r was ins e r t e d into an Amp 530954-6 f e r r u l e . The f i b e r was fi x e d i n the f e r r u l e 95 Figure 3 .34 The setup used to a l i g n the c a p i l l a r i e s / f i b e r s with the device (a) with the l i g h t s on and (b) i n the dark. 96 using Epotek 302 Op t i c a l Epoxy. The f i b e r end was then polished using the same p o l i s h i n g procedure as that described i n Section 3.7 except that now an Amp 53022-1 p o l i s h i n g bushing was used as the p o l i s h i n g j i g . With the already attached f i b e r inserted i n a detector the second f i b e r was aligned and attached. Since we could continue to use th i s f i b e r as the input f i b e r i t was not necessary to remove the cladding mode s t r i p p i n g end. However, i t was s t i l l desirable to remove the excess c a p i l l a r y from the end butted to the c r y s t a l . This was done and the excess c a p i l l a r y was moved down toward the input end where i t was attached to the f i b e r with some masking tape. We could now mount the micropositioner with the f i b e r s attached on the capacitive d i v i d e r port. Figure 3.35 shows the microprobe s t a t i o n with both f i b e r s attached to the device and mounted on the capacitive divider port. Figure 3 . 35 The microprobe s t a t i o n with both f i b e r s attached and mounted on the c a p a c i t i v e d i v i d e r port. 98 Chapter 4 Results 4.1 Introduction In t h i s chapter the device parameters a f f e c t i n g the v o l t a g e - i n / o p t i c a l -intensity-out transfer functions of the devices that we constructed are given. These are the half-wave voltage, the i n t r i n s i c phase, and the e x t i n c t i o n r a t i o . The impedance measurements made on the capacitive d i v i d e r as well as the measured d i v i d e r r a t i o s are given. The method of determining the number of modes i n , and the e f f e c t i v e mode r e f r a c t i v e indices of the d i f f u s e d waveguides i s d e t a i l e d and the measured values are given. The r e s u l t s of a 60Hz high voltage test on a sensor, employing the c a p a c i t i v e d i v i d e r and a separate IMZ, are given. F i n a l l y , the p r i n c i p l e s of operation of a voltage induced waveguide device are described and measurements made on a prototype are presented. 4.2 Device Parameters The most common form of the v o l t a g e - i n / o p t i c a l - i n t e n s i t y - o u t transfer function i s given by equation A2.13 as I - (I /2)[1 + COS(TCV/V + 4> ) ] . 4.1 out i n TI I The parameters of t h i s equation are the half-wave voltage, , and the i n t r i n s i c phase d i f f e r e n c e , 4>^ . In t h i s equation i t i s assumed that the e x t i n c t i o n r a t i o i s 100%. E x t i n c t i o n r a t i o s of 98% [Leonberger, Woodward, and Spears 1979] and 99% [Becker 1984a] have been reported. The e x t i n c t i o n r a t i o i s the r a t i o of the peak to peak i n t e n s i t y of the modulated s i g n a l , I , to the peak output i n t e n s i t y , 1,^^ o f t n e output of the IMZ. It i s u s u a l l y given i n percent as 99 R = (I /I ) x 100. 4.2 pp max x y Figures 4.1a and b show the E and E po l a r i z a t i o n s of the modulated outputs of a 5mm long 4um IMZ. From figure 4.1a the ex t i n c t i o n r a t i o i s given a s (3.7/3.9) x 100 or 95% and from figure 4.1b as (3.1/3.15) x 100 or 98%. The half-wave voltage i s the voltage that must be applied to the electrodes to achieve a r e l a t i v e change i n phase of T t r a d between the outputs of the two branches a f t e r they emerge from the propagation constant modulation region of the two branches. The half-wave voltage i s given i n equation A2.5 as V - X g/(2n 3roL). 4.3 Tt O x From fig u r e 4.2, showing the E p o l a r i z a t i o n of the output of a 10mm long 4um device, we can c a l c u l a t e as the voltage necessary to drive the output s i g n a l from a minimum to a maximum. From fig u r e 4.2 we calculate to be 4V. The value of the f i e l d overlap f a c t o r , o, can be calculated for a p a r t i c u l a r device structure as o = X g/(2n 3rLV ) 4.4 o it using the measured value of V . The overlap factors for the devices made during t h i s work were i n the range .4 - .5, for example, the device whose output i s shown i n fi g u r e 4.2 has a value of o of ~.48. The i n t r i n s i c phase diffe r e n c e i s the b u i l t - i n phase diffe r e n c e that e x i s t s at the output of the device due to geometrical differences i n the waveguides of the two branches of the device. This can be calculated from 4>, - -rc(V /V ) 4.5 I p Tt where V i s the voltage that must be applied to achieve the peak output P i n t e n s i t y . Figure 4.3 shows the E p o l a r i z a t i o n of the output of a 1mm long 100 f o r Figure 4.2 The modulating signal and E x polarization output signal for a 4um IMZ with L - 10mm. Mod. Sig. (xlO) Out. Sig. iff I 23 li l l l l l l l l l l l i l lBilHI! a i n i i i i i i i i i gy | i 11 IilfiiIIIIIiiI.il II i§KIi.IliltiII» Figure 4.3 The modulating signal and E x polarization output aignal for a 4um IMZ with L • 1mm. 102 4um device with an i n t r i n s i c phase difference of 110°. Note that the i n t r i n s i c phase difference may a c t u a l l y include phase differences of more than ±2n which are not Included i n t h i s d e f i n i t i o n . This d e f i n i t i o n i s purely for defining a p r a c t i c a l measure of the i n t r i n s i c phase. If the x y device supports more than one mode of eit h e r type (E or E ) then the i n t r i n s i c phase of each mode may be d i f f e r e n t . Table A . l gives the e x t i n c t i o n r a t i o s , half-wave voltages, and i n t r i n s i c phase differences of a number of d i f f e r e n t devices. The e x t i n c t i o n r a t i o s of these devices are comparable to the highest that have, to the best of our knowledge, been reported i n the l i t e r a t u r e . Figure A.Aa shows the output of the E y p o l a r i z a t i o n of a device with a 98% e x t i n c t i o n r a t i o at maximum output (with the l i g h t confined to the output waveguide) and 4.4b shows the same device at minimum output (with the l i g h t radiated into the bul k ) . 4.3 The Capacitive Divider Our capacitive d i v i d e r consisted of a .5*18*18mm piece of z-cut LiNb0 3 with Ni deposited onto one of the faces. It was mounted on a port as shown i n f i g u r e 4.5. A 6" strand of 30 gauge wire was soldered to the deposited Ni coat. LiNb0 3 was chosen as the d i e l e c t r i c because the p o t e n t i a l exists to combine the capacitive d i v i d e r and the IMZ m o n o l i t h i c a l l y [see Section 2.2]. The z-cut was chosen since LiNb0 3 i s a p i e z o e l e c t r i c c r y s t a l with a small change i n the r e l a t i v e p e r m i t t i v i t y , as the c r y s t a l goes from the "free" to the "clamped" state, f o r f i e l d s applied p a r a l l e l to the z axis but with a large change for f i e l d s applied perpendicular to the z axis [Raeuber 1978]. The quote of the p e r m i t t i v i t i e s supplied by the manufacturer are 103 Figure 4.4 The p o l a r i z a t i o n of an IMZ for (a) the case i n which the l i g h t i s confined to the output waveguide and (b) the case i n which the l i g h t i s radiated i n t o the bulk of the c r y s t a l . Figure 4.5 The port and capacitive d i v i d e r . Device Pol. L R I • l D10-J14 TM 5mm 24V 0° D13-J17 TE 1mm 95<* 45 V 60° D5-J18 TE 10mm 9H 4v -80° D5-J18 TM 10mm 98% 12V -90° D9-J18 TE 5mm 95% 9V -100° D9-J18 TM 5mm 24V -65° D9-J19 TE 5mm 95% 10V 50° D14-J19 TE 1mm 88% 43V 110° Table 4.1 Device parameters. 1 0 6 e 23 = •254nF/m and e 33 = .247nF/m where e ^ i s the p e r m i t t i v i t y under g constant stress (free) and e ^3 * s the p e r m i t t i v i t y under constant s t r a i n (clamped). Using these values for the p e r m i t t i v i t i e s and the formula for the capacitance of a p a r a l l e l plate capacitor (C «= eA/d) we calculated the capacitance of the free and the clamped di v i d e r to be 165pf and 160pf r e s p e c t i v e l y . The capacitance, C £, and the d i s s i p a t i o n factor of the c r y s t a l were measured on a Hewlet-Packard LCR meter at ten points between 10kHz and 10MHz and are given i n figu r e 4.6. The Impedance of the di v i d e r was then measured on a Hewlett-Packard Vector Impedance Meter for 1000 separate points i n the range of 400kHz to 110MHz which indicated that the f i r s t major p i e z o e l e c t r i c resonance occured at ~4.5MHz. Figure 4.7 i s a plot of 1000 sample points i n the frequency range l-10MHz. Both figures i n d i c a t e that the div i d e r i s very nearly purely capacitive i n the range 10kHz-2MHz. In that range the can be read capacitances d i r e c t l y from fig u r e 4.6 as ranging from a low of 205pf (at 400kHz) to a high of 230pf (at 2MHz). In order to simulate an SF 6 bus duct we used a test j i g c o n s i s t i n g of two concentric c i r c u l a r electrodes that were 2m long. The inner electrode had an outer radius of 89mm and the outer conductor had an inner radius of 248mm. A port 254mm i n diameter was cut i n the outer electrode i n order to give us access to the f i e l d to be measured. The port f i x t u r e , with the capa c i t i v e d i v i d e r attached, was inserted i n the port and the capacitance measurements were made to determine the capacitance from the d i v i d e r to the inner electrode, C . Once C was determined the voltage reduction of the 107 CRPRCITHNCE (*) RND DISSIPRTION FRCTOR (+) SHMPLE> DIVIDER(SERIRL) xlE-Bl 2 xlE-10 4 r a 1 o r-U tr u. 2 O ,5 -1 -LO O 2 cr cr a. in in o tr a. tr o 0 + 0 1E+04 1E+05 1E+0G FREQUENCY (Hz) 1E+07 Figure 4.6 The capacitance and dissipation factor of the capacitive divider measured at ten discrete points between 10kHz and 10MHz. 108 Figure 4.7 The impedence, (a) phase and (b) magnitude, of the capacitive d i v i d e r (plus a connecting wire) measured at 1000 discrete points between 1MHz and 10MHz. 109 d i v i d e r could also be determined from equation 2.1 [see Section 2.2]. The data was taken with a high voltage 60Hz s i g n a l , a low voltage varying frequency s i g n a l , and a high voltage impulse applied across the electrodes. The high voltage 60Hz capacitance measurements were made with 10, 20, 30, 40, 50, and 55kV rms across the electrode p a i r . The calculated values f o r C were e i n the range of 37-38fF (femtoFarads). Figure 4.8 shows the input and output s i g n a l s from the di v i d e r at 50kV. Figure 4.9 i s a plo t of the calculated values of C g at the various applied voltages. The low voltage measurements were made with 20V applied across the electrodes at 600, 6000, and 60000Hz. P P The values f o r these measurements gave values of C g i n the range from 23-30fF. Figure 4.10 shows the input and output signals at 6000Hz. F i n a l l y the impulse response measurements were made with r i s e times of 200us and 1.5LIS with peak voltages of 23.8kV and 26.3kV r e s p e c t i v e l y . The slow impulse measurement, figure 4.11a, gave a value for C of 30-35fF. The fast impulse measurement, fig u r e 4.11b, was not used to determine the value of C £ because of the rin g i n g on the output. This i s believed to be due to the high frequency p i e z o e l e c t r i c resonances of the c r y s t a l . Using these values f o r C g and s e t t i n g C £ • 220pF we were able to predict that our di v i d e r r a t i o would be i n the range 110-190*10" 6. Thus with an applied voltage of 50kV rms we expected a s i g n a l voltage of between 5.5 and 9.5Vrms or 15.5 and 2 7 v p p * The e f f e c t of the cap a c i t i v e loading of the IMZ on the c a p a c i t i v e d i v i d e r i s n e g l i g i b l e . Figure 4.12 i s a plo t of the capacitance and d i s s i p a t i o n factor of a device with a modulation length L of 5mm. 110 In. Sig. (x28560) Out. Sig (xlO) Figure 4 . 