SOLUTION OF THE VECTOR WAVE-EQUATION USING GREEN-FUNCTION TECHNIQUES

Polarized solutions of the vector wave equation are computed for two-dimensional waveguides using a Green's function perturbative approach. By solving the vector wave equation, the discontinuities in the normal electric field across internal boundaries are automatically taken into account, which obviates the need for imposing internal boundary conditions. Both the effective indices and the electric field profiles can be obtained for structures containing arbitrary index of refraction profiles. In order to obtain field profiles to the same order of accuracy as the effective indices, the iterated Galerkin method is used to improve the wave equation eigenfunctions. Compared with comparable finite element or finite difference-based codes, the computed effective indices and electric field profiles are determined to be in excellent agreement.