Control And Synchronization Of Hyperchaos In Erbium-doped Fiber Lasers And Spatiotemporal Optical Patterns

Erbium-doped fiber laser has attracted much more attentions for its greatly potential application. It upbuilds good theory and experimental foundation for the application of erbium-doped fiber lasers in optic communication, optic detection etc. to study control and synchronization of chaotic erbium-doped fiber lasers. The investigation of the optical spatiotemporal pattern is a forward topic in nonlinear scientific field. It has basic significance to study the chaos of Erbium-doped fiber laser and optical spatiotemporal pattern.In this dissertation, we mainly investigate the control and synchronization of chaos/hyperchaos in dual-ring erbium-doped fiber lasers (DREFL) and optical spatiotemporal pattern of medium with two energy levels in a ring optic cavity. At the same time, we also do a pilot study for the application of the synchronization of the chaotic DREFLs in secure communication. The dissertation can be divided into two parts: the control, synchronization of DREFLs and its application; optical spatiotemporal pattern in a ring optic cavity.In part one, firstly, the dynamic equation of the DREFL is deeply investigated and the stability of its stable solution is analyzed, the condition of the threshold is determined. We roundly investigate the chaos and hyperchaos of DREFL from different aspect embodying the character of chaos and find that DREFL can be in chaotic or hyperchaotic state at some conditions. It is firstly founded that the DREFL has two attracting basin at some conditions. Secondly, the chaos and hyperchaos of DREFL is successfully controlled by three methods-period-parameter-modulation, delay nonlinear-feedbackparameter-modulation and outer-period-signal-drive. The latter two methods are new methods that we present based on original methods for control chaos and considering the character of DREFL, the results of controlling the chaos and hyperchaos of DREFL is satisfying. Thirdly, we investigate the generalized synchronization and accurate synchronization of two chaotic/hyperchaotic DREFLs. The generalized synchronization present an advantageous way for multi chaotic DREFLs realizing accurate synchronization at the same time. Based on the generalized synchronization and method of controlling chaos, we present two new methods to realize acute synchronization of two chaotic DREFLs, i.e., delay-feedback-injection and delay-outer-chaotic-signal-feedback. It is shown thatthe method delay-feedback-injection is robust by numerical simulation, which is the base for its application in practice. Finally, it is investigated that optic secure communication is realized by using synchronization of chaotic DREFLs based on the method delay-feedback-injection, the numerical result is heart stirring.In part two, the optical spatiotemporal pattern in ring optic cavity is investigated. Using delay feedback with spatial perturbation method, the system shows roll, square, hexagon, homocentric circle, "honeycomb" and "snowflower" pattern with different spatial perturbation functions. Different patterns can be coexist and compete each other with the same perturbation function, which is the new character of this optical system with delay feedback.