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Updated: Jun 22, 2026

Fabrication And Characterization Of Photonic Crystal Slow Light Waveguides And Cavities
Published on: November 30, 2012
Gap-edge Asymptotics of defect modes in 2D Photonic Crystals
K B Dossou1, R C McPhedran, L C Botten
1CUDOS, Department of Mathematical Sciences, University of Technology, Sydney, NSW 2007, Australia. Kokou.Dossou@uts.edu.au
Abstract:
We consider defect modes created in complete gaps of 2D photonic crystals by perturbing the dielectric constant in some region. We study their evolution from a band edge with increasing perturbation using an asymptotic method that approximates the Green function by its dominant component which is associated with the bulk mode at the band edge. From this, we derive a simple exponential law which links the frequency difference between the defect mode and the band edge to the relative change in the electric energy. We present numerical results which demonstrate the accuracy of the exponential law, for TE and TM polarizations, hexagonal and square arrays, and in each of the first and second band gaps.
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