Dynamics And Applications Of Nonlinear Photonic Crystals

We have investigated the dynamics and applications of nonlinear photonic crystals (PCs) by theoretical analysis and numerical simulation.First, we examine the dynamics of PC molecules with Kerr nonlinearity by numerical simulations in a pump-probe scheme. In order to clearly identify the dynamical responses of nonlinear PC molecules, the constitutional PC atoms are intentionally chosen to be multimode. We reveal that the coupling between the PC atoms plays an important role in determining the dynamical responses of nonlinear PC molecules to the excitation of ultrashort pulses and find that PC molecules with different spectral shapes exhibit different dynamical response behaviors.Second, we present an analytical description for the pump-probe simulations used to characterize the dynamical responses of nonlinear PCs. Some important physical processes clarified recently for the dynamics of nonlinear PCs have been taken into account, including the strong dependence of the lifetime of the probe pulse on the power density of the pump pulse as well as the interaction of the excited PC structure with the probe pulse. The transmission spectra for nonlinear PC atoms derived based on the analytical model are in good agreement with the simulation results obtained previously and the evolution of the transmission spectrum for a nonlinear defect mode observed previously in the experiments can be easily explained by this model. In addition, we reveal that the transient spectrum of a nonlinear PC atom can be captured if the lifetime of the probe pulse inside the PC atom is sufficiently short. It in return confirms the validity of our analytical model to investigate the dynamics of the nonlinear PC.Finally, we investigate the unidirectional transmission behavior of PC molecules consisting of nonlinear defect pairs by use of the coupled mode theory and the finite-difference time-domain technique. As compared with a single asymmetrically confined PC atom, a significant enhancement in the transmission contrast is achieved. The tolerance of the resulting optical diodes against the fabrication error is discussed and it is reasonable for present fabrication technology. Furthermore, it is revealed that the figure of merit, which is defined as the product of the threshold transmission and the transmission contrast, can be greatly improved by dropping the use of air defects and some abnormal and intriguing transmission behaviors are observed in this kind of PC molecules.