The Theory Research Of Transmittance Characteristic Of Nonlinear Photonic Crystatls

During the past decade, the photonic band gap structure has attracted considerable research attentiono In general, nonlinear photonic band gap structures are structures in which the nonlinear susceptibility is a periodic function in space. The nonlinear effects include steady state optical bistability and band gap solitary waves in nonlinear photonic band gap structure have been studied. The large omnidirectional band gaps in metallodielectric photonic band gap structures have been studied. And the two-dimensional photonic band gap optical limiter in the visible has been investigated.In the one-dimensional photonic band gap structure studied previously, a multilayer stack of dielectric material is arranged in such a way that alternating layers with a high index of refraction and a low index of refraction is alternated. And the thickness of each layer also alternates. The thicknesses are a and b which are constants.In this paper, the variation of the transmission and the dispersion relation with respect to the frequency in one-dimensional linear photonic band gap structure with variable period is demonstrated by numerical simulation, in which the thickness of the layers with high and low index of refraction is not constant that is different from the general one-dimensional photonic band gap structure. It is shown that the position of the photonic band gap will shift to the red side with the increase of the changing thickness of the layers. This effect becomes obvious with the increasing of frequency. And for the same structure, it can be shown that the photonic band gaps shift to the red side and the transmission with respect to the frequency becomes larger with the increasing of the applied intensity.And in this paper, the variation of the transmission and the dispersion relation with respect to the frequency of one-dimensional linear photonic band gap structure with variable period is demonstrated by numerical simulation.In this paper, the intense second harmonic field induces a nonlinear phase changeon a fundamental field simultaneously through cascaded second order processes is demonstrated by numerical simulation. It was shown that, the phase change dependson both the propagation length and input fundamental power density Ex.And the variations of the complex amplitude of the third wave at frequency 2>a> in one-dimensional photonic crystal are obtained through cascaded second order nonlinear processes by numerical simulation. Compared with a smaller amplitude of the second harmonic field, for a larger amplitude of the second harmonic field, in the procedure that the amplitude of the third field decreases quickly with the increase of the wavelength of the fundamental wave, there is a range of the refractive index in that the amplitude of the third field increases slowly. With the increase of the refractive index, the change of the amplitude of the third field exhibits special property.