Study On The Propagation Properties Of Peregrine Soliton In Doped Fiber

The rogue waves are originated from a giant wave in the ocean.Its peak is usually two to three times higher than the surrounding water,and instantaneous disappearance without any signs.They have a great destructive power in the ocean,so they aroused people's attention widespreadly.Because the rogue waves in the ocean are difficult to monitor,people begin to explore other areas of rogue wave phenomenon.In optics,Solli and other people firstly observed the presence of rogue waves from supercontinuum spectroscopy generation in fibers in experiment.The discovery of rogue wave on the optical platform provides a convenience to study the mechanism of the generation of rogue waves.At present,there are many explanations about the reasons for the formation of rogue waves.One of the most important reasons is modulation instability,which can lead to the modulation of the steady state through the interaction of dispersion and nonlinear in the anomalous dispersion region,as a result that the quasi-continuous wave split into a series of high peak pulse train.The growth and decay of modulation instability can be described by a set of exact soliton solutions on plane wave backgrounds of the nonlinear Schr?dinger equation.The soliton solutions on the background waves can be divided into Akhmediev breathers solution(ABs),Kuznetsov-Ma soliton(KM)and Peregrine soliton(PS)solution.The Peregrine soliton solution is a single pulse that localized both in time and space.The Peregrine soliton is now commonly used to describe optical wave.In this paper,we mainly study the transmission of Peregrine soliton in doped fiber.Specific content includes the following four aspects:(1)Introduce the basic concept,the forming reasons,the research progress and the application areas of rogue wave.(2)From the Maxwell equation,the nonlinear Schr?dinger equation for optical pulses transmitted in fiber is deduced.The soliton solutions of Akhmediev breathers(AB),Kuznetsov-Ma soliton(KM)and Peregrine soliton(PS)are discussed.The numerical model for the optical pulse transmitting in doped fiber is derived.And the split-step Fourier numerical method is introduced.(3)The transmission characteristics are studied that the initial waveform of the Peregrine soliton solution as the initial input pulse transmitted in the doped fiber.It is found that the Peregrine soliton is affected by the parameters such as small signal gain and saturation energy of the doped fiber.The higher the gain of the small signal,the higher the saturation energy,the pulse intensity gradually increases with the width narrower and the space interval gradually reduced.In addition,three different initial inputs,the Peregrine soliton,the Gaussian pulse and the hyperbolic secant pulse on the plane wave background are transmitted in the doped fiber,and the similar Peregrine soliton can be generated due to the modulation instability.(4)The Peregrine soliton cannot stably transmit in the doped fiber because of the high peak single pulse divided into more sub-pulses.In order to obtain the high-peak pulse of stable transmission,the background wave is eliminated by coherent superposition and filtering methods.Then the pulses as the initial waveform input into the doped fiber.The results show that the high peak pulse obtained by the two methods can be stably transmitted in the doped fiber.And the pulse width presents breathing variation with the intensity periodically oscillated and the average of the intensity increased.