Spectrum of the Maxwell equations for a flat interface between homogeneous dispersive media

Brown, Malcolm ORCID: https://orcid.org/0000-0002-2871-6591, Dohnal, Tomáš, Plum, Michael and Wood, Ian 2024. Spectrum of the Maxwell equations for a flat interface between homogeneous dispersive media. Communications in Mathematical Physics 406 (1) , 3. 10.1007/s00220-024-05154-9

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Abstract

The paper determines and classifies the spectrum of a non-self-adjoint operator pencil generated by the time-harmonic Maxwell problem with a nonlinear dependence on the frequency for the case of two homogeneous materials joined at a planar interface. We study spatially one-dimensional and two-dimensional reductions in the whole space R and R2. The dependence on the spectral parameter, i.e. the frequency, is in the dielectric function and we make no assumptions on its form. These function values determine the spectral sets. In order to allow also for non-conservative media, the dielectric function is allowed to be complex, yielding a non-self-adjoint problem. The whole spectrum consists of eigenvalues and the essential spectrum, but the various standard types of essential spectra do not coincide in all cases. The main tool for determining the essential spectra are Weyl sequences.

Item Type:	Article
Date Type:	Published Online
Status:	Published
Schools:	Computer Science & Informatics
Additional Information:	License information from Publisher: LICENSE 1: URL: http://creativecommons.org/licenses/by/4.0/, Type: open-access
Publisher:	Springer
ISSN:	0010-3616
Date of First Compliant Deposit:	11 December 2024
Date of Acceptance:	29 September 2024
Last Modified:	11 Dec 2024 10:00
URI:	https://orca.cardiff.ac.uk/id/eprint/174676

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