THE UNIVERSITY OF MICHIGAN 011764-501-M 20 March 1973 Memo to: File From: T.B.A. Senior Subject: Front Edge Scattering For plane wave incidence on a two-dimensional body at whose surface an impedanoe boundary condition is applied, the transformation r-> 1/n connects the results for E and H polarizations. This has an unfortunate practical consequence. The front edge of a metallic ogival cylinder is a relatively strong source of scattering for E polarization, but a weak source for H polarization (the dominant source then being the rear). To reduce the E-polarized return for E polarization, it is natural to impose a non-zero surface impedance; however, this serves to increase the H-polarized return, suggesting that there is a fundamental limit below which the average return for all polarizations cannot be reduced. It may be that the saving grace is that an actual material will present different surface impedances to the two polarizations, particularly close to the edge where the field behaviors on the metallic body are so different. But if this is not the case, dan we attempt to estimate the amount by which the average scattering regardless of polarization could be reduced? A simple problem for which we can do so is backscattering from an impedance half plane at edge-on incidence. For a metallic half plane, the two dimensional diffraction coefficients for edge-on backscattering are Knott Senior File 11764-501-M = RL-2225

011764-50 1-M i P H(0) = EH 2 where a time convention e has been employed. If the surface impedance r7 is non-zero, the analogous results are K (k) *iE 4 K+(-k) L O) i PH( = 4 L+(-k) where K (C), L (O) are the Wiener-Hopf split functions deflied by Senior (1954). We note that L (f) differ from K+(t) in having 77 replaced by 1/rn. Although the above functions could be computed for any given r] using the expressions in Senior (1954), we shall use instead the simpler expanded forms on p. 70 valid for r << 1, viz K r) = - t {I+n ( -t+sin ) +r(log -1) +~(n) KL() = n/ (2 [ 1) + (n )} implying K(~) = +Skk {+~f[~ik2 (j+sin.')+ (logn -1) +0(t2)} k w k2- k ~2 implying L( = 1/2 1+ (4j +sin k )+O (2)} Note that the time convention employed is e 2

011764-50 1-M Hence P (1 = - i- (ilg)+o(n2) PH( 4- r{i+o(t2} from which we conclude -2 (,.log [),<< i P 2 PE (0) E 1 I>> 1 The anlogous results for H-polariation follow on replacing r) by 1/n. The above simplified formulae are plotted in Fig. 1. The broken line is a reasonable extrapolation between them and suggests that, for all polarizations, we might hope for a reduction of the E-polarized return by 10 dB by asing a (lossy) surface impedance having (obviously) jr | = 1. Reference T. B. A. Senior (1954) Ph.D. Thesis (Cambridge University). 3

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