LIST OF FIGURES .............................................. xiii
LIST OF TABLES ................................................ xix
PREFACE ....................................................... xxi
ACKNOWLEDGMENTS ............................................. xxiii
I FUNDAMENTALS ................................................. 1
1 ELECTRO-OPTIC EFFECT ......................................... 5
1.1 Light propagation in crystals ............................ 5
1.1.1 Wave propagation in anisotropic media .............. 6
1.1.2 General wave equation .............................. 6
1.1.3 Index ellipsoid .................................... 7
1.2 Tensorial Analysis ....................................... 9
1.3 Electro-optic effect .................................... 10
1.3.1 Sillenite-type crystal ............................ 11
1.3.2 Lithium niobate ................................... 16
1.3.3 KDP-(KH2PO4) ...................................... 17
1.4 Concluding Remarks ...................................... 18
2 PHOTOACTIVE CENTERS AND PHOTOCONDUCTIVITY ................... 19
2.1 Photoactive centers: Deep and shallow traps ............. 21
2.1.1 Cadmium telluride ................................. 21
2.1.2 Sillenite-type crystals ........................... 23
2.1.3 Lithium niobate ................................... 26
2.2 Photoconductivity ....................................... 26
2.2.1 Localized states: traps and recombination
centers ........................................... 27
2.2.2 Theoretical models ................................ 29
2.2.2.1 One-center model .......................... 33
2.2.2.1.1 Steady state under uniform
illumination .................... 34
2.2.2.2 Two-center/one-charge carrier model ....... 35
2.2.2.2.1 Steady state under uniform
illumination .................... 36
2.2.2.2.2 Light-induced absorption ........ 38
2.2.2.3 Dark conductivity and dopants ............. 38
2.2.3 Photoconductivity in bulk material ................ 39
2.3 Photochromic effect ..................................... 39
2.3.1 Transmittance with light-induced absorption ....... 40
II HOLOGRAPHIC RECORDING ....................................... 45
3 RECORDING A SPACE-CHARGE ELECTRIC FIELD ..................... 47
3.1 Index of refraction modulation .......................... 50
3.2 General formulation ..................................... 54
3.2.1 Rate equations .................................... 56
3.2.2 Solution for steady state ......................... 56
3.3 First spatial harmonic approximation .................... 59
3.3.1 Steady-state stationary process ................... 62
3.3.1.1 Diffraction efficiency .................... 63
3.3.1.2 Hologram phase shift ...................... 64
3.3.2 Time-evolution process: Constant modulation ....... 65
3.4 Steady-state nonstationary process ...................... 67
3.4.1 Running holograms with hole-electron
competition ....................................... 71
3.4.1.1 Mathematical model ........................ 75
3.5 Photovoltaic Materials .................................. 79
3.5.1 Uniform illumination: ∂N/∂x = 0 ................... 80
3.5.2 Interference pattern of light ..................... 81
3.5.2.1 Influence of donor density ................ 82
4 VOLUME HOLOGRAM WITH WAVE MIXING ............................ 85
4.1 Coupled wave theory: Fixed grating ...................... 85
4.1.1 Out of Bragg condition ............................ 88
4.2 Dynamic coupled wave theory ............................. 89
4.2.1 Combined phase-amplitude stationary gratings ...... 90
4.2.1.1 Fundamental properties .................... 92
4.2.1.2 Irradiance ................................ 93
4.2.2 Pure phase grating ................................ 95
4.2.2.1 Time evolution ............................ 95
4.2.2.1.1 Undepleted pump approximation ... 96
4.2.2.1.2 Response time with feedback ..... 98
4.2.2.2 Stationary hologram ...................... 101
4.2.2.2.1 Diffraction .................... 104
4.2.2.3 Steady-state nonstationary hologram
with bulk absorption ..................... 108
4.2.2.3.1 Diffraction efficiency ......... 110
4.2.2.3.2 Output beams phase shift ....... 112
4.3 Phase modulation ....................................... 114
4.3.1 Phase Modulation in dynamically recorded
gratings ......................................... 118
4.3.1.1 Phase modulation in the signal beam ...... 119
4.3.1.1.1 Unshifted hologram ............. 119
4.3.1.1.2 Shifted hologram ............... 120
4.3.1.2 Output phase shift ....................... 120
4.4 Four-wave mixing ....................................... 122
4.5 Final remarks .......................................... 123
5 ANISOTROPIC DIFFRACTION .................................... 125
5.1 Coupled wave with anisotropic diffraction .............. 125
5.2 Anisotropic diffraction and optical activity ........... 127
5.2.1 Diffraction efficiency with optical activity p ... 128
5.2.2 Output polarization direction .................... 130
6 STABILIZED HOLOGRAPHIC RECORDING ........................... 131
6.1 Introduction ........................................... 131
6.2 Mathematical formulation ............................... 133
6.2.1 Stabilized stationary recording .................. 136
6.2.1.1 Stable equilibrium condition ............. 137
6.2.2 Stabilized recording of running (nonstationary)
holograms ........................................ 138
6.2.2.1 Stable equilibrium condition ............. 140
6.2.2.2 Speed of the fringe-locked running
hologram ................................. 140
6.2.3 Self-stabilized recording with arbitrarily
selected phase shift ............................. 141
