A higher-order spectral element method for modeling eccentric anisotropic multilayered waveguides via transformation optics

We present a higher-order spectral element method (SEM) for analyzing eccentric anisotropic multilayered waveguides. The formulation uses conformal transformation optics to map the original eccentric waveguide to an equivalent concentric one. This transformation is extended to handle anisotropic non-reciprocal media characterized by non-symmetric and non-Hermitian tensors. In the transformed concentric domain, higher-order two-dimensional basis functions associated with the zeros of the completed Lobatto polynomial are used to expand the fields. To simulate radially unbounded problems, we employ a complex-stretched perfectly matched layer to mimic open space. The method is validated with radially bounded two-layer and three-layer waveguides and radially unbounded three-layer waveguides. Comparisons with the finite element method (FEM) demonstrate that our SEM approach requires significantly fewer degrees of freedom than FEM.