Diffraction by semi-infinite cone formed with electric and magnetic surfaces: analytical regularization and Wiener–Hopf techniques

Abstract

The problem of axially symmetric E-polarized electromagnetic waves diffraction from the circular cone formed by the junction of the perfectly electro-conducting (PEC) semi-infinite truncated cone and the perfectly magneto-conducting (PMC) finite cone is studied rigorously by applying the Kontorovich–Lebedev integral transformation technique, the mode-matching method, and the analytical regularization procedure. The convolution-type operator and its inverse operator are used to conduct the regularization procedure and to reduce the problem to the infinite systems of linear algebraic equations of the second kind. The left side and the right side of the regularization procedures are considered. Transition from the cone to the PEC plane with the circular magnetic window is analysed. The exact solution of the problem is obtained for the static limit, and the low-frequency approximate is derived. The Wiener–Hopf technique is also applied to obtain the solution. Both solutions obtained using the analytical regularization method and by the Wiener–Hopf technique are compared, and the relation between them is derived. Within the framework of the Macdonald’s model, the solution is applied to analyse the far field scattered from the two partially absorbing conical scatterers; (1) the PEC semi-infinite cone with the “black” vertex; and (2) the semi-infinite PMC cone with the “black” truncated conical surface.