Research On Nonlinear Transmission Chaos Based On Controllable Noise Sources

In the nonlinear optics,chaos is one of the most important research hotspots.Optical chaos has many unique properties,such as inherent randomness,sensitivity to initial values,long-term unpredictability,etc.It has broad application prospects in terms of secure communication,optical image encryption,and true random number generation.At present,the optical chaos phenomenon caused by nonlinear phenomena such as phase conjugation,second harmonic wave,stimulated Brillouin scattering,etc.has been widely studied,but there is less research on the chaos phenomenon caused by modulation instability.In this paper,the optical pulse modulated by a controllable random noise are used as the initial condition,and the mechanism of the chaos phenomenon is studied.Firstly,by adding a perturbation to the steady-state solution of the nonlinear Schrodinger equation,the dispersion relation and gain function of the modulation instability are obtained by linear stability analysis.Then the mean gain formula is introduced,and the gain of the Gaussian pulse at a single point frequency is calculated using the cosine modulation.The gain spectrum of the Gaussian pulse is obtained by numerical fitting.Second,a bandwidth-controllable random noise model is established,which can be controlled by setting the correlation length.Based on this random noise theoretical model,a method of generating a bandwidth-controllable optical random signal source is proposed.By analyzing the impact of random noise on the transmission of different optical pulses,the transmission characteristics of random noise are discussed.It is found that the smaller the bandwidth of random noise is,the smaller the influence of noise on pulse transmission is,and the random noise-modulated Airy pulse and super-Gaussian pulse will evolves into a chaotic light field,and there is a rogue wave generation.In addition,random noise can destroy the stability of higher-order soliton pulses except the ground state solitons.Finally,the chaotic phenomenon of the Gaussian pulse with controllable noise modulation in the nonlinear transmission process is studied.The influence of the initial parameters of the incident pulse on the generation of the rogue wave in the chaotic field is analyzed.According to the different nonlinear effects dominated during Gaussian pulses evolution and the pulse evolution in different propagation distances,the evolution of Gaussian pulses is divided into two stage,modulation instability(MI)stage and rogue wave(RW)stage.In MI stage,the evolution of Gaussian pulse is mainly affected by modulation instability,and some noise frequencies have exponential growth.In RW stage,the rogue waves split and merge irregularly under the influence of nonlinear effects.The evolution of the light field during the RW phase is chaotic.Increasing the noise correlation length,modulation depth,and initial power will cause the Gaussian pulse to evolve into a chaotic field faster,and the required transmission distance for generating a rogue wave also becomes shorter.Increasing the initial power and pulse width of the Gaussian pulse will increase the number of generated rogue wave.Only the initial power of the initial parameters of the incident pulse affects the modulation instability gain of the Gaussian pulse.In addition,it has been verified through simulation that the chaotic light field obtained using random noise or the method of generating the flow chopped wave has a certain resistance to power jitter.