Impacts Of Cross-phase Modulation On Modulation Instability Of Airy Pulses

In recent years,modulation instability(MI)is one of the research focuses in the field of nonlinear fiber optics.When two or more pulses are transmitted in the optical fiber,cross phase modulation(XPM)makes the modulation instability in both normal and anomalous dispersion regions.The finite energy Airy pulse has many characteristics,such as self-healing,the lateral acceleration,non-diffraction and multi peak structure.It has been widely used in plasma channel,spatiotemporal airy light bullets,optically mediated microparticle control and so on.At present,the modulation instability of Airy pulse is mainly concentrated in the case of single pulse transmission,but there are less research on the modulation instability of Airy pulse under the effect of cross phase modulation.In this paper,we study the modulation instability of the main lobe and sides lobe of the Airy pulse under the cross-phase modulation by using the nonlinear coupling between the pump soliton and the Airy pulse.Firstly,we analyze the coupled nonlinear Schrodinger equation(NLSE)by using the linear stability theory,and the dispersion relation of perturbation and the MI gain spectrum are also obtained.Then the expressions of Airy pulse and pump soliton with cosine modulation are introduced,combined with the theory of cross phase modulation instability,the approximation analytical expression of modulation instability gain spectrum of Airy pulse is derived.Secondly,the influence of cross phase modulation on the modulation instability of the main lobe of Airy pulse is systematically studied,the research found that the gain of MI is related to modulation frequency,the initial power ratio of two pulses and the truncation factor of Airy pulse.When there is not cosine modulation,the peak power of the main lobe increases slowly,and the sidelobe is almost unaffected.The main lobe split into the multimodal and peak power increases sharply with cosine modulation,exhibit the obvious modulation instability phenomenon.At this time,the maximum intensity growth rate of the main lobe is larger than that without modulation.Then the MI gain spectrum of Airy pulse main lobe is analyzed,the different modulation frequencies correspond to different gain.The gain spectrum is first increased and then decreased,and the maximum value is obtained at the fastest growth rate.When the power ratio is fixed,the MI gain spectrum is inversely proportional to the Airy pulse truncation coefficient;In the case of fixed truncation coefficient,the stronger the pump soliton power,the larger the MI gain spectrum of the main lobe.The MI gain spectrum of Gauss pulse and main lobe are compared,The MI gain spectrum of the main lobe is larger than that of the Gauss pulse under the pump soliton.Lastly,the effect of pump soliton on MI of side lobes of Airy pulse is researched,there are inconsistency to be found.Side lobes occupy a considerable portion of the Airy pulse energy,side lobes is modulated by the pump soliton,the pump soliton can be adjusted so that it can be fully nonlinear coupled with side lobes.It is found that the modulation instability is similar to that of the main lobe,the MI gain spectrum decreases with increasing truncation coefficient,and the gain spectrum of MI increases with the increase of power ratio.However,due to the weaker initial power,compared with the main lobe,the amplitude of the MI gain spectrum is smaller.