Modulation Instability Dynamics Of Coupling Pulses With Different Powers In Nonlinear Relaxation Fibers

In the nonlinear optical fiber,the nonlinear interaction between the copropagation of two pulses with different powers can lead to dramatic changes in temporal,spatial,and spectral properties,and modulation instability plays a crucial role for these changes.The nonlinear interaction between a high-power pulse and a low-power pulse has received significant attention,such as soliton trapping,pump probe,self-focusing and filamentation.Thus,the study of modulation instability between the co-propagation of two pulses with different powers becomes very important.Firstly,with some mathematical treatments and analysis,the conventional coupled nonlinear Schr?dinger equation can be changed to the simplified nonlinear propagation equations contained the influence of different power ratios of two co-propagating optical pulses and the nonlinear relaxation response contribution which is the function of the relaxation time.Then,the dispersion relationship and the gain spectrum of modulation instability,which contain power ratios and the relaxation time,can be obtained.Secondly,the modulation instability dynamics under the influence of different power ratios of two co-propagating optical pulses is analyzed based on the simplified nonlinear propagation equations contained the influence of power ratios and nonlinear relaxation response contribution in the relaxation response fiber.The researches show that different power ratios affect modulation instability in the instantaneous band and the relaxational band simultaneously,and the increase of the power ratio leads to the decrease of gain and the shrink of the main unstable frequency range.In the anomalous group velocity dispersion regime,the effect of different power ratios resembles the case in the normal group velocity dispersion,but modulation instability in the anomalous group velocity dispersion regime is more visible with the aid of self-phase modulation.Then,the numerical simulations of the phenomenology has reported in this paper,and it coincides well with the theoretical investigation.Lastly,in view of this theoretical basis,the modulation instability dynamics are investigated systematically under the effect of relaxation time with a fixed power ratio in the relaxation response fiber.It is evident that the relaxation time mainly affect the relaxation band,and the gain curves are suppressed as the relaxation time becomes larger,the smaller input pulses powers ratio leads to the larger gain peak and the broader unstable frequency range.Then,the results of numerical simulations are in excellent agreement with the aforementioned conclusions which are presented in the theoretical model.