Numerical Analysis of Localized Defect Modes in a Photonic Crystal: Two-Dimensional Triangular Lattice with Square Rods

We report the results of numerical calculation for localized defect modes in a two-dimensional triangular photonic crystal composed of square air-rods formed in silicon. The eigenfrequencies and eigenfunctions of the defect modes were calculated by means of the numerical simulation of the radiation process of a virtual oscillating dipole moment. We found that a defect mode of the A 1 spatial symmetry appears when one of the air-rods is missing. We also found that defect modes with all possible symmetries appear when the dielectric constant of the defect rod is varied. The consequence of their spatial symmetry is discussed.