8 The input and output signals from the capacitive divider for a 50kV applied signal. 1+0.5 1+0 -39 -e (tr) 38 37 -36.5 Figure 4.9 C versus applied voltage. 112 Figure 4 . 1 0 The input and output signals from the capacitive d i v i d e r f 6000Hz applied s i g n a l . (b) A.11 The (a) slow and (b) f a s t r i s e time impulse measurements. CRPflCITRNCE (*) RND DI5SIPRTI0N FRCTOR ( + ) SRMPLE- D10 ,J IB(SERIRL) x l E - 0 1 x l E - 1 2 -3 u z cr u CX Q_ cr u 0 1E+04 1E+05 1E+0B FREQUENCY (Hz) 1E+07 Figure 4.12 The capacitance and d i s s i p a t i o n factor of a device with L " 5mm. 115 4.4 Waveguide E f f e c t i v e Mode Refractive Index Measurements To determine the e f f e c t i v e mode r e f r a c t i v e indices of our waveguides we made a prism coupler. The setup i s depicted i n figure 4.13. Light was "end - f i r e " coupled into a polished edge of the waveguide. The l i g h t propagating i n the waveguide was then coupled out of the waveguide and projected onto a screen using a high r e f r a c t i v e index prism. Due to the necessity of tangential f i e l d continuity at the waveguide/prism interface the e f f e c t i v e r e f r a c t i v e index of the mode can be related to the angle of ra d i a t i o n Into the prism, a, by the r e l a t i o n s h i p : cos(a) « n ,,,/n 4.6 ef f p where n i s the r e f r a c t i v e index of the prism. P A further a p p l i c a t i o n of the continuity condition (Snell's Law) and a knowledge of the base angle of the prism, c, allow the angle that the l i g h t r adiates from the prism surface, e, to be calculated e = 90° - c - d 4.7 where d i s given by d - s i n _ 1 [ ( n In )sin(b)] 4.8 and b by b = 90° - a - c 4.9 and n i s the r e f r a c t i v e index of a i r . By knowing the distance from the screen to the point at which the l i g h t radiates from the prism, D, as well as the height on the screen at which the l i g h t 6pot i n t e r s e c t s the screen, H, we can c a l c u l a t e the angle, e. Our c a l c u l a t i o n s showed that the assumption that the point at which the l i g h t radiates from such a small prism was constant would r e s u l t i n an error i n n of < .0001 over the expected range of values e f f 116 Figure 4.13 Drawing of the prism coupler used to measure the waveguide e f f e c t i v e mode r e f r a c t i v e i n d i c e s . 117 of the propagation constants (2.202 - 2.242 for E X modes and 2.289 - 2 .329 y f o r E modes). Figure 4.14 i s a picture of the setup used. The prism used was made of r u t i l e which i s a u n i a x i a l b i r e f r i n g e n t c r y s t a l . It was supplied to us by B e l l Northern Research. It was quoted as having a value f o r the extraordinary r e f r a c t i v e index, n g, of 2.871 and for the ordinary r e f r a c t i v e index, n Q, of 2.584. The z axis of the c r y s t a l was oriented so as to be perpendicular to the p a r a l l e l sides of the prism ( i . e . into/out of the paper i n figu r e 4.13). The angle, c, was measured by a l i g n i n g the base of the prism so that i t was perpendicular to a laser beam and adjusting i t s p o s i t i o n so that the corner of i n t e r e s t bisected the l a s e r beam. The p o s i t i o n of the I n t e r n a l l y r e f l e c t e d half-spot was then recorded on the opposite face (fi g u r e 4.15). Using t h i s technique the angle, c, was found to be 46.58°. Due to t h e i r small dimensions i t was impractical to use the smaller waveguides to measure the e f f e c t i v e r e f r a c t i v e indices of the confined modes. Instead a sample was prepared with 40nm of T i on a piece of LiNb0 3 and i t s device w e l l d e l i n e a t i o n marks were used. The d i f f u s i o n was car r i e d out i n 0 2 bubbled through 8" of D.I. water. The input face was polished to a 9um p o l i s h . A 20* microscope objective was used to couple l i g h t into the waveguide i n order to achieve a more uniform i l l u m i n a t i o n of the Input face (leading to the e x c i t a t i o n of a l l modes). The waveguide was found to support x v x only E m 0 and E m Q modes. The e f f e c t i v e mode r e f r a c t i v e index for the E m Q modes was 2.219 ±.004 and for E y _ modes was 2.301 ±.004. mu 118 Figure 4.14 Picture of the prism coupler used to measure the waveguide e f f e c t i v e mode r e f r a c t i v e i n d i c e s . L a s e r beam Figure A.15 Arrangement used for measuring the base angle of the pri 120 4.5 High Voltage Test Measurements on the capacitive d i v i d e r described i n section 4.3 indicated that the d i v i d e r would produce a peak to peak d r i v i n g voltage, V , PP i n the range of 15.5 to 27V. The device that would be used would have to have a half-wave voltage i n excess of 27V. Therefore only the 1mm long devices could be used. Furthermore the i n t r i n s i c phase of the device should be nearly ±7t/2 (with a maximum allowable deviation of Tt/2(1-V /V ) ) . pp n, Figure 4.16 shows the output of the device that was used. V^ for t h i s device i s 45V, 4> i s -80°, and R i s 21%. Using the value of 45V for V^ we expect the peak applied voltage (50kV rms) to cause a peak change i n phase of between 30° and 54° for E mQ modes V V and between 10° and 18° for E „ modes (since V for E modes i s ~3 times V mO TC it f o r E x modes; r ^ = r23 " ^'^ a n ( * r33 = J ^ * ^ ) * Representing the output s i g n a l shown i n figure 4.16 by P /2)cos(TtV/V + « ) 4.10 out dc pp 71 i or P - P J + ( P / 2 ) [C O S ( T I V / V ) C O S ( 0 , ) - sin (7tV/V )sin (0 , )] 4.11 O U t dc pp TC I 71 1 where P ^ C represents the unchanging portion of the output power and P represents the peak to peak change i n the output power due to the modulating s i g n a l . Taking into account the measured value of the I n t r i n s i c phase (-80°) and ignoring the term P . equation 4.11 can be rewritten as dc P / P - 1/2[.17COS(TCV/V ) + .98sin(TcV/V )] 4.12 O U t pp 1 TC TC 121 Mod. S i g . Out. S i g . Figure 4.16 The modulation and output signals of the device used i n our high voltage sensor. 122 which has been plotted i n figure 4.17. In equation 4.12 we have ignored the DC term since i t can be f i l t e r e d out of any measurements to be made. The high voltage test was c a r r i e d out at 60Hz for applied signals of 10, 20, 30, 40, and 50kV rms (28.3, 56.6, 84.9, 113.1, and 141.4kV peak to peak). Using the measured d i v i d e r r a t i o s for these voltages the corresponding predicted peak to peak d r i v i n g voltages for the IMZ are 4.9, 9.8, 14.8, 19.8, and 24.1V and the induced peak phase changes are 9.8, 19.6, 29.6, 39.6, and 50.2°. The predicted values of the output s i g n a l , normalized with respect to the lOkV rms output s i g n a l , are shown i n figure 4.18. The measured outputs are plotted i n fi g u r e 4.19. The l i n e drawn between the data points i n fi g u r e 4.19 i s a le a s t squares f i t to the data. Figures 4.20a and b show the applied signals and the corresponding output signals f o r the 20 and 50kV rms sig n a l s r e s p e c t i v e l y . Figure 4.21 shows the test setup used to make the high voltage measurements. 4.5 The Voltage Induced Waveguide In 1971 Channin reported a voltage induced o p t i c a l waveguide [Channin 1971]. He deposited electrodes on x-cut LiNb0 3 i n such a way that the l i g h t confined to the induced waveguide would propagate p a r a l l e l to the c r y s t a l ' s y a x i s . The in t e r e l e c t r o d e gap was 7CLim and the length of the c r y s t a l was 1.7cm. The turn-on voltages reported by Channin were i n excess of 300V. Since Channin's i n i t i a l report we are unaware of any subsequent work on voltage induced waveguides. We believe t h i s to be due to the large turn-on voltages he reported. We have reduced the turn-on voltage by decreasing the int e r e l e c t r o d e gap. We have also Introduced a d i e l e c t r i c buffer layer 123 P J? -.5 -90^ 90^  Figure 4.17 Plot of ^ /V . 124 (Arb. units) 25 50 75 100 125 (kV p-p) 150 175 200 Figure A.18 The predicted values of the output s i g n a l based on the measured ca p a c i t i v e d i v i d e r r a t i o s . 125 Figure 4.19 The measured outputs of our high voltage sensor 126 Applied signal Output signal (a) Applied signal Output signal HUftflllliHIil. ( b ) Figure 4.20 The applied and output signals for an applied voltage of (a) 20 and (b) 50kVrms. 127 Figure 4.21 The test setup used to make the high voltage measurements. 128 between the c r y s t a l and the electrodes to i s o l a t e the electrodes from the waveguide. The waveguides were fabricated by f i r s t sputtering a 200nm layer of Si0 2 onto a piece of x-cut LiNb0 3. Second, A l was evaporated onto the sample and was patterned to form two 23mm long electrodes with a 4um wide interelectrode gap. The electrodes were patterned so that the l i g h t i n the waveguide would propagate p a r a l l e l to the c r y s t a l ' s y a x i s . Third, the ends of the c r y s t a l were polished. Figure 4.22 depicts the cross section of the voltage induced waveguide. The device works by applying a voltage across the i n t e r e l e c t r o d e gap and thus e s t a b l i s h i n g an e l e c t r i c f i e l d i n the c r y s t a l . The r e f r a c t i v e index of the region between the electrodes i s increased v i a the e l e c t r o o p i t c e f f e c t for one f i e l d d i r e c t i o n and i s decreased for the opposite f i e l d d i r e c t i o n . The main f i e l d component i n the region of the interelectrode gap i s p a r a l l e l to the c r y s t a l ' s z axis thus u t i l i z i n g the and r 1 3 e l e c t r o o p t i c c o e f f i c i e n t s . It follows that the lowest order mode w i l l be an E mode. The device was tested using the same setup as that described i n Section 3.5. Figure 4.23 shows the output power of the voltage induced waveguide as a function of the voltage applied across the electrodes. The on/off r a t i o for the output shown i n f i g u r e 4.23 i s ~23dB. Larger r a t i o s were obtained f o r l a r ger applied voltages. Figure 4.24 shows the output spot of the waveguide when 35V were applied across the electrodes. 4.22 The cross section of a voltage induced waveguide. Figure 4 . 2 3 The output power of the voltage induced waveguide as a function of the voltage applied across the electrodes. Figure 4 . 2 4 The output spot of the voltage induced waveguide with 35V applied across the electrodes. 