Reflection of a plane electromagnetic wave in a right-angled interior wedge with anisotropic faces

Abstract

We consider the reflection of a plane electromagnetic wave incident obliquely in a right-angled corner region with anisotropic faces (in this paper, we mean by “corner” an intersection of two planes). This geometry is a useful model for a variety of applications. In radar applications, for example, the corner is a basic model of a dihedral corner reflector which is used for calibration of radars. Similar, dihedral-like, geometries are encountered in RCS simulations if a target has flat facets at 90 degrees to each other or if a target is placed over a ground plane. The corner geometry is also relevant to rectangular waveguides with corrugated walls and to the propagation of radio waves inside buildings, and the examples from wireless propagation are junctions of walls in a room, or a corner between a building wall and the ground in a street environment. To describe material properties of the corner faces, we use impedance boundary conditions in their most general tensor form. The impedance boundary condition [Senior and Volakis, Approximate Boundary Conditions in Electromagnetics, IEE, 1995] is a convenient tool for simulating the material properties of a surface. For most materials the surface impedance is a scalar, but there are materials whose properties are anisotropic for which a tensor impedance is required. The simplest cases are those for which the tensors are diagonal but recent work with metamaterials has made possible the creation of very general materials for which the tensor may be non-diagonal. These are the focus of the present study. We show that in general the solution consists of plane waves reflected off the two faces of the wedge and a diffracted field associated with the edge of the wedge, but if the surface impedances satisfy certain restrictions the diffracted field disappears. The exact solution is then the sum of four plane waves, one of which is the incident field. We derive the restrictions on the impedances for which this is so, and present a number of images showing the simulated behavior of the field in the corner region with various impedance tensors.