Photorefractive Materials Fundamental

Photorefractive Materials presents an overview of the basic features and properties of photorefractive materials, covering a wide array of related topics. It provides a coherent approach suitable for introductory and advanced students seeking to learn or review the fundamentals, as well as senior researchers who need a reference while investigating more specialized areas.

Jaime Frejlich graduated as a chemical engineer at the Universidad de la República, Uruguay (1973) and earned his PhD in physics/optics at Université Pierre et Marie Curie in Paris, France, in 1977. He has been a professor at Universidade Estadual de Campinas, Instituto de Física do Laboratório de ?ptica in Brazil since 1978. Professor Frejlich has published more than eighty scientific papers in specialized journals. His present research interests are in photorefractive materials, effects, processes, and applications.

LIST OF FIGURES

xiii

LIST OF TABLES

xix

PREFACE

xxi

ACKNOWLEDGMENTS

xxiii

I FUNDAMENTALS

1

(44)

1 ELECTRO-OPTIC EFFECT

5

(14)

1.1 Light propagation in crystals

5

(4)

1.1.1 Wave propagation in anisotropic media

6

(1)

1.1.2 General wave equation

6

(1)

1.1.3 Index ellipsoid

7

(2)

1.2 Tensorial Analysis

9

(1)

1.3 Electro-optic effect

10

(8)

1.3.1 Sillenite-type crystal

11

(5)

1.3.2 Lithium niobate

16

(1)

1.3.3 KDP-(KH2PO4)

17

(1)

1.4 Concluding Remarks

18

(1)

2 PHOTOACTIVE CENTERS AND PHOTOCONDUCTIVITY

19

(26)

2.1 Photoactive centers: Deep and shallow traps

21

(5)

2.1.1 Cadmium telluride

21

(2)

2.1.2 Sillenite-type crystals

23

(3)

2.1.3 Lithium niobate

26

(1)

2.2 Photoconductivity

26

(13)

2.2.1 Localized states: traps and recombination centers

27

(2)

2.2.2 Theoretical models

29

(10)

2.2.2.1 One-center model

33

(1)

2.2.2.1.1 Steady state under uniform illumination

34

(1)

2.2.2.2 Two-center/one-charge carrier model

35

(1)

2.2.2.2.1 Steady state under uniform illumination

36

(1)

2.2.2.2.2 Light-induced absorption

38

(1)

2.2.2.3 Dark conductivity and dopants

38

(1)

2.2.3 Photoconductivity in bulk material

39

(1)

2.3 Photochromic effect

39

(8)

2.3.1 Transmittance with light-induced absorption

40

(5)

II HOLOGRAPHIC RECORDING

45

(118)

3 RECORDING A SPACE-CHARGE ELECTRIC FIELD

47

(38)

3.1 Index of refraction modulation

50

(4)

3.2 General formulation

54

(5)

3.2.1 Rate equations

56

(1)

3.2.2 Solution for steady state

56

(3)

3.3 First spatial harmonic approximation

59

(8)

3.3.1 Steady-state stationary process

62

(3)

3.3.1.1 Diffraction efficiency

63

(1)

3.3.1.2 Hologram phase shift

64

(1)

3.3.2 Time-evolution process: Constant modulation

65

(2)

3.4 Steady-state nonstationary process

67

(12)

3.4.1 Running holograms with hole–electron competition

71

(8)

3.4.1.1 Mathematical model

75

(4)

3.5 Photovoltaic Materials

79

(6)

3.5.1 Uniform illumination: N/ x = 0

80

(1)

3.5.2 Interference pattern of light

81

(4)

3.5.2.1 Influence of donor density

82

(3)

4 VOLUME HOLOGRAM WITH WAVE MIXING

85

(40)

4.1 Coupled wave theory: Fixed grating

85

(4)

4.1.1 Out of Bragg condition

88

(1)

4.2 Dynamic coupled wave theory

89

(25)

