Diffraction of evanescent plane waves by a resistive half-plane

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.

Download Full-text

DIFFRACTION BY A CONDUCTING HALF-PLANE IN AN ANISOTROPIC PLASMA

Canadian Journal of Physics ◽

10.1139/p64-133 ◽

1964 ◽

Vol 42 (8) ◽

pp. 1455-1468 ◽

Cited By ~ 21

Author(s):

E. V. Jull

Keyword(s):

Magnetic Field ◽

Half Plane ◽

Scattered Field ◽

Plane Electromagnetic Wave ◽

Plane Waves ◽

Angular Spectrum ◽

Anisotropic Plasma ◽

Angle Of Incidence ◽

Dual Integral Equations ◽

Magnetostatic Field

The diffraction of a plane electromagnetic wave by a perfectly conducting half-plane in an anisotropic plasma is considered. The plasma is characterized by a permittivity tensor and the wave is assumed to propagate in a direction normal to the magnetostatic field and the diffracting edge, but its angle of incidence is otherwise arbitrary. Only the H-polarized wave of the incident field, which has a single magnetic field component parallel to the edge, is affected by the anisotropy and the analysis is restricted accordingly. Representing the scattered field as an angular spectrum of plane waves leads to dual integral equations from which an expression for the scattered field is obtained. The total field is then reduced to Fresnel integrals and its far-field behavior is investigated. Agreement with Seshadri and Rajagopal's result for a wave normally incident on the conductor, which was obtained by using the Wiener–Hopf technique, is found. The differences between isotropic and anisotropic solutions to this problem, which arise from the differing boundary conditions on the tangential magnetic field, are examined.

Download Full-text