Efficient light extraction from various two-dimensional photonic crystal slab structures is studied. By using the finite-difference time-domain method, effects of finite air-hole depth, and the cladding refractive index on the light extraction efficiency are investigated. The largest extraction efficiency is obtained in the photonic crystal slab with entirely drilled air hole patterns and large index contrast with the bottom cladding. Using InGaAsP quantum wells emitting at 1.5 /spl mu/m large enhancement of photoluminescence is observed from the slab structures with air-hole patterns fully transferred through the active medium and the bottom cladding. The photoluminescence enhancement relative to the as-grown wafer is /spl sim/8 in the oxide-supported slab and /spl sim/13 in the free-standing slab. The large light extraction enhancement results from the coupling to leaky modes above the light line of a band structure. In addition, the extraction behaviors of a triangular lattice and a square lattice are compared, and it is shown that their distinctive extraction characteristics well reflect the features of each band structure.