A vector Galerkin's method based on E fields

To find approximate solutions of the vector wave equation for general dielectric optical waveguides, a vector Galerkin's method based on the transverse electric field (E formulation) is formulated and presented. The method is compared with the exact solution for a circular step-index fiber, and a agreement in beta /k to 0.4% with 16 basis functions in each of the two orthogonal directions is found. It is noted that the Hermite-Gaussian basis functions can overcome the difficulties in the choice of the adequate size of the enclosed domain.<
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