Diffraction by a half plane in a gyrotropic medium (normal incidence)

Abstract

An exact, closed-form solution is found for the following problem of half-plane diffraction in a gyrotropic medium. (i) A perfectly conducting half-plane is parallel to the distinguished axis of the medium with the edge perpendicular to the axis. (ii) The incident-wave direction is normal to the edge of the half-plane.The problem is phrased as a boundary-value problem for a system of two coupled second-order partial differential equations. Two basic properties characterize the problem. (i) It is two-moded; that is, superpositions of both ordinary and extraordinary waves are necessary for the spectral representation of the solution. (ii) It involves reflection coupling of the modes; that is, modes couple on reflection from an entire plane.The formulation of the problem leads to two uncoupled Wiener–Hopf equations that are solved in the classical manner. This is in contrast to previous two-mode half-plane gyrotropic problems where Wiener–Hopf equations were coupled, requiring advanced techniques for their solution. Basic properties of the solution (for example, excitation of surface waves) are briefly discussed.