Optical Filter Design and Analysis: A Signal Processing Approach

CHAPTER TWO

Fundamentals of Electromagnetic Waves and Waveguides

The plane wave is the most fundamental electromagnetic wave and is a particular solution of Maxwell's equations. It will be used as an example to develop the fundamentals of electromagnetic waves in dielectric media including solutions to Maxwell's equations, phase velocity, group velocity, polarization, boundary conditions, and total internal reflection, which makes it possible for optical signals to propagate and be guided in waveguides. Based on the concepts developed for plane waves, planar one-dimensional waveguides will be presented, followed by the study of rectangular two-dimensional waveguides. Fundamental concepts for wave propagation in waveguides such as modes, orthogonality and completeness of modes, dispersion, and losses are discussed. A review of waveguide-based directional couplers, the fundamental building block for planar waveguide filters, is followed by a brief presentation of star couplers and multi-mode interference couplers, which are important for multi-port filters. The chapter concludes with a discussion of material properties and fabrication processes that are important to filter design, with a focus on planar waveguide implementations.

2.1 THE PLANE WAVE

2.1.1 Maxwell's Equations

The governing equations for electromagnetic wave propagation are Maxwell's equations. In fact, Maxwell's equations describe not only wave propagation at high frequencies, but also zero Hz static electromagnetic ...