4.2.1 Combined phase-amplitude stationary gratings

90

(5)

4.2.1.1 Fundamental properties

92

(1)

4.2.1.2 Irradiance

93

(2)

4.2.2 Pure phase grating

95

(19)

4.2.2.1 Time evolution

95

(1)

4.2.2.1.1 Undepleted pump approximation

96

(1)

4.2.2.1.2 Response time with feedback

98

(3)

4.2.2.2 Stationary hologram

101

(1)

4.2.2.2.1 Diffraction

104

(4)

4.2.2.3 Steady-state nonstationary hologram with bulk absorption

108

(1)

4.2.2.3.1 Diffraction efficiency

110

(1)

4.2.2.3.2 Output beams phase shift

112

(2)

4.3 Phase modulation

114

(8)

4.3.1 Phase Modulation in dynamically recorded gratings

118

(9)

4.3.1.1 Phase modulation in the signal beam

119

(1)

4.3.1.1.1 Unshifted hologram

119

(1)

4.3.1.1.2 Shifted hologram

120

(1)

4.3.1.2 Output phase shift

120

(2)

4.4 Four-wave mixing

122

(1)

4.5 Final remarks

123

(2)

5 ANISOTROPIC DIFFRACTION

125

(6)

5.1 Coupled wave with anisotropic diffraction

125

(2)

5.2 Anisotropic diffraction and optical activity

127

(4)

5.2.1 Diffraction efficiency with optical activity ρ

128

(2)

5.2.2 Output polarization direction

130

(1)

6 STABILIZED HOLOGRAPHIC RECORDING

131

(32)

6.1 Introduction

131

(2)

6.2 Mathematical formulation

133

(11)

6.2.1 Stabilized stationary recording

136

(2)

6.2.1.1 Stable equilibrium condition

137

(1)

6.2.2 Stabilized recording of running (nonstationary) holograms

138

(3)

6.2.2.1 Stable equilibrium condition

140

(1)

6.2.2.2 Speed of the fringe-locked running hologram

140

(1)

6.2.3 Self-stabilized recording with arbitrarily selected phase shift

141

(3)

6.3 Self-stabilized recording in actual materials

144

(21)

6.3.1 Self-stabilized recording in Sillenites

144

(1)

6.3.2 Self-stabilized recording in LiNbO3

145

(25)

6.3.2.1 Holographic recording without constraints

145

(1)

6.3.2.1.1 Space-charge electric field build-up

147

(1)

6.3.2.1.2 Hologram phase shift

148

(1)

6.3.2.1.3 Diffraction efficiency with wave mixing

149

(3)

6.3.2.2 Self-stabilized recording

152

(1)

6.3.2.2.1 Effect of light polarization

157

(1)

6.3.2.2.2 Glass plate-stabilized recording

159

(4)

III MATERIALS CHARACTERIZATION

163

(80)

7 NONHOLOGRAPHIC OPTICAL METHODS

165

(16)

7.1 Light-induced absorption

165

(5)

7.2 Photoconductivity

170

(9)

7.2.1 Alternating current technique

171

(5)

7.2.1.1 Wavelength-resolved photoconductivity

174

(2)

7.2.2 Modulated photoconductivity

176

(5)

7.2.2.1 Quantum efficiency and mobility-lifetime product

178

(1)

7.3 Electro-optic coefficient

179

(2)

8 HOLOGRAPHIC TECHNIQUES

181

(44)

8.1 Direct holographic techniques

181

(13)

8.1.1 Energy coupling

182

(3)

8.1.2 Diffraction efficiency

185

(1)

8.1.3 Holographic sensitivity

186

(2)

8.1.4 Hologram recording and erasure

188

(3)

8.1.4.1 Dark conductivity

190

(1)

8.1.5 Hole–electron competition

191

(3)

8.2 Phase modulation techniques

194

(31)

8.2.1 Holographic sensitivity

194

(2)

