Semivectorial polarised finite difference method for optical waveguides with arbitrary index profiles

A simple accurate method, which automatically takes full account of the discontinuities in the normal electric field components across any arbitrary distribution of internal dielectric interfaces, is presented for the determination of polarised solutions of the Helmholtz wave equation. The application of the shifted inverse power iteration method to the resulting matrices, enables any required propagation eigenvalue (not necessarily the fundamanetal mode) to be determined, together with its corresponding electric field profile. It is found that the results, which are presented for various semiconductor rib waveguide structures, compare favourably with published vector finite element and scalar results.