Spectral-domain determination of the propagation constant in biaxial planar media

The problem of finding the propagation constant (and other related characteristics) of biaxial medium planar waveguide structures is formulated in terms of Maxwell's equations. The special case of a diagonalized biaxial permittivity tensor in the coordinate system of interest is treated. From the approach given, the tensor Green's function in the Fourier (spectral) transform domain is found for three longitudinal-to-an-axis coupled electric-magnetic field sets applied to a simple layered structure. These Green's functions, which are analogous to circuit immittance matrices, are of use in the method of moments numerical calculations employing techniques such as Galerkin's method for finding the propagation constant. It is also demonstrated that the biaxial treatment properly reduces to the biaxial case. The treatment is applicable to the frequency-dispersive regimes of planar structures.