Improvement of finite difference methods for step-index optical waveguides

Abstract

New 3-point finite difference formulae with equally spaced grid points are given for the analysis of scalar or semivectorial fields in waveguides with discontinuous refractive index profiles. The new formulae lead to more accurate calculations for the modes than the previously known methods, irrespective of the location of the discontinuities with respect to the grid points and without averaging the permittivity over meshes.