Finite-element full-vectorial propagation analysis for three dimensional z-varying optical waveguides

A finite-element-based full-vectorial beam propagationmethod (BPM) for the analysis of the electromagneticfield evolution in three-dimensional (3-D) dielectric waveguides ispresented. The approach has been derived in order to be suitablefor the numerical discretization through finite elements and tofully account for the vectorial nature of the electromagnetic field.To this aim the problem related to the permittivity derivativeat dielectric interface has been addressed and overcome. Theadvantages and the potentialities of the finite elements usageare discussed. The precision and the correctness of the proposedapproach is demonstrated through numerical examples. Typicalintegrated optics structures, as a tapered waveguide and a Y -junction, are analyzed to assess the applicability of the method.