## 1. Introduction

[2] In the framework of high-frequency scattering and radiation phenomena, the diffraction of arbitrarily polarized plane waves obliquely incident on the edge of impedance half and full planes represents an important canonical problem. In the case of isotropic impedance boundary conditions (IBCs), rigorous integral solutions and related uniform high-frequency field expressions are available [*Senior and Volakis*, 1995]. Conversely, when anisotropic IBCs are introduced the complexity of the scattering problem increases, and the most general problem relevant to oblique incidence and arbitrary surface impedance tensors is still unsolved. Nevertheless, present-day applications (e.g., frequency/polarization selective surfaces, radar targets realized by new absorbing materials) explicitly demand for a characterization of the scattering by electrical and/or geometrical discontinuities in material surfaces which may be modeled by means of anisotropic IBCs.

[3] Solutions to the scattering from discontinuities in anisotropic impedance surfaces available in the literature are based on either numerical approaches or analytical techniques. Analytical solutions have been obtained by alternatively applying two basic techniques, namely, the Wiener-Hopf method [*Daniele*, 1984] and the Sommerfeld-Maliuzhinets method [*Maliuzhinets*, 1958; *Osipov and Norris*, 1999]. Despite of the numerous and continuous variations/extensions of both the above analytical techniques, it is worth noting that exact closed form solutions for the scattering from anisotropic impedance wedges have been derived only for specific electrical and geometrical configurations. For the sake of brevity, an overview of the previous work will be limited to the most recent papers.

[4] The difficulties arising in solving the wedge scattering problem by applying the Sommerfeld-Maliuzhinets technique are due to the fact that the angular spectra for the field components parallel to the edge appear in a system of coupled functional equations. Generally speaking, an exact spectral solution can be derived whenever a couple of suitable field components can be identified, giving rise to decoupled boundary conditions on both wedge faces. These field components are obtained as linear combinations of the electric and magnetic field components parallel to the edge, and their spatial derivatives. By following this approach, rigorous analytical solutions to the scattering by anisotropic impedance wedges or half planes with specific impedance tensors have been presented in [*Manara et al.*, 2000; *Nepa et al.*, 2001; *Lyalinov and Zhu*, 2003; *Manara et al.*, 2004]. Among alternative approaches, it is worth mentioning the procedure proposed by *Senior and Legault* [2000], *Senior et al.* [2001], and more recently applied by *Legault and Senior* [2002], where the system of coupled functional equations obtained by applying the Somerfeld-Maliuzhinets method is reduced to a second-order functional equation for a linear combination of the angular spectra of the field components parallel to the edge. *Lyalinov and Zhu* [2005] reduced the solution of the second-order functional equation to the numerical evaluation of an equivalent Fredholm integral equation of the second kind. A simple approach to solve the second-order difference functional equation was presented in [*Senior et al.*, 2001; *Senior and Topsakal*, 2002], where the original problem is reduced to an inhomogeneous nonsingular integral equation that can be solved by using only a few terms in a Taylor series expansion of the unknown. A similar hybrid analytical-numerical approach has been applied by *Osipov and Senior* [2005] directly to the first order coupled functional equations to analyze the scattering from an isotropic impedance wedge. Other rigorous analytical solutions valid for specific classes of impedance tensors have been recently derived by resorting to the Wiener-Hopf method [*Sendag and Serbest*, 2001; *Büyükaksoy et al.*, 1996].

[5] The main objective of this paper is to provide a rigorous analytical solution for the fields scattered by a new class of anisotropic impedance half- and full-plane configurations, illuminated at oblique incidence by an arbitrarily polarized plane wave. Anisotropic IBCs hold on the half- and full-plane faces, the principal anisotropy axes being parallel and perpendicular to the diffracting edge. Although limited to specific geometrical and electric configurations, these analytical solutions do represent important benchmarks in the analysis of the scattering from composite surfaces of finite extent. Indeed, they provide a set of useful reference cases that can be used to check the accuracy of numerical, hybrid or approximate analytical methods, valid for more general configurations. Also, they can be chosen as the starting point for developing perturbative as well as heuristic solutions. Furthermore, they can suggest extensions of the adopted analytical method toward the solution of more general and complex configurations.

[6] The paper is organized as follows. The formulation of the problem is provided in section 2. Exact integral representations for the electric and magnetic field longitudinal components are derived by the Sommerfeld-Maliuzhinets method in section 3. In section 4, the integral representations are asymptotically evaluated to obtain uniform high-frequency expressions in the UTD format [*Kouyoumjian and Pathak*, 1974]. Finally, samples of numerical results are presented in section 5.