Fundamentals of the Physical Theory of Diffraction, 2nd Edition

5 First-Order Diffraction at Strips and Polygonal Cylinders

The relationships u_s = E_z and u_h = H_z exist between the acoustic and electromagnetic fields for these problems.

In Chapters 3 and 4 we have built a foundation for the solution of two-dimensional diffraction problems. General asymptotic expressions have been derived for first-order edge-diffracted waves generated by both uniform and nonuniform components of the surface sources. In this chapter this general theory is applied to high-frequency diffraction at strips and cylinders with triangular cross-sections. These specific diffraction problems have been studied comprehensively and reported in the literature. In particular, the uniform asymptotic expressions (with arbitrary high asymptotic precision) for the directivity pattern and for the surface field at the strips have been derived by Ufimtsev (1969, 1970, 2003, 2009). In these publications one can also find many other references related to the strip diffraction problem. Among them we should note the first and classical solution by Schwarzschild (1902). High-frequency diffraction at polygonal cylinders was investigated by Morse (1964) and Borovikov (1966). We consider these problems again here, to demonstrate the first applications of PTD.

5.1 Diffraction at a Strip

The geometry of the problem is shown in Figure 5.1. Soft (1.5) or hard (1.6) boundary conditions are imposed at the strip. The incident wave is given by

(5.1)

Figure 5.1 Cross-section of ...