Diffraction by a half-plane perpendicular to the distinguished axis of a general gyrotropic medium

Abstract

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.

Scattering by a screen with fluid flow.

“…The aim here is to solve this mixed boundary value problem for a cylindrical wave in the presence of a moving fluid. The present analysis is also related to Wiener-Hopf solutions for structural elements composed of plates joined end to end, [6][7][8][9][10][11][12][13][14][15] although such configurations are quite distnict from the present one. The solution of the problem is obtained using Jones' method and the Wiener-Hopf technique.16) It is found that results for the still air case can be deduced easily by taking the Mach number (=U/C,U is the fluid velocity) to be zero.…”

“…For subsonic flow, |M|<1 and for analytic convenience we assume k=kr+iki(kr, ki>0). It is assumed that a solution can be written in the form (5) where which, together with the substitution (9) reduce the boundary value problem to (10)…”

On the matrix factorization of Wiener-Hopf Kernel

“…Thus a considerable effort has been made in recent years both to extend this class and to find new methods for cMculating matrix factorization, especially with reference to particular physical problems. Examples of these specific problems solved by achieving the matrix factorization can be found in the papers by Rawlins [3], Przezdziecki and Hurd [4], Hurd and Przezdziecki [5], Hurd and Lª [6], Abraham and Wickham [7] and Jones [8]. Some important techniques for factorization of certain class of matrices have been developed by Hurd [9], Daniele [10], Khrapkov [11], Rawlins and Williams [12] and Jones [13].…”

Diffraction of a cylindrical pulse by a half plane under mixed boundary conditions

“…Hurd (2), when treating the problem of diffraction of an incident plane wave on a half plane with different face impedances, gave an ingeneous method of reducing the system of WienerHopf equations to a system of Hilbert problems and then solved them by a well-known function theoretic method. This method of Hurd is referred to as the Wiener-Hopf-Hilbert (WHH) method in the literature (2,4).…”

“…We then deduce, in Sect. 4 case of plane wave incidence is also considered. The infinite series solution obtained in the latter case has been summed and the final solution is presented in closed form involving an improper integral which behaves like a complementary error function for large values of the argument.…”