Scattering of a plane electromagnetic wave by a hollow circular cone with thin semi-transparent walls

• Published in: IMA journal of applied mathematics Vol. 75; no. 5; pp. 676 - 719
• Main Authors: Lyalinov, M. A., Zhu, N. Y., Smyshlyaev, V. P.
• Format: Journal Article
• Language: English
• Published: Oxford University Press 01.10.2010
• Subjects: Asymptotic properties; Circular cones; Diffraction; functional difference equations; Integral equations; Integrals; Mathematical analysis; Mathematical models; numerical evaluation of the vertex diffracted wave; Plane waves; Representations; semi-transparent cone; the far-field asymptotics
• ISSN: 0272-4960; 1464-3634
• DOI: 10.1093/imamat/hxq030

We study electromagnetic plane wave diffraction by a hollow circular cone with thin walls modelled by the so-called impedance-sheet boundary conditions. By means of Kontorovich–Lebedev integral representations for the Debye potentials and a ‘partial’ separation of variables, the problem is reduced to coupled functional difference (FD) equations for the relevant spectral functions. For a circular cone, the FD equations are then further reduced to integral equations, which are subsequently shown to be Fredholm-type equations via a semi-inversion by use of Dixon's resolvent. We then solve the integral equations numerically using an appropriate quadrature method. Certain useful further integral representations for the solution of ‘Watson–Bessel’ and Sommerfeld types are developed, which gives a theoretical basis for subsequent calculation of the far-field (high-frequency) asymptotics for the diffracted field. Based on this asymptotics, the radar cross section in the domain, which is free from both the reflected and the surface waves, has been computed numerically.