A Higher-Order Spectral Element Method to Model Eccentric Anisotropic Two-Layer Waveguides via Conformal Transformation Optics

We present an improved spectral element method (SEM) to analyze eccentric two-layer waveguides filled with anisotropic non-reciprocal media. The formulation employs conformal transformation optics (TO) theory to map the original eccentric waveguide into an equivalent concentric problem. The TO is extended to include non-symmetric and non-Hermitian media tensors. In the concentric domain, we apply higher-order two-dimensional basis functions associated with the zeros of the completed Lobatto polynomial to model the fields. We validated our approach against finite-element method (FEM) solutions, and the preliminary results show that our technique requires far fewer degrees of freedom than FEM.