Scattering characteristics of a rectangular groove in a reactive surface

The diffraction of a plane electromagnetic wave by a rectangular groove in a reactive plane is studied rigorously through the Fourier transform technique. The corresponding boundary value problem is Formulated into a modified Wiener-Hopf equation of the third kind whose approximate solution involves two sets of infinite number of unknown constants satisfying two infinite systems of linear algebraic equations. Numerical solutions of these systems are obtained for various values of the surface reactance and the sizes of the groove through which the effects of these parameters on the diffraction phenomenon are studied.