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Gap localization of multiple TE‐Modes by arbitrarily weak defects

Brown, B. M., Hoang, V., Plum, M., Radosz, M., Wood, Ian (2020) Gap localization of multiple TE‐Modes by arbitrarily weak defects. Journal of the London Mathematical Society, . ISSN 0024-6107. (doi:10.1112/jlms.12337) (KAR id:81758)

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https://doi.org/10.1112/jlms.12337

Abstract

This paper considers the propagation of TE‐modes in photonic crystal waveguides. The waveguide is created by introducing a linear defect into a periodic background medium. Both the periodic background problem and the perturbed problem are modelled by a divergence type equation. A feature of our analysis is that we allow discontinuities in the coefficients of the operator, which is required to model many photonic crystals. Using the Floquet–Bloch theory in negative‐order Sobolev spaces, we characterize the precise number of eigenvalues created by the line defect in terms of the band functions of the original periodic background medium for arbitrarily weak defects.

Item Type: Article
DOI/Identification number: 10.1112/jlms.12337
Uncontrolled keywords: 35J15, 35P05, 47A10, 78A48 (primary), 35B20, 78A50 (secondary)
Subjects: Q Science > QA Mathematics (inc Computing science)
Divisions: Faculties > Sciences > School of Mathematics Statistics and Actuarial Science
Depositing User: Ian Wood
Date Deposited: 18 Jun 2020 08:31 UTC
Last Modified: 18 Jun 2020 08:33 UTC
Resource URI: https://kar.kent.ac.uk/id/eprint/81758 (The current URI for this page, for reference purposes)
Wood, Ian: https://orcid.org/0000-0001-7181-7075
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