131 Chapter 5 Summary and Conclusions In this work a number of things have been accomplished. In Chapter 2 two device types are proposed for the determination of voltages on high voltage l i n e s . One type uses capacitive voltage dividers i n conjunction with an IMZ. It i s proposed to integrate the capacitive d i v i d e r and the IMZ mo n o l i t h i c a l l y and an example of such a device i s given. The second type Includes two Immersion devices. One i s based on an asymmetric slab waveguide design. The other uses strip-loaded diffused waveguides. Examples of both immersion devices are given. In Chapter 3 the f a b r i c a t i o n of our devices i s given i n d e t a i l . The designs of the masks, the process of f a b r i c a t i n g IMZs with Ti:LiNb0 3 waveguides, and the methods of p o l i s h i n g the edges of the c r y s t a l s and ends of the o p t i c a l f i b e r s i s explained. The bench te s t i n g procedure and the method of attaching f i b e r s to the c r y s t a l are also described. Following these steps we were able to fa b r i c a t e very long IMZs with excellent e x t i n c t i o n r a t i o s . In Chapter 4 the device parameters of IMZs made during t h i s work are given. The e x t i n c t i o n r a t i o s of the devices are comparable to the highest that have been reported i n the l i t e r a t u r e . A capacitive d i v i d e r made from a t h i n z-cut slab of LiNb0 3 was shown to be nearly purely capacitive below ~2MHz and to have i t s f i r s t p i e z o e l e c t r i c resonance at ~4.5MHz. The divider r a t i o of the capac i t i v e d i v i d e r was c a l c u l a t e d . The capacitive d i v i d e r was used i n conjunction with a separate IMZ to form a high voltage sensor. The 132 sensor, accessed by mono-mode o p t i c a l f i b e r s , was tested under high voltage conditions and was found to give a l i n e a r output for applied voltages i n the range from 10-50kV rms at 60Hz. A device using a voltage induced waveguide was proposed and demonstrated. The output power was measured as a function of applied voltage and the on/off r a t i o ( for the peak to peak applied voltage) was found to be ~23dB. This work shows that i t i s possible to fabricate IMZs with state-of-the-a r t e x t i n c t i o n r a t i o s and which have large enough dimensions to allow them to be combined on a sing l e substrate with a capacitive voltage d i v i d e r using electron beam generated masks and by following the steps outlined i n Chapter 3. Also i t i s possible to use capacitive dividers i n conjunction with IMZs as high voltage sensors i n gas insulated bus ducts where the sensor i s accessed by mono-mode o p t i c a l f i b e r s thus i s o l a t i n g the rest of the monitoring apparatus from the high voltage environment. F i n a l l y i t i s possible to f a b r i c a t e voltage induced waveguide devices with low turn-on voltages and large enough on/off r a t i o s to make them a t t r a c t i v e as o p t i c a l switches. Suggestions for further work include f a b r i c a t i o n of a capacitive d i v i d e r and an IMZ m o n o l i t h i c a l l y on a z-cut LiNb0 3 wafer f o r the high voltage measurement a p p l i c a t i o n . Further reduction of the wafer's thickness should r e s u l t i n the f i r s t p i e z o e l e c t r i c resonance occurring at a higher frequency thus allowing the device to measure higher frequency t r a n s i e n t s . Also the f a b r i c a t i o n of the immersion type devices described i n Section 2.3 should be attempted. F i n a l l y voltage induced waveguides with narrower interelectrode gaps should be made to further reduce the turn-on voltage. 133 Appendix 1 Waveguide Analysis A l .1 Introduction The propagation of electromagnetic waves i n planar and channel waveguide structures i s discussed. The eigenvalue equations for TE and TM modes i n the asymmetric slab and exponential r e f r a c t i v e index p r o f i l e planar waveguides are given. M a r c a t i l i ' s method of analyzing channel waveguides i s presented x v and the properties of E and E modes are discussed. Al.2 Planar Waveguides The name "planar waveguide" i s commonly used In the l i t e r a t u r e to refer to a d i e l e c t r i c waveguide i n which the r e f r a c t i v e index changes i n only one d i r e c t i o n and i s invariant i n planes perpendicular to that d i r e c t i o n ( i . e . the r e f r a c t i v e index d i s t r i b u t i o n i s a function of a single v a r i a b l e ) . Figure A l . l a shows the cross section of a symmetric slab waveguide structure. The r e f r a c t i v e index i s constant i n planes p a r a l l e l to the x-z plane and v a r i e s only i n the y d i r e c t i o n . In f i g u r e A l . l b the r e f r a c t i v e index d i s t r i b u t i o n , n(y), f o r the symmetric slab waveguide i s shown as i t i s commonly represented. While i t i s not possible to construct planar waveguides of i n f i n i t e extent I t i s s t i l l u s e f u l to study the waveguiding behavior of these structures i n order to predict the behavior of more p r a c t i c a l structures such as wide waveguides with thick substrates and superstrates and channel waveguides. From Maxwell's equations two equations can be derived for the propagation of electromagnetic waves In a current and charge free medium; for 134 y Fieure A l . l (a) The cross section of a symmetric slab waveguide, (b) The ^ refractive index distribution, n(y), for the symmetric slab waveguide• 135 the e l e c t r i c f i e l d , E , we have the vector wave equation V 2 E + V ( E • Vlog ee) + Vlog eu x ( V x I) - U E E " = 0 A 1 , 1 and for the magnetic f i e l d , H V 2 H + V ( H • Vlog gu) + V l o g E E x ( V x H ) - U E H " = 0 A1.2 where E i s the p e r m i t t i v i t y and u i s the permeability of the medium within which the wave i s propagating (the prime stands for the p a r t i a l d erivative with respect to time). [Derivations of equations A l . l and A1.2 can be found i n e.g. Born and Wolf 1980, Snyder and Love 1983, and Yariv and Yeh 1984]. In the case of a planar waveguide, that i s e l e c t r i c a l l y and magnetically i s o t r o p i c , using a few s i m p i l i f y i n g assumptions about the nature of the guided electromagnetic wave we can replace the vector wave equations A l . l and A1.2 with the two scalar wave equations [Love and Ghatak 1979] d 2 E /by2 + ( n 2 ( y ) k 2 - p 2 )E « 0 A1.3 x x w ' o r i x and d 2 H /by2 - (Slog n 2(y)/oy)(5H /dy) + (n 2 (y)k 2 - p 2 )H «= 0 A1.4 X 6 X O 1 X r e s p e c t i v e l y , where k Q Is the free space propagation constant ( k Q = 2 r t / \ o ) , and p, i s the propagation constant of the i * * 1 mode. The s i m i p l i f y i n g assumptions used to a r r i v e at equations A1.3 and A1.4 are that the wave propagating i n the waveguide has planes of constant phase which are perpendicular to the d i r e c t i o n of propagation, that the permeability of the material i s equal to that of free space, that our coordinate system i s arranged so that the d i r e c t i o n of propagation i s p a r a l l e l to the z axis, that the z dependencies of the modes are of the form exp(-ip.z), that the time 136 dependencies are of the form exp(lwt)., and that the f i e l d s , l i k e the waveguide, are invarient i n the x d i r e c t i o n ( i . e . o/dx m 0). Using equations A1.3 and A1.4 we can define two mode types; the transverse e l e c t r i c (TE) and the transverse magnetic (TM) modes. Equation A1.3 provides the solutions for TE modes. In a TE mode the E f i e l d i s taken to have only one component which i s p a r a l l e l to the x axis ( i . e . E = ^ x x ) . From the s o l u t i o n for E x one can cal c u l a t e the associated H f i e l d components H and H from the r e l a t i o n s y z H - p,E /ion A1.5 y i x o and H - (-i/uu )oE /by. A1.6 Z ^O X S i m i l a r l y equation A1.4 provides the solutions for TM modes. In a TM mode the H f i e l d i s taken to have only one component which i s p a r a l l e l to the x axis ( i . e . H = H xx). From the s o l u t i o n for H x one can ca l c u l a t e the associated E f i e l d components E^ and E z from the r e l a t i o n s E - -p.H / U E A1.7 y i x and E •* ( 1 / U E ) O H /by. A1.8 Z X When a p a r t i c u l a r mode i s indicated a subscript i s included In the notation such as f o r the T E Q or T M ^ mode. In t h i s notation the subscript refers to the number of nodes (zeros) of the transverse f i e l d d i s t r i b u t i o n . In order to study the behavior of the modes of propagation of electromagnetic waves ( l i g h t ) In planar waveguides we need to be able to 137 obtain solutions to equations A1.3 and A1.4 for the r e f r a c t i v e index p r o f i l e of the structure, n(y) (or rather the r e l a t i v e p e r m i t t i v i t y p r o f i l e e(y) = n 2(y))« Exact solutions to equation A1.3 have been derived for the p r o f i l e s : n 2 ( y ) = constant [Marcuse 1974], n 2 ( y ) «= n f e 2 + 2n bAnexp(-|y|/d) (the exponential taper p r o f i l e ) [Conwell 1973], and n 2(y) • n 2 + (n 2 - n 2 ) y / y . (the l i n e a r taper p r o f i l e ) [Marcuse 1973]. For equation A1.4 exact solutions e x i s t for the p r o f i l e s : n 2 ( y ) - constant [Marcuse 1974], n 2 ( y ) = n 2exp(-2|y|/d), n 2 ( y ) - n 2 s e c h 2 ( 2 y / d ) , and n 2 ( y ) - n 2/(l+2|y|/d) 2 [Love and S S 8 Ghatak 1979]. Where n i s the r e f r a c t i v e index at y » 0 and n. i s the i s J b r e f r a c t i v e index deep i n the bulk. An approximate sol u t i o n to equation A1.4 a l s o e x i s t s for the p r o f i l e n 2(y) » i ^ 2 + 2n bAnexp(-|y|/d)[Conwell 1973]. Obtainment of exact solutions to equations A1.3 and A1.4 i s not the only method of analyzing the behavior of l i g h t i n a planar waveguide, however, whenever possib l e , i t i s preferable to expensive computer intensive methods. One method developed by Hocker and Burns [Hocker and Burns 1975] i s based on the progression of a wave, In a waveguide, i n which the r e f r a c t i v e index i s approximated by many thi n slabs of constant r e f r a c t i v e index. In this t r e a t -ment the r e f r a c t i v e index of each slab and the mode propagation constant are used to determine the change i n phase i n the y d i r e c t i o n across the slab and then the t o t a l change i n phase as the wave progresses between the waveguide boundaries i s summed up and added to the changes at the boundaries. The propagation constants of the modes are then found by f o r c i n g the t o t a l changes In phase to be even multiples of 7t. In essence the method of Hocker and Burns i s an adaptation of the older zigzag method [Tien 1971] applied to slab waveguides where the s i n g l e high r e f r a c t i v e index slab has been replaced 138 by hundreds of very t h i n slabs. Figure A1.2 i s a wave-vector diagram such as would be used to determine the change i n phase i n the slabs. A second method i s the Linear Segment Method (LSM) [Marcuse 1973; Noda and Fukuma 1980] i n which the r e f r a c t i v e index d i s t r i b u t i o n i s approximated by l i n e a r segments ( f i g u r e A1.3). The boundary conditions of tangential f i e l d c o ntinuity and power confinement are applied to the solutions of equation A1.3, for each region, i n order to obtain the eigenvalue equation for the structure. Besides being computer intensive the LSM has the further l i m i t a t i o n that i t i s only applicable to the analysis of TE modes. A s i m i l a r method using constant r e f r a c t i v e index slabs has also been used (fig u r e A1.4) [Suematsu and Furuya 1972; Shubert], however, i t s accuracy i s not good i n regions i n which the slope of the r e f r a c t i v e index d i s t r i b u t i o n i s steep. Another method of analyzing waveguides i s the Wentzel-Kramers-Brillouin (WKB) method. It has been used to study the properties of planar waveguides supporting a large number of modes [Marcuse 1973; Tien et a l . 