Dynamic Holography Using
`
`Ferroelectric Liquid Crystal on Silicon
`
`Spatial Light Modulators
`
`A dissertation submitted for the degree of
`
`Doctor of Philosophy
`
`at the University of Cambridge
`
`UNIVERSITY
`LIBRARY
`OAUBRIOG£
`
`Kim Leong Tan
`
`Wolfson College
`
`February 1999
`
`FINISAR 1006
`
`

`
`Declaration
`
`This dissertation contains the results of research undertaken by the author between October
`
`1995 and December 1998 at the Engineering Department of Cambridge University. No part
`
`of this dissertation is the result of work done in collaboration with others, except where
`
`explicitly described or cited within the text. The contents have not been submitted, in whole
`
`or in part, for any other University degree or diploma.
`
`Kim Leong Tan
`
`Cambridge, February 1999
`
`

`
`Keywords
`
`CMOS VLSI silicon backplane, computer generated holograms, diffraction efficiency,
`
`dynamic holography, ferroelectric liquid crystals, free-space holographic switch, multi-level
`
`phase holograms, spatial light modulators.
`
`11
`
`

`
`Summary
`
`Optical networking is expected to evolve from the current point-to-point photonic transport
`
`networks. Optical wavelength-
`
`and space-division
`
`interconnects allow for a fuller
`
`exploitation of the intrinsic bandwidths of optical fibres as the transmission medium. The use
`
`of costly electronic Time Division Multiplexing (TOM) switches
`
`in high bit-rate
`
`telecommunications systems can also be reduced/eliminated. These networks require
`
`dynamic and transparent Wavelength Division Multiplexing (WDM) filters and Optical
`
`Cross-Connects (OXC). Dynamic holograms recorded on reconfigurable ferroelectric liquid
`
`crystal (FLC) spatial light modulators (SLM) have the potential to meet these requirements.
`
`The research outlined in this dissertation relates to an original theoretical analysis, validated
`
`by numerical simulations and experimental measurements, of the performance of these
`
`routing holograms when used in 4f coherent optical systems. The principal analytical results
`
`demonstrated are the dependence of the hologram replay crosstalk on the clipping of the
`
`Gaussian beam by the hologram aperture and the predictability of the locations and
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`intensities of the hologram replay peaks. The level of sidelobe ripple noise and the effects of
`
`phase quantisation, arrangement of phase elements, spatial quantisation and SLM pixel dead(cid:173)
`
`space are quantified within the valid regime of paraxial diffraction theory. The understanding
`
`of routing hologram replay has been exploited to devise a novel deterministic hologram
`
`generation algorithm and to determine the scalability of these switches as constrained by the
`
`switch path, temporal loss variations and optical bandwidths. It can be also used to design
`
`hologram configurations for a large free-space optical matrix switch.
`
`The first silicon backplane for driving a holographic SLM was designed and commercially
`
`fabricated during the course of this research. The emphasis of the backplane design and the
`
`SLM assembly was to obtain good optical modulation for coherent applications. The
`
`backplane contains a binary and a quaternary modulator array having 540 x 1 pixels. The
`
`silicon backplane and all assembled SLMs were fully tested and characterised. The binary(cid:173)
`
`phase SLM, with a high quality post-processed mirror array, was to be used in a collaborative
`
`free-space 1 x 8 optical switch demonstration . Several optical experiments were performed
`
`using a fixed intensity grating on glass and a reconfigurable binary-phase SLM with a view
`
`of verifying the crosstalk isolation and insertion loss aspects of routing hologram analyses .
`
`These experiments simulating infinite switch configurations gave > 50 dB crosstalk figures
`
`and insertion losses to within 3 dB of the theoretical values. Two hologram refresh schemes
`
`for maintaining a holographic interconnect over a long period were also evaluated.
`
`Ill
`
`

