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Zapiski Nauchnykh Seminarov LOMI, 1991, Volume 195, Pages 40–47
(Mi znsl5024)
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On completeness of asymptotic formulae for amplitudes of the plane waves diffracted by a smooth periodic boundary
V. V. Zalipaev, M. M. Popov
Abstract:
It is almost evident that in the shortwave approximation
various parts of a smooth periodic boundary are responsible for
the amplitudes of appropriate plane waves diffracted by the boundary.
(It follows from the Green's formula and the stationary
phase method.) It is clear also that under the grazing incidence
only top part of the boundary hills is illuminated while the main
part of it turns out to be in a deep shadow.
In the previous paper [3] two different types of asymptotic
formulae for the diffracted wave amplitudes have been obtained.
One of it is originated by the Fock's region near the top of boundary
hill. The other type is originated by illuminated part of the
boundary arc adjoining to the Fock's region. Different mathematics
has been used to derive the formulae.
It is shown in this paper that both type of the formulae are
overlaped in some intermediate region of the diffraction agles.
Thus these formulae describe complete asymptotics of diffracted
wave amplitudes except those which are originated by shadow part
of the boundary and therefore are small in the shortwave approximation.
Citation:
V. V. Zalipaev, M. M. Popov, “On completeness of asymptotic formulae for amplitudes of the plane waves diffracted by a smooth periodic boundary”, Zap. Nauchn. Sem. LOMI, 195, 1991, 40–47; J. Soviet Math., 62:6 (1992), 3076–3080
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