Finite-difference time-domain investigation of band-edge resonant modes in finite-size two-dimensional photonic crystal slab

We investigate characteristics of optical modes near band edges of finite-size two-dimensional photonic crystals and photonic crystal slab structures by using finite-difference time-domain calculations. Mode patterns, spectra, and quality factors are calculated near several photonic band edges of triangular lattice air-hole structures. As the size of a photonic crystal pattern increases, the spectral peak approaches the photonic band edge and the quality factor increases. It is interesting to find that, in spite of out-of-plane radiation loss, band-edge quality factors of the photonic crystal slab is larger than those of the two-dimensional photonic crystal with equivalent effective refractive index. This fact originates from the slower group velocity near band edges of photonic crystal slab structures compared with two-dimensional photonic crystals. High quality factors $>2000$ are achieved from the second Γ point of the photonic crystal air-bridge slab with only 15 layers of air holes.