`
`Acknowledgements
`
`The work reported here owes much to the unique environment in the Photonics and Sensors
`
`Group. For that, I would like to thank Bill Crossland with the help of Caryn Wilkinson, for
`
`leading the group and providing the resources and interactions with fellow researchers from
`
`elsewhere in my chosen field of research. Many thanks are also due to Bill for sorting out my
`
`maintenance support. My gratitude is also extended to Mike Robinson at Sharp Labs. Europe
`
`for starting the ball rolling by suggesting work on analogue SLMs. I would like to thank
`
`Robert Mears, my supervisor at Cambridge, for his occasional but critical appraisals of my
`
`work and for the tremendous help in the preparation of papers and this dissertation.
`
`I would especially like to thank Tim for his help in SLM processing/fabrications and proof
`
`reading the draft dissertation; Steve for fruitful interactions on hologram analysis and replay;
`
`Maura for liquid crystal alignment work; llias for help in mounting the fibre on the quarter
`
`disc and optical system aligning; Ping Chiek for varied assistance throughout the two and a
`
`half years as well as encouragement when I have been frustrated and dispirited; James
`
`Collington for demonstrating the VLSI layout using Mentor Graphics; Ian Underwood and
`
`David Holburn for contributing to the chip design review; Mike Hands for loaning the
`
`stepper motor stages; Mike Bradley for helping with C-programrning; Mike Parker for
`
`discussions on quaternary hologram analysis; Sazzad Nasir at Wolfson college for numerous
`
`mid-night discussions on the wonderful world of physics and mathematics research; Tony
`
`Davey for his critical opinions on liquid crystals; Eddie, Sabesan, Cheng-Ruan, Karsten,
`
`Anna, Huan, Jeon, Clarence, Terence, Faheem, Louis, Niall, Adam, Brian, Mark and many
`
`others for friendship, help, comments, advice, etc.; Overseas Research Studentship,
`
`Cambridge Commonwealth Trust and Thomas Swan Co. Ltd. for providing financial
`
`assistance and making my existence at Cambridge possible!
`
`The support by the workshop technicians, Russell, Steve, Adrian and Mick is greatly
`
`appreciated. The Roses project with its industrial and university partners has provided many
`
`opportunities for interactions and the funding for the chip development. My sincere thanks to
`
`them all and especially to CRL for bonding the SLMs.
`
`Lastly, I am indebted to my wife, Sian, for her never ending love and support and in putting
`
`up with the inevitable maniacal work routines during the final stages of my Ph.D.
`
`Author's note: the image on the cover page is the fibre-scan intensity pattern of a grating replay, see §8.5.1.
`
`iv
`
`

`
`To Sim;
`To Sian
`
`(writ!
`and
`
`ourfamilies
`ourfimtifies
`
`v
`
`

`
`Contents
`
`List of figures
`
`List of tables
`
`CHAPTERl
`
`Introduction
`
`CHAPTER2
`
`Spatial light modulators: active devices for optical processing
`
`xii
`
`xviii
`
`1
`
`6
`
`2.1 Introduction ......... .. ... ........... ...... .. ........................................................ .... .... .................. 6
`
`2.2 SLMs for use in coherent optical processing systems .. .. ............................................... 7
`
`2.2.1 Nematic liquid crystal (NLC) modulators .......................................................... 8
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`2.2.2 Photorefractive crystals ... .... .... .. ... .. .. .. .. ............ ..... ........ ... ......... ....... ................. ... 8
`
`2.3 Smart-pixel arrays for free-space optical interconnects (FSOI) .................................... 9
`
`2.3. l SEED modulators ..................................... .................. ... ....................................... 9
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`2.3.2 Electro-absorption (EA) modulators ................ ...................... ................ ............ 10
`
`2.4 SLMs for use in free-space optical switches ............................................................... 11
`
`2.4.1 Opto-mechanical modulators ............................................................................. 13
`
`2.4.2 Magneto-optic modulators ........................ ............... .. ............ ... ......................... 13
`
`2.4.3 Si-PLZT modulators ......................................... ............... ................................... 13
`
`-
`
`

