In this paper, a new vectorial boundary element method is introduced and applied to the modal analysis of dielectric waveguides with piecewise homogeneous refractive indexes. The procedure, which is free of spurious modes,determines the full field distribution from the longitudinal fields at the refractive index boundaries. Singular kernels are evaluated through series solutions while the electric field discontinuity at corners is accommodated through either a grid refinement technique or a semianalytic approach. Our formalism generates propagation constants and modal field distributions for several representative refractive index profiles with far higher accuracy than standard finite-difference or finite-element procedures.
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