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On the spectrum of waveguides in planar photonic bandgap structures

Brown, B. M., Hoang, V., Plum, M. and Wood, I. 2015. On the spectrum of waveguides in planar photonic bandgap structures. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 471 (2176) , 20140673. 10.1098/rspa.2014.0673

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We study a Helmholtz-type spectral problem related to the propagation of electromagnetic waves in photonic crystal waveguides. The waveguide is created by introducing a linear defect into a two-dimensional periodic medium; the defect is infinitely extended and aligned with one of the coordinate axes. This perturbation introduces guided mode spectrum inside the band gaps of the fully periodic, unperturbed spectral problem. In the first part of the paper, we prove that guided mode spectrum can be created by arbitrarily ‘small’ perturbations. Secondly, we show that, after performing a Floquet decomposition in the axial direction of the waveguide, for any fixed value of the quasi-momentum kx, the perturbation generates at most finitely many new eigenvalues inside the gap

Item Type: Article
Date Type: Publication
Status: Published
Schools: Computer Science & Informatics
Subjects: Q Science > QA Mathematics
Q Science > QA Mathematics > QA75 Electronic computers. Computer science
Additional Information: Pdf uploaded in accordance with publisher's policy at
Publisher: Royal Society, The
ISSN: 1364-5021
Date of First Compliant Deposit: 30 March 2016
Date of Acceptance: 24 February 2015
Last Modified: 05 Aug 2022 01:55

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