Scattering from Finite Periodic Surfaces: a Comparison between Integral Equation and Ray Techniques

The electromagnetic scattering from a large planar strip composed of parallel free-standing dense metallic strips is addressed. The scattered field is evaluated by resorting to a couple of different methods: an asymptotic technique, namely the Uniform Geometrical Theory of Diffraction (UTD), and a numerical method (the Method of Moments, MoM). The results of a numerical investigation are presented with the aim of demonstrating the effectiveness and the accuracy of the ray technique. Specific attention is also devoted to the phenomenon of surface wave excitation. INTRODUCTION In the latest years, an increasing interest has been devoted to the design and fabrication of composite materials (Ziolkowski and Engheta [1], Munk [2]). Artificial surfaces, as for instance, metamaterial slabs, dichroic screens, frequency/polarization selective reflectors, absorbers, or more general multi-layer and periodic surfaces, are being more and more often applied in antenna and microwave device technology. Their analysis is usually focused on their reflection and transmission properties; indeed, it is often performed by considering an infinite surface under plane wave or, more rarely, dipole excitation. However, in many applications it is important to include edge effects. In this framework, efficient numerical methods have been developed to study electrically large finite periodic surfaces, and accurate diffraction coefficients have been proposed to evaluate the scattering from edges in artificial surfaces when they can be characterized by proper impedance boundary conditions. In particular, the latter approach represents an extension of analytical high frequency techniques (e.g., the Uniform Geometrical Theory of Diffraction, UTD, and the Physical Theory of Diffraction, PTD) to the analysis of edge effects in non-metallic composite surfaces and it seems to be a very promising alternative to pure numerical methods, when dealing with large reflectors or screens. The first step in deriving closed form expressions for the edge diffracted field is the development of an analytical model of the surface. This model should be able to recover the reflecting and transmitting properties of the material slab, in a given frequency interval and for a sufficiently wide angular sector around normal incidence (Tretyakov [3]). Starting from the analytical model of the surface, a canonical diffraction problem can be defined. The most suitable techniques for solving the above canonical diffraction problem are the Wiener-Hopf and the Maliuzhinets methods. In spite of their recent significant extensions with respect to what presented in the corresponding original papers, the solutions to the diffraction from some composite material slabs require the calculation of complicated special functions and in many cases the problem cannot be solved in a closed form. This is due the fact that the analytical models available to characterize the above mentioned artificially composite material surfaces are usually more involved than standard impedance boundary condition. Consequently, major research activities are focused on the extension of exact solutions valid for specific scattering problems, with the objective of deriving more general heuristic or approximate diffraction coefficients, able to efficiently evaluate the most important edge field contributions in the scattering from non-metallic surfaces. In this context, this paper is aimed at presenting some numerical results relevant to the analysis of the scattering from a large planar strip (see Fig. 1) made of parallel free-standing metallic strips (one-dimensional, 1D, periodic surface). The distance between the two edges of the planar strip is equal to L. The parallel metallic strips are in air, their periodicity and width are denoted by p and w, respectively. The orientation of the metallic strips with respect to the edge is defined by the angle γ ( γ =π/2 or γ =0, when the strips are parallel or perpendicular to the edge, respectively). Gratings of parallel metallic wires or strips behave as polarization selective screens and are widely employed in reflector antennas with high levels of