Vectorial finite difference scheme for isotropic dielectric waveguides: transverse electric field representation

The authors demonstrate a computer program for calculating the two-dimensional transversal vectorial field in longitudinally invariant isotropic optical waveguides by applying a simple finite difference approach using successive overrelaxation on a Gauss-Seidel algorithm and estimation of the propagation constant using the Rayleigh quotient. The method is formulated in terms of the transverse electric field that implicitly satisfies the boundary conditions to the order of the discretisation step. The implementation is such that it allows the computations, even of structures with complex refractive index, to be performed on a personal computer