Gap-edge asymptotics of defect modes in twodimensional photonic crystals
- Optical Society of America
- Publication Type:
- Journal article
- Dossou Kokou et al. 2007, 'Gap-edge asymptotics of defect modes in two-dimensional photonic crystals', Optical Soc Amer, vol. 15, no. 8, pp. 4753-4762.
- Issue Date:
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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