Single and coupled degenerate defect modes in two-dimensional photonic crystal band gaps

We investigate the formation and coupling of defect modes in two-dimensional photonic crystal (PC) band gaps associated with degenerate edges. Using a method based on Green's functions and perturbation theory, we derive a condition for the degeneracy of a defect mode in a PC band gap. We show that the interaction between multiple degenerate defects splits this degeneracy and provide a semi-analytic model for the splitting using a 4×4 tight-binding matrix. We observe that the structure of this tight-binding matrix is related to the overlap and corresponding symmetry of the defect modes. We confirm our analysis by comparing with numerical results.