Oblique Incidence Diffraction by Edges in Anisotropic Impedance Surfaces: A Collection of Exact Solutions for Specific Non-Axial Tensor Boundary Conditions

Abstract

The electromagnetic scattering of an arbitrarily polarized plane wave obliquely impinging on the edge of anisotropic impedance half-planes and planar junctions featuring inclined anisotropy axes is analyzed. Exact spectral representations for the total field are derived when the wedge faces are characterized by a set of specific homogeneous anisotropic impedance boundary conditions exhibiting an impedance matrix with no vanishing diagonal terms, as implied by the arbitrary orientation of the principal anisotropy axes with respect to the edge. The proposed solutions, which extend previous formulations valid for direction of the anisotropy axes either parallel or perpendicular to the edge, are derived by resorting to the Sommerfeld-Maliuzhinets method and exploiting the properties of the special function ˆ, originally introduced in the study of the scattering from wedges in gyroelectric media. Explicit uniform asymptotic expressions for the fields are provided along with samples of numerical results proving their validity.

Analytic theory of an edge mode between impedance surfaces

“…The TM and TE polarized wave are coupled for the oblique incidence, which makes the Maliuzhinets method no longer valid. Based on the Sommerfeld-Maliuzhinets technique, the diffraction of an electromagnetic skew-incident wave by a wedge with anisotropic impedance boundary condition is solved analytically [15,16]. The scattered wave generated by a Hertzian dipole placed over an impedance wedge can be calculated by expanding the dipole field into plane waves and extending to complex angles of incidence [17].…”