Optical Filter Design and Analysis: A Signal Processing Approach

CHAPTER ONE

Introduction

The field of signal processing provides a host of mathematical tools, such as linear system theory and Fourier transforms, which are used extensively in optics for the description of diffraction, spatial filtering, and holography [1–2]. Optical filters can also benefit from the research already done in signal processing. In this book, digital signal processing concepts are applied to the design and analysis of optical filters. In particular, digital signal processing provides a readily available mathematical framework, the Z-transform, for the design of complex optical filters. More conventional approaches, such as coupled-mode theory, are also included for comparison. The relationship between digital filters and optical filters is explored in Section 1.1, and a brief historical overview of optical waveguide filters is given. Previously, spectrum analysis was the main application for optical filters. Recently, the demand for optical filters is increasing rapidly because of the deployment of commercial wavelength division multiplexed (WDM) optical communication systems. With low loss optical fibers and broadband optical amplifiers, WDM systems have the potential to harness a huge bandwidth, and optical filters are essential to realizing this goal. In addition to traditional designs such as bandpass filters, new applications have emerged such as the need for filters to perform gain equalization and dispersion compensation. Filter applications for WDM systems ...