Finite‐element analysis of anisotropic waveguides with tensor permittivity

A finite‐element expression for an anisotropic waveguide with a tensor permittivity is derived based on the variational expression in terms of all three components of the magnetic field. Since only the Hermitian condition is imposed on the permittivity tensor, the expression can handle an arbitrary anisotropic dielectric and a gyrostatic material. The spurious modes do not appear in the region of effective index of refraction larger than a specific value. From these points of view, the present finite‐element representation is considered to be one of the analysis methods useful for millimeter waveguides and optical waveguides. In this paper, a waveguide with a rectangular cross section is treated which is a fundamental structure for millimeter‐wave and otical integrated circuits. Specifically, rectangular anisotropic dielectric waveguides and rectangular gyrotropic waveguides are analyzed. The effect of off‐diagonal elements of the permittivity tensor on the guided mode characteristics is investigated.