On the Transformation of the Maxwell Equations for Inhomogeneous and Anisotropic Media into a Numerically Stable Eigenproblem and its Applications

We show that the Maxwell equations for inhomogeneous and fully-anisotropic media can be transformed into an equivalent Eigenproblem. The method is well-suited for implementation in digital computers and allows the electromagnetic wave analysis in nonflat surface-, flat surface-, single layer-, and multilayer-problems. Here, as a special application, the method is used for derivation of dyadic Green´s functions for shielded, layered, and anisotropic media. The structure of slowness surfaces in isotropic and anisotropic media are discussed. The method is combined with Floquet´s theorem to construct periodic dyadic Green´s functions for printed phased antennas on anisotropic substrates. Consecutively, the method of weighted residuals is applied to solve for the associated field distribution.