Shallow defect states in two-dimensional photonic crystals

Abstract

We investigate localized defect states near the edge of a band gap in a two-dimensional photonic crystal. An asymptotic approach based on Green's functions leads to analytical results both for the frequency and for the spatial behavior of the defect states. In particular, we find a simple exponential law which relates the change in frequency of the defect states to the relative change in electrical energy of the Bloch modes on the band edge, and to the density of states in the photonic crystal. We find that the symmetries of the Bloch modes at band extrema play an important role in the manifestation and evolution of defect states. We confirm the analysis with numerical simulations based on the fictitious source superposition method.