Electromagnetic scattering by a circular impedance cone: diffraction coefficients and surface waves

This paper is devoted to the study of electromagnetic scattering of a plane wave by a circular cone with impedance boundary conditions on its surface. The technique developed in the previous works is extended and applied to the electromagnetic diffraction problem with the aim of computing the far-field. It is known that by means of the Kontorovich-Lebedev integral representations for the Debye potentials and a 'partial' separation of variables, the problem is reduced to coupled functional difference equations for the relevant spectral functions. For a circular cone, the functional-difference equations are then further reduced to integral equations which are shown to be of Fredholm type. Certain useful integral representations for the solution of 'Watson-Bessel' and Sommerfeld types are exploited, which gives a theoretical basis for subsequent evaluation of the far-field (high-frequency) asymptotics for the diffracted field. To that end, we study analytic properties of the integrands in the Sommerfeld integrals. We also discuss the asymptotic expressions for the surface waves propagating from the conical vertex to infinity and give new expressions of the diffraction coefficients for the spherical wave in the domain illuminated by the rays reflected from the cone (in the so-called 'non-oasis' domain M '').