Nonlinear Optical Properties Investigation On Photonic Crystals

In 1987,E. Yablonovitch and S. John pointed out that the behavior of photons can be changed when propagating in the material with periodically distributed dielectric constant, and termed such material photonic crystal. As known, photonic crystal has a photon band gap (PBG) structure, in which the electromagnetic wave is forbidden for some optical frequencies. Moreover, if certain impurity or defect is doped in PBG, the photons are localized without any spontaneous emission. Such features have become a topic of intense research and would find potential applications in many areas such as optical communications, information storage, and full-optical switching. In this dissertation, we focus our attention on the structure of photonic crystal, and discuss its nonlinear optical properties and its potential applications. First, we study and develop the transfer matrix, Green's function, and finite differential time domain (FDTD) methods. By using these theoretical methods, we demonstrate numerically the transmission and reflection spectra, and the other nonlinear optical effects, based on the 1D photonic crystal and 1D optical superlattice models, respectively. It is shown that our numerical simulations are in perfect agreement with the previous theoretical results. Then in theory, we discuss the nonlinear optical effects, especially the second-harmonic generation (SHG) and bistablility in photonic crystal in detail. As for SHG, we show that the efficiency of SHG in PBG can be greatly enhanced if the phase match condition is met. In the meantime, the influence factors on SHG, e.g., the structure of PBG, periodicity of dielectric constant, refractive index, and defect state are also studied. To be specific, we analyze the SHGs in the Ag-doped photonic crystal and in 2D defect photonic crystal, and simulate them by using FDTD method. Many important results are found. On the other hand, we investigate the bistablities in 1D and 2D nonlinear photonic crystals both theoretically and numerically. It is found that the periodicity in material with high-low refractive index, the thickness of defect layer, the incident frequency, etc., have an important impact on these bistablities. Concretely, the stronger optical field in defect layer or the thinner the line band becomes, the more easily the bistable state is obtained. By the same token, the increase in periodicity number and in thickness of defect layer can also contribute to the generation of bistable state. In fact, these physical reasons are easily understood. When the light intensity increase, there occurs red-shift in defect mode frequency. To make the threshold value more lower, it is required that the incident frequency should be red-shifted as well, achieving close resonance with defect mode. This will be helpful for the generation of bistable state. As one might expect, a bistable state with low threshold value suggests extensive applications in the design of optical switching and optical instruments.