Silicon Photonics: Electromagnetic Theory

by Wouter Westerveld

Overview

This book is a concise introduction to the fundamental theories of integrated optics that focuses on modern silicon photonic technology. It offers analytical mathematical treatments and practical guidelines for the design of silicon-photonic circuits including examples to further emphasize the material presented.

Product Details

ISBN-13:	9780750313872
Publisher:	Iop Publishing Ltd
Publication date:	02/10/2018
Pages:	164
Product dimensions:	7.27(w) x 10.46(h) x 0.60(d)

Table of Contents

Preface viii

Further reading x

Author biographies xii

List of symbols xiii

1 Introduction 1-1

1.1 Photonics 1-1

1.2 Integrated photonics 1-1

1.3 Silicon photonics 1-2

1.4 Silicon-on-insulator technology in this book 1-3

References 1-3

2 Waveguides 2-1

2.1 Maxwell's equations for linear, passive materials 2-1

2.2 Dielectric slab waveguides 2-2

2.2.1 TE modes 2-4

2.2.2 TM modes 2-5

2.3 General properties of modes in dielectric waveguides 2-7

2.3.1 Guided waves described by E_x E_y, H_x and H_y 2-7

2.3.2 Guided waves described by E_z and H_z 2-9

2.3.3 Orthogonality 2-11

2.3.4 Power flow 2-13

2.3.5 Mode normalization 2-14

2.3.6 Mode expansion conjecture 2-14

2.3.7 Waveguides with losses and bends 2-16

2.4 Rectangular Si waveguides: extension of Marcatili's approach 2-18

2.4.1 Ansatz for the shape of the field 2-18

2.4.2 Boundary conditions 2-20

2.4.3 Approximate methods 2-22

2.4.4 Avoided crossing of modes with similar propagation constants 2-26

2.4.5 Dispersion: effective group index 2-30

2.5 Rigorous numerical mode-solvers 2-32

2.6 Typical silicon-on-insulator waveguides 2-33

References 2-35

3 Components 3-1

3.1 Directional couplers 3-1

3.1.1 Coupled mode theory 3-1

3.1.2 Eigenmode expansion (EME) 3-3

3.1.3 Rigorous FDTD simulations 3-5

3.2 Multimode interference (MMI) couplers 3-8

3.2.1 Approximate description of the guided modes 3-8

3.2.2 Multimode propagation and interference 3-11

3.2.3 Imaging and power splitting 3-13

3.2.4 A 2 × 2 MMI coupler 3-15

3.2.5 Comparison with rigorous numerical simulations 3-17

3.3 Fibre to chip coupling 3-19

3.3.1 Inverted optical taper (fibre to chip coupler) 3-22

3.3.2 Basic out-of-plane grating couplers 3-23

3.3.3 Advanced grating couplers 3-28

3.4 Ring and racetrack resonators 3-30

3.4.1 Silicon ring resonators with directional couplers 3-32

3.4.2 Ring resonator resonances 3-32

3.4.3 Ring resonators with a non-uniform waveguide 3-35

3.5 Mach-Zehnder interferometers 3-36

References 3-39

4 Computational methods 4-1

4.1 Finite difference time domain (FDTD) 4-1

4.2 The eigenmode expansion method 4-6

4.2.1 Properties of unidirectional modes 4-7

4.2.2 Number of modes 4-7

4.2.3 Mode matching 4-8

4.2.4 The T-matrix scheme 4-10

4.2.5 The S-matrix scheme 4-11

4.2.6 Examples: MMI coupler and grating coupler 4-13

References 4-15

5 Devices 5-1

5.1 Ring resonator sensors 5-2

5.1.1 Ring resonators 5-2

5.1.2 Temperature sensors 5-3

5.1.3 Sensor systems and interrogation 5-4

5.1.4 Influence of an external effect on rectangular silicon waveguides 5-4

5.1.5 Biosensors 5-6

5.1.6 Ultrasound sensors 5-7

5.2 Silicon photonic modulators based on carrier-depletion in a MZI 5-11

5.2.1 Modulation formats: on-off keying 5-12

5.2.2 Electro-optical conversion: pn-junction carrier depletion 5-12

5.2.3 Phase to amplitude: Mach-Zehnder inferometer 5-15

5.2.4 A 40 GBit/s optical modulator 5-16

5.3 Fabrication technology and design of optical circuits 5-17

5.3.1 Example: design of racetrack for ultrasound sensor 5-20

References 5-21

Appendices

A Coupled mode theory of parallel waveguides A-1

B Lossless transmission matrix B-1

C Semiconductor physics of pn-junctions C-1