The Mixed Spectral-Element Method for Anisotropic, Lossy, and Open Waveguides

The higher order mixed spectral-element method (SEM) is proposed for the analysis of anisotropic, lossy, and open waveguides. The new variational formulation incorporating Gauss’ law into the vectorial wave equation is completely free of spurious modes. It utilizes the edge-based curl-conforming Gauss–Lobatto–Legendre (GLL) polynomials to approximate the tangential vector of the electric field and the nodal-based scalar GLL basis functions to discretize its longitudinal component to obtain the highly accurate solution. By employing the mass-lumping technique, only a smaller generalized eigenvalue problem needs to be solved. Several numerical examples are given to verify that the mixed SEM is free of any spurious eigenmode and has spectral accuracy with the propagation constant.