`
`CONTENTS
`
`vii
`
`2.4.4 Ferroelectric liquid crystal (FLC) modulators ...... ...... ... ........... ....... ... ............... 14
`
`2.4.5 Digital-micro-mirror-device (DMD) ..... .. ........ .. ..... .... ... ... .. ............ .... ................ 15
`
`2.5 Conclusions ........ .... ... .................... ...................... ....................... ...... ........................... 16
`
`CHAPTER3
`
`Analysis of fibre-to-fibre l:N switch coupling efficiency
`
`17
`
`3.1 Introduction ... .............. ............. ...................... .... ....... ................ ...... ..... ........ .. ............. 17
`
`3.2 Weakly-guiding approximation for the fundamental (HE 11 ) fibre mode .. ........ .. ...... .. 17
`
`3.3 Analysis of the replay field profile using Gaussian fibre mode description ........... .... 19
`
`3 .4 Analysis of the coupling intensity profile using Gaussian fibre mode description ..... 22
`
`3.4.1 Coupling intensity with lateral offsets (u,v) ... ................... ................. ................ 26
`
`3.4.2 Coupling intensity with angular tilts (Ox,(Jy) ...... .. ....... .... ... .... ...... ......... ..... ......... 30
`
`3.5 Numerical simulations of the replay field and coupling intensity profiles ... ....... ....... 32
`
`3 .5 .1 Approximate replay peak descriptions .... ............................ ..... .......................... 34
`
`3.5.2 Approximate coupling intensity with a 1-D lateral offset, u .. .... ....................... 36
`
`3.5.3 Coupling intensity with a 1-D angular tilt, Ox ............. .. ........... ..... .... ................. 38
`
`3.6 Conclusions ... .... .......................... ....... ... ..... .. ...... ........ ...... ....... .... ... .......... ....... ............ 40
`
`CHAPTER4
`
`Theory of the replay of routing holograms written onto a programmable SLM
`
`42
`
`4.1 Introduction .... ...... .......... .... ............... ..... ....... ........ ... ...... .. .... ... .. ... .. ........ ... ..... ...... ....... 42
`
`4.2 Phase quantisation and the distribution of quantised phase elements ............. ... ...... .. .43
`
`4.2.1 Fractional representation for the replay of routing holograms .. .... ........ ...... .. .. .. 44
`
`4.2.2 The replay intensities of grating holograms ........... ..... .... .... ..... ....... ........... .... .... 45
`
`4.2.3 The replay locations of general holograms .................................. ... ....... ............ 49
`
`4.3 The effect of pixellation and dead-space (spatial quantisation) .......... ..... ................... 52
`
`4.3. l Numerical simulations of 1-D hologram replay ....... ...... ... .. ...... ............... .... ...... 54
`
`4.3.2 The upper-bound of the replay efficiency of routing holograms ....... ........... ..... 58
`
`4.4 Inadequate phase modulation (phase mismatch) ............ ..... ... ..... ........ .. .. .......... ... ... ... . 59
`
`4.4.1 The zero orders for phase-mismatched holograms .......... ...... ............................ 60
`
`

