Power Transfer in a Large Parallel Array of Coupled Dielectric Waveguides

This paper presents a compact analytical solution to the conventional coupled-mode equations for a large parallel coupled array of identical dielectric waveguides. Such arrays could be used as couplers in millimeter-wave or fiber-optic communication. The approach here is to characterize the array response to a signal injected into single waveguide first. This approach drastically simplifies the double Fourier sums called for in dealing with multiple waveguide injections. Regardless of the size of an array, the response consists of a series of Bessel functions, six of which suffice to give good accuracy. The general solution is then obtained by a linear superposition of responses when multiple waveguides are injected. Quasi-3-D profiles of waves propagating and spreading in a large array of 100 coupled guides can be quickly displayed using Microsoft Excel. Remarkably clear characteristics of power transfer such as self-focusing and boundary reflection are observed. Since the solution involves Bessel functions of high orders that diminish rapidly in value, the solution for very large arrays can be computed just as efficiently as for smaller arrays.