Title :
Spectral domain solution and asymptotics for the diffraction by an impedance cone
Author :
Bernard, J.M.L. ; Lyalinov, M.A.
Author_Institution :
Departement de Phys. Theor. et Appliquee, CEA, Bruyeres le Chatel, France
fDate :
12/1/2001 12:00:00 AM
Abstract :
The problem of diffraction of a plane wave by a cone with impedance condition on its surface is studied, for a scalar wave field satisfying the Helmholtz equation. The integral Kontorovich-Lebedev, Sommerfeld-Maliuzhinets and Fourier transformations are exploited to investigate the problem and to separate the radial variable. The problem in question is reduced to that for a spectral function satisfying a Laplace-Beltrami type equation on the unit sphere with a hole cut out by the conical surface. An impedance type boundary condition with a nonlocal impedance operator is determined on the boundary of the hole. Then the problem for the spectral function can be transformed to a second kind integral equation with a nonoscillatory kernel. In the particular case of a circular impedance cone the problem is simplified. As an application, a closed form expression for the scattering diagram (or pattern) is deduced in the narrow cone approximation. The leading and first correction terms are represented
Keywords :
Helmholtz equations; Laplace equations; Laplace transforms; boundary-value problems; electric impedance; electromagnetic wave diffraction; electromagnetic wave scattering; integral equations; spectral-domain analysis; Fourier transformations; Helmholtz equation; Laplace-Beltrami type equation; Sommerfeld-Maliuzhinets transformation; asymptotics; circular impedance cone; closed form expression; correction terms; hole boundary; impedance type boundary condition; integral Kontorovich-Lebedev transformation; integral equation; narrow cone approximation; nonlocal impedance operator; nonoscillatory kernel; plane wave diffraction; radial variable; scalar incident plane wave; scalar wave field; scattering diagram; scattering pattern; spectral domain solution; spectral function; unit sphere; Acoustic diffraction; Boundary conditions; Electromagnetic diffraction; Geometry; Integral equations; Kernel; Laplace equations; Physics; Surface impedance; Surface waves;
Journal_Title :
Antennas and Propagation, IEEE Transactions on