We calculate linear and nonlinear optical effective refractive indices of finite period one-dimensional photonic
crystals, Bragg reflectors and photonic crystal microcavities, by using numerical dispersion relation. We discuss
optical dispersive properties of both the Bragg reflectors and the photonic crystal microcavities. For Bragg
reflectors, optical Kerr nonlinearity is enhanced at bandgap edges, and the singularity problem at bandgap
edges, occurred in Bloch index for infinite structure, is removed by the numerical dispersion relation. Also, the
numerical dispersion relation is adopted to describe optical property of photonic crystal microcavities, for which
Bloch index is not available. Optical Kerr nonlinearity in photonic crystal microcavities is found to be more
enhanced at optical defect modes than at bandgap edges. Z-scan profiles of a Bragg reflector and a photonic
crystal microcavity are numerically simulated based on the calculated nonlinear effective refractive indices, which
show peaks at bandgap edges and defect mode incurred by dispersion anomaly.
We fabricated SiO2/TiO2 one-dimensional photonic crystals by a sol-gel method. A picosecond pump-probe nonlinear optical measurement was performed in the one-dimensional photonic crystal, with the pump wavelength fixed at 355nm and the probe wavelength fixed at 532nm falling on the bandgap edges. The third order nonlinear optical response in an anatase TiO2 film composing the one-dimensional photonic crystal is found to be responsible for the nonlinear optical transmission changes at both bandgap edges.
We analyzed the depolarized hyper-Rayleigh scattering from molecular system with a partial macroscopic polar ordering. It is shown that hyperpolarizability tensor ratio and molecular dipole moment can be determined simultaneously by the depolarization measurement as a function of the external field strength. As an experimental example, we performed a quantitative analysi sof the electric-field dependent depolarized hyper-Rayleigh signal from a poly-γ-benzyl-L-glutamate solution, obtaining the dipole moment and the ratio of hyperpolarizability components as 4.0 Debye and β311/β333=-0.81.
A cholesteric liquid crystal cell was fabricated possessing 1-D photonic bandgap structure. From the measurement of the linear absorption spectrum of the cell, a bandgap was identified, centered at 1.08 eV (1143 nm) with the gap width of 0.1 eV (100 nm). Based on the linear absorption spectra, the dispersion of the principal refractive indices along the parallel and perpendicular directions of the molecule was determined as 1.631 and 1.476 at the wavelength of 1064 nm through Berreman matrix method. A Q-switched Nd:YAG laser (1064 nm) was employed to investigate the nonlinear optical changes of photonic bandgap. As the laser intensity was increased to 320 MW/cm2, the transmittance decreased from 0.51 to 0.47, corresponding to an 8% change. The nonlinear transmittance change was analyzed numerically by Berreman matrix method with the incorporation of Kerr nonlinearity in the optical response of the molecules forming cholesteric liquid crystal. The changes in the refractive indices along the parallel and perpendicular directions were 3.46 and 1.51 X 10-10 (cm2/W). The changes in the position and width of bandgap were 0.02 eV and 0.03 eV at the laser intensity of 320 MW/cm2.