Localized defect modes in a two-dimensional triangular photonic crystal

Abstract

By using a finite-difference time-domain numerical method based on introducing an oscillating dipole at a proper position in a two-dimensional photonic crystal consisting of an array of dielectric cylinders, we numerically solve the inhomogeneous wave equation discretized in both space and time to calculate the eigenfrequency and the eigenfunction of a localized defect mode. We study the spatial distribution of the electric field and the radiated power associated with the defect modes produced by introducing a defect cylinder into an otherwise periodic two-dimensional triangular photonic crystal. We have obtained excellent agreement for the defect mode of ${A}_{1}$ symmetry created by removing a single cylinder from the center of the region of cylinders arrayed in a triangular lattice with the experimental result of Smith et al. [J. Opt. Soc. Am. B 10, 314 (1993)]. We have also examined systems in which defect states are introduced by varying the radius of a single cylinder and when both the dielectric strength and the radius of the defect cylinder are changed. The calculated values of the donor and acceptor levels associated with the exponentially decaying defect modes of ${A}_{1}$ symmetry induced by changing the radius are in good quantitative agreement with the nondegenerate donor and acceptor levels obtained by the supercell method within the plane-wave approach reported recently by Feng et al. [Jpn. J. Appl. Phys. 36, 120 (1997)].