`
`CONTENTS
`
`viii
`
`4.4.2 The replay of non-zero orders for phase-mismatched holograms ...................... 62
`
`4.5 Conclusions ...... ...................... ...... ............ .......... ......... .............. .... ........................... ... 63
`
`CHAPTERS
`
`Applications of coupling intensity and discrete hologram replay descriptions
`
`65
`
`5 .1 Introduction ................................................................................................................. 65
`
`5 .2 The design limitations of a large 1 :N holographic switch ............ .... ........ ..... .............. 65
`
`5.2.1 On-beam-axis coupling efficiency and off-beam-axis crosstalk power. ............ 67
`
`5.2.2 The number of hologram repeats for a l:N holographic switch ........................ 68
`
`5.2.3 Prospective 1 :N switch using a highly specified SLM ... ..... ......... ..................... 72
`
`5.3 Deterministic routing hologram generation ..................................................... ............ 75
`
`5.3.1 1-D hologram generation by choosing a combination of x 0 phase elements ..... 76
`
`5.3.2 Offsetting the 1-D combinations to provide 2-D routing patterns ..................... 78
`
`5.3.3 The advantages of the skip-rotate hologram generation technique ............ ........ 79
`
`5.4 Conclusions ................................................................................................................. 80
`
`CHAPTER 6
`
`FLC on CMOSNLSI Si spatial light modulators for holographic applications
`
`81
`
`6.1 Introduction ............................. ................. ... ..... .................. ............................ .... .... ..... 81
`
`6.2 Polarisation rotation as a means of phase modulation ........ ....................................... . 82
`
`6.2.1 Multi-level modulation .. ......... .. ................................. ... ..... ..... ......... ....... ... ..... ... 82
`
`6.2.2 Binary modulation .............................................................................................. 86
`
`6.3 Fast four-level phase-only modulation by polarisation rotation .................................. 88
`
`6.3 .1 Analysis of enhanced switching using a double-pass configuration ... .. ... .. ....... 89
`
`6.3 .2 Double-pass devices .. .......................... .......... ....... ............... ... .................... ... ..... 91
`
`6.4 Processing digital data input for analogue devices ................................. ... ... ......... ..... 93
`
`6.4.1 Global DA Cs .................. ........ .. .. ...... .. .................. ................. ............................. 94
`
`6.4.2 Column-select DA Cs ......................................................................................... 95
`
`6.4.3 Pixel-level DA Cs ............. ............................. .... ... .... ...... .... ..... ............ ......... .. .... 96
`
`6.4.4 Choice of DAC location for the demonstrator chip ........................................... 98
`
`6.5 Pixel design for coherent optical phase modulation ........ ... ...... ......... ...... ............... .... . 98
`
`

`
`CONTENTS
`
`ix
`
`6.5.1 Enhanced optical reflectors for the binary SLM .. ... .... ....................................... 98
`
`6.5.2 Transmissive pixels for quaternary SLM ........................................................... 99
`
`6.6 Semiconductor fabrication process ................... .......................................................... 99
`
`6.6.1 CBH lOV 2-µm CMOS process .... .. ... ............................................................. . 100
`
`6.6.2 CBY 50V 2-µm DMOS process ...................................................................... 103
`
`6.7 Conclusions ................................... .. ........................................... ........ ....... ................ 106
`
`CHAPTER 7
`
`Circuit design and layout of the Roses chip
`
`108
`
`7 .1 Introduction ..... ........................ .......................... ...... ................... ............. ... ... ............ 108
`
`7 .2 Specifications for the binary and quaternary modulators .......... .... ........ .. .................. 109
`
`7 .2.1 The reflective binary array .................................... ........ ................. ...... .... ........ 110
`
`7.2.2 The transmissive quaternary array ...... .... ... ...................................................... 111
`
`7 .3 Overall floor-plan ................................... ..... ........ ... ................................... ... ............. 111
`
`7.4 Features and simulated performance of the Roses chip ............................................ 113
`
`7 .5 Circuit design for binary modulation ..................................... ..... .............................. 116
`
`7.5 .1 Binary driver schematics and functionality ..................................................... 116
`
`7.5.2 Asynchronous global blanking ........ ........................................... ........... .......... . 118
`
`7.5.3 Standard geometry MOSFET design .................. ............................ .......... ....... 118
`
`7 .5 .4 Current-limiting in sizing level shifter transistors ........ ......... .......................... 118
`
`7 .5 .5 Speed versus current-limiting trade-off in sizing buffering transistors ........... 118
`
`7 .6 Layout of the binary backplane ............ ... ..... .. .. ..... ....................... .... .. ..... .................. 119
`
`7 .6.1 Standard geometry MOSFET layout.. .............................................................. 119
`
`7.6.2 Protecting supply lines from peak current effects .................... ........................ 119
`
`7 .6.3 Increasing the decoupling-capacitance of power lines ........................ ............ 120
`
`7 .6.4 Routing driver outputs to the pixel array .................. ....... ................................ 120
`
`7.6.5 Pixel tabs to contact MET3 pixels ............................ ......... ...... ........................ 120
`
`7.7 Circuit design for four-level modulation ...... ................................. .... ............... .... ..... 121
`
`7.7.1 Quaternary driver schematics and functionality .... ..... ............. ........................ 121
`
`7.7.2 Standard geometry MOSFET design ....................................... ... ............. ........ 123
`
`

