In 1968, physicist V.G. Beselago pointed out that there always exists negative refractive index in materials when their electric constant and magnetic permeability μ are both negative, and therefore the propagation properties of the EM wave in such materials behave distinctively from those in media with positive refractive index (RI). In this paper, we construct two types of one-dimensional photonic crystals made up with positive and negative RI materials and
investigate their nonlinear optical properties. One type of photonic crystals consists of materials with both negative linear and positive third-order nonlinear RIs, the other are mainly made up with a Bragg micro-cavity constructed with both linear positive and negative RIs which contains Kerr media. We show that both types of photonic crystals exhibit bistable switching characteristics. Moreover, as compared with the crystals involved pure positive RI, our photonic
crystals possess even lower threshold valve in optical switching.
In this paper, the propagation properties of the electromagnetic (EM) waves in one-dimension photonic crystals (PC) with nonlinear defects layer closed by periodic layered structures are reported. It is shown that in the presence of the nonlinearity, the transmission properties are strongly modulated by both the frequency and intensity, and the system exhibits bistability and multistability. Moreover, we find that both the switching-up and switching-down intensities of the bistable response can be made very low, when the intensity of the incident wave matches the defect mode of the structure. By use of the nonlinear finite-difference time-domain (NFDTD) method, we simulate the bistable threshold of the nonlinear photonic crystals with the kerr medium and the feasibility of making a switch utilizing such a structure. Bistable swithching with a low threshold intensity of 0.0007 kW/cm<sup>2</sup> is obtained. The numerical experiments describenoptimal bistable switching in a nonlinear photonic crystal system. A photonic crystal enables the device to operate innsingle-mode fashion, as if it were effectively one-dimensional. This provides optimal control over the input and outputnand facilitates further large-scale optical integration.
We present an analytical model and numerical experiments to describe optimal bistable switching involving photonic crystals nonlinear cavity. The involving photonic crystals nonlinear cavity is particularly suitable for large-scale all-optical integration. It is interesting to show that the refractive index of the system can be altered by the incident intensity when the incident frequency is tuned to the evanescent mode and the cavity contains a nonlinear Kerr medium. The response of this system to high-intensity incident waves is studied in detail. A cavity host a localized mode at 1.55 um with a Q of 4000 and a mode volume of 0.055 um3, we predict the onset of bistable reflection at incident powers of ~40 mW. The downstream reflections lead to hysteresis loops in the reflectivity that are topologically distinct from conventional Lorentzian-derived loops characteristic of isolated Fabry-Perot cavities. We provide a stability argument that reveals the unstable branches of these unique hysteresis loops, and we illustrate some of the rich bistable behaviors that can be engineered with such downstream sources, this fact may be used to obtain more flexibility in designing nonlinear devices.