Detailed treatment of the Nonlinear optical properties of nonlinear photonic crystals

Nonlinear photonic crystals were designed such that the center wavelength of the photonic bandgap could be located near 800 nm. The transmission spectrum was obtained by applying the optical transfer matrix formalism to the photonic crystal. The transmission spectrum of the photonic crystal revealed a defect mode resonance and a broad photonic band gap. The spatial optical intensity distribution was obtained by applying the Helmholtz equation to the photonic crystal structure. The intensity distribution exhibited strong confinement of the optical field inside the defect layer. The spatial variation of the electric permittivity was induced by the spatial optical intensity distribution inside the nonlinear defect layer. The nonlinear optical properties of these nonlinear photonic crystals were investigated by applying the finite-difference time-domain method (FDTD) to the photonic crystal structure with a spatially varying electric permittivity. The nonlinear transmission characteristics obtained by using the FDTD method were compared with those obtained by using the spatial average of the spatial optical intensity distribution. The effects of the nonlinear absorption, the nonlinear refraction, and the optical intensity on the nonlinear transmission were investigated.