Plane wave scattering by a dielectric loaded slit in a thick impedance screen

The electromagnetic scattering of the plane wave by a slit loaded with dielectric in a thick impedance screen is considered for a rather general case where the surface impedances of the screen planes and vertical sides of the slit have different values. Because of the symmetry of the scattering structure, the image bisection principle is used and the original problem is splitted up into even and odd excitation cases. By introducing the Fourier transform for each case yields a modified Wiener–Hopf equation of the second kind for each excitation. After decoupling these equations by standard transformation, each modified Wiener–Hopf equation is reduced to a pair of coupled Fredholm integral equations of the second kind. The solution of each integral equation involves two sets of infinitely many constants satisfying two infinite systems of linear algebraic equations and Branch-cut integrals which are evaluated approximately. Numerical solutions of these systems are obtained for various values of the parameters such as the surface impedance of the screen, the vertical wall impedance of the slit, the width and the thickness of the slit and the permittivity of the filling material of the slit which permit one to study the effect of these parameters on the diffraction phenomenon. In order to validate the present Wiener–Hopf solution, experimental verification of the dielectric loaded thick metallic slit has been implemented in microwave frequencies with good agreements.