Native 2-D-FEM/Mode-Matching Formulation for Second-Order Symmetric Waveguide Devices

Abstract

In this work we present, taking a holistic approach, the integration between the 2-D finite element method (FEM) and mode-matching (MM) for devices exhibiting second-order rotational symmetry and, optionally, first-order axial symmetry. Using a tailored approach, involving adequate inner products, the formulation allows for the rotationally symmetric modes with complex-valued eigenfunctions to keep their useful physical and mathematical properties. Mode class orthogonality and degeneracy discrimination are kept throughout the pipeline. The approach leads to a more efficient and accurate analysis of devices with these geometrical properties, significantly reducing the dimensionality of the problem, both in the inner-product calculation and in the generalized scattering matrix (GSM) derivation, while providing physical insight regarding modal discrimination.