The problem of plane wave scattering by a half-plane with different face impedances is reexamined by means of the Wiener-Hopf-Hilbert technique. The mode of attack is altered somewhat from that employed in a previous paper by Hurd, and the analysis is more carefully done. We show that the same solution is obtained whether upper or lower branch cut formulations are used. We also show that our solution is identical to that of Maliuzhinets. and that it satisfies the principle of reciprocity.Le probleme de la diffraction d'une onde par un demi-plan dont les deux faces ont des impedances differentes est reexamine au moyen de la technique Wiener-Hopf-Hilbert. La f a~o n d'attaquer le probleme est quelque peu modifiee par rapport a celle qu'on avait utilisee dans un travail anterieur par Hurd, et I'analyse est faite avec plus de soin. Nous montrons qu'on obtient la mtme solution avec les coupures relatives aux points de branchement dans la partie superieure ou dans la partie inferieure du plan. Nous montrons aussi que notre solution est identique a celle de Maliuzhinets et qu'elle satisfait au principe de reciprocite.[Traduit par le journal]Can.

An exact, closed form solution is presented for a diffraction problem by a half-plane embedded in a chiral medium. The incidence direction of an electromagnetic plane wave is assumed to be normal to the edge of the half-plane. The problem has been reduced to a boundary value problem for two modal potentials satisfying distinct Helmholtz equations and coupled by the boundary conditions at the half-plane. A solution is constructed with the aid of the Wiener-Hopf technique. A basic feature of the problem is its two-mode character exhibited by: two families of diffracted rays, reflection coupling of the modes, excitation of lateral waves.

An exact, closed-form solution is found for the following half-plane diffraction problem: (I) The medium surrounding the half-plane is both electrically and magnetically gyrotropic. (II) The scattering half-plane is perfectly conducting and oriented perpendicular to the distinguished axis of the medium. (III) The incident electromagnetic plane wave propagates in a direction normal to the edge of the half-plane.The formulation of the problem leads to a coupled pair of Wiener–Hopf equations. These had previously been thought insoluble by quadratures, but yield to a newly discovered technique : the Wiener–Hopf–Hilbert method. A basic feature of the problem is its two-mode character i.e. plane waves of both modes are necessary for the spectral representation of the solution. The coupling of these modes is purely due to edge diffraction, there being no reflection coupling. The solution obtained is simple in that the Fourier transforms of the field components are just algebraic functions. Properties of the solution are investigated in some special cases.

The diffraction problem of a plane wave obliquely incident on a half-plane embedded in a gyrotropic medium whose distinguished axis is parallel to the half-plane's edge is considered. The problem is a generalization of previous work by JOn who treated normal incidence of a plane wave. The generalization is not trivial: indeed for many years the problem bad been thought insoluble. We have found that the Wiener-Hopf-Hilbert (WHH) method provides a factorization of the Wiener-Hopf maxtrix encountered, and we obtain an exact closed-form solution.