A powerful method of solving diffraction problems is described. In it, a system of Wiener–Hopf equations is transformed into a system of Hilbert problems. The latter apparently can be solved fora wider range of problems than the former. As an example, the diffraction problem of a plane wave incident on a half-plane with different face impedances is considered. This problem is not solvable by ordinary Wiener–Hopf techniques, but yields to the new method. Possible applications to some unsolved problems are mentioned.

The azimuthal radiation pattern of an axial slot in a dielectric-coated circular cylinder is derived. Some patterns are computed, and a comparison with experiment made.'Manuscript received March 12, 1956.

Propagation of an electromagnetic wave along an infinite corrugated surface whose slot walls are vanishingly thin is investigated using a method based on the calculus of residues. The method yields expressions for the amplitudes and phase velocities which are highly accurate near cutoff when the number of slots per wavelength is greater than about five.

A low-frequency solution to the diffraction problem of an E-polarized plane wave incident on a dielectric-loaded trough in a conducting plane is obtained. The dielectric loading consists of a circular cylinder which fits the semicircular trough in the conducting plane. The method used is a powerful low-frequency technique which has been succesfully applied to other problems of cylindrical geometry.

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.