## 1. Introduction

[2] Among many electromagnetic (EM) issues (radiation, scattering, and propagation), the wedge-shaped objects and their special case, the half plane, have been always acted as classic forms and structures of these types of issues, and they are most important objects in the study of EM problems. In recent years, with increasing interest in anisotropic composites, considerable attention has been drawn to the study of the electromagnetic scattering properties of surfaces coated with these materials. The anisotropic impedance boundary conditions [*Senior and Volakis*, 1991] are the simplest and most effective way to describe these problems. While in the case of skew incidence, so far, there do not exist good solutions to the difference equations generated by the boundary conditions in Maliuzhinets' approach [*Maliuzhinets*, 1958]. The main difficulty is the lack of techniques to solve the four coupled functional difference equations [*Syed and Volakis*, 1995]. To the authors' knowledge, those that can be solved analytically are limited to specific face impedances or geometrical configurations, [*Vaccaro*, 1980; *Senior and Volakis*, 1986; *Rojas*, 1988; *Lyalinov*, 1994; *Lyalinov and Zhu*, 1999, 2003; *Manara et al.*, 1996; *Manara and Nepa*, 2000; *Bernard*, 1987, 1998]. *Pelosi et al.* [1998] has given an asymptotic solution using a perturbation technique based on the solution for normal incident. However, this asymptotic solution is valid only in the region deviating at most 30° from normal incidence. It is worth noting that in the case of very skew incidence, few researches have been carried out to provide a satisfactory solution.

[3] This paper analyzes the electromagnetic scattering of a plane wave obliquely incident on a wedge of an arbitrary open angle with anisotropic impedance faces, in which the impedance tensor has its principal anisotropy axes along the directions parallel and perpendicular to the edge. As indicated by *Pelosi et al.* [1998], first, the first-order anisotropic impedance boundary conditions are introduced to prescribe the wedge faces, and then followed the well-known Sommerfeld-Maliuzhinets method, the longitudinal components of the total fields are represented as Sommerfeld spectral integrals. Next, the boundary conditions are imposed to yield a group of functional difference equations. The approximate integral expressions of the spectral functions are then determined by applying the perturbation technique which is based on two analytical solutions (normal incidence [*Maliuzhinets*, 1958] and grazing to the edge incidence [*Lyalinov and Zhu*, 1999]) to decoupling the functional difference equations. Then by the residue theorem, the asymptotic evaluation of the spectral integrals is performed in the framework of the uniform geometrical theory of diffraction (UTD), with the high-frequency representation for the fields diffracted by anisotropic impedance wedge valid at close to normal incidence and almost grazing to the edge incidence. Finally, some examples of the numerical results are given and compared with those obtained also by the perturbation method [*Pelosi et al.*, 1998] and the analytical solutions [*Manara and Nepa*, 2000] to demonstrate the uniform and continuous behavior of the fields in the absence of the wedge region.

[4] Though this work does not exactly solve the whole problem because of the limitation of the perturbation technique, the solution given here includes all the possible cases which can utilize the perturbation technique to derive the diffraction field for an anisotropic impedance wedge of an arbitrary open angle at skew incident, and should be at least as a practical way to obtain a comparatively good approximation to the field behavior at the general case of skew incidence, and comparison with other pure numerical or hybrid methods.