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XVI.—Creeping Waves in an Inhomogeneous Medium*

Published online by Cambridge University Press:  14 February 2012

W. G. C. Boyd
W. G. C. Boyd
Affiliation:
Department of Mathematics, University of Dundee.
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Synopsis

This paper is concerned with high-frequency scattering in a medium, the square of whose refractive index varies linearly with height from a plane boundary. Two asymptotic methods are examined, namely the method of stationary phase and evaluation by residue series. The first of these corresponds to geometric optics and gives the high-frequency field in the illuminated region, while the second complements the first in the sense that if thsre is no point of stationary phase, the residue series is an asymptotic expansion of the field. The Airy functions in the residue series can be replaced by their asymptotic developments in terms of exponentials, and when this is done only the first term or first creeping wave is of genuine significance.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 69 , Issue 3 , 1971 , pp. 227 - 245
Copyright
Copyright © Royal Society of Edinburgh 1971

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References

References to Literature

[1]Jones, D. S., 1963. ‘High-frequency refraction and diffraction in general media’, Phil. Trans., 255A, 341–387.Google Scholar
[2]Jones, D. S., 1964. The Theory of Electromagnetism. Oxford: Pergamon.Google Scholar
[3]Keller, J. B., 1953. The geometrical theory of diffraction. Proc. Symp. Microwave Optics. McGill Univ.Google Scholar
[4]Keller, J. B., 1956. ‘Diffraction by a convex cylinder’, I.R.E. Trans. Antennas Propag., 4, 312–321.CrossRefGoogle Scholar
[5]Leppington, F. G., 1967. ‘Creeping waves in the shadow of an elliptic cylinder’, J. Inst. Maths Applies, 3, 388–402.CrossRefGoogle Scholar
[6]Seckler, B. D. and Keller, J. B., 1959. ‘Geometrical theory of diffraction’, J. Accoust. Soc. Am., 31, 192–205.CrossRefGoogle Scholar
[7]Seckler, B. D. and Keller, J. B., 1959. ‘Asymptotic theory of diffraction’, J. Accoust. Soc. Am., 31, 206–216.CrossRefGoogle Scholar
[8]Titchmarsh, E. C., 1939. The Theory of Functions (2nd Edn.). O.U.P.Google Scholar
[9]Ursell, F., 1968. ‘Creeping modes in a shadow’, Proc. Camb. Phil. Soc. Math. Phys. Sci., 64, 171–191.CrossRefGoogle Scholar