Geometrical Theory of Diffraction for Electromagnetic Waves
The continuous development of the Geometrical Theory of Diffraction (GTD), from its conception in the 1950s, has now established it as a leading analytical technique in the prediction of high-frequency electromagnetic radiation and scattering phenomena. Consequently, there is an increasing demand for research workers and students in electromagnetic waves to be familiar with this technique. In this book they will find a thorough and clear exposition of the GTD formulation for vector fields. It begins by describing the foundations of the theory in canonical problems and then proceeds to develop the method to treat a variety of circumstances. Where applicable, the relationship between GTD and other high-frequency methods, such as aperture field and the physical optics approximation, is stressed throughout the text. The purpose of the book, apart from expounding the GTD method, is to present useful formulations that can be readily applied to solve practical engineering problems. To this end, the final chapter supplies some fully worked examples to demonstrate the practical application of the GTD techniques developed in the earlier chapters.
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Canonical problems for GTD
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Airy function asymptotic evaluation asymptotic expansion canonical problems caustic contour creeping wave curvature matrix deﬁned derived diffracted ﬁeld diffraction coefﬁcients diffraction term discontinuity in curvature edge diffracted ﬁeld edge diffraction electric ﬁeld electric polarisation equation exact solution ﬁeld components ﬁeld given ﬁnite ﬁrst order geometrical optics ﬁeld given by eqn given in Section gives half-space Hankel functions Helmholtz equation illuminated region illustrated in Fig incident ﬁeld inﬁnite interface leading term line source magnetic ﬁeld magnetic polarisation medium modiﬁed Fresnel integral normal incidence obtain optical boundaries perfectly conducting physical optics physical optics approximation plane wave plane wave incidence principal radii radiation radii of curvature reﬂected ﬁeld reﬂection and refraction reﬂection boundary reﬂector antenna result scattered ﬁeld shadow boundary shown in Fig slightly lossy slope-diffraction smooth convex surface stationary phase point straight edge theory of diffraction total ﬁeld transition region wavefront waveguide wedge face yields zero