A parasite-free non-orthogonal frequency-domain finite difference method for the electromagnetic analysis of anisotropic waveguides

A methodology is presented for the development of a discrete vector eigenvalue problem for the dispersive analysis of inhomogeneous, anisotropic waveguiding structures. The methodology is based on the discretization of the the frequency-dependent Maxwell's equations on a non-orthogonal grid using covariant and contravariant representation for the fields and a simple point-matching procedure. The occurrence of spurious modes is avoided by the direct enforcement of Gauss' law in the development of the matrix eigenvalue problem. Results from the application of the proposed method to the dispersive analysis of planar, anisotropic microwave and optical waveguides compare favorably with published data obtained using alternative finite element formulations.