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Singularities of the transmission coefficient and anomalous scattering by a dielectric slab
University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electronics, Mathematics and Natural Sciences, Mathematics.
2018 (English)In: Journal of Mathematical Physics, ISSN 0022-2488, E-ISSN 1089-7658, Vol. 59, no 3, article id 033507Article in journal (Refereed) Published
Abstract [en]

We prove the existence and describe the distribution on the complex plane of the singularities, resonant states (RSs), of the transmission coefficient in the problem of the plane wave scattering by a parallel-plate dielectric slab in free space. It is shown that the transmission coefficient has isolated poles all with nonzero imaginary parts that form countable sets in the complex plane of the refraction index or permittivity of the slab with the only accumulation point at infinity. The transmission coefficient never vanishes and anomalous scattering, when its modulus exceeds unity, occurs at arbitrarily small loss of the dielectric filling the layer. These results are extended to the cases of scattering by arbitrary multi-layer parallel-plane media. Connections are established between RSs, spectral singularities, eigenvalues of the associated Sturm-Liouville problems on the line, and zeros of the corresponding Jost function.

Place, publisher, year, edition, pages
American Institute of Physics Inc. , 2018. Vol. 59, no 3, article id 033507
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Mathematics
Identifiers
URN: urn:nbn:se:hig:diva-26671DOI: 10.1063/1.5027195ISI: 000428902300037Scopus ID: 2-s2.0-85044305243OAI: oai:DiVA.org:hig-26671DiVA, id: diva2:1211908
Available from: 2018-05-31 Created: 2018-05-31 Last updated: 2018-05-31Bibliographically approved

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Shestopalov, Yury

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