Radio Science, Volume 17,Number 5, pages 1199-1210,September-October 1982 Scattering by a strip with two face impedances at edge-on incidence R. Tiberio, F. Bessi,G. Manara, and G. Pelosi Istituto di Elettronica, Universityof Florence, 50139 Florence, Italy (Received November 13, 1981; revised April 28, 1982; accepted April 28, 1982.) A high-frequencysolution for the diffraction from a strip with two arbitrary face impedances, illuminated at edge-on incidence, is obtained by a spectral extensionof the geometricaltheory of diffraction. An asymptotic approximation of the solution given by Maliuzhinets for the half plane is used.Uniform expressions for the scattered far field are given for cylindrical and plane wave illumi- nations. Incidenceperpendicular to the edges of the strip is considered in both TE and TM cases. In the case of planewave illumination the expressions for the field are greatly simplified. Numerical results are presented. In particular for resistive strips, the backscattered field calculatedfrom this solution compares very well with that calculated by other techniques. 1. INTRODUCTION The diffraction by edgeson a non-perfectly con- ducting surface has recently focused an increasing interest not only becauseof the importance of this problem in diffraction theory, but also because of its relevance for many applications. Resistive and dielec- tric coated sheets are important in the designof low radar cross-section targets. Diffraction by solar cell panelson satellites, diffraction by the loaded rim of high-performance antennas,and diffraction by im- pedance discontinuities in a ground plane are also examples of the practical importance of this problem. The high-frequency diffraction by a strip with two faceimpedances is considered in this paper. Although the electromagnetic diffraction by a perfectly conduc- ting strip has been studiedextensively [Millar, 1957; Jones, 1964; Corriher and Byron, 1965; Fialkovskiy, 1966; Bowman et al., 1969; Freeland et al., 1970; Ti- berio and Kouyournjian, 1979], the more general and difficult problem of a strip with arbitrary face im- pedances has been treated by few authors. This ex- ample hasbeenconsidered by Bowman [1967] for the case of a broadside illumination. The most significant contribution to the problem of the scatteringby re- sistive strips has been recently given by Senior [1979a, b]. Preliminary resultsfor the problem con- sidered here have been presented by Bessi et al [1980]. Other analogous configurationshave beer_ Copyright 1982 by the AmericanGeophysical Union. Paper number 2S0670. 0048-6604/82/0910-0670508.00 studied by Tiberio and Pelosi [1981] and by P. H. Pathak (personal communication,1981). In this paper the geometricaltheory of diffraction is usedto obtain uniform expressions for the far field scattered by an impedance strip illuminated at edge- on incidence. As in the work by Tiberio and Kouy- ournjian [1979], the high-frequency scatteredfield is obtained as the sum of contributions from rays singly, doubly, and triply diffractedfrom the edges of the strip. At grazingincidence, in the cases of doubly and triply diffracted rays,the second edgeof the strip is illuminated by the shadow boundary field of the first edge.This is a non-ray optical field, and in de- termining the field of the doubly and triply diffracted rays the same spectralextension is employed,which has been used by Tiberio and Kouyournjiarn [1979, 1982a,b] in the caseof edges on a perfectly conduc- ting surface. However, there the basic asymptotic solution for single diffraction of ordinary, slowly varyingwaves was givenby the uniform geometrical theory of diffraction (UTD) [Kouyournjian and Pathak, 1974]. In the present example, the basic solu- tion for single diffraction is given by a uniform, asymptotic approximation of the exact solution for the diffractionof a plane wave at the edgeof a half plane with two arbitrary face impedances [Ma- liuzhinets,1958]. An asymptotic approximation of the Maliuzhinets solution has been employed by Bowman [1967]. However, the approximation used there is not uniform and of course is not sutiable for our problem.A uniform asymptotic evaluationof the solution given by Maliuzhinets, which has also been discussed by Christiansen [1974] and Senior[1978], 1199