Pattern Dynamics In Optical Resonator With Nonlinear Material

Pattern dynamics, including pattern formation and selection, spatio-temporal chaos (STC) control, synchronization and applications, has become the most important area in nonlinear optical research, which indicating tremendously applying potentialities.Optical pattern dynamics is mainly divided into two parts: laser pattern dynamics and pattern dynamics in optical resonator with nonlinear material. We mainly investigate the second kind. Linear stability analysis and numerical simulations will be used, and the evolution equation of a nonlinear resonator filled with Kerr medium, the mean-field model for a nonlinear resonator filled with two-level atomic medium, second-harmonic generation system (SHG) with quadratically nonlinear material, complex Ginzburg- Landau equation (CGLE), and coupled map lattice model (CML) will be considered in this dissertation. The paper can be divided into three parts: pattern formation, pattern selection and control of STC, the synchronization and applications of STC.In part one, a survey of the development of chaos research and optical pattern dynamics are presented, the basic theories of pattern dynamics are introduced, and the achievements of optical pattern dynamics are described also. Taking the evolution equation of a Kerr resonator and CGLE for example, we discuss pattern formation with system boundary effects. Spatial modulated instability induced pattern formation in SHG is discuss also. Detail of linear stability analysis, numerical simulations and their consistencies are presented. A new type of complex pattern is obtained when Turing and Hopf bifurcation are both existed.In part two, we mainly discuss pattern selection and control of STC. Taking the mean-field model of a nonlinear resonator filled with two-level atomic medium as an example, we use spatial Fourier filter techniques toselect optical pattern, and first introduce the discrete random filter method which proved to be flexible and effective for the system having rotary invariability. Taking CGLE for example, we first introduce spatial grid filter technique to control the system turbulence states and obtain multiform regular spatial distributions, both with the time evolution keeping to be chaos or changing to be period. And we also control STC in CGLE by using delay feedback method.In part three, the synchronization and applications of STC are investigated. Realized STC synchronization in CGLE by using several methods, such as noise induced synchronization, chaos signal driven synchronization, regular signal driven synchronization, substituted signal driven synchronization. The generalized synchronization in DT (defect turbulence) regime and PT (phase turbulence) regime of CGLE using coupled method is first put forward. Finally, we also discuss the fully development of STC in CML and its synchronization, using this kind of STC we realize secure communication with multi-road spread spectrum method and realize information storage. All these topics have attracted a great deal of attention in recent years.