Elementary Edge Waves and the Physical Theory of Diffraction

Abstract

ABSTRACT A more general and rigorous form of the physical theory of diffraction (PTD) is presented. This theory is concerned with the field scattered by perfectly conducting bodies whose surfaces have sharp edges and whose linear dimensions and curvature radii are large in comparison with a wavelength. The PTD proposed here is based on the conception of elementary edge waves (EEWs). These are the waves scattered by the vicinity of an edge infinitesimal element. Their high-frequency asymptotics are given. Various definitions of EEWs (Maggi, Bateman, Rubinowicz, Mitzner, Michaeli) are discussed. Total edge waves (TEWs) scattered by the whole edge are found to be a linear superposition of all EEWs. PTD enables one to determine correctly the first (leading) term in the high-frequency asymptotic expansions for primary and multiple TEWs both in ray regions and diffraction regions such as caustics, shadow boundaries, and focal lines. Some examples of these asymptotics are given. The connection of PTD with other asymptotic theories is established. Particularly, the directivity patterns of EEWs are the same hypothetical edge currents which are introduced in the method of equivalent currents.