Brown, Malcolm S. and Hoang, Vu and Plum, Michael and Wood, Ian
(2012)
*On the spectrum of waveguides in planar photonic bandgap structures.*
arxiv.org
.
pp. 1-19.
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Official URL http://arxiv.org/abs/1204.0998 |

## Abstract

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. The perturbation is expected to introduce guided mode spectrum inside the band gaps of the fully periodic, unperturbed spectral problem. In the first part of the paper, we prove that, somewhat unexpectedly, 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 $k_x$ the perturbation generates at most finitely many new eigenvalues inside the gap.

Item Type: | Article |
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Uncontrolled keywords: | Spectral Theory; Mathematical Physics |

Subjects: | Q Science > QA Mathematics (inc Computing science) > QA299 Analysis, Calculus Q Science > QA Mathematics (inc Computing science) > QA377 Partial differential equations Q Science > QC Physics > QC20 Mathematical Physics |

Divisions: | Faculties > Science Technology and Medical Studies > School of Mathematics Statistics and Actuarial Science |

Depositing User: | Ian Wood |

Date Deposited: | 12 Oct 2012 15:38 |

Last Modified: | 28 Jul 2014 08:02 |

Resource URI: | http://kar.kent.ac.uk/id/eprint/31659 (The current URI for this page, for reference purposes) |

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