Electrooptics PHENOMENA, MATERIALS

A N D APPLICATIONS

Fernando Agullö-Löpez Departemente de Fisica de Materiales

Universidad Autönoma de Madrid, Spain

, ; > ' '

Jose Manuel Cabrera Departemente de Fisica de Materiales

Universidad Autönoma de Madrid, Spain

Fernando Agullo-Rueda Institute de Ciencia de Materiales

de Madrid (CSIC), Spain

A, N.

ACADEMIC PRESS Harcourt Brace & Company, Publishers

London San Diego New York Boston Sydney Tokyo Toronto

Contents

Series Foreword xiii Preface xv

1. T h e Vast Wor ld of Electrooptics

/ . / . Introduction I

1.2. Historical notes 2

1.3. Injection electroluminescence: LEDs 4

1.3.1. Polymer LEDs 1.3.2. Porous silicon

1.4. Bulk electroluminescence 6

1.4.1. Powder electroluminescence devices 1.4.2. Thin-film electroluminescence devices (TFEL)

1.5. Diode lasers 9

1.5.1. Narrow-line and tunable lasers

1.5.2. Blue lasers

1.5.3. Quantum well lasers 1.5.4. Surface-emitting lasers (SEL): microlasers

1.6. Electrochromism 14

2. Light Propagation in Anisotropic Media

2.1. Introduction 19

2.2. Birefringence and dichroism: a microscopic picture 19

2.3. Macroscopic Maxwell equations 21

2.4. The dielectric tensor 22

2.4.1. Clamped and undamped static dielectric constant

2.5. General properties of the dielectric tensor 23

2.6. Fresnel and index ellipsoids 25

2.7. Propagation of a monochromatic plane wave in an anisotropic medium 26

2.7./ . Geometrical considerations

2.7.2. Wave equation: Eigenmodes

2.7.3. Propagation along principal axes

2.7.4. Propagation along arbitrary directions

2.8. Analysis of the polarization 30

2.8.1. Algebraic method

2.8.2. Graphical method

2.9. Phase velocity, energy velocity and group velocity 33

2.10. The optical classification of crystals 34

2 . / / . Uniaxial crystals 34

V

ELECTROOPTICS

2.12. Biaxial crystals 40 2.13. Refraction at a boundary of an anisotropic crystal 41 2.14. Optically active materials 42 2. /5. Plane monochromatic waves in optically active media 45

3. Electrooptics: Concepts, Phenomena and Techniques

3.1. Introduction 49 3.1.1. EJectrogyration

3.2. Electrooptic coefficients 50 3.2.1. Contracted matrix representation

3.3. Equivalent formulations 51 3.4. Electroabsorption 52 3.5. Pockels effect: electronic and ionic contributions 53

3.5.1. Response times 3.5.2. Relationship between Raman and Pockels effects

3.6. Frequency dispersion behaviour 56 3.6.1. Miller's parameter

3.7. Kerr effect 57 3.7.1 Kerr effect in liquids

3.8. Symmetry restrictions on electrooptic coefficients 58 3.9. A microscopic model: the anharmonic oscillator 59

3.9.1. Pockels effect 3.9.2. Linear electroabsorption 3.9.3. Kerr response

3.10. Simple estimate of the nonresonant electronic coefficients r and s 63 3.10.1. Pockels coefficients 3.10.2. Kerr coefficients

3.11. Optical wave propagation through a Pockels medium 64 3.1 I.I. Determination of new principal indexes and directions 3.11.2. Field-induced birefringence 3.11.3. Effective electrooptic coefficients

3.12. Light propagation in isotropic Kerr media 70 3.12.1. Propagation of a plane monochromatic wave

3.13. Measurement of electrooptic coefficients 3.13.1. Single beam methods (noninterferometric) 3.13.2. Interferometric methods 3.1.3.3. Raman spectroscopy measurements Appendix ЗА. Pockels tensors for noncentrosymmetric crystallographic point groups 82 Appendix 3B. Kerr tensors for crystallographic point groups 85

4. Electrooptics and Nonlinear Optics

4.1. Introduction 87 4.2. Nonlinear wave propagation 87

4.2.1. Slowly-varying amplitude approximation 4.3. Nonlinear polarization and nonlinear optical effects 89

4.3.1. Nonlinear optical effects

CONTENTS vii

4.4. Second-harmonic generation: phenomenological approach 92 4.4.1. Efficiency 4.4.2. Phase (index) matching 4.4.3. Index matching: corpuscular view

4.5. Experimental methods for phase matching 96 4.6. Dispersive behaviour: frequency dependence of x"1 97

4.6.1. Second-order susceptibilities 4.7. Symmetry properties of the susceptibilities 100

4.7.1. Point-group symmetry relations 4.7.2. Intrinsic symmetry properties

4.8. Nonlinear processes and susceptibilities 102 4.9. Electrooptic coefficients and susceptibilities 103

Comparison between e/ectroopt/c and optical wave-mixing experiments 4.10. Molecular formulation: hyperpolarizabilities 104

