A Novel Finite-Element Method for Propagation Analysis of Open Dielectric Waveguides

Abstract

A modified finite-element method for propagation analysis of open dielectric waveguides, such as optical fibers and integrated optical waveguides, is presented. The method is based on the full vectorial finite-element formulation (Svedin [6]), which has been found to be absent of spurious modes. An asymptotically correct, exponentially decaying approximation of thie radial field behaviour has been incorporated in the infinite-element expansion used for the exterior region. The exponential decay is hereby controlled by a set of transversal wavenumbers related to each medium. The linearity of the original finite-element method has been conserved, which results in a sparse generalized eigenvalue problem. Numerical examples including both optical fibers and integrated optical waveguides, isotropic as well as anisotropic, have been analyzed in order to confinm the validity of the method. The observed correspondence with analytical or elsewhere reported solutions has been found excellent. For some waveguides a high accuracy near cut-off has been obtained by adding a special near-field wavenumber. No spurious modes have been observed using the proposed method.