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Variational Analysis of a Dually Polarized Waveguide Skew Loaded by Dielectric Slab

An expression for the propagation constant, cutoff frequency, and associated fields of the first two modes in a waveguide filled with a tilted slab of the dielectric is derived using the variational analysis. The solution to such a problem is divided into two parts. First, the slab is assumed to be parallel with the walls of the waveguide with no tilt. In this part, the effective permittivities of the first two orthogonally polarized modes are derived from two different variational expressions for the transversal resonance frequencies. This results in a diagonal tensorial permittivity that represents an effective uniaxial anisotropic medium. Next, this tensorial permittivity is transformed into a tilted set of coordinates representing the required tilt angle. In the new set of coordinates, a variational expression for the propagation constant is solved using the Rayleigh–Ritz procedure. The resulting analytic expressions are verified using a full-wave analysis and a prototype measurement.