1974; Conwell 1974]. However, t h i s approximate method i s not suitable for analyzing the properties of waveguides supporting only the lowest order mode. Exact s o l u t i o n s , on the other hand, allow the obtainment of a n a l y t i c solutions that are e a s i l y studied and are v a l i d for any number of modes. Two of the r e f r a c t i v e index p r o f i l e s that allow a n a l y t i c solutions to be found for both equations A1.3 and A1.4 have received the most attention i n the l i t e r a t u r e ; they are the slab and exponential p r o f i l e s . As mentioned above the s o l u t i o n to equation A1.4 for the exponential p r o f i l e i s only approximate. H r- 1 •—I 1 • y ~ Actual distribution Linear segments Figure A1.3 A piecewise linear approximation to an arbitrary refractive index distribution. n(y) 140 n 0 ' n, X V1 H r- y — — — — Actual d i s t r i b u t i o n Constant r e f r a c t i v e index slabs Figure A1.4 A constant r e f r a c t i v e index slab approximation to an a r b i t r a r y r e f r a c t i v e index d i s t r i b u t i o n 141 Al.2.1 The Asymmetric Slab Waveguide The asymmetric slab waveguide i s a structure that i s both easy to r e a l i z e and easy to analyze. Since the beginning of integrated o p t i c s , waveguides have been formed by depositing films with high r e f r a c t i v e indices on substrates with lower r e f r a c t i v e indices [Tien 1971]. High r e f r a c t i v e index materials are usually r f sputtered onto a substrate [Tien 1971; Futura, Noda, and Ihaya 1974; Terui and Kobashi 1981] or else a metal, such as Ta, Is deposited and i s then thermally oxidized [Hensler et a l . 1971]. The r e s u l t i s an asymmetric slab waveguide such as that shown i n fi g u r e A1.5. Various properties of the f i l m , such as f i l m thickness or r e f r a c t i v e index, can then be studied by launching guided waves i n the films and comparing the measured behavior of the modes with the predicted behavior. In any of the three regions of the waveguide E x and H x must provide solutions to equations A1.3 and A1.4 r e s p e c t i v e l y . Since n 2 ( y ) i s constant i n each region equations A1.3 and A1.4 can be reduced to the form o2cj>/dy2 + vcp = 0 Al .9 where 4» replaces E x or H x and v = (n 2 k 2 - p 2)1/2 j o r i f o r each of the three regions; j = 1,2,3. The general so l u t i o n to equation A1.5 i s tMy) - C e x p [ 1 ( 1 x ^ 2 - P i 2 ) l / 2 y ] + C 2 j e x p [ - i ( n j 2 k o 2 - P i 2 ) 1 / 2 y ] . A L I O Using equation Al.lO and imposing the boundary conditions that the tangential components of the E and H f i e l d s must be continuous at the Figure A1.5 (a) The cross section of an asymmetric slab waveguide, refractive index distribution 143 boundaries of the regions with d i f f e r e n t r e f r a c t i v e indices and that the power i n a guided wave must be confined to the region of the waveguide ( i . e . (|,(+OD) = o) we can f i n d the eigenvalue equations for both the TE and TM modes of the structure. F i r s t we can write equation A1.10 for the TE and TM modes, i n each of the three regions, by s u b s t i t u t i n g E x ( y ) or H x ( y ) , re s p e c t i v e l y , for 4>(y) as I C 1 1 e x p [ - ( p 1 2 - n 1 2 k Q 2 ) 1 / 2 y ] 0 < y < » A l . l l a C 1 2 e x p [ i ( n 2 2 k o 2 - P i 2 ) 1 / 2 y ] + C 2 2 e x p [ - i ( n 2 2 k o 2 - P i 2 ) 1 / 2 y ] A l . l l b - t < y < 0 C 2 3exp [ ( p ± 2 - n 3 2 k Q 2 ) 1 / 2 ( y + t ) ] — < y < - t . A l . l l c Then using r e l a t i o n s A1.6 for TE modes and A1.8 for TM modes and the remaining boundary conditions we a r r i v e at the eigenvalue equations for TE modes tan(ht) - h(p + q)/(h 2 - pq) A1.12 and f o r TM modes tan(ht) - h(p' + q')/(h 2 - p'q') A1.13 where h = ( n 2 2 k Q 2 - P l 2 ) 1 / 2 , q = ( P i 2 - n f * ? * ' * , P « ( P i 2 - n 3 2 k o 2 ) l / 2 , q« - ( n 2 2 / n i 2 ) q , and p' - ( n 2 2 / n 3 2 ) p . Using equations A1.12 and A1.13 we can f i n d the values of p for each of the 144 modes supported by the waveguide. Figure A1.6 shows typical f i e l d distributions for the Oth and 4th order modes of an asymmetric slab waveguide. Al.2.2 The Exponential Waveguide The solutions to the scalar wave equations A1.3 and Al.4 for a waveguide with an exponential refractive Index profile were f i r s t presented by Conwell in 1973 [Conwell 1973] to describe the modes of waveguides formed by diffusion. Figure A1.7 shows the refractive index distribution of an exponentially tapered waveguide covered by a medium with a constant refrac-tive index. It is not unreasonable to assume that diffusion would lead to impurity concentration profiles other than the complementary error function or Gaussian profiles as there may be more than one diffusion mechanism at work, the diffusion profile may be at an intermediate state between the two idealized profiles, etc. Furthermore the change in the refractive index, from the undoped value, need not be linearly proportional to the dopant concentration as has been determined for the change in the ordinary refractive index of Ti indiffused LiNb03 [Minakata et a l . 1978]. Even without justifying their use as tools for analyzing the modes of diffused waveguides the solutions are valuable as they provide a means of checking the accuracy of other techniques designed for the analysis of waveguides with arbitrary refractive index profiles [Marcuse 1973; Tien et a l . 1974; Hocker and Burns 1975]. In 1974 Carruthers, Kaminow, and Stulz showed that for waveguides formed by the out-diffusion of L i 2 0 from LiNb0 3 and LiTa0 3 a good f i t between the refractive index distribution of the out-diffused region (as measured using 145 Figure A1.6 (a) The r e f r a c t i v e Index d i s t r i b u t i o n of an asymmetric slab Figure A1.6 C ^ ™ ^ f ± M d i s t r l b u t i o n B of (b) the 0 t h order mode and (c) the 4 t h order mode. 146 Figure A1.7 The r e f r a c t i v e index d i s t r i b u t i o n of an exponentially tapered waveguide covered by a medium with a constant r e f r a c t i v e index. 147 an interference microscope) and an exponential r e f r a c t i v e index p r o f i l e could be obtained [Carruthers, Kaminow, and Stulz 1974]. That same year Schmidt and Kaminow estimated the change i n the surface r e f r a c t i v e index and the d i f f u s i o n depth of waveguides, formed by the d i f f u s i o n of various t r a n s i t i o n metals into LiNb03, by f i t t i n g the measured mode parameters to those predicted for the modes of waveguides with exponential r e f r a c t i v e index p r o f i l e s [Schmidt and Kaminow 1974]. In 1975 Hocker and Burns generated a set of un i v e r s a l curves for the exponential waveguide using t h e i r approximate method [Hocker and Burns 1975]. Later Noda et a l . used the solutions to predict the behavior of strip-loaded diffused channel waveguides [Noda et a l . 1978]. Similar work was done by Ahmed and Young i n 1983 i n which a loading s t r i p with a variable r e f r a c t i v e index was used to tune an integrated Mach-Zehnder modulator [Ahmed and Young 1983]. Assuming a r e f r a c t i v e index p r o f i l e of the form n(y) = + Anexp(-|y|/d), A1.14 where An i s the difference between the surface and the bulk r e f r a c t i v e i n d i c e s , i f An « n f e then we can write the expression for the r e l a t i v e p e r m i t t i v i t y p r o f i l e as e(y) - n 2 ( y ) = i ^ 2 + 2n bAnexp(-|y|/d) Al.15 where the term An 2exp(-2|y|/d) has been ignored since i t s contribution i s extremely small. Inserting equation Al.15 i n t o equation A1.3 and making the s u b s t i t u t i o n of variables u » exp(-|y|/2d) we can rewrite equation A1.3 as 148 ir^a E /ou 2 + uBE x/5u + ( B 2 ^ - q 2 ) E x » 0. A1.16 The general s o l u t i o n to equation A1.16 i s E x ( y ) = C ^ I g C y ) ] + C 2 Y q [ q ( y ) ] A1.17 where J^[g(y)] i s a Bessel function of the f i r s t kind, Y^[g(y)] i s a Bessel function of the second kind, q • 2d(p^ 2 - n ^ 2 ^ 2 ) 1 ' 2 , and g(y) - Bu - 2 d k ) ( 2 i i b A n ) 1 / 2 exp(-|y|/2d). Since one of our boundary conditions i s that the f i e l d must be contained i n the region of the waveguide we can drop the term in v o l v i n g the Bessel function of the second kind by s e t t i n g the c o e f f i c i e n t equal to zero as a l l Bessel functions of the second kind w i l l be I n f i n i t e when |y| • ». Thus we are l e f t with the so l u t i o n E - AJ [ g(y)]. A1.18 x q Given that the r e f r a c t i v e index of the covering medium i s constant and i s lower than that of the surface of the diffused waveguide we can use equation A l . l O to describe the f i e l d , of a bound mode, i n the covering medium as E (y) - Bexp[-(p 2 - n 2 k 2 ) 1 / 2 y ) ] . A1.19 x I / O Applying the boundary conditions of tangential f i e l d c o ntinuity at the in t e r f a c e between the covering medium and the di f f u s e d region and using r e l a t i o n A1.6 we can derive the eigenvalue equation for the TE modes of the dif f u s e d waveguide (Jq-ll8(°)] " Vl [ 8 (° ) 1 ) / Jq [ 8 ( 0 ) 1 ' -nPi2-n22%2)l/2/ko{2nbLn)l/2. A1.20 In order to derive an eigenvalue equation f o r the TM modes i n the dif f u s e d waveguide the approximations are made that n^ 2 » 2n^An and d » X /2rtn. , both of which are generally true for d i f f u s e d waveguides. Thus we O D can neglect the term (-Q lo^tt? ( y ) ^ y ) < Q y) i n equation Al.4 and write i t 149 as 5 2H /By2 + (e(y)k 2 - p 2 )H = 0 A1.21 x x w ' o i x which has as i t s s o l u t i o n H (y) - AJ [g(y>] A1.22 x <4 where we have again dropped the term inv o l v i n g the Bessel function of the second kind. Again we assume that the r e f r a c t i v e index of the covering medium i s constant and i s lower than that of the surface of the diffused waveguide and we use equation A L I O to describe the f i e l d , of a bound mode, i n the covering medium as H x(y) = B e x p [ - ( P i 2 - n 2 2 k o 2 ) l / 2 y ) ] . A1.23 Applying the boundary conditions and using r e l a t i o n A1.8 we a r r i v e at the eigenvalue equation for the TM modes of the diffused waveguide J ^ I g C O ) ] - J ^ I g ^ ) ] _ - 2 ( 1 ^ + A n ) 2 ( P l 2 - n 2 2 k Q 2 ) 1 / 2 J q [ 8 ( 0 ) ] n f 2 k o ( 2 n b A n ) l / 2 A1.24 These equations can be used to f i n d p^ for the bound modes of such a st r u c t u r e . Figure A1.8 shows t y p i c a l f i e l d d i s t r i b u t i o n s for the 0th and 4th order modes r e s p e c t i v e l y . A1.3 Channel Waveguides When speaking of channel waveguides one i s r e f e r r i n g to waveguides formed by imbedding a high r e f r a c t i v e index rectangular rod into materials of lower r e f r a c t i v e index or by d i f f u s i n g impurities i n t o a substrate r e s u l t i n g i n a region of high r e f r a c t i v e index ( i . e . T i d i f f u s i o n Into LiNb0 3). Figure A1.9 6hows a rectangular rod of r e f r a c t i v e index n 2 embedded i n a substrate 150 Figure Al . B (a) The refractive index distribution and <b> the 0<» and (c) Figure ai.o ^ o f m e x p 0 „ e n t i a l waveguide. a i r Figure A1.9 A rectangular rod embedded i n a substrate and covered by a i r . 