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.PACS Nos.: 42.25.Bs, 42.25.Gy, 42.82.Et