Optical Filter Design and Analysis: A Signal Processing Approach

Contents

Preface

1 Introduction

1.1 Optical Filters

1.2 Filter Applications in WDM Systems

1.2.1 Bandpass Filters for Multiplexing, Demultiplexing, and Add/Drop

1.2.2 Gain Equalization Filters

1.2.3 Dispersion Compensation Filters

1.3 Scope of the Book

References

2 Fundamentals of Electromagnetic Waves and Waveguides

2.1 The Plane Wave

2.1.1 Maxwell's Equations

2.1.2 The Wave Equation in a Dielectric Medium

2.1.3 Solutions of the Wave Equation

2.1.4 Phase Velocity and Group Velocity

2.1.5 Reflection and Refraction at Dielectric Interfaces

2.2 Slab Waveguides

2.2.1 The Guided Wave Condition

2.2.2 Characteristic Equations for the Slab Waveguide

2.2.3 Waveguide Modes

2.2.4 Orthogonality and Completeness of Modes

2.2.5 Dispersion

2.2.6 Loss and Signal Attenuation

2.3 Rectangular Waveguides

2.3.1 Wave Equation Analysis

2.3.2 The Effective Index Method

2.3.3 Perturbation Corrections

2.4 Splitters and Combiners

2.4.1 Directional Couplers

2.4.2 Star Couplers

2.4.3 Multi-Mode Interference Couplers

2.5 Material Properties and Fabrication Processes

2.5.1 Materials

2.5.2 Fabrication

References

Problems

3 Digital Filter Concepts for Optical Filters

3.1 Linear Time-Invariant Systems

3.1.1 Continuous Signals

3.1.2 Discrete Signals

3.2 Digital Filters

3.2.1 The Z-Transform

3.2.2 Poles and Zeros

3.2.3 Stability and Causality

3.2.4 Magnitude Response

3.2.5 Group Delay and Dispersion

3.2.6 Minimurn-, Maximum-, and Linear-Phase Filters

3.3 Single-Stage Optical Filters

3.3.1 A Single-Stage MA Filter ...