Analytical Study Of Generalized Nonlinear Schrodinger Equation In Fiber Lasers

Due to its advantages of large transmission capacity,long transmission distance,and good confidentiality,optical fiber communication has become an important method in today’s communication field[1].Keeping the waveform,velocity and amplitude unchanged during transmission,optical soliton has become the most promising medium in optical fiber communication[2-4].The main experimental platform of optical soliton research is mode-locked fiber laser,so it is necessary to study the theory of fiber laser.Theoretically,optical soliton propagation in optical fiber can be modeled by nonlinear Schrodinger equation[5].Soliton solution is an important aspect in the study of nonlinear model.In this paper,the generalized nonlinear Schrodinger equation in fiber laser is studied theoretically.The soliton solution of the equation is obtained by Hirota method,and its theory and application are both analyzed.The specific research contents are as follows:(1)The analytical study of traditional nonlinear Schrodinger equation:The third-order nonlinear Schrodinger equation is selected as the research model.The two-soliton and three-soliton solutions are obtained by virtue of Hirota method,and the transmission characteristics of solitons are analyzed based on the solutions obtained.The results show that the amplitude of soliton can be controlled by adjusting the value of third-order dispersion,which can be used in optical amplifiers.The shape of soliton envelope can also be changed by adjusting the function type of third-order dispersion,which may be helpful in the design of optical switch.In addition,by adjusting the group velocity dispersion and correlation coefficient,we can control the position and degree of interaction between solitons,which can provide theoretical guidance for improving the transmission performance of optical solitons,and ultimately improves the communication quality.(2)The analytical study of coupled equations:the(2+1)-dimensional coupled nonlinear Schrodinger equation is selected as the research model.Its one-and two-bright soliton solutions are obtained by Hirota method.The effects of four wave mixing parameters and free parameters on soliton transmission are explored.It is found that four wave mixing parameters can affect the amplitude of solitons,and one can control the direction and velocity of solitons by adjusting the value of free parameters.The energy transfer phenomenon when solitons are separated after collision is also discussed.The results given here may be applied to the multimode fiber and realize the control of soliton transmission direction and the improvement of communication quality.(3)The analytical study of Ginzburg-Landau equation:The Ginzburg-Landau equation is selected as the research model.Because the composition of this kind of equation is different from that of the traditional nonlinear Schrodinger equation,the modified bilinear method is chosen to solve the equation,and the transformation form is different.Based on the solution obtained,the influence of the parameters in the equation on soliton propagation is discussed.The analysis shows that the free parameter in the equation will affect the propagation direction and amplitude of the soliton.In addition,the value of dispersion can determine the envelope shape and amplification degree of soliton,which can be applied to soliton amplification and reshaping.The results may be helpful for the amplification and direction control of optical solitons in multimode fibers.