Sommerfeld type integrals for discrete diffraction problems

08/05/2019

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by   A. V. Shanin, et al.

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Three discrete problems for Helmholtz equation is studied analytically using Sommerfeld integral approach. They are the problem with point source on a whole plane, the problem of diffraction by a half-plane, and the problem of diffraction by a right-angled wedge. It is showed that total field is represented as an integral from an algebraic function on a manifold. The latter is torus. For the problem with a point source a recursive relation is introduced. For half-plane and wedge problems solutions are obtained in terms of Sommerfeld integral.