4.10.1. Estimate of the harmonic-generation efficiencies 4.11. Local field corrections 106

4.1 I.I. Lorentz correction factor 4.11.2. Onsager correction factor

4.12. Calculation of susceptibilities: theoretical approaches 108 4.12.1. SOS method 4.12.2. Finite-field method 4.12.3. Phenomenological models

4.13. Resonances 110 4.14. Relation between the molecular and the bulk nonlinear response 110 4.15. Example: oriented thin film I I I 4. /6 . Second-order processes: three wave mixing 113 4. / 7. Reanalysis of second harmonic generation 114 4.18. Third-order processes: four wave mixing I 15 4.19. Experimental methods 118

4.19.1. Second-order susceptibilities 4.19.2. Powder method 4.19.3. Third-order susceptibilities Appendix 4A. Derivation of the nonlinear equation for plane waves 123 Appendix 4B. Effective nonlinear coefficients deff for crystallographic point groups 124 Appendix 4C. Structure of the dit tensor assuming Kleinmann symmetry 125

5. Inorganic Electrooptic Materials

5.1. Introduction 127 5.2. Dielectric and ferroelectric single crystals 129

5.2./ . General considerations 5.2.2. Bond anharmonic polarizability descriptions 5.2.3. Effects related to the ferroelectric transition

5.3. KDP-family crystals 132 5.4. Oxide ferroelectrics 133

5.4.1. В0ТЮ3 5.4.2. LiNbOi

viii

5.4.3. KTP

Nonferroelectric oxides

5.5.1. Silknites

5.5.2. Borate-family crystals

Electrooptic ceramics

PLZT ceramics

5.7.1. Introduction

5.7.2. Compositions and microstructure

5.7.3. Dielectric properties

5.7.4. Optical properties

5.7.5. Electrooptic properties

Semiconductors

5.8.1. Optical properties

Electrooptic behaviour of semiconductors

Physical mechanisms

5.10.1. Bound electrons: bond anharmonic models

5.10.2. Phillips spectroscopic models

5.10.3. Franz-Keldysh effect

5.10.4. Exciton effects

5.10.5. Free electron contribution (intraband effects)

Kerr materials: glasses

5.1 I.I. Homogeneous glasses

5.11.2. Composite glasses

6. Organic Electrooptic Materials

6. f. Introduction

6.2. Structural features of organic materials

6.3. Design criteria for electrooptic and nonlinear organic molecules

6.3.1. Second-order nonlinear response

6.3.2. Third-order nonlinear response

6.4. Macroscopic electrooptic (nonlinear) response

6.5. Organic single crystals

6.6. Langmuir-Blodgett (LB) films

6.7. Polymeric materials

6.7.1. Inorganic hosts

6.8. Liquid crystals: an introduction

6.9. Nematic liquid crystals

6.9./ . Energy considerations: continuum elastic model

6.9.2. Molecular anchoring at walls

6.9.3. Twisted nematics (TN)

6.9.4. Dielectric and optical properties

6.10. Electrooptics of nematic liquid crystals

6.10.1. Variable birefringence. Fredericksz transition

6.10.2. Dichroic absorption by dissolved dyes

6.10.3. Convective instabilities: dynamic light scattering

6.11. Cholesteric liquid crystals

S.S.

5.6. 5.7.

5.8.

5.9.

5.10.

5.11.

6.1 I.I. Energy considerations: continuum elastic model 6.11.2. Dielectric and optical properties 6.11.3. Electrooptics of cholesteric liquid crystals

