Finite-difference vectorial-beam-propagation method using Yee’s discretization scheme for modal fields

Abstract

A novel finite-difference vectorial-beam-propagation method using Yee’s mesh is demonstrated to be a simple, efficient, and versatile method to analyze the modal characteristics of waveguide structures with arbitrary cross section. The method is derived from directly discretizing Maxwell’s equations with the use of Yee’s mesh. A von Neumann stability analysis indicates that there is a stable region for the wave front to propagate along the imaginary waveguide axis. Such a direct propagation method is efficient in terms of CPU time and memory requirements. Therefore the propagation constants and their corresponding vectorial-modal-field distributions for waveguides of variable cross sections are obtained efficiently and simultaneously. Results in close agreement with published results using either analytic or numerical methods for several waveguides are shown.