# On the spectrum of waveguides in planar photonic bandgap structures

@article{Brown2012OnTS, title={On the spectrum of waveguides in planar photonic bandgap structures}, author={B. M. Brown and Vu Hoang and Michael Plum and Ian Wood}, journal={Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences}, year={2012}, volume={471} }

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…

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