`
`CONTENTS
`
`x
`
`7 .7.3 Converting drive voltages by digital selection of power rails ...... .. .. ...... ...... .. . 123
`
`7.7.4 Current limiting by sizing select transistors ............................ .. .. .... ............ .. ... 123
`
`7.8 Layout of the quaternary backplane .... .. .. .. ..................... ......... ......... .... .... .. ............... 124
`
`7 .8.1 Layout of the quaternary drivers ...................... .. ........ ............................... .. .. ... 124
`
`7 .8.2 Layout of the quaternary pixel array ........................ .. ............... .. ....... .. ........ .... 124
`
`7.9 Buffering of control signals ............ .. ... ....... .... ...... .... ... .. ... .. .. .. ........ .. .. ....................... 126
`
`7.10 Bonding pads ..... .... .... .. ........ ... ...... ... .. .... ..... ... ............... ..... ...... ........... ... .. ................ 126
`
`7 .11 Functionality tests .... ... .. .. ... .. ..... .... ... ..... .... .. ... ..... .. ..... ....... ...... .... .... ... ...................... 127
`
`7 .11.1 Test of the dynamic shift register data latching and shifting .. .. .. ........ ....... .... 127
`
`7.11.2 Test of frame update, level shifting and DIA conversion .......... ...... .. .. .. .. ...... 127
`
`7.12 Conclusions ...................................... .... ... ....... ... .................. .. ...... .... .. ....... ............... 129
`
`CHAPTERS
`
`Characterisation of fabricated Roses devices
`
`130
`
`8.1 Introduction ....................................... .. ........ .. ... ..... ..... ... ... ............... .. .... ...... .. ...... .. .... 130
`
`8.2 Initial tests of an unprocessed wafer .. ............ .. ............ .... ....... ....... .. ........ .. ....... .. .. .. .. 130
`
`8.2.1 Binary array .. .. .. ......................... .. ... .... ........ .. ... ..... .. .... .... .. .... .......... .. ................ 131
`
`8.2.2 Quaternary array .............. .. .......... ........ .. .......... .... .. .. ... .. ........ .... .... .. .. ...... .. .. ..... 133
`
`8.3 Processing silicon backplane devices and SLM assembly ................................ ........ 135
`
`8.3 .1 Optical quality mirror deposition ......... .. ..... .. ..................................... ....... .. .... . 135
`
`8.3 .2 Al-etch of protective mirror coating .... .. ...................... .. .... .. .. ... .... .............. .. ... 135
`
`8.3.3 Assembly of silicon backplane SLMs .... ... .... .. ................... .. .... .. .... .. .... ... ..... .... 135
`
`8.4 Tests of assembled SLMs ..... .... ..... .................. ............ ........ .... ................ ...... ...... ...... 136
`
`8.4.1 Initial optical inspection using the probe-station ...... ... .... ..... .... .. ..... .. .. .......... .. 136
`
`8.4.2 SLM interface and carrier design ... .. ........ .. .. .... ..... ..... .. .. .. ...... .. ... ..... .. .............. 139
`
`8.4.3 Imaging optical modulating using a polarising microscope ...... .. .. .... .... ... ... .... 140
`
`8 .5 Holographic SLM demonstrator ...... .. ...... .... .... .. ... .. ... .............. .. ... .. ........ .. .... .. ........... 143
`
`8.5.1 Replay field mapping using intensity modulation ... ... ... .. ..... .. .. ..... .................. 143
`
`8.5 .2 Reflective binary-phase holographic operation .... .... .. .... .. .. .. .. .. .. .. ................... 151
`
`8.6 Drive schemes issues for holographic applications ........................ .... .... .. .... .. .......... . 156
`
`