1 5 2 of r e f r a c t i v e index n 3 and covered by a i r , n^. The pred i c t i o n that waveguides s i m i l a r to t h i s one would be the basic b u i l d i n g blocks of integrated optics provided M a r c a t i l i with the impetus for deriving a set of eigenvalue equations to describe the behavior of the modes of propagation of l i g h t confined to such structures [ M a r c a t i l i 1969]. We w i l l present the theory and r e s u l t s a r r i v e d at by M a r c a t i l i . He found that by means of a few si m p l i f y i n g assumptions a set of eigenvalue equations could be derived describing the behavior of the modes of the waveguide structure the cross section of which i s shown i n figure A l . l O . The primary assumption i s that the bound modes are f a r from c u t o f f . Under t h i s assumption the o p t i c a l f i e l d s are well confined to the core (region 1) of the structure and i t i s therefore possible to neglect those portions of the f i e l d which extend into the regions which have been shaded i n figure A l . l O . Mathematically t h i s assumption implies that p, * n, k A1.25 i 1 o and since n 2k 2 = p 2 + p 2 + 2 A 1 . 2 6 j o *xj *yj where j « 1-5 (see figu r e Al.lO) that P i » Pxl o r p y l A 1 , 2 7 where p ^ and p are the x and y propagation constants i n the core. In planar waveguide structures we can always resolve the bound wave into TE and TM modes, however, i n channel waveguides the modes are hybrid with y both E and H f i e l d components i n a l l d i r e c t i o n s . M a r c a t i l i defined an E p q mode as a mode that has i t s E f i e l d predominantly polarized p a r a l l e l to the y axis In figu r e A l . l O . S i m i l a r l y an E X mode has i t s e l e c t r i c f i e l d pq predominantly 153 Figure A L I O The cross section of the waveguide used by M a r c a t i l i . 154 polarized p a r a l l e l to the x a x i s . The subscripts p and q indicate the number of extrema i n the f i e l d d i s t r i b u t i o n i n the x and y d i r e c t i o n s respectively ( i n t h i s thesis the subscripts m and n are used, instead, i n d i c a t i n g the number of nodes i n the f i e l d d i s t r i b u t i o n i n each of the d i r e c t i o n s which i s more consistent with the convention adopted for TE and TM modes). To describe E y modes H . i s set equal to 0 and Maxwell's equations are mn y j used to derive the following r e l a t i o n s : H J = - ( i / p , )o 2H ,/oxoy, A1.28a z j r i ' x j E . = - ( i / u > E n J 2p,)& 2H 7ox&y, A1.28b x j o j r i x j E . = [(n 2 k 2 - p .2)/coe n 2 p , ]H A1.28c yj j o * y j o j r i J x j ' E . = (i/coe n 2)BH Jby, A1.28d z j v o j x j where M 1 c o s ( p x l x + a ) c o s ( p y l y + b) for j = 1 A1.28e M 2 c o s ( p x l x + a ) e x p ( - i p y 2 y ) for j - 2 A1.28f H x j = \ M 3 C o s ( p y l y + b ) e x P ( _ 1 P x 3 x ) for j - 3 A1.28g M,cos(p ,x + a)exp(ip .y) for j - 4 A1.28h 4 r x l ry4' M 5 c o s ( p y l y + b ) e x p ( i p x 5 x ) for j - 5 A1.28I i n which m u l t i p l i c a t i o n of each term by exp(icot - ip^z) i s implied, the constants a and b locate the f i e l d maxima i n the x and y d i r e c t i o n s r e s p e c t i v e l y , and the constants M^  give the f i e l d amplitudes (these equations are taken from Hunsperger [Hunsperger 1984]). Also equations A1.28e-i assume that A1.29a P x l " Px2 " Px4 and 155 Pyl = Py3 = Py5- A 1 ' 2 9 b F i n a l l y M a r c a t i l i assumed that the r e f r a c t i v e index of the core was only s l i g h t l y larger than that of the surrounding regions. This assumption implies that i n e q u a l i t y A1.27 holds i n a l l regions of the waveguiding structure ( i . e . p. » p . or p . ) • It follows, a f t e r inspection of equations A1.23b, A1.28d and A1.28e-i, that the magnitude of the z component of the E f i e l d w i l l be much greater than the x component. Therefore the x component i s neglected and the z component i s matched at the boundaries. By matching the remaining tangential f i e l d components at the boundaries a set of eigenvalue equations may be obtained that w i l l y i e l d the values of p y ^ and P xi« For p y ^ we obtain [Marcuse 197A] and f o r p x ^ t a n ( p x l t x ) - p x l ( p x 3 + P x 5 ) / ( P x l 2 - P x 3 P x 5 ) . A1.31 Equations A1.30 and A1.31 ( a f t e r making some minor substitutions) are i d e n t i c a l to equations A1.13 and A1.12 re s p e c t i v e l y . The r e s u l t being that y the properties of well guided E modes may be studied by replacing the pq structure depicted i n figu r e Al.lO with the two planar, slab waveguide, structures of figures A l . l l a and b. The value of p A may be determined by fi n d i n g the value of h (as i n equations A1.12 and A1.13) for the TM modes of the structure of figu r e A l . l l a and the value of h for the TE modes of the structure of figu r e A l . l l b . x An equivalent set of eigenvalue equations may be obtained for the E ^ 156 n n ( a ) y n. t x (b) n Figure A l . l l The equivalent structures for f i n d i n g (a) P y l and (b) p x l -157 nodes by following the same reasoning. However, i t i s assumed that the x component of the E f i e l d i s dominant and H . i s set equal to 0. The r e s u l t i n g equation for c a l c u l a t i n g p y ^ i s t a n ( p y l t y ) = P y l ( p y 2 + P y 4 ) / ( P y l 2 " P y 2 P y 4 ) A1.32 and for c a l c u l a t i n g p^^ i s , n l 2 P x l ( n 3 2 p x 3 * n5 2 px5> „ tan(p . t ) . A1.33 X < n 3 2 n 5 2 p x l 2 " n l 2 p 3 p x 5 > y y Figure A1.12 shows the f i e l d d i s t r i b u t i o n for a t y p i c a l E QQ mode (an E ^ mode following M a r c a t i l i ' s notation). One of the main r e s u l t s of M a r c a t i l i ' s solutions for well guided modes i n channel waveguides was that the e l e c t r i c and magnetic f i e l d d i s t r i b u t i o n s can be treated as separable functions of x and y. The re s u l t s of M a r c a t i l i ' s paper have been used extensively since they f i r s t appeared. Among other things they have been used to predict the coupling e f f i c i e n c i e s of tapered horns [Nelson 1975; Milton and Burns 1977], to predict the waveguiding properties of strip-loaded waveguides [Futura, Noda, and Ihaya 1974], to study mode dispersion i n diffused channel waveguides [Hocker and Burns 1977], and to analyze the behavior of strip-loaded d i f f u s e d channel waveguides [Noda et a l . 1978]. Figure A1.12 The f i e l d distribution of an E y 0 0 159 Appendix 2 The Integrated Mach-Zehnder Modulator A2.1 Introduction The theory of the IMZ modulator i s reviewed. A mathematical development of the v o l t a g e - i n / o p t i c a l - i n t e n s i t y - o u t transfer function i s presented. A discussion of the design considerations as well as t h e o r e t i c a l and experimental j u s t i f i c a t i o n s for assumptions made during the mathematical development i s included. A2.2 The Integrated Mach-Zehnder Modulator The IMZ i s an e l e c t r o o p t i c modulator. Other e l e c t r o o p t i c modulators include d i r e c t i o n a l couplers [Papuchon et a l . 1975; Cross and Schmidt 1979], the BOA [Papuchon, Roy, and Ostrowski 1977], and the p o l a r i z a t i o n converter [Alferness 1980]. The IMZ modulator i s shown i n figure A2.1. The IMZ i s a beam s p l i t t i n g modulator. The beam i s s p i l t by equal d i v i s i o n of the input power between two arms of a Y-branch. The l i g h t then propagates down the two branches and i s recombined at a second Y-branch. The modulation of the output i n t e n s i t y i s achieved by c o n t r o l l i n g the propagation constants of the l i g h t i n one or both of the branches. IMZ modulators are usually made by d i f f u s i n g appropriate materials into e l e c t r o o p t i c substrates; e.g. Cd into ZnSe [Martin 1975] or T i into LiNb0 3 [Leonberger 1980]. Electrodes are then deposited beside and/or above [Alferness 1982] the waveguides as shown i n figures A2.2a-c. By applying a p o t e n t i a l d i f f e r e n c e between the electrodes an e l e c t r i c f i e l d i s established i n the c r y s t a l ( substrate). The e l e c t r i c f i e l d induces a change i n the r e f r a c t i v e index of the c r y s t a l v i a the e l e c t r o o p t i c e f f e c t [Nye 1979, 160 P 2 = 0 - r ) R n H i g h r e f r a c t i v e i n d e x r e g i o n Low r e f r a c t i v e r e g i o n _^ D i r e c t i o n o f p r o p a g a t i o n Figure A2.1 The integrated Mach-Zehnder modulator (IMZ). The input power, P<„, i s divided between the two branches of the device and i s i n " recombined at the output. Figure A2.2 IMZs with electrodes (a) beside, (b) above and beside, an (c) above the waveguides of an IMZ. 162 Chapter 13]. The change i n the e f f e c t i v e mode r e f r a c t i v e index, A n e ^ , of the waveguide, for a p a r t i c u l a r mode, can then be expressed as a function of the applied voltage, V, as A n g f f ( V ) * (n 3r / 2)Vo/g A2.1 where g i s the gap width between the electrodes, n i s the r e f r a c t i v e index, r i s the relevant e l e c t r o o p t i c c o e f f i c i e n t , and o i s the f i e l d overlap factor (a factor which r e f l e c t s the fact that neither the e l e c t r i c f i e l d nor the o p t i c a l f i e l d i s uniform i n the overlap region). It follows that the change i n the propagation constant as a function of V, Ap^(V), i n each of the branches i s given by A P l ( V ) = k A n e f f ( V ) = (7tn 3 r A 0)Vo/g A2.2 where k Q i s the free space propagation constant (k^ • 2 n A 0 ) « The half-wave voltage of an IMZ, , i s the voltage that must be applied to the device to achieve a change of itrad between the outputs of the two branches. i s calculated by using the formula A0 - TtV/V A2.3 TC where A0 i s the r e l a t i v e phase change caused by the applied voltage, V. For the device configuration shown i n figu r e A2.2a a r e l a t i v e phase change of icrad between the branches i s achieved i f the phase i n one branch i s enhanced by ic/2rad and retarded by Tc/2rad i n the other. The change i n phase i n one of the arms, A0 , i s given by fl*. Ill A0 =Ap, (V)L A2.4 arm i where L i s the length of the modulated region of the branch. When a voltage i s applied to the electrodes the e l e c t r i c f i e l d induced i n the c r y s t a l i s i n opposite d i r e c t i o n s i n each of the branches thus giving r i s e to equal and 163 opposite changes i n the mode propagation constants. Therefore A 0 i s equivalent to 2 A 0 a r m * Using equation A2.3 becomes V = TtV/(2Ap,(V)L) - X g/(2n 3roL). A2 .5 it i o The voltage-In/optical-intensity-out transfer function (V. /I ) of the i n out IMZ modulator i s a function of the r e l a t i v e phase change and therefore a function of the applied voltage. The i n t e n s i t y at a p a r t i c u l a r point i n the waveguide's cross section i s equivalent to the time average of the magnitude of the Poynting vector at that point T/2 I(x,y) = (1/T) / |S(x,y)|dt - (p / 2 L O U )E (x,y) • E.