8.2.2 Holographic phase-shift measurement

196

(1)

8.2.2.1 Wave-mixing effects

197

(1)

8.2.3 Photorefractive response time

197

(4)

8.2.4 Selective two-wave mixing

201

(5)

8.2.4.1 Amplitude and phase effects in GaAs

203

(3)

8.2.5 Running holograms

206

(6)

8.2.6 Photo-electromotive-force techniques

212

(17)

8.2.6.1 Holographic photo-emf

212

(13)

9 SELF-STABILIZED HOLOGRAPHIC TECHNIQUES

225

(18)

9.1 Holographic phase shift

225

(4)

9.2 Fringe-locked running holograms

229

(9)

9.2.1 Absorbing materials

230

(2)

9.2.1.1 Low-absorption approximation

232

(1)

9.2.2 Characterization of materials

232

(14)

9.2.2.1 Measurements

232

(1)

9.2.2.1.1 Hologram speed K

232

(1)

9.2.2.1.2 Diffraction efficiency

233

(1)

9.2.2.2 Theoretical fitting

234

(4)

9.3 Characterization of LiNbO3:Fe

238

(5)

IV APPLICATIONS

243

(1)

10 VIBRATIONS AND DEFORMATIONS

245

(22)

10.1 Measurement of Vibration and Deformation

246

(1)

10.2 Experimental Setup

246

(13)

10.2.1 Reading of Dynamic Holograms

246

(2)

10.2.2 Optimization of illumination

248

(3)

10.2.2.1 Target illumination

249

(1)

10.2.2.2 Distribution of light among reference and object beams

249

(2)

10.2.3 Self-stabilization Feedback Loop

251

(1)

10.2.4 Vibrations

252

(3)

10.2.5 Deformation and tilting

255

(4)

11 FIXED HOLOGRAMS

259

(11)

11.1 Introduction

259

(1)

11.2 Fixed holograms in LiNbO3

260

(1)

11.3 Theory

260

(2)

11.4 Experiment

262

(5)

V APPENDICES

267

(1)

A DETECTING A REVERSIBLE REAL-TIME HOLOGRAM

269

(24)

A.1 Naked-eye detection

270

(1)

A.1.1 Diffraction

270

(1)

A.1.2 Interference

270

(1)

A.2 Instrumental detection

271

(2)

B DIFFRACTION EFFICIENCY MEASUREMENT: REVERSIBLE VOLUME HOLOGRAMS

273

(1)

B.1 Angular Bragg selectivity

273

(5)

B.1.1 In-Bragg recording beams

274

(1)

B.1.2 Probe beam

274

(4)

B.2 Reversible holograms

278

(1)

B.3 High index of refraction material

278

(3)

C EFFECTIVELY APPLIED ELECTRIC FIELD

281

(2)

D PHYSICAL MEANING OF SOME FUNDAMENTAL PARAMETERS

283

(1)

D.1 Debye screening length

283

(2)

D.1.1 Temperature

283

(1)

D.1.2 Debye screening length

284

(1)

D.2 Diffusion and mobility

285

(2)

E PHOTODIODES

287

(2)

E.1 Photovoltaic regime

289

(1)

E.2 Photoconductive regime

290

(1)

E.3 Operational amplifier operated

291

(2)

BIBLIOGRAPHY

293

(12)

INDEX

305

What is included with this book?

The New copy of this book will include any supplemental materials advertised. Please check the title of the book to determine if it should include any access cards, study guides, lab manuals, CDs, etc.

The Used, Rental and eBook copies of this book are not guaranteed to include any supplemental materials. Typically, only the book itself is included. This is true even if the title states it includes any access cards, study guides, lab manuals, CDs, etc.

FREE SHIPPING

Amazon no longer offers textbook rentals. We do!

Photorefractive Materials Fundamental Concepts, Holographic Recording and Materials Characterization

Summary

Author Biography

Table of Contents

Supplemental Materials