Study Of Photonic Band Gap Structure And Nonlinear Characteristics

The Photonic Crystal is a new concept proposed at the end of 1980's. For its characteristics of controlling the movement of photons, this structure has a widespread application prospect in many fields,and has become a hot spot of the international academic communityFirstly the present paper introduced the basic surveys of the photon crystal, including its concept, the characteristics, especially research progress of nonlinear photonic crystal, the application and the development and so on.As the periodic structure of photonic crystal is intricate, it is very hard to make a mathematical analysis. So people usually analyze a photonic crystal through numerical simulations. Therefore, it is essential to study numerical methods in the theoretical research of photonic crystals. After comparing the different numerical method on the base of detailed understanding, Transfer Matrix Method(TMM),Finite Different Time Domain(FDTD) and the plane wave method(PWM) is chosen to be the main algorithm. The basic conception and theoretical methods based on plane wave method are reviewed in this paper.The 1D photonic band gap structures are derived and analysed using TMM. The tight relation between bang gap and parameters such as number of periods,refractive index ratio,incidence angle is studied. The light propagation in 1D photonic crystals with defects is analyzed by numeral simulated calculation.We have has emphatically studied the mode establishment of the 2D photonic crystal, then general computational routines are programmed to calculate photonic crystal band gap using MATLAB, influence of changing structure,permittivity and filling contrast。Parameters for widest band gap are found. The theoretic design of photonic crystals will benefit from these.We discuss the defect mode of 2D photonic crystal, and calculated bang structure with point defect and line defect. Optical devices based on resonance are dicussed. The theoretic design of photonic crystals will benefit from these.The study is made of nonlinear effect of photonic crystal. By Modeling the photonic crystal wave-guide with kerr nonlinear dielectric media, the transmission characteristics, as well as with non-linear evolution are derived. Research shows that when the introduction of nonlinear effect, the waveguide transmission characteristics seen tremendous changes, and there have been some new nonlinear transmission peak. Under such circumstances, Intrinsic localized modes which is similar to the soliton model, arise in nonlinear material. Discussing the Categories of nonlinear model by analyzing the corresponding distribution of these nonlinear transfer modes. The conclusion will be helpful for the extensive applications in the design of optical switching and optical instruments.