(x,y)* -T/2 l o t t = ( P i/2u)u o)|E t(x,y) 2| A2.6 where S i s the Poynting vector and E t(x,y) i s the time independent transverse 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 ( i . e . E(x,y,z,t) » (E t(x,y) + E z ( x , y ) n z ) e x p ( i t o t - i p ^ z ) ) . The power flow i n a p a r t i c u l a r mode of the waveguide i s given by CO CO OO OO ^ P ± - / / I i(x,y)dxdy = ( P i / 2 u ) L i o ) | a ± | 2 / / e t i ( x , y ) • e t i ( x , y ) dxdy CO CD = (p /2u>u )|a | 2 / / e (x,y)*dxdy A2.7 —CD -CD where | | i s the mode's peak magnitude and e t i ( x , y ) i s the transverse 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 such that E t i ( x , y ) = l a j e ^ x . y ) and the subscript i re f e r s to the i t h mode. Throughout the rest of th i s section only the f i e l d d i s t r i b u t i o n of the lowest order mode w i l l be considered, 164 therefore the subscript i w i l l be dropped from the f i e l d d i s t r i b u t i o n term and [a^| w i l l be written as a^ ( i . e . la^Je (x,y) => a i e t ( x , y ) ) . After the o p t i c a l power has been evenly divided by the beam s p l i t t i n g Y-branch the l i g h t propagates down the p a r a l l e l waveguide sections, where the voltage dependent phase difference i s induced, u n t i l i t reaches the recombining Y-branch. Ideall y the recombining Y-branch should be designed i n 6uch a way as to radiate a l l but the lowest order transverse mode which i t should transmit a d i a b a t i c a l l y ( i . e . without coupling to or from other modes and without losses due to radiation) [Ranganath and Wang 1977a]. Upon entering the recombining Y-branch (while the waveguides are s t i l l many decay constants of the evanescent f i e l d apart) the perturbation of the 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 i n either of the branches due to the presence of the other branch i s n e g l i g i b l e and the t o t a l 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 may be viewed as being the sum of the d i s t r i b u t i o n s of the orthogonal l o c a l normal modes of the two branches (fig u r e A2.3). Assuming that each branch i s a mono-mode x v waveguide (supporting either an E QQ or E QQ mode [see Section A1.3]) we may write the combined transverse f i e l d d i s t r i b u t i o n i n the two branches as the sum of an even and an odd transverse l o c a l normal mode, of the two waveguide structure, such that a e * t e < X , y ) " ( 1 / 2 ) I V t l ( x , y ) + a 0 2 * t 2 ( x ' y ) + a 0 1 * t l ( ~ X , y ) + a 0 2 ® t 2 ( " X , y ) 1 A 2 * 8 a and 165 Figure A2.3 E(x) and n(x) along a l i n e perpendicular to the d i r e c t i o n of propagation i n the recombining Y-branch of an IMZ at a f i x e d moment i n time. An a r b i t r a r y r e l a t i v e phase d i f f e r e n c e , between the two branches, has been assumed. a o e t o ( x , y ) - (1/2) [ a ^ e ^ (x,y) + a 0 2 e t 2 ( x , y ) -a 0 1 * t l ( ~ X , y ^ ~ a 0 2 * t 2 ( - x , y ^ A 2 , 8 b where the subscripts e and o stand for the even and the odd d i s t r i b u t i o n s r e s p e c t i v e l y and the subscripts 1 and 2 r e f e r to the branch. Assuming that the two waveguides are i d e n t i c a l and that each has a r e f r a c t i v e index p r o f i l e that i s symmetric about i t s center i n the x d i r e c t i o n , for a l l values of y, we may write e t l ( x , y ) = e ^ x - x ^ y ) A2.9a and e t 2 ( x , y ) = e t(x-rx 1,y)exp(-iA<))) A2.9b where e t(x,y) i s the transverse 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 of an equivalent waveguide centered at x = 0 and the branch waveguides are centered at ± x^. One of the advantages of describing the modes of the waveguides i n terms of x y E and E modes i s that the f i e l d components of these modes are separable mn mn functions of x and y [see Section A1.3]. In figure A2.A we i l l u s t r a t e the x •*• dependence of e t ( x , y ) , e t l ( x , y ) , and e t 2 ( x , y ) . The values of and a^ c a n be calculated from the condition of power conservation; P. « rP. and P. - ( l - r ) P . ( f i g u r e A2.1). If the power i s 1 In £• i n evenly divided between the branches ( i . e . r • 1/2) then a Q 1 » a^ 2 • a Q i n / 2 1 / 2 . Using equations A2.9a and b equations A2.8a and b become V t e ( x ' y ) " ( l / 2 ) ( a 0 i n / 2 1 / 2 ) [ l + exp(-iA$)] * [ e t ( x - x 1 > y ) + e t ( x + x 1 > y ) ] A2.10a 167 Figure A2.4 The x dependence of e t ( x , y ) , e t l ( x , y ) , and e t 2 ( x , y ) A4> • Orad. 168 and a o e t o ( x , y ) = ( l / 2 ) ( a ( ) i n / 2 1 / 2 )[1 - exp(-iAO)] * [e t(x-x 1,y) - e t ( x + x 1 , y ) ] . A2.10b Using equations A2.7 and A2.10a and bearing i n mind that only the lowest order mode contributes to the output power, ^ o u t ( x » y ^ > ^ o u t ^ X ' ^ * S £ * v e n by P o u t ( x , y ) = ( p 0 / 2 u ) t i o ) ( a 0 i n 2 / 4 ) [ l + cos(A$)] x 00 GO / / [ e t ( x - x 1 , y ) 2 + e t(x-x 1,y)e t(x+x 1,y) + • ••OP OD e j ;(x+x 1 ,y)e t(x-x 1 ,y) + e t (x-b^ ,y) 2 ]dxdy A2.11a or P o u t ( x , y ) = ( p 0 / 2 c o u o ) ( a 0 . n 2 / 2 ) [ l + cos(A$)] / / e t(x,y) 2dxdy —CD -CO OD CD - / / I o u t ( x , y ) d x d y . A2.11b Also using equation A2.6 we can ca l c u l a t e the input i n t e n s i t y , I ^ n ( x , y ) , as I l n ( x , y ) = < p 0 / 2 w u o ) ( a 0 i n ) 2 e t ( x , y ) 2 . A2.12 Combining equations A2.11b and A2.12 ( i . e . w r i t i n g I o u t - ( x » y ) = ( p 0 / 2 a ) u o ) ( a Q i n 2 ) [1 + cosA<J>,]et(x,y)2 ) leads to the standard form of the V. /I ^transfer function [Leonberger 19801 i n out 1 I = (I . /2)[1 + cos(A<t>)] - (I, /2)[1 + COS(TCV/V + $,)] A2.13 out In In TC I which i s often given i n the form [Becker 1984b, Ahmed and Young 1985] I - I , COS2(TCV/2V + 4>./2). A2.14 out i n TC i In equations A2.13 and A2.14 the i n c l u s i o n of the term, 4>A, r e f l e c t s the fact 169 that an a r b i t r a r y i n i t i a l phase difference i s to be expected due to the f a b r i c a t i o n tolerance being much larger than the e f f e c t i v e wavelength of the guided l i g h t . Both equations can also be written to express the output power, P Q u t » as a function of the applied voltage Pout = ( P i n / 2 ) [ 1 + c o s ( * v / v n A 2 ' 1 5 and P * P, C O S 2 ( T C V / 2 V +<t>,/2). A2.16 out i n v it Y i ' A2.3 Design Considerations In order for an actual IMZ modulator's V . /I transfer function to be i n out a reasonable approximation of equation A2.13 ce r t a i n design considerations must be addressed: 1. The waveguide should be mono-mode. 2. The input Y-branch should s p l i t the l i g h t evenly. 3. The output Y-branch should recombine the l i g h t evenly. 4. The Y-branches' transmissions should be large for the m • 0 mode. 5. The recombining Y-branch should t o t a l l y radiate the m •= 1 mode into the substrate. There are two reasons for making sure that the waveguides are mono-mode. Each of the reasons concerns the number of modes and i s not so concerned with the mode type since e i t h e r p o l a r i z a t i o n can be removed using a polarizer or be independently preserved using a b i r e f r i n g e n t o p t i c a l f i b e r at the output X V of the device. Figures A 2.5a and b show the E and E polarizations of the output of an IMZ with 2 8 V peak to peak applied to i t s electrodes (note that the E y p o l a r i z a t i o n does not go through a complete cycle) and figure A2.5c i s 170 Figure A2.5 The output s i g n a l of an IMZ with a t r i a n g l e wave applied to i t s electrodes, (a) The E x p o l a r i z a t i o n and (b) the E y p o l a r i z a t i o n . 171 Figure A2.5 (cont.)> (c) The output s i g n a l of E X + E y . the output of E X + E y . Assuming the waveguide supports more than one mode of either the E oe y E type each mode w i l l have i t s own propagation constant. Since the branches of the IMZ modulator are many thousands of e f f e c t i v e wavelengths long i t would not be possible to con t r o l t h e i r widths and thicknesses to the degree necessary to ensure a non-arbitrary i n t r i n s i c phase difference between the contributions to the transverse component of the output e l e c t r i c f i e l d from each of the branches. Furthermore the difference i n the branch lengths, A L D , would have to be co n t r o l l e d to within a small portion of one quarter of a the e f f e c t i v e wavelength of the confined mode with the highest propagation constant X o / ( 4 n e f f 0 ) » A L B A 2' 1 7 derived from TC/2 » PQALJ = ^ ^ e f f O ^ ^ B ^ o * ^ n e s e f a b r i c a t i o n constraints are c l e a r l y not achievable for a number of reasons such as current mask f a b r i c a t i o n and lithography techniques. The output power of such a multi-mode waveguide would be the sum of the powers i n each of the modes excited i n the output waveguide thus degrading the output s i g n a l . Assuming now that the waveguides support modes of either the E ^ or E y type odd and even modes w i l l be acted upon by the Y-branches i n mU d i f f e r e n t fashions. Since the d i v i s i o n and recombination of the modes i n the Y-branches are s i m i l a r problems they w i l l be discussed together. The Y-branch can be broken down in t o 3 separate sections; the input/output waveguide, the horn, and the output/input waveguides ( f i g u r e A2.6). The region i n which the input/output waveguides are close enough together for s i g n i f i c a n t coupling of the f i e l d s i n the two branches to occur i s also k input/output horn »|« output/input Figure A2.6 The Y-branch of an IMZ. The three regions of the Y-branch are the input/output waveguide, the horn, and the output/input waveguides. 174 referred to as the fork. It has already been pointed out that i d e a l l y the recombining Y-branch should transmit the lowest order mode a d i a b a t i c a l l y ( t h i s i s true for the beam s p l i t t i n g Y-branch as well) since It i s desirable that a confined mode that enters the narrow end w i l l propagate down the e n t i r e length without s i g n i f i c a n t r a d i a t i o n loss and without s i g n i f i c a n t coupling to other modes. This has been shown to be the case for horns [Winn and Harris 1975; Nelson 1975; Milton and Burns 1977] with l i n e a r , parabolic, and exponential tapers and with small taper angles and short lengths. Piecewise l i n e a r parabolic horns of both the d i v i d i n g and recombining types have been formed by T i i n d i f f u s i o n i n LiNb0 3 with expansion/contraction r a t i o s of 7.5:1 and single mode transmission e f f i c i e n c i e s of > 87% [Burns, Milton, and Lee 1977; Chen, Tangonan, and Lee 1977]. The horn i n the Y-branches of the IMZ modulator has an expansion/contraction r a t i o of 2:1 and taper angles comparable to those of the i n i t i a l branch angles of the experimental horns ~ 1 ° . T h e o r e t i c a l l y the amount of intermodal coupling increases with Increased horn width and v i r t u a l l y 100% coupling for the lowest order mode across such a horn for taper angles of 1° or less i s predicted. Working IMZ modulators have been reported with branch angles of 2° [Leonberger, Woodward, and Spears 1979; Leonberger 1980] and with a t o t a l i n s e r t i o n loss of ~ldB more than that of a st r a i g h t waveguide. S i m i l a r l y , when the Y-branch i s being used to recombine modes i t i s desirable to have the mode enter the wide end of the horn and exit from the narrow end without s i g n i f i c a n t coupling to other modes. However, i t w i l l be shown that for the IMZ modulator to function properly i t i s necessary for modes with m > 0 to be completely l o s t to r a d i a t i o n modes. This i s due to 175 what one could c a l l the "mode c o n v e r t i n g / s p l i t t i n g " behavior of the Y-branch. It has been shown [Burns and Milton 1975] that separating waveguides can behave either as power di v i d e r s (beam s p l i t t e r s ) or as mode s p l i t t e r s . A power d i v i d e r divides the power of a given input mode evenly between the two branches of the IMZ whereas a mode s p l i t t e r channels the power of a p a r t i c u l a r mode into one of the branches only. When i t i s desired that the forking region act as a power div i d e r i t i s necessary for the branching angle to be large (giving r i s e to greater r a d i a t i o n losses) or for the branch to be highly symmetric. When i t i s desired to have the fork behave as a mode s p l i t t e r the branching angle must be small, allowing for more coupling between the symmetric and asymmetric modes of the structure, and the branch must be asymmetrical. Optical waveguide branches, made by i n d i f f u s i o n of T i i n LiNb0 3, have been studied [Burns et a l . 