6.3 Self-stabilized recording in actual materials .......... 144
6.3.1 Self-stabilized recording in Sillenites .......... 144
6.3.2 Self-stabilized recording in LiNbO3 .............. 145
6.3.2.1 Holographic recording without
constraints .............................. 145
6.3.2.1.1 Space-charge electric field
build-up ....................... 147
6.3.2.1.2 Hologram phase shift ........... 148
6.3.2.1.3 Diffraction efficiency with
wave mixing .................... 149
6.3.2.2 Self-stabilized recording ................ 152
6.3.2.2.1 Effect of light
polarization ................... 157
6.3.2.2.2 Glass plate-stabilized
recording ...................... 159
III MATERIALS CHARACTERIZATION ................................ 163
7 NONHOLOGRAPHIC OPTICAL METHODS ............................. 165
7.1 Light-induced absorption ............................... 165
7.2 Photoconductivity ...................................... 170
7.2.1 Alternating current technique .................... 171
7.2.1.1 Wavelength-resolved photoconductivity .... 174
7.2.2 Modulated photoconductivity ...................... 176
7.2.2.1 Quantum efficiency and
mobility-lifetime product ................ 178
7.3 Electro-optic coefficient .............................. 179
8 HOLOGRAPHIC TECHNIQUES ..................................... 181
8.1 Direct holographic techniques .......................... 181
8.1.1 Energy coupling .................................. 182
8.1.2 Diffraction efficiency ........................... 185
8.1.3 Holographic sensitivity .......................... 186
8.1.4 Hologram recording and erasure ................... 188
8.1.4.1 Dark conductivity ........................ 190
8.1.5 Hole-electron competition ........................ 191
8.2 Phase modulation techniques ............................. 194
8.2.1 Holographic sensitivity .......................... 194
8.2.2 Holographic phase-shift measurement .............. 196
8.2.2.1 Wave-mixing effects ...................... 197
8.2.3 Photorefractive response time .................... 197
8.2.4 Selective two-wave mixing ........................ 201
8.2.4.1 Amplitude and phase effects in GaAs ...... 203
8.2.5 Running holograms ................................ 206
8.2.6 Photo-electromotive-force techniques ............. 212
8.2.6.1 Holographic photo-emf .................... 212
9 SELF-STABILIZED HOLOGRAPHIC TECHNIQUES ..................... 225
9.1 Holographic phase shift ................................ 225
9.2 Fringe-locked running holograms ........................ 229
9.2.1 Absorbing materials .............................. 230
9.2.1.1 Low-absorption approximation ............. 232
9.2.2 Characterization of materials .................... 232
9.2.2.1 Measurements ............................. 232
9.2.2.1.1 Hologram speed Kv .............. 232
9.2.2.1.2 Diffraction efficiency ......... 233
9.2.2.2 Theoretical fitting ...................... 234
9.3 Characterization of LiNbO3:Fe ........................... 238
IV APPLICATIONS ............................................... 243
10 VIBRATIONS AND DEFORMATIONS ................................ 245
10.1 Measurement of Vibration and Deformation .............. 246
10.2 Experimental Setup .................................... 246
10.2.1 Reading of Dynamic Holograms ................... 246
10.2.2 Optimization of illumination ................... 248
10.2.2.1 Target illumination ................... 249
10.2.2.2 Distribution of light among
reference and object beams ............ 249
10.2.3 Self-stabilization Feedback Loop ............... 251
10.2.4 Vibrations ..................................... 252
10.2.5 Deformation and tilting ........................ 255
11 FIXED HOLOGRAMS ............................................ 259
11.1 Introduction .......................................... 259
11.2 Fixed holograms in LiNbO3 ............................. 260
11.3 Theory ................................................ 260
11.4 Experiment ............................................ 262
V APPENDICES ................................................. 267
A DETECTING A REVERSIBLE REAL-TIME HOLOGRAM .................. 269
A.1 Naked-eye detection .................................... 270
A.1.1 Diffraction ...................................... 270
A.1.2 Interference ..................................... 270
A.2 Instrumental detection ................................. 271
B DIFFRACTION EFFICIENCY MEASUREMENT: REVERSIBLE VOLUME
HOLOGRAMS .................................................. 273
B.1 Angular Bragg selectivity .............................. 273
B.1.1 In-Bragg recording beams ......................... 274
B.1.2 Probe beam ....................................... 274
B.2 Reversible holograms ................................... 278
B.3 High index of refraction material ...................... 278
C EFFECTIVELY APPLIED ELECTRIC FIELD ......................... 281
D PHYSICAL MEANING OF SOME FUNDAMENTAL PARAMETERS ............ 283
D.1 Debye screening length ................................. 283
D.1.1 Temperature ...................................... 283
D.1.2 Debye screening length ........................... 284
D.2 Diffusion and mobility ................................. 285
E PHOTODIODES ................................................ 287
E.1 Photovoltaic regime .................................... 289
E.2 Photoconductive regime ................................. 290
E.3 Operational amplifier operated ......................... 291
BIBLIOGRAPHY .................................................. 293
INDEX ......................................................... 305
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