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

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Abstract
A computer program is demonstrated 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. Using this implementation technique (based on successively more accurate approximations of the field), the first few higher order modes can be obtained without difficulty, which is usually one of the problems with this method. The comparison of results is given for standard passive structures examined and for waveguides in the index gain guiding regime.

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