An Efficient Finite-Element Formulation for Anisotrpic Wave-Guides without Spurious Modes

A numerically efficient finite element formulation is presented for the analysis of arbitrary shaped waveguides with anisotropic material characteristics. The electromagnetic field is described either by the three components of a magnetic vector potential and an electric scalar potential or by the three components of an electric vector potential and a magnetic scalar potential. The uniqueness of the potentials is ensured by the incorporation of the Coulomb gauge and by proper boundary conditions. Owing to the correct description of the electromagnetic field, no spurious modes appear. Standard finite element techniques are employed for the numerical solution leading to a generalized eigenvalue problem with symmetric, sparse matrices. This is solved by means of the bisection method with the sparsity of the matrices fully utilized. Waveguides with closed and open boundaries and including both isotropic and anisotropic materials and sharp edges are presented as examples.