1980] i n which the branch asymmetry was Induced geometrically (as opposed to r e f r a c t i v e index induced asymmetry) and compared to high symmetry devices. It was found that the power t r a n s f e r , P ,/(P ,+P ^ ~ ) , f o r the asymmetric structure (w. = 2um ou t l o u t l out2 1 and w2 = 3um) i s r e l a t i v e l y low .1 - .25 at the output of the narrow branch, whereas i t i6 r e l a t i v e l y high .42 - .5 for the symmetric structures (w^ = w 2). It was also shown that the transmission loss i s lower and the power t r a n s f e r i s higher for wider waveguides, w • 4.8um, than i t i s for narrower waveguides, w » 3.0um, i n the symmetric branches. Ranganath and Wang used the symmetry of the Y-branch to argue that the input/output waveguide should be mono-mode [Ranganath and Wang 1977a]. It i s proposed that E ^ and E Q input modes are converted to lower/higher order modes of the same kind i n the output waveguides/waveguide of the beam splitting/recombining Y-branch. In the beam s p l i t t i n g Y-branch the modes with even values of m are s p l i t so that the mode number i n one of the output waveguides far from the fork, m a r m » i s given by m « in, 12 A2.18a arm i and for odd values of m by m = (m - l ) / 2 A2.18b arm i where m^  i s the l a t e r a l mode number of the input mode. Figures A2.7a through d show the mode converting behavior of the beam s p l i t t i n g fork for m^  = 0 through 3 r e s p e c t i v e l y . The serious e f f e c t that such a s i t u a t i o n could have on the i n t e n s i t y d i s t r i b u t i o n between the two branches i s obvious since far from the fork the i n t e n s i t y d i s t r i b u t i o n In each branch w i l l be the r e s u l t of interference between the contributions made by each of the input modes. Figures A2.8a and b depict the cases i n which the lowest order modes of the two waveguides recombine with the outputs of the two branches having phase differences of 0 and urad r e s p e c t i v e l y . In the case that the phase d i f f e r e n c e i s Orad they couple into the m " 0 mode of the output J r out waveguide, however, i f the phase differ e n c e i s urad they couple into the m = 1 mode. From the preceding discussion i t follows that the output out waveguide should be mono-mode so that any power that i s coupled into the m o u t • 1 mode of the horn w i l l be l o s t to r a d i a t i o n modes when the horn width i s too narrow to support such a mode. If t h i s i s not the case then the output of the IMZ modulator w i l l be the s p a t i a l interference of the two (or more) 177 input (b) output Figure A2.7 The mode converting behaviour of the beam splitting Y-branch of an IMZ for (a) the m - 0 and (b) the m± - 1 modes. 178 o u t p u t ( c ) o u t p u t (a) Fieure A2.7 (cont.) The mode converting behaviour of the beam splitting Figure A2 Q f ^ ^ f n ^ m ± m 2 a n d ( d ) t h e m ± . 3 modes 179 Figure A2.8 The mode converting behaviour of the recombining Y-branch of an IMZ for the m a r m " 0 modes of the Input waveguides with phase differences between the modes in the two arms of (a) 0 and (b) TI radians. 180 modes. Figures A2.9a and b show the output s i g n a l s , for the E p o l a r i z a t i o n , f o r a multi-mode and a mono-mode IMZ modulator r e s p e c t i v e l y . Assuming that the waveguides are mono-mode and that the m • 1 mode i s radiated by the recombining horn we w i l l show that i n th i s i d e a l i z e d case the odd and the even modes remain uncoupled as they propagate down the Y-branch to the output waveguide. We do this using a small step approximation to the p e r f e c t l y symmetric Y-branch and consider the coupling of l o c a l normal modes across the step [Milton and Burns 1979] (figure A2.10). It can be shown that the coupling c o e f f i c i e n t between modes on eit h e r side of the step i s [Milton and Burns 1977] O D O O J / [<E i 0 * H *) + (E * x 1 )j . ^ d x d y c = A2.19 CO CD CO OD 1 3 2[ / / (E x H ) • n dxdy / / (E * H )• n d x d y ] 1 / 2 — Q O -*EO - 4 0 — C D *J *^  where the subscripts I and j indicate the mode and 0 and 1 refer to the side of the step. It can be further shown that the orthogonality r e l a t i o n s h i p for modes across a small step i s given by [Milton and Burns 1977] ( P 1 0 - P J J . ) / / K E I 0 * V * + X " i O ) ] - \ d X d y " •J - co —oo J J OO 00 ^ k o ' ' ( n 0 2 _ n l 2 ) ( ^ 1 l • \ o ) d x d y * A 2 , 2 ° m 111 *J If the r e f r a c t i v e index d i s t r i b u t i o n s n Q and n^ are assumed to be r e a l , even functions of x then n^ 2 - n^ 2 Is also a r e a l , even function of x. It follows * > that i f E J J • E^Q i s also an even function of x that the integration of the right-hand side of equation A2.20 over a l l x has a f i n i t e s olution and that i f i t i s an odd function of x that i n t e g r a t i o n over x i s zero. From 181 183 this symmetry argument we see that even and odd modes of a perfectly symmetric Y-branch are orthogonal and i t follows that any arbitrary f i e l d distribution may be expressed as the sum of even and odd modes even at step boundaries. Furthermore using equation A2.20 to substitute into A2.19 we see that the coupling coefficient, c^j» * s zero between even and odd modes. y Figures A2.11a and b show the E polarization of the output of an IMZ with the light confined to the waveguiding region and with the light being radiated into the substrate respectively. If the Y-branches deviate from being perfectly symmetrical the output w i l l be degraded. This is the result of unequal coupling of the fields into each of the branches and then the unequal coupling of the f i e l d in the branches into the m = 0 mode of the output waveguide. The ratio of the peak to peak output intensity deviation to the maximum output intensity obtainable i s referred to as the extinction ratio. It i s usually given in percent or dB. It i s a measure of how close to the ideal IMZ modulator's operation a particular device's operation comes. Extinction ratios, for devices made by Ti diffusion into LiNb0 3, of 98% (17dB) have been reported [Leonberger, Woodward, and Spears 1979] and even some in excess of 20dB (99%) [Becker y 1984a]. Figure A2.12 shows the output signal for the E' polarization of a device made during this work. It has an extinction ratio of ~98%, an Intrinsic phase of ~65°, and a of 24V. 184 (a) O) Figure A2.ll The Eypolari«?ation of the output of an IMZ for (a) the case i n which the light i s confined to the output waveguide and (b ) the case In which the light is radiated into the bulk of the crystal. 185 Figure A2.12 The output signal of the polarization of an IMZ made during this work. The device has an extinction ratio of ~98%, an Intrinsic phase of ~ 6 5 Z , and a of 24V 186 Appendix 3 A3.1 Introduction The wave equations f o r the E and H f i e l d s of an electromagnetic wave propagating i n an anisotropic medium, where the f i e l d vector i s p a r a l l e l to one of the p r i n i c p a l axes, are derived. The eigenvalue equations for TE and TM modes of an asymmetric slab waveguide with a well oriented anisotropic substrate are presented. A discussion of the choice of the f i l m thickness used i n the example of an immersion device with an asymmetric slab waveguide structure [Section 2.3.1] i s included. The wave equations for the E and H f i e l d s of an electromagnetic wave propagating i n a u n i a x i a l medium with a slowly varying p e r m i t t i v i t y d i s t r i b u t i o n , where the f i e l d vector i s p a r a l l e l to the optic axis, are derived. The eigenvalue equation for TE and TM modes of a strip-loaded d i f f u s e d waveguide with an exponential r e f r a c t i v e index p r o f i l e i s presented. A discussion of the choice of waveguide parameters used i n the example of an immersion device with a strip-loaded d i f f u s e d waveguide structure [Section 2.3.2] i s included. A3.2 The Asymmetric Slab Waveguide With an Anisotropic Substrate For a current and charge free d i e l e c t r i c Maxwell's equations can be written as V x i - - B ' , V x H = D', A3, la A3, lb 7 • D - 0, A3.1c and V • B «= 0 A3. Id where the prime indicates the p a r t i a l d e r i v a t i v e with respect to time. In the case that the medium of i n t e r e s t i s e l e c t r i c a l l y anisotropic we must remember that the p e r m i t t i v i t y , e, i s a tensor of rank 2; i . e . D » eE. A3.2 For cases i n which the p e r m i t t i v i t y tensor i s referred to the p r i n c i p a l axes of the medium e can be written as e l l 0 0 E X 0 0 0 e22 0 • E O 0 £ y 0 A3.3 0 0 e33 0 0 E Z leading to three separate equations f o r D x, D y, and T>^ D = E E E = n 2e E , X X O X x o x' E E E y o y n  l z E , y o y» and E E E = n 2 E E z o z z o z A3.4a A3.4b A3.4c (on the right-hand sides of equations A3.4a-c the s u b s t i t u t i o n of the square of the p r i n c i p a l r e f r a c t i v e index f or the r e l a t i v e p e r m i t t i v i t y has been made). Using equations A3.4a-c equations A3.la and A3.lb become A3. 5a A3.5b A3.5c A3.5d A3.5e dE z/dy - &E y/Bz - -lwu QH x, BE /Bz - BE /3x - -iuu H , x z r o y' BE /dx - BE /By • -iuu H , y x "o z BH /By - BH /Bz « iun 2 E E , z y x o x BH /Bz - BH /Bx « i o n 2 E E , x z y o y and BH /Bx - BH /By " ium 2e E y x z o z A3.5f 188 where both f i e l d s have been assumed to have a time dependence of the form e x p ( i u t ) . The derivations are considerably simpler i f i t i s assumed that for TE modes the e l e c t r i c f i e l d i s p a r a l l e l to one of the p r i n c i p a l axes of the medium, say the x a x i s . This assumption implies that = 0 and that a l l f i e l d component values are Independent of t h e i r p o s i t i o n along the x axis ( i . e . 