`
`CONTENTS
`
`xi
`
`8.6.1 Non-DC balanced refreshing to maintain holograms for long periods .......... .. 157
`
`8.6.2 DC-balanced refreshing to maintain holograms for long periods ..... ..... .... ...... 160
`
`8.7 Conclusions .... ....... .... ............. ............. .. ..... ........ ..... .... ...... ..... ... ........... ..................... 163
`
`CHAPTER9
`
`Conclusions and further work
`
`164
`
`9 .1 Conclusions ..... ... .............. .... .... ...... .... ... ............ ........... ......... ... .......... ............. ... ..... .. 164
`
`9 .2 Further work ....... .... ........... .... ...... ... ...... .. ....... .. ...... ........ ................. ... .... .. ............ ..... . 167
`
`9.2.1 Single discrete description for numerical hologram replay ....... ..... ..... ............ 167
`
`9.2.2 Single continuous description of optical hologram replay ..... .. ..... .................. 167
`
`9.2.3 Hologram synthesis for multiple replay fractions ..... ....... ... .... ........ ...... ........... 167
`
`9.2.4 Silicon design for a low dimension DMOS process ........... ..... .......... .. .. .... .. .... 167
`
`9.2.5 Hologram efficiency measurements ....... ......... ............ .... .... ...... ... ........... ...... ... 168
`
`9.2.6 Experiments using moderate and high number of phase levels ..... .... ........ ...... 168
`
`Bibliography
`
`APPENDIX A
`
`Derivation of the replay field approximation
`
`APPENDIXB
`
`DC undiffracted light for multi-level polarisation rotation
`
`APPENDIXC
`
`Associated publications
`
`APPENDIXD
`
`Glossary
`
`169
`
`179
`
`183
`
`187
`
`188
`
`D.1 Abbreviations and acronyms .... ..... ...... ......... ... ........ .......... ...... ... .. .... .... ...... .............. 188
`
`D.2 Holographic terminology .... .... ..... .. ...... ............. ...... ......... .... ....... .. ..... .. ... .. ....... ......... 189
`
`

`
`List of figures
`
`2.1: Basic arrangement for coherent optical filtering . .......... ............... ........... ... ........................ 6
`
`2.2: General structure of an SLM ............... ....... .......... ....... ............. ............... .................. ... ...... 7
`
`2.3: Generalised SEED device . .. ..... .. .................. ..... ................ ........... ..... ...... .......................... 10
`
`2.4: Schematic view of an electro-absorption modulator. ...... ... .. ... .. ........ .... ... ........ .... ..... .. .. ... 11
`
`2.5: Single-mode fibre to fibre free-space switch techniques ............... ........ ... ........... ............. 12
`
`2.6: Binary (bistable) ferroelectric liquid crystal orientations ...... ......... ................. ... .............. 14
`
`2.7: N x N free-space optical switching using DMDs ............................................. ....... ...... .... 15
`
`3.1: The replay of a blank hologram using a 4f coherent optical configuration . ....... ... ......... .. 20
`
`3.2: Asymptotic approximation of the replay field of a blank hologram illuminated by a
`Gaussian beam with w,. = 5.06 µm ... ........ ....... ...... .. ........ ... ......... .... ........ ............... .. ........ 21
`
`3.3: Power coupling of the blank hologram replay and the weakly-guiding fibre mode
`
`with an angular-tilt and a lateral-shift in a 4f holographic routing architecture ......... .... . 22
`
`3.4: Numerical integration of the coupling intensity into an output fibre with ID lateral
`
`offsets and angular tilts . ........ ........................ ........ ........ .... ............................................... 25
`
`3.5: 1-D coupling intensity profile using asymptotic approximation for w,. = 5.06 µm ......... . 27
`
`3.6: Coupling intensity for an output fibre with two-dimensional lateral offsets (u,v) for a
`symmetric truncation with ratio y = 2 and similar input/output fibre modes ........... ........ 29
`
`3.7: Absolute intensity error values incurred by including only one term in the asymptotic
`
`

