May 2014
Intermediate
496 pages
12h 21m
English
Content preview from Fundamentals of the Physical Theory of Diffraction, 2nd Edition
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2 Wedge Diffraction: Exact Solution and Asymptotics
2.1 Classical Solutions
Diffraction at a wedge with a straight edge and infinite planar faces is an appropriate canonical problem to derive asymptotic expressions for edge waves scattered from arbitrary curved edges. In the particular case of the wedge, which is a semi-infinite half-plane, the exact solution of this canonical problem was found by Sommerfeld (1896), who constructed branched wave functions. Analysis of this work by Ufimtsev (1998) shows that Sommerfeld also developed almost everything that was necessary to obtain the solution for a wedge with an arbitrary angle between its faces. However, he missed the last step, which led directly to this solution. This more general solution was found by Macdonald (1902) using the classical method of separation of variables in the wave equation. Later, Sommerfeld also solved the wedge diffraction problem by his method of branched wave functions and derived simple asymptotic expressions for the edge-diffracted waves (Sommerfeld, 1935). ...
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