Cutoff frequencies in planar optical waveguides with arbitrary index profiles: An efficient numerical method

摘要: A numerical method for obtaining mode cutoffs planar waveguides with arbitrary index profiles is developed. The based on the Galerkin in which wave equation modes at cutoff converted to a matrix eigenvalue using set of orthogonal basis functions. Due different boundary conditions, we have identified two separate cases; one, cover and substrate indices are identical leading same behavior field these regions and, other, hence, behaves differently. We accordingly chosen functions cases. results generalized problem has been standard symmetric analytically. used obtain variety profiles. Comparisons available exact show that very good accuracies can be obtained moderate sizes.