On the geometrical optics of curved surfaces with periodic impedance properties

Abstract

In a p revious publication, a t wo-dimensional Green's fun ction has been deriv ed for a c ircula r cylinder whose su rface impedance aroun d t he peripher y deviates from a constan t value by a s inusoidal va riation of small amplit ude u. H ere, t his solut ion is eva luated asymptoticall y in t he illuminated region under t he assumpt ion t hat t he cylinder radius is la rge co mpared with Lhe wavelength of t he in ciden t fi eld . The asymptotic resul t is i nte rpreted. in te rms of geometrica~ opt ics generalized to ap ply to cylindrically curved, convex reflect ion grat ings, and comprIses t he first a nd higher-o rder diffracted rays associated wit h a plane grating, together with geometrical divergence coe ffi cien ts acco unting fo r t he surface curvature. Genera l properties of the spectru m of reflected rays a re observed . T he behav ior of t he firs t-order diffracted rays, a nd in part icular t heir domain of ex isten ce as a fUllet ion of s urface pe riod icity, is discussed in detail.