Spectral Element Method for Modeling Eccentric Coaxial Waveguides Filled with Anisotropic Media via Conformal Transformation Optics
In this work, a spectral element method (SEM) in cylindrical coordinates is explored for analyzing the electromagnetic field propagation in eccentric coaxial waveguides filled with anisotropic media. The proposed formulation employs conformal transformation optics to map the original problem into an equivalent concentric coaxial waveguide. Our novel cylindrical-coordinate-based SEM facilitates the mapping between reference and curvilinear elements for waveguides that present cylindrical-conforming boundaries. The proposed approach was validated against perturbation and finite-difference-based solutions, and preliminary results show that our solution excels because of its accuracy and low computational cost. With a few adaptations, the present cylindrical SEM formulation can be extended for modeling a large class of problems involving complex media such as metamaterial devices and geophysical exploration sensors.