The Research Of Simulation Experiment About Chaotic Synchronization Based On Erbium Doped Fiber Laser

Chaos is common in nature and human society, chaos is a irregular movement seeming like random that appears in a certain system, it is a both universal and complex phenomenon, and it is the most typical behavior in nonlinear system.The French scholar Pang Jialai discovered the phenomenon of chaos in the early 20th century, Lorenz discovered the "butterfly effect" in 1960s,after that, Feigenbaum discovered the universal constant in period-doubling bifurcation to chaos, this caused a particular concern on the research of chaos in academic circles. People give a great concern on chaos as soon as these characteristics were found. Now chaos theory and its application have extended to physics, chemistry, biology, medicine and many other natural and social sciences. Chaotic dynamics has extended to other areas of research, and it has became a comprehensive, interdisciplinary and cross-cutting science. The establishment of chaotic dynamics changed people's understanding of the objective world.Currently, erbium-doped fiber laser study focused on the research of double-loop erbium-doped fiber laser chaos,Hyperchaotic and Synchronization,but on the study of single-ring erbium-doped fiber laser chaos and chaos synchronization is relatively rare.This paper started from the analysis of single-ring erbium-doped fiber laser dynamics equation, by the methods of modulating pump parameters and increasing delayed feedback loop in the laser system to achieve chaos of a single-ring of chaotic erbium-doped fiber laser. On this basis, respectively, the nonlinear feedback parameter modulation synchronization method, delay-driven synchronization method and linear delayed feedback synchronization method to achieve two single-ring erbium-doped fiber laser synchronization.The paper is divided into two parts:First of all, the principle of erbium-doped fiber is introduced. As the polarization variable relaxation time is very small, fiber lasers are classified as class B. According to the principle of system to produce chaos, B class laser requires at least an additional degree of freedom was possible laser chaos, For erbium-doped fiber laser system to achieve chaos, we can increase the system's degree of freedom to become a multi-dimensional erbium-doped fiber laser system, under certain conditions can be achieved chaos of the system. By the dynamic equations theory analysis of single loop erbium-doped fiber laser shows that the pump intensity modulation and the additional delay feedback loop can increase the system's degrees of freedom, under certain conditions of realization of the chaotic system. In the appropriate system parameters, we carried out these two methods of simulation. On the simulation results of the system attractor, bifurcation diagram, power spectrum, and the output light intensity with time evolution diagram analysis shows that the two methods can achieve chaos of a single ring erbium-doped fiber laser.Second, in the chaos of single-ring erbium-doped fiber laser based on the premise, respectively, the nonlinear feedback parameter modulation synchronization method, delay-driven synchronous method and the linear feedback law is analyzed theoretically.Synchronization of nonlinear feedback parameter modulation principle is: Both chaotic system of single ring erbium-doped fiber laser system with identical parameters were used as a drive system and response system, the output drive system and response system of nonlinear difference signal as the feedback signal to control the response system loss parameter modulator, after the transient process, the drive system and response system can achieve chaos synchronization.Principle of delay-driven synchronization is: Two identical chaotic single-ring erbium-doped fiber laser, a drive system as the other as a response system. So as the drive system of the laser output light intensity after a period of delay, part of the response as a drive signal is injected into the system, another part of the feedback to the drive system. The two systems on the same drive signal achieve synchronization of chaos.Principle of linear feedback synchronization: Drive system and response system has the same structure and system parameters. A variable of drive system sent to the response system, select the appropriate system in the relevant driving factor case allows both systems to achieve precise synchronization.Thus the two systems can achieve synchronization, the key is to select the appropriate drive factor.Using Runge - Kutta method to solve nonlinear equations for the three methods , and making a experiment of numerical simulation. Simulation results show that the three synchronization methods can achieve the two single-ring erbium-doped fiber laser synchronization.