Study On Dispersion And Nonlinearity Of Ultra - Short Avery Pulse In Kerr Medium

In 2007, Siviloglou and Christodoulides, first predicted the existence of finite energy Airy beams, which have the characteristic of maintain long-distance transmission without diffraction by using the paraxial approximation wave equation. Since then, the generation, transmission and application of limited energy Airy beam has always been a hot research field.Since the low-order group velocity dispersion plays a major role in the group velocity dispersion, we always tend to ignore the role of high-order dispersion. However, through the theoretical analysis and numerical simulation in this dissertation, we can find that high-order dispersion also has a great impact on the airy pulse’s transmission. Therefore, in order to obtain a high quality airy profile, the high-order dispersion will be a non-negligible factor. In this dissertation, we simulated and analyzed airy pulse dispersion effect by the split-step Fourier transform method (SSFM). The wave transmission characteristic of Airy pulse under second and third-order dispersion effects is discussed. Furthermore, we studied the influence of the initial chirp and weakly nonlinear effects. The results showed that the positive third-order dispersion effect will lead to pulse compression and amplitude increase. On the other hand, the negative third-order dispersion effects will lead to pulse broadening and amplitude decrease. When taking the effect of the initial chirp and weakly nonlinear effects into account, we found that as the third-order dispersion effects growing, the quality of airy pulse will reduce.