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A high-accuracy finite-difference time-domain method based on what are called nonstandard finite differences was used to simulate optical propagation in a two-dimensional photonic crystal with a point defect. We used a photonic crystal consisting of a triangular lattice of air columns embedded in a high-refractive index medium. We found that the transmittance spectrum has four peaks in the photonic band-gap region, and that these peaks correspond to the resonant energies of light localized at the point defect. For a point defect consisting of an air hole with a radius smaller than that of the air holes of the photonic crystal, these peaks shift to higher energy. The peak shift of the resonant mode that is associated with the electric field concentrated about the center of the point defect is larger than the peak shift of the other modes. © 2002 American Institute of Physics.