Gap-edge asymptotics of defect modes in two-dimensional photonic crystals

Optical Soc Amer
Publication Type:
Journal Article
Optics Express, 2007, 15 (8), pp. 4753 - 4762
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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 componenet wich 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 andthe band edge to the relative change in the electric energy. We rpesent numerical results which deminstrate 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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