All integrated optical components and devices make use of "waveguides", where light is confined by total internal reflection. The elements in such "photonic chip" are interconnected through waveguides, and also the integrated optics components themselves are fabricated using waveguide configuration, such as couplers, switches, modulators, multiplexors, amplifiers and lasers, etc. These components are integrated in a single substrate, thus resulting in a compact and robust photonic device, which can be optically connected through optical fibres. With and increase in the number of integrated optical components and devices emerging from the research laboratories to the market place an up-to-date book is essential in collecting, summarizing and presenting the new developed photonic devices. This includes fundamental aspects, technical aspects (such as fabrication techniques and materials) and characterisation and performance. This is an advanced text aimed at specialists in the field of photonics, but who may be new to the field of integrated photonics. The fundamental aspects have been carefully considered, and all the topics covered by the book start at a medium level, making it highly relevant for undergraduate and post-graduate students following this discipline.

Ginés Lifante is the author of Integrated Photonics: Fundamentals, published by Wiley.

Preface

xi

About the Author

xiii

Introduction to Integrated Photonics

1

(23)

Introduction

1

(1)

Integrated Photonics

1

(3)

Brief History of Integrated Photonics

4

(2)

Characteristics of the Integrated Photonic Components

6

(4)

Integrated Photonics Technology

10

(3)

Basic Integrated Photonic Components

13

(5)

Some Examples of Integrated Photonics Devices

18

(3)

Structure of the Book

21

(3)

References

22

(1)

Further Reading

23

(1)

Review of the Electromagnetic Theory of Light

24

(28)

Introduction

24

(1)

Electromagnetic Waves

25

(12)

Maxwell's equations: wave equation

25

(2)

Wave equation in dielectric media

27

(2)

Monochromatic waves

29

(1)

Monochromatic plane waves in dielectric media

30

(2)

Polarisation of electromagnetic waves

32

(2)

Light propagation in absorbing media

34

(3)

EM Waves at Planar Dielectric Interfaces

37

(15)

Boundary conditions at the interface

37

(3)

Reflection and transmission coefficients: reflectance and transmittance

40

(7)

Total internal reflection

47

(3)

References

50

(1)

Further Reading

51

(1)

Theory of Integrated Optic Waveguides

52

(46)

Introduction

52

(1)

Optical Waveguides: Basic Geometries

52

(6)

Types of Modes in Planar Optical Waveguides

58

(3)

Wave Equation in Planar Waveguides

61

(5)

Guided Modes in Step-index Planar Waveguides

66

(7)

Graded-index Planar Waveguides

73

(10)

Multi-layer approximation

74

(2)

The ray approximation

76

(4)

Reconstruction of index profiles: the inverse WKB method

80

(3)

Guided Modes in Channel Waveguides

83

(15)

Marcatili's method

85

(6)

The effective index method

91

(5)

Notes

96

(1)

References

96

(2)

Coupled Mode Theory: Waveguide Gratings

98

(38)

Introduction

98

(1)

Modal Coupling

98

(23)

Modal orthogonality and normalisation

98

(2)

Modal expansion of the electromagnetic field

100

(2)

Coupled mode equations: coupling coefficients

102

(4)

Coupling mode theory

106

(4)

Co-directional coupling

110

(6)

Contra-directional coupling

116

(5)

Diffraction Gratings in Waveguides

121

(15)

Waveguide diffraction gratings

121

(1)

Mathematical description of waveguide gratings

122

(2)

Collinear mode coupling induced by gratings

124

(3)

Coupling coefficients calculation

127

(1)

Coupling coefficients in modulation index gratings

128

(3)

Coupling coefficients in relief diffraction gratings

131

(3)

References

134

(1)

Further Reading

135

(1)

Light Propagation in Waveguides: The Beam Propagation Method

136

(27)

Introduction

136

(1)

Paraxial Propagation: Fresnel Equation

137

(1)

Fast Fourier Transform Method (FFT-BPM)

138

(4)

Solution based on discrete fourier transform

139

(3)

Method Based on Finite Differences (FD-BPM)

142

(4)

Boundary Conditions

146

(4)

Transparent boundary conditions

148

(2)

Spatial Frequencies Filtering

150

(3)

Modal Description Based on BPM

153

(10)

Modal field calculation using BPM

157

(4)

Notes

161

(1)

References

161

(1)

Further Reading

162

(1)

Appendix 1 Complex Notation of the Electric and Magnetic Fields

163

(1)

Appendix 2 Phase Shifts for TE and TM Incidence

164

(2)

Appendix 3 Marcatili's Method for Solving Guided Modes in Rectangular Channel Waveguides

166

(5)

Appendix 4 Demonstration of Formula (4.3)

171

(1)

Appendix 5 Derivation of Formula (4.4)

172

(2)

Appendix 6 Fast Fourier Algorithm

174

(2)

Appendix 7 Implementation of the Crank-Nicolson Propagation Scheme

176

(3)

Appendix 8 List of Abbreviations

179

(1)

Appendix 9 Some Useful Physical Constants

180

(1)

Index

181

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