Abstract
The asymptotic coefficients of the eigenfunctions of the continuous spectrum of a periodic lightguide are investigated. Integral equations, describing the spectrum of scattering matrices and other symplectic matrices that connect the asymptotic coefficients, are obtained. The directed motion of the eigenvalues of the scattering matrices and of certain groups of eigenvalues of symplectic matrices, under a parametric monotonic change in the medium of the lightguide, is established.
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References
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Additional information
Translated from Problemy Matematicheskogo Analiza, No. 11, pp. 161–176, 1990.
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Derguzov, V.I. Properties of asymptotic coefficients of the functions of the continuous spectrum of a lightguide. J Math Sci 64, 1331–1340 (1993). https://doi.org/10.1007/BF01098024
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DOI: https://doi.org/10.1007/BF01098024