Study On The Algorithm And Characteristics Of Optical Solitons To The NLS Type Equations In Optical Fiber Communications

Optical soliton is a kind of electromagnetic wave that can keep its own speed,amplitude and pulse width unchanged in long distance transmission.Because of these unique properties of optical soliton.optical soliton,as the most ideal information transmission carrier,is widely used in long-distance optical communication and ultra fast signal processing systems.Compared with traditional optical fiber communication,optical soliton communication has the advantages of long transmission distance,high information capacity,high transmission rate,low bit error rate,good confidentiality and strong anti-interference ability.In nonlinear fiber optics,the propagation of optical pulses in nonlinear media is generally described by nonlinear Schrodinger equation(NLS)model.Exploring the analytical solutions of NLS type equations,especially the soliton solutions,lays the foundation for studying the characteristics of different kinds of optical solitons,such as dispersion managed optical solitons,solitons in passively mode-locked erbium-doped fiber lasers,and optical solitons in highly birefringent fibers.Because nonlinear NLS equations are often not integrable,the algorithm research of optical soliton solutions is very important,and the study of optical soliton characteristics is of great significance.This thesis studies the optical soliton solutions and transmission characteristics of several NLS type equations in optical fiber communication based on relevant algorithms such as exact solutions and numerical solutions,which lays a theoretical foundation for the construction of a new generation of all optical soliton communication system with ultra long distance,ultra high code rate and ultra large capacity in the future,and provides a new idea for solving the technical problems of optical soliton communication.The specific work of this thesis is as follows:(1)Based on Schrodinger-Hirota(SH)equation,the management and regulation of high-order dispersive optical solitons are studied.Firstly,the highorder NLS equation is transformed into SH equation by Lie transformation.The modulation instability conditions of plane waves with small perturbation are derived by using the linear stability method for nonlinear systems.It is proved that the modulation instability depends on the plane wave amplitude,wave number and third-order dispersion coefficient.Based on the Hirota method,the bilinear form of SH equation is given and the analytical solutions of single,double and triple solitons are calculated,and the transport modes of high-order dispersive optical solitons are simulated.The influence of different parameters on the transmission of solitons is studied and the dynamics characteristics of solitons are analyzed.Finally,the asymptotic analysis of the three-soliton solution is given to prove the collision behavior of multiple solitons.The results of this thesis theoretically realize the management and parameter regulation of high-order dispersive optical solitons,reveal the transmission characteristics of high-order dispersive optical solitons and the mechanism of elastic collision of multi-solitons,and provide theoretical analysis and basis for the application of ultra-short solitons pulses in dense wavelength division multiplexing systems.(2)Based on the cubic Ginzburg-Landau(CGL)equation,the transmission characteristics of optical pulses in passively mode-locked Erbium-doped fiber lasers are studied.Because of the inintegrability of the CGL equation,it is impossible to solve the double soliton solution of the equation analytically.The barycenter interpolation collocation method is introduced to solve the double soliton solution of CGL equation numerically.The efficiency and accuracy of the numerical method have been analyzed.For bright single solitons,the increase of nonlinear coefficient will make the peak value of optical solitons smaller,while the broadening of optical solitons slightly increases but is not significant.The increase of dispersion coefficient will make the transmission width of soliton wider,the transmission speed of soliton slower,and the peak value larger.For dark solitons,when the dispersion coefficient increases,the dark solitons broaden,and the dark soliton peak value increases slightly,but not significantly.In our thesis,based on CGL equation,the propagation of optical pulses in passively mode-locked erbiumdoped fiber lasers are investigated.The effects of nonlinear coefficient and dispersion coefficient on soliton pulses,as well as the physical meaning and dynamic behavior of different free parameter solutions are analyzed,which lays a foundation for finding the specific expression of middle soliton molecules.(3)Based on the coupled nonlinear Schrodinger(NLS)model,the modulation instability and optical switching mechanism of optical pulses in high birefringence fibers are studied.The analytical single and double soliton solutions are derived.Based on the interaction analysis of the double solitons,the all-optical switching mechanism and the influence of different soliton parameters on the all-optical switching are discussed.By controlling the related soliton parameters,the control mechanism of the logic structure of the all-optical switch is explored,and the on and off functions of different optical signals are realized.For zero birefringence and linear birefringence respectively,the modulation instability gain in the normal and abnormal dispersion regions are discussed.We find that when the perturbation frequency is zero,there is no unstable gain,and there is a pair of unstable blades on either side of the zero-perturbation frequency.The greater the difference between the incident power values of the two components of the optical pulse,the worse the stability of the system.When the incident power of the two components is equal,the unstable region of the system is the smallest and the system is the most stable.With the increase of the total power value,the gain gradually increases,the gain band becomes wider,and the instability range becomes larger.The research results of modulation instability and optical switching mechanism of optical pulse in high birefringence fiber provide a theoretical basis for the construction of information systems such as optical computer,optical information processing,optical fiber network and photonic integrated circuit.