Numerical method for localized defect modes in photonic lattices

We formulated a numerical method to calculate the eigenfrequencies and the eigenfunctions of localized defect modes in arbitrary photonic lattices based on the simulation of the excitation process of the defect modes by a virtual oscillating dipole moment. We applied this method to a two-dimensional square lattice, and obtained excellent agreement with the experimental result by McCall et nl. [Phys. Rev. Lett. 67, 2017 (1991)]. We also found that localized defect modes of all possible symmetries appear when we change the dielectric constant of the defect, and we investigated their eigenfunctions in detail.