Wiener-Hopf analysis of the parallel plate wave guide with opposing rectangular dielectric-filled grooves

Abstract

The purpose of the present work is to provide a rigorous analysis of the parallel plate wave guide with two opposing rectangular grooves of different depths and filled with different dielectric materials. This configuration may be used as a band-stop filter. The representation of the solution to the three-part mixed boundary-value problem in terms of Fourier integrals leads to a couple of simultaneous modified Wiener-Hopf equations. By using the analytical properties of the functions that occur, the simultaneous modified Wiener-Hopf equations are reduced to the solution of four infinite systems of linear algebraic equations. These systems are solved numerically, and the band-stop filter characteristics of the reflection coefficient are studied in terms of frequency, groove sizes, and the parameters of the filling dielectric material.