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Canonical problems for GTD
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Airy function aperture applied asymptotic evaluation asymptotic expansion axis canonical problem caustic contour creeping wave curvature matrix cylinder deﬁned derive diffracted ﬁeld diffraction term discontinuity in curvature edge diffracted ﬁeld edge diffraction electric ﬁeld electric polarisation equation exact solution field ﬁeld components ﬁeld given ﬁnite ﬁrst order Fock functions geometrical optics ﬁeld given by eqn gives GTD formulation half-plane half-space Helmholtz equation higher order illustrated in Fig incident ﬁeld inﬁnite interface Keller leading term line source magnetic ﬁeld magnetic polarisation modiﬁed Fresnel integral normal incidence oblique incidence obtain optical boundaries path perfectly conducting physical optics physical optics approximation plane wave principal radii radiation radii of curvature reﬂected ﬁeld reﬂection and refraction reﬂection boundary result shadow boundary shadow region shown in Fig slightly lossy stationary phase point theory of diffraction total ﬁeld transition region uniform solution wavefront waveguide wedge face yields zero