`
`LIST OF FIGURES
`
`xiii
`
`series expansion for y = 2 and w,. = 5.06 µm ......................... .. ........................................ . 30
`
`3.8: Coupling intensity for tilted fibres .... .......... ...... ........ ................ .................... .......... ...... .... 31
`
`3.9: Coupling intensity profile for an output fibre with 2-D angular tilts, ( 8,JJy) ........ ........ .. . 32
`
`3.10: The field profiles at the (a) input, (b) hologram and (c) replay planes for
`
`numerical simulations .... .... .............. .. .............. .. .................... .... ...... .... ......... ........ ..... .... 34
`
`3.11: Approximate replay field magnitude using analytic expression and numerical
`!ft of the blank hologram field at the exit pupil ...... .......... ...................... .. .. ................ .. .. 35
`
`3 .12: Absolute errors of the replay field magnitude by using asymptotic approximation
`
`compared to numericalffi .. ................ ............................................... ..... .... .. ... .. .. .... .... .... 35
`
`3.13: Coupling intensity for an output fibre with a lateral offset u, Gaussian beam radius w, =
`5.06 µm and truncation ratio y= 2 ............... ...... .................. .... ...... ...... .................. .. .... .. 37
`
`3.14: Coupling intensity errors using the asymptotic approximation expression as
`
`compared to numerical results ....................................................... .... ............................. 37
`
`3 .15: Coupling intensity for an output fibre with an angular tilt ex for Gaussian beam
`radius w,. = 5.06 µm and truncation ratio y= 2 ..................................................... ......... 39
`
`3.16: Coupling intensity errors using the e1f and scaled Marcuse's expressions as
`
`compared to numerical results ................. ............................ ........................................... 39
`
`4.1: Higher orders overlap in the numerical replay grid of binary gratings .. .. .. ...................... .46
`
`4.2: Modulo-I shift-rule used to locate higher order replay peaks of quaternary replay
`fraction cr = 1/10 ... .......................... ....... ..... ... .... .. .......... ... ... ........ ... ...... ...... ... ......... .. .... .... 49
`
`4.3: Modulo-I shift-rule to locate higher orders of cr = 115 quaternary hologram replay ........ 51
`
`4.4: Pixel dimensions, transmittance and a 1-D cross-section of pixels .................................. 52
`
`4.5: Real holograms depicted by the 1-D convolution of each calculated hologram point
`
`with the pixel transmittance and multiplied by the finite hologram illumination ............ 52
`
`4.6: Composite effects of spatial and phase quantisation on the intensity of a phase-
`
`matched 3/8 quaternary replay fraction ................................. ....... ................................ .... 56
`
`4.7: Separating the hologram term (delta function plot) and the single pixel aperture
`
`term (dotted line) ........... .................. ............. .... .. ...... .... ... ................................ .... ..... ........ 56
`
`

