Half-plane diffraction in a chiral medium

Abstract

An exact, closed-form solution is presented for the problem of diffraction of an electromagnetic plane wave by a perfectly conducting half-plane embedded in a chiral (optically active) medium. The direction of incidence is arbitrary (3D case). The fundamental feature of the problem is its two-mode character. A chiral medium is isotropic but handed and supports two modal fields propagating with distinct velocities. The modes couple at the screen and its edge. Arising phenomena are exemplified by the two cones of diffracted rays and the excitation of lateral waves at the half-plane. The problem is a generalization of the previously solved 2D case of normal incidence and this motivates the adopted approach via the modal Hertz potentials. A subtle role in this context is played by the modal ghost potentials, i.e. peculiar potentials corresponding to the zero electromagnetic field. The mathematical core structure underlying the problem is defined by a boundary value problem for two scalar functions satisfying distinct Helmholtz equations and subject to a pair of boundary conditions at the half-plane. Required solutions to this problem are obtained with the aid of the Wiener–Hopf technique. The main result of the paper consists in showing how to generate, via relevant operators, the 3D electromagnetic solution from three appropriate solutions to the core problem. These solutions are, in essence, available from the 2D case. Basic properties of the solution are briefly discussed. Definitions of the diffraction coefficients indicate the canonical role of the problem for a geometrical theory of diffraction in chiral media.