Limits on quality factors of localized defect modes in photonic crystals due to dielectric loss

The spectral widths of defect modes localized at line defects formed in a two-dimensional photonic crystal composed of a square lattice of dielectric cylinders were analyzed theoretically. The transmission spectra calculated by the layer-doubling method based on the vector–cylindrical–wave expansion of the internal field showed a rapid decrease of the spectral width with increasing number of the lattice layers when the dielectric loss is absent. Quality factors larger than 107 were predicted for the total lattice layers of 18. However, the numerical evaluation of the decay constant of the defect modes due to the imaginary part of the dielectric constant showed that the actual quality factor is limited by the dielectric loss. The calculated widths agreed qualitatively with the experimental observations by Lin et al. [Appl. Phys. Lett. 68, 3233 (1996)].