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Gap localization of multiple TE‐Modes by arbitrarily weak defects

Brown, B. M., Hoang, V., Plum, M., Radosz, M. and Wood, I. 2020. Gap localization of multiple TE‐Modes by arbitrarily weak defects. Journal of the London Mathematical Society 10.1112/jlms.12337

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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
Date Type: Published Online
Status: In Press
Schools: Mathematics
Computer Science & Informatics
Publisher: Wiley
ISSN: 0024-6107
Date of First Compliant Deposit: 29 May 2020
Date of Acceptance: 9 March 2019
Last Modified: 29 Jul 2020 13:25
URI: http://orca.cf.ac.uk/id/eprint/131972

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