Arbitrary-order three-point finite difference method for the modal analysis of chiral waveguides

Abstract

A three-point finite difference method with an arbitrary order of accuracy is proposed for the modal analysis of chiral planar waveguides. The elaborate application of a nonuniform grid, compact finite difference technique, and boundary conditions results in an efficient, easily implemented, and versatile tool for the modal analysis of chiral planar waveguides with an arbitrarily discontinuous profile of permittivity, permeability, and chirality. In particular, this method efficiently resolves the fine structures in plasmon and photonic crystal waveguides. For the test model of a chiral-metallic plasmon waveguide, stable convergence up to a sixteenth order of accuracy can be obtained, which produces a relative error on the effective index that approaches the machine precision with only eighty grid points.