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On the Rayleigh assumption in scattering by a periodic surface. II

Published online by Cambridge University Press:  24 October 2008

R. F. Millar
R. F. Millar
Affiliation:
Radio and Electrical Engineering Division, National Research Council, Ottawa, Canada
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Abstract

The Rayleigh assumption, which concerns the domain of validity of a representation for the field scattered by a periodic surface under time-harmonic plane-wave excitation, is re-examined. The analysis employs a technique developed to locate singularities of solutions to the Helmholtz equation. When applied to the surface profile v = b cos κu (-∞ < u < ∞) considered originally by Lord Rayleigh, it is found that the Rayleigh assumption is valid if 0 ≤ κb < 0·448 and is not valid if κb > 0·448; this is more precise than an earlier result. It is shown how these findings may be reconciled with the work of others who have suggested, or concluded, that the Rayleigh assumption is never valid.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 69 , Issue 1 , January 1971 , pp. 217 - 225
Copyright
Copyright © Cambridge Philosophical Society 1971

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References

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