`
`LIST OF FIGURES
`
`xiv
`
`4.8: Sine squared scaling due to 1-D spatial quantisation ... ....... ......... ....... .......... .... .......... ...... 57
`
`4.9: The ratio of pixellation scaling for p = 0.9 and 1.0 ... ......... ...................... .... .................... 57
`
`4.10: The intensity of the first order replay peaks within the central replication ............ ... ..... 59
`
`4.11: (a) The intensities of the central first and zero order replay peaks.
`
`(b) The intensities of the central zero order for phase-mismatched binary holograms .. 61
`
`4.12: Replay intensity for a phase-mismatched quaternary replay fraction cr = 3/8 ............. ... 63
`
`5 .1 : Coupling of holographic replay power into output fibres ......................... ... ....... .............. 66
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`5.2: The dependence of coupling and replay intensity on the truncation ratio, y .... ........ ....... 67
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`5.3: Crosstalk level at 30 µm offset due to the replay of a single beam .......... ........ ........ ........ 68
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`5.4: (a) The largest x0 of a base hologram to adequately resolve the replay.
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`(b) The corresponding hologram repeats for N = 1200 . ........ ................... ........ ............... 69
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`5 .5: The coupling intensity profile at the replay plane for y = 6.15 and cr = 1/20 ................... 70
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`5.6: The coupling intensity profile at the replay plane for y = 6.15 and cr = 91200 . ................ 71
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`5.7: The coupling intensity profile at the replay plane for y = 3.07 and cr = 91200 . ................ 71
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`5.8: (a) The largest beam steering angle using 'A= 1.55 µm.
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`(b) The fraction of power loss due to a 1 µm dead-space .. .... .... ............. ..... .. .... ............ .. 73
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`5.9: (a) The size of the central replay replication ford= 10 µm and 'A= 1.55 µm.
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`(b) The corresponding focal length in order to achieve they values above .................... 73
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`5.10: Modulo-x0 skip and rotate rule used for generating 1-D holograms . .. ...... ...................... ??
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`5.11: Flowchart of the algorithm for generating determinstic multi-level phase-only
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`routing holograms ............................. ......... .............................................. ....................... 79
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`6.1: (a) m switched states of a CSLC cell
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`(b) Two linear orthogonal polarisation components of the illuminating beam ............... 82
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`6.2: Four-level polarisation rotation given an input polarisation and four CSLC states ......... 84
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`6.3: Four-level phase modulation using optically active and isotropic media ... ................. .. ... 85
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`6.4: Binary polarisation rotation given an input polarisation and two FLC states .................. 87
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`6.5: The first order efficiencies of binary and quaternary phase-only holograms ................ ... 88
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`

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`LIST OF FIGURES
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`xv
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`6.6: Double-pass holographic optical element structure .............. .... .............. .... ...................... 90
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`6.7: A silicon backplane SLM integrated with a thin-film A/4 wave plate .............................. 91
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`6.8: A double-pass silicon backplane SLM with fused reactive monomers on glass .............. 91
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`6.9: A double-pass silicon backplane SLM with a rigid solid crystal /..J4 wave plate ............. 92
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`6.10: Approximation of the diffraction within a single pixel aperture ............................... ..... 93
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`6.11 : A general layout of an SLM driven from global DACs .................................................. 94
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`6.12: Column-select DIA conversion for CMOS/VLSI SLMs . ............................................... 95
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`6.13: Combinational logic circuits for a column-select DAC .................................................. 96
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`6.14: Pixel layout using a single DRAM transistor. .......... .. .................................................... 96
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`6.15: Equivalent circuit components of a LC/DRAM pixel. ................................................... 97
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`6.16: Six-transistor SRAM memory element. .................... ................ ........ ...... ........................ 97
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`6.17: Transistor-level schematics of a complimentary n-fet/p-fet switch (transmission
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`gate) and a CMOS inverter ............................................................................ .. ........ ..... 101
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`6.18: 1-bit dynamic shift register with two non-overlapping clock signals ........................... 102
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`6.19: 1-bit static shift register using positive feedback .......................................................... 102
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`6.20: Level shifting from [O,VDD] to [O,VDDH] using cross-coupled p-fets ..............