6.12. Ferroelectric liquid crystals

6.12.1. Structural considerations 6.12.2. Electrooptics of surface stabilized ferroelectric liquid crystals (SSFLC)

6.13. Recent developments: polymer dispersed liquid crystals (PDLC)

Bulk Electrooptic Applications

7.1. Introduction

7.2. Deflectors and scanners

7.2./. Analogue deflectors

7.2.2. Digital defectors

7.2.3. Index gradient deflectors

7.3. Light modulators

7.4. Phase modulators

7.4.1. Frequency shifters 7.4.2. Pulse chirping

7.5. Polarization modulators

7.5.1. Optical isolator

7.6. Amplitude (intensity) modulators

7.6.1. Longitudinal Pockets modulators

7.6.2. Transverse Pockets modulators 7.6.3. Kerr modulators

7.6.4. Some practical considerations 7.7. Other noncrystalline devices

7.7./. PLZT shutters

7.7.2. Variable liquid crystal wavelength filters and phase retarders

7.7.3. Smart windows

7.8. High-frequency modulators

7.8.1. Resonant modulators 7.8.2. Travelling-wave modulators

7.9. Fabry-Perot modulators

7.9. /. Amplitude modulators 7.9.2. Phase modulators

7.10. Performance parameters for modulators

7.10.1. Figures of merit

7.11. Spatial light modulators (SLMs)

7.1 I.I. Performance parameters

7.12. Electrically addressed spatial light modulators (EASLMs)

7.13. Optically addressed spatial light modulators (OASLMs)

7.13.1. Liquid crystal light valves (LCLVs)

7.13.2. Pockels read-out modulators (PROMs)

7.13.3. MicroChannel spatial light modulators

7.14. Displays

7.15. Liquid crystal displays (LCDs)

7. /5. / . Simple LCD

ELECTROOPTICS

7. /5.2. Matrix-addressed displays 7.15.3. Ferroelectric LCDs

7.16. PLZT displays 216

8. Electrooptics and Integrated Optics

8.1. Introduction 219 8.2. Light propagation in optical waveguides: modes 220

8.2.1. Dispersion equation of the step-index planar guide 8.2.2. The Goos-Hänchen shift and the effective guide thickness 8.2.3. Field distributions for the step-index planar guide 8.2.4. Other waveguide geometries

8.3. Inorganic electrooptic waveguides 226 8.3.1. LiNbOi waveguides 8.3.2. Semiconductor waveguides

8.4. Organic electrooptic waveguides 232 8.5. Electrooptic modulation in waveguides 233

8.5.1. Single-waveguide electrooptic modulators 8.5.2. Mach-Zehnder type modulators 8.5.3. Electrooptic Bragg modulators

8.6. Coupled-mode formalism 237 8.7. Directional couplers 239 8.8. Other electrooptic devices 242 8.9. Measurement of electrooptic coefficients in waveguides 244

8.9.1. The Mach-Zenhder interferometer method 8.9.2. Attenuated total reflection (ATR)

9. Semiconductor Quantum Wells and Superlattices

9.1. Introduction 251 9.2. Fabrication of quantum wells and superlattices 252 9.3. Fabrication of quantum well electrooptic devices 254 9.4. Electronic structure 255

9.4.1. Electronic properties of a single quantum well 9.4.2. Electronic properties of coupled quantum wells and superlattices 9.4.3. Electronic properties of quantum wires and quantum dots

9.5. Optical properties of quantum wells 260 9.5./. Excitonic effects

9.6. Electrooptic effects in a quantum well 262 9.6.1. Electroabsorption 9.6.2. Electrorefraction. Electrooptic coefficients

9.7. Electrooptics of coupled quantum wells and superlattices 268 9.8. Electrooptics of quantum wires and quantum dots 270 9.9. Electrooptic applications 271 9.10. The self-electrooptic-effect device (SEED) 273 9.11. Concluding remarks 275

10. The Photorefractive Effect

CONTENTS xi

10.1. Introduction 279

/0.2. Holographie recording and erasure 280

10.3. Reading the hologram: diffraction efficiency 282

10.4. Microscopic mechanisms for the photorefractive effect 285

10.4.1. Charge-transport processes

10.4.2. Transport lengths

10.4.3. Carrier dynamics 10.5. Rate equations 289

10.5.1. Main approximations 10.5.2. Steady state recording (low modulation depths, m <£ I)

10.5.3. Kinetics of optical erasure

10.6. Fixing of holographic gratings 294

/0.7. Wave-coupling effects 295

10.7.1. beam amplification 10.7.2. Fringe bending

10.8. Short-pulse experiments 298

10.9. Four-wave mixing experiments: phase conjugation 299

10.9.1. Self-pumping

10.10. Photorefractive materials and active centres 302

10.10.1. Inorganic crystals and ceramics 10.10.2. Semiconductor crystals and nanostructures 10.10.3. Organic materials

10.11. Performance parameters 306

11. Photorefractive Applications

/ / . / . Introduction 31 I

11.2. Information storage 311 11.3. Real-time holographic interferometry 312

11.4. Beam modulators, deflectors and interference filters 314

11.5. Optical amplifiers 316

11.5.1. Image amplifiers 11.5.2. Laser beam clean-up

11.6. Optical phase conjugation 318

11.6.1. Lensless and speckle-free imaging

11.6.2. Imaging through a phase disturbing medium 11.6.3. Phase distortion correcbon in laser cavibes

11.6.4. Self-sweeping of the frequency of a dye laser

11.6.5. Phase-locking of independent lasers

11.6.6. Phase-conjugate mirrors in interferometers

11.7. Optical information processing and computing 323

11.7.1. Optical image processing

11.7.2. Optical computing: optical interconnects 11.7.3. Optical neural networks: associative memories

11.8. Determination of material parameters 328

Index 332