## 1. Introduction

[2] Diffraction of electromagnetic waves in wedge-shaped regions remains the subject matter of many works since the seminal paper of *Sommerfeld* [1896], and is analyzed often with the Sommerfeld-Malyuzhinets method [cf. *Senior and Volakis*, 1995; *Buldyrev and Lyalinov*, 2001; *Babich et al.*, 2004]. The key step of the Sommerfeld-Malyuzhinets technique lies in solving the resulting functional difference equations of higher order. Recently, it has been shown that a generalized Malyuzhinets function *χ*_{Φ} [*Bobrovnikov and Fisanov*, 1988; *Avdeev*, 1994] and the so-called S integral [*Tuzhlin*, 1973] can be combined to convert a functional difference (FD) equation of the second order to a Fredholm integral equation of the second kind with the integral equation solved numerically by quadrature method [*Lyalinov and Zhu*, 2003b]. Furthermore, this approach has been extended to solve an FD equation of higher order resulting from diffraction of a skew incident plane electromagnetic wave by a wedge with scalar impedance faces [*Lyalinov and Zhu*, 2006].

[3] In the present paper, this approach is applied, with due modification, to a more general diffraction problem, namely, diffraction of a skew incident plane electromagnetic wave by a wedge with axially anisotropic impedance faces. The extensions are direct and within the framework of the general procedure for the isotropic impedance faces.

[4] It is worth mentioning that recently, this problem has been tackled on use of two other ways: the probabilistic random-walk method [*Budaev and Bogy*, 2006] and a generalized Wiener-Hopf technique [*Daniele and Lombardi*, 2006]. These two approaches manage to deal with more general anisotropic impedance faces than the way which is followed in the present paper. This notwithstanding, the authors do believe that for problems solvable using all three approaches, the present one is at least as efficient as the other two in terms of accuracy and computational speed (see section 3), thanks to the nonsingular, wave number–free and rapidly decreasing kernel of the resulting Fredholm integral equation obtained on use of, among other things, the special function *χ*_{Φ}. Furthermore, just like the Wiener-Hopf technique, which was regarded for many decades as not being suitable for wedge problems but now has outperformed the Sommerfeld-Malyuzhinets technique in certain aspects, the Sommerfeld-Malyuzhinets technique could one day get the upper hand again. In addition, a closed-form explicit solution to the problem under study ought to be found yet (for such solutions in special cases see, for instance, *Lyalinov and Zhu* [1999, 2003a] and *Antipov and Silvestrov* [2006]). Hence this solution procedure deserves to be presented to the electromagnetics community.