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.
