A Circular-Harmonic Computer Analysis of Rectangular Dielectric Waveguides

TLDR

The study presents a computer analysis of propagating modes in a rectangular dielectric waveguide. The analysis expands the electromagnetic field into circular harmonics, matches core and cladding fields at the boundary, and solves the resulting equations on a computer to obtain propagation constants and mode configurations. The computations yield propagation‑constant curves and mode patterns that are refractive‑index independent for small core‑cladding index differences relevant to integrated optics, and also provide results for larger index differences typical of microwave applications.

Abstract

This paper describes a computer analysis of the propagating modes of a rectangular dielectric waveguide. The analysis is based on an expansion of the electromagnetic field in terms of a series of circular harmonics, that is, Bessel and modified Bessel functions multiplied by trigonometric functions. The electric and magnetic fields inside the waveguide core are matched to those outside the core at appropriate points on the boundary to yield equations which are then solved on a computer for the propagation constants and field configurations of the various modes. The paper presents the results of the computations in the form of curves of the propagation constants and as computer generated mode patterns. The propagation curves are presented in a form which makes them refractive-index independent as long as the difference of the index of the core and the surrounding medium is small, the case which applies to integrated optics. In addition to those for small index difference, it also gives results for larger index differences such as might be encountered for microwave applications.