## 1. Introduction

[2] High-frequency methods are based on the definition of a suitable set of diffraction coefficients, which are determined by analytically solving specific canonical scattering problems. Each canonical problem is characterized by simple geometries (as for instance wedges, tips, corners), which however well approximate the exterior surface of the scattering body in the vicinity of the pertinent scattering center.

[3] In this context, the present paper deals with a high-frequency analysis of the diffraction of an inhomogeneous plane wave, impinging on the edge of a perfectly electric conducting (PEC) wedge at oblique incidence. The incident plane wave is arbitrarily polarized and exhibits an exponential variation of the field amplitude along an arbitrary direction in the plane perpendicular to the propagation direction. This situation may arise in practice when the incident field is a surface wave, a leaky wave, a lateral wave, or when propagation occurs in a lossy medium. For instance, a homogeneous plane wave impinging from air onto a planar interface between air and a lossy medium (ground) generates an inhomogeneous plane wave into the lossy medium. Consequently, a diffraction coefficient for inhomogeneous plane waves can be considered an important tool in the analysis of the interaction between electromagnetic waves and metallic objects buried underground [*Bertoncini et al.*, 2001, 2004].

[4] A uniform geometrical theory of diffraction (UTD) solution [*Kouyoumjian and Pathak*, 1974] for inhomogeneous plane wave scattering by a PEC wedge has been presented by *Kouyoumjian et al.* [1996], when both the incidence and the exponential decay directions lie in the plane transverse to the edge. Here, the above analysis is extended to treat the more general case of skew incidence and completely arbitrary orientation of the exponential decay direction of the evanescent incident field. First, a representation of the incident field in terms of a plane wave with complex incidence angles is provided for a completely arbitrary incident inhomogeneous plane wave. Then, an exact integral representation for the total field is obtained by analytically continuing the Sommerfeld solution to complex incidence angles. The exact integral representation of the field is asymptotically evaluated by deforming the original Sommerfeld integration contour onto the two steepest descent paths (SDPs) through the saddle points at *π* and −*π*. The residue contributions of the poles that are captured in the contour deformation process are associated with the geometrical optics (GO) field contributions. The diffracted field contribution is obtained by asymptotically evaluating the integrals along the SDPs. To obtain the total field continuity at both the shadow boundaries (SBs) of the incident and reflected fields, all terms of order *K*^{−1/2} must be retained in the asymptotic approximation of the longitudinal field components, where *K* is the large parameter. Uniform asymptotic expressions are then derived for all the scattered field components, which are needed to construct a generalized dyadic diffraction coefficient. The asymptotic solution contains the conventional UTD transition function that is extended to complex arguments, as outlined by *Kouyoumjian et al.* [1996].

[5] The organization of the paper is described next. The canonical problem relevant to an inhomogeneous electromagnetic plane wave obliquely incident on a PEC wedge is formulated in section 2, where a detailed description of the electric and magnetic incident field is also given. An exact eigenfunction solution is provided in section 3. High-frequency uniform expressions for both the longitudinal and transverse components of the diffracted field are presented in section 4, and a generalized UTD dyadic diffraction coefficient is derived in section 5. Finally, samples of numerical results are shown in section 6, both to demonstrate the continuity of the total field across the GO SBs and to examine the accuracy of this high-frequency solution through comparisons with calculations based on the exact eigenfunction solution, as a function of the distance of the observation point from the diffracting edge.