A generalization of the Wiener-Hopf approach to direct and inverse scattering problems connected with non-homogeneous half-spaces bounded by n-part boundaries

Abstract

The classical Wiener-Hopf method connected with mixed two-part boundary-value problems is generalized to cover n-part boundaries. To this end one starts from an ad-hoc representation for the Green function, which involves n unknown functions having certain analytical properties. Thus the problem is reduced to a functional equation involving n unknowns, which constitutes a generalization of the classical Wiener-Hopf equation in two unknowns. To solve this latter which cannot be solved exactly when n greater than or equal to 3, one establishes a new method permitting one to obtain the asymptotic expressions valid when the wavelength is sufficiently small as compared with the widths of the inner strips of the boundary. The essentials of the method are elucidated through a concrete inverse scattering problem whose aim is to determine the constitutive electromagnetic parameters of a slab and a half-space bounded by an n-part impedance plane. Some illustrative numerical examples show the applicability as well as the accuracy of the method.