VECTORIAL FINITE-DIFFERENCE SCHEME FOR ISOTROPIC DIELECTRIC WAVE-GUIDES - TRANSVERSE ELECTRIC-FIELD REPRESENTATION

A computer program is demonstrated for calculating the two-dimensional transversal vectorial field in longitudinally invariant isotropic opt ical waveguides by applying a simple finite difference approach using successive overrelaxation on a Gauss-Seidel algorithm and estimation o f the propagation constant using the Rayleigh quotient. The method is formulated in terms of the transverse electric field that implicitly s atisfies the boundary conditions to the order of the discretisation st ep. The implementation is such that it allows the computations, even o f structures with complex refractive index, to be performed on a perso nal computer. Using this implementation technique (based on successive ly more accurate approximations of the field), the first few higher, o rder 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.