Exact numerical technique for the analysis of step discontinuities and tapers in optical dielectric waveguides

Abstract

In this paper, we first review the existing analytical methods used to analyze step discontinuities and tapers in optical dielectric waveguides. We then develop an exact numerical technique for determining the transmitted, reflected, and radiated power that is due to a step discontinuity or a taper in an optical dielectric waveguide. We demonstrate the method by evaluating step discontinuities and tapers in various symmetric and asymmetric slab waveguides. Unlike with previous analytical methods, no physical approximations are made throughout the entire analysis. For this reason, our method can be used to evaluate a step discontinuity or a taper in a dielectric waveguide of arbitrary cross section, regardless of the magnitude of the geometrical mismatch between the input and the output waveguide sections.