By Birkhoff G.D.
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4). 45) shows that σ tot = 4π Im k (ϑ = 0). 53) This equation is well known as the Optical Theorem (Born and Wolf, 1980). 4 Basic Notions in Acoustic and Electromagnetic Diffraction Problems Introducing the Notion of “Shadow Radiation” This notion was introduced for electromagnetic waves by Uﬁmtsev (1968). It was additionally investigated in Uﬁmtsev (1990) and discussed in Uﬁmtsev (1996). A signiﬁcant part of the results relating to electromagnetic shadow radiation was included in Theory of Edge Diffraction in Electromagnetics (Uﬁmtsev, 2003).
It was extensively investigated both experimentally (Willis, 1991) and theoretically [Bowman et al. (1987)]. The numerical data for the ﬁeld scattered by acoustically soft and hard objects, as well as perfectly conducting objects, presented in the work of Bowman et al. (1987), clearly illustrate the existence of this phenomenon. Our present analysis of the PO approximation reveals the nature of this phenomenon, which is inherent for scattering at any large opaque objects. 2 in the present book.
First we derive this solution in the form of inﬁnite series and then convert it to the Sommerfeld integrals convenient for asymptotic analysis. 7, is a scalar version of the theory developed by the author for electromagnetic waves (Uﬁmtsev, 1962). Fundamentals of the Physical Theory of Diffraction. By Pyotr Ya. Uﬁmtsev Copyright © 2007 John Wiley & Sons, Inc. 1 A wedge is excited by a ﬁlamentary source located at the line r = r0 , ϕ = ϕ0 . 1. A wedge with inﬁnite planar faces ϕ = 0 and ϕ = α is located in a homogeneous medium.