A finite-element-based full-vectorial beam propagation method (BPM) for the analysis of the electromagnetic field evolution in three-dimensional (3-D) dielectric waveguides is presented. The approach has been derived in order to be suitable for the numerical discretization through finite elements and to fully account for the vectorial nature of the electromagnetic field. To this aim the problem related to the permittivity derivative at dielectric interface has been addressed and overcome. The advantages and the potentialities of the finite elements usage are discussed. The precision and the correctness of the proposed approach is demonstrated through numerical examples. Typical integrated optics structures, as a tapered waveguide and a Y-junction, are analyzed to assess the applicability of the method.
Ettore Montanari, Stefano Selleri, Luca Vincetti, and Maurizio Zoboli, "Finite-Element Full-Vectorial Propagation Analysis for Three-Dimensional z-Varying Optical Waveguides," J. Lightwave Technol. 16, 703- (1998)