Practical Vectorial Mode Solver for Dielectric Waveguides Based on Finite Differences

This study presents a finite-difference-based numerical solver designed for the electric field formulation of vector wave equations in optically linear, non-magnetic, dielectric waveguides. We construct a generalized eigenvalue problem by incorporating all three components of the electric field into a self-consistent formulation. This ensures accurate enforcement of boundary conditions and reduces numerical artifacts, particularly at permittivity discontinuities. We validate the solver's performance through two representative waveguide structures, demonstrating its accuracy in computing both propagation constants and mode profiles.