New full-wave theory for scattering from rough metal surfaces—the correction current method: the TE-polarization case

Abstract

A new full-wave theory of scattering from metal surfaces with one-dimensional roughness profiles is presented. A primary field and a complete system of modal functions (radiation modes) are defined to be relatively simple in structure (plane-wave-type fields) and to satisfy the boundary conditions at the rough surface, individually and rigorously. These fields will not necessarily satisfy Maxwell's equations. But compliance with these equations is enforced by the introduction of fictitious current distributions, associated with each of these fields, and chosen such that these ‘passive’ currents compensate for any field errors. In addition, each radiation mode is assumed to include an ‘active’ current distribution in the form of a current sheet which generates this mode. The composite field, formulated as a superposition of the primary field and the radiation modes, must be source free. It cannot involve any active or passive currents; and this zero-current requirement is then used to solve the scatter problem by an iterative procedure which, in a step-by-step fashion, eliminates the passive currents of the primary field and radiation modes by the active currents of the radiation modes. The result is a composite field that satisfies all requirements (Maxwell's equations, boundary conditions and radiation condition) while all fictitious current distributions are eliminated by mutual compensation. This composite field is therefore the solution of the scatter problem. This new theory—involving fictitious current distributions—is unconventional. But after definition of the primary field and the radiation modes, it is straightforward and conceptually transparent. The first-order scatter pattern is reciprocal and bridges the gap between the small-perturbation method and the physical optics method. Since the passive currents quantify the field errors, the theory allows the establishment of an error criterion which indicates when field errors can be expected to be small. The results are compared with those of existing theories. The present paper presents the TE case; the TM case, which is more complex, will be described in a follow-on paper. (Some figures in this article are in colour only in the electronic version)