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Method of double-scale expansions for refractive waveguides and conditions for its applicability

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Abstract

The problem of waveguide propagation for refractive waveguides is solved by the method of double-scale expansions. In analyzing the formula for the second approximation, it is shown that the method of double-scale expansions can be applied also at high frequencies under the condition ɛm ≪ 1, where ɛ is a small parameter characterizing the slowness of variation of the properties of the medium in the direction of the 0x axis and m is the number of nodes of the eigenfunction of the waveguide in the variable z for a fixed value of the variable x.

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Authors
  1. V. S. Buldyrev
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  2. N. S. Grigor'eva
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Additional information

Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 104, pp. 33–48, 1981.

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Buldyrev, V.S., Grigor'eva, N.S. Method of double-scale expansions for refractive waveguides and conditions for its applicability. J Math Sci 20, 1766–1776 (1982). https://doi.org/10.1007/BF01119358

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  • DOI: https://doi.org/10.1007/BF01119358

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