3/3x = 0). These conditions reduce equations A3.5a-f to only three equations BE /dz = -itou H , A3.6a x o y BE /ay • iiou H , A3.6b X o z and aH /ay - BH /az = iwn 2e E . A3.6c z y x o x S i m i l a r l y f o r TM mode propagation we w i l l assume that the magnetic f i e l d i s p a r a l l e l to the medium's x a x i s . Thus E x = 0 and 8/Bx = 0. In t h i s case equations A3.5 a-f reduce to BE /ay - BE /Bz - -itou H , A3.7a z ' y *o x' BH /Bz • iam 2e E , A3.7b x y o y and BH /By " -Iwn 2e E . A3.7c X z o z Sub s t i t u t i o n of equations A3.6a and b into A3.6c and A3.7b and c int o A3.7a plus the further substitutions of B/Bz « - i p . and w2u e «= k 2 lead to the r 1 o o o wave equations f o r TE and TM modes in the region occupied by the anisotropic medium B 2E /By 2 + (n 2 k 2 - p 2 ) E - 0 A3.8a X X O i X and o 2H /oy 2 + (n 2 / n 2 ) ( n 2 k 2 - p 2 ) H =0. A3.8b x z y y o r i x Equation A3.8a shows that i n an anisotropic medium the wave equation for E x i s i d e n t i c a l to equation A1.9 provided that E x i s p a r a l l e l to one of the p r i n c i p a l axes. Equation A3.8b i s s l i g h t l y d i f f e r e n t from equation A1.9 i n that v has been modified by the i n c l u s i o n of the factor n 2 / n 2 . This z y r e f l e c t s the fac t that f o r TM modes, i n an anisotropic medium, the e l e c t r i c f i e l d vector i s not ( i n general) p a r a l l e l to the e l e c t r i c displacement vector. The general solutions to equations A3.8a and b are E •= C.exp[i(n 2 k 2 - p 2 ) 1 / 2 y ] + C 0exp[-i(n 2 k 2 - p 2 ) 1 / 2 y ] A3.9a x l r L x o r i ' 2 r x o 1 ' 1 and H x = C i e x p [ i ( n 2 / n y ) ( n y 2 k o 2 - p ^ / ^ y ] + C 2 e x p [ - i ( n 2 / n y ) ( n y 2 k o 2 - P i 2 ) 1 / 2 y ] A3.9b i n which the time dependence of the f i e l d s has been removed. Using equations A3.9a and A3.9b and following the method described i n Section Al.2.1 the eigenvalue equations f o r the TE and TM modes for the asymmetric slab waveguide depicted i n fig u r e A3.1 can be derived. They are tan(ht) - M p * ^ A3.10a h 2 - pq and h<P' A3.10b h 2 -r e s p e c t i v e l y , where g tan(ht) 2  p V h - (n 2 k 2 - p . 2 ) 1 / 2 , g o I y nx>ny;nz x u z Figure A3.1 An asymmetric slab waveguide with an anisotropic substrate. and q » (P 2 - n 2 k 2 ) 1 / 2 , l m o p = (p 2 - n 2 k 2)1/2 r v r i x o ' q« - (n 2/n 2 ) q g m p' = (n 2/ n n ) ( p 2 _ n 2 k 2)1/2 r g y z i y o i n which n i s the slab r e f r a c t i v e index, n i6 the superstrate r e f r a c t i v e g m r index, and t i s the slab thickness. In Section 2.3.1 an immersion type high voltage sensor with an asymmetric slab waveguide structure i s proposed. Its substrate i s z-cut LiNb0 3 and the slab i s ZnS. Z-cut LiNb0 3 was chosen as the substrate so that the e f f e c t being demonstrated would be largest for the T M Q mode of the s t r u c t u r e . The T M Q mode Is desirable because the cutoff thickness for a TM mode of an asymmetric waveguide i s greater than that for a corresponding TE mode. For the device proposed the value for the f i l m thickness t should be i n the range between the cutoff thicknesses for the T M Q and TM^ modes of the two branches. It should also be less than the cutoff thickness of the T E Q mode i n the region with n • 1.000. The cutoff thicknesses for the TE and T M m modes are given by t „ - 2 2 - + i tan-l MP±SLl 3.11a cutoff h h .? I r -pq and , . + 1 t a n - l Mp'+q') 3 > U b cutoff h h .o , , h^- p'q' r e s p e c t i v e l y where m i s the mode number. The cutoff condition for the T E Q mode i n the branch with n - 1.000 i s that p. - n k y i e l d i n g a cutoff 192 thickness of ~.27um. The cutoff condition f o r the T M Q and TM^ modes i n the same region i s • n e ^ 0 a n d t* i e c u t o ^ thicknesses are ~.18um and ~.57^m. The cutoff condition for the TMQ and T ^ modes i n the region with n m = 2.2 136 i s p. = n k and the cutoff thicknesses are ~.04um and ~.46um. Therefore our r i m o lower and upper bounds for the waveguide thickness are .18um and .27um re s p e c t i v e l y . We have chosen a value f o r t closer to the cutoff thickness for the T M Q mode because the e f f e c t we are attempting to show i s l a r g e r c l o s e r to c u t o f f . A3.3 The Strip-Loaded Diffused Waveguide With an Anisotropic Substrate Following the same procedure as i n section A3.2 Maxwell's equations are reduced to a set of three equations for TE modes: BE /Bz = -iiou H , A3.12a x r o y ' BE /By = IJJU H , A3.12b X o z and BH /By - BH /By - iwz E E A3. 12C z y x o x and three equations for TM modes: BE /By - BE /Bz = -ILOU H , A3.13a z ' y o x BH /Bz « iwE E E , A3.13b x y o y and BH /By » - I W E E E A3.13c X z o z where the s u b s t i t u t i o n of the square of the r e f r a c t i v e index for the r e l a t i v e p e r m i t t i v i t y has not yet been made. Substitution of equations A3.12a and b i n t o A3.12c and A3.13b and c i n t o A3.13a lead to the wave equations for the TE and TM modes i n the region occupied by the anisotropic medium B 2E /By2 + (E (y)k 2 - p 2) - o A3.14a X X O I \ 193 and d 2H /dy 2 - (Slog e (y)/oy)(dH / b y ) +' ( £ (y)/e (y))(£ ( y ) k 2 - p . )H = x 6 2 x z y v o A x 0.A3.14b Equation A3.14a i s i n exactly the same form as equation A1.3 (with the su b s t i t u t i o n of e x ( y ) f ° r n 2 ( y ) ) and shows that If the e l e c t r i c f i e l d vector i s p a r a l l e l to one of the p r i n c i p a l axes of an anisotropic medium then the wave equation for the e l e c t r i c f i e l d i s i d e n t i c a l to that of a wave i n an Is o t r o p i c medium with a r e f r a c t i v e index p r o f i l e equal to n x(y)» After making the approximation that the second term on the left-hand side of equation A3.14b can be neglected (see Section Al.2.2) we can rewrite equation A3.14b as In the case that the medium i s a u n i a x i a l c r y s t a l (such as LiNb0 3), with the magnetic f i e l d vector p a r a l l e l to the optic axis, equation A3.15 reduces to the form of equation A1.21, which i s the wave equation for the magnetic f i e l d of a wave i n an i s o t r o p i c medium with a r e f r a c t i v e index p r o f i l e equal to The s o l u t i o n to equation A3.14a for a waveguide with an exponentially tapered r e f r a c t i v e index p r o f i l e (provided that the e l e c t r i c f i e l d i s p a r a l l e l to a p r i n c i p a l axis) i s given by equation A1.18 and the solu t i o n to equation A3.15 (provided that the magnetic f i e l d i s p a r a l l e l to the optic axis of a u n i a x i a l medium) i s given by equation A1.22. Noda et a l . developed an eigenvalue equation for the waveguide depicted i n f i g u r e A3.2 [Noda et a l . 1978] & 2H x/dy 2 + (£ z(y)/£ y(y))(£ y(y)k o 2 - P i - 0. A3.15 n <y) (« n ( y ) ) . y z VilsCQ)] - J q + 1 [g(0)] Jq[g(0)] k (2n,An) o v b 2h S - tan(ht) I 1 + Stan(ht) J A3.16 where 1 9 4 y n n(y) a Figure A3.2 A strip-loaded d i f f u s e d waveguide with an exponential r e f r a c t i v e index p r o f i l e . 195 g(0) = 2 d k ) ( 2 n b A n ) 1 / 2 , q = 2 d ( P i 2 - n ^ 2 ) 1 ' 2 , h = ( n f 2 k Q 2 - P i 2 ) 1 / 2 , (p 2 - n 2 k 2 ) 1 / 2 / ( n 2 k 2 - p 2 ) 1 / 2 for TE modes 1 S O I O 1. s = (n 2/n 2 ) ( p 2 - n 2 k 2 ) 1 / 2 / ( n 2 k 2 - p , 2 ) 1 / 2 for TM modes, 1* A x d o I O 1 and 1 for TE modes ( n b + A n ) 2 / n f 2 for TM modes, where n^, n^, and n^ are the bulk, f i l m , and a i r r e f r a c t i v e i n d i c e s . An i s the diffe r e n c e between the surface and bulk r e f r a c t i v e indices and d i s the d i f f u s i o n depth. In t h e i r work Noda et a l . appear to have neglected the anisotropy of LiNb0 3 by using equation A3.16 to ca l c u l a t e the propagation constants (and f i e l d d i s t r i b u t i o n s ) of TM modes i n z-cut LiNb0 3. In order to do t h i s one must assume that equation A1.22 provides a so l u t i o n to equation A3.15 when n (z) * n ( y ) . We can i l l u s t r a t e our concern by inspecting the term y 2 ( e z ( y ) / e y ( y ) ) ( e y ( y ) k o 2 - p^ 2) of equation A3.15. F i r s t the term i s written as (E (y)k 2 + f(y ) p 2 - <£.(—)/e ( — ) ) p . 2 ) where z o x z y l f ( y ) - ( E z ( - ) / E y ( - > ) ) - ( E z ( y ) / E y ( y ) ) . For bound modes of t h i s waveguide [ E Z ( - 0 D ) / E Y ( - 0 0 ) J p ^ > n z b 2 k Q 2 or p ^ > n y b 2 k 0 2 . We can write f ( y ) i n the form 196 2n , An e n . n .An /An - n . 2 £ , <. zb z r zb yb y z yb i £ ( y ) [ yb yb yb y 2n .An e ~ ' y ' / d n ,n vAn /An - n 2 ^ zb z ^ zb yb y z yb j n . 2 n 2 + 2n .An yb yb yb y which leads to the i n e q u a l i t y f ( y ) p 2 > A(2n An e ' ' y l / d k 2 ) i zb z o where (An /An - n ,/n , ) v y z yb zb A •= n , . . zb n , + 2An yb y A was calculated using measured values of An • An = .01 and An = An = .04 z o y e [Schmidt and Kaminow 1974] and our values of n , • n • 2.2884 and n . = n = 1 zb o yb e 2.2017 and found f ( y ) P i 2 >3(2n z bAn zeHy|/^ k o2 ). Since both sides of t h i s equation go to zero i n the l i m i t as y -»• - 0 D one should be cautious about the p o s s i b i l i t y of neglecting the term f ( y ) p i 2 that -Ivl/d o may dominate the other term n ^ A ^ e , J ' ^ 0 • Therefore even though Noda et a l . ' s approximation may be appropriate under c e r t a i n conditions we have avoided i t i n preference to the exact solutions obtainable for modes propagating i n the x-cut LiNb0 3 substrates with propagation p a r a l l e l to the c r y s t a l ' s y a x i s . [Since the substrate i s x-cut LiNb0 3 such an immersion device would have to be oriented with the surface containing the device p a r a l l e l to the f i e l d to be measured i n order to be able to make use of the large r ^ e l e c t r o o p t i c c o e f f i c i e n t . ] 197 t , d, and An are a l l chosen to ensure that only the T E Q and T M Q modes propagate i n the waveguides for the example i n Section 2.3.2. To analyze the device operation we rewrite equation A3.16 using the cutoff condition P i 2 - n b V J l I e ( 0 ) ] = „ [ S' - tan(h't) ] V S ( 0 ) J ( 2 n b A n ) 1 / 2 1 + S ' ^ h ' t ) - 1 where h' = k Q ( n f 2 - t^2)1'2 and ( n b 2 " n z 2 > 1 / 2 / < n f 2 " ° b 2 ) 1 / 2 f o r T E m o d e s S' = (n 2/n 2 ) ( n 2 - n 2 ) 1 / 2 / ( n } - n . 2 ) for T M modes. v f a ' v b a ' f b Since for the unloaded waveguide (t=0) the right-hand side of equation A3.17 i s always p o s i t i v e and since the left-hand side i s always increasing from 0 to » on the Int e r v a l 0 < g(0) < g z Q (where g z Q i s the value of g(0) at which •J0lg(°)] n a s i t s f i r s t zero) and from —> to 0 on the i n t e r v a l g z Q < g(0) < g , (where g , i s the value of g(0) at which J.[g(0)] has i t s second zero) z l z l l only the TE and TM modes w i l l e x i s t f o r g < g(0) < g . Therefore, 0 \) z u z i d ( A n ) 1 / 2 must be on the i n t e r v a l 8 z 0 ^ ° < d(An)l/2 < ! f i ^ 2 A3.18 4 T t ( 2 n b ) 1 / 2 4 T c ( 2 n b ) 1 / 2 f o r both the TE- and TM„ modes i n LiNbO,. Minakata et a l . have shown that 0 0 3 f o r small An (An < 3xl0~ 3) the changes i n n g and n Q due to d i f f u s i o n , An g and An , are both l i n e a r functions of the T i concentration [Minakata et a l . o 1978]. In t h i s range An^ i s larger than An g (a s i t u a t i o n that changes at An ~5*10~ 3) and the two appear to be rela t e d by An Q « 1.5An e. The range of values for d i s found to be between 1.83 and 2.33um where n g ™ 2.2017 and An • .001 are used to f i n d the lower bound on d and n • 2.2884 and e o An = .0015 are used to f i n d the upper bound. 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