Study On Nonlinear Dynamics Of Two-Photon Lasers

All the systems in nature including physical system, chemical system, biological system, microscopic particle, and celestial body in astrospace exhibit nonlinear dynamic behaviors. The studies on nonlinear dynamic systems mainly contain two aspects, one for coherent dynamic structure of the nonlinear system, for example solition, gyre, and complex pattern, and another for research on the stability of nonlinear system, such as bifurcation, cataclysm, and their induced chaos and turbulence. In the last two decades, the nonlinear subject undergoes a rapid development, and it has become a interdiscipline subject. This paper mainly studies chaotic dynamics of the two-photon laser field.We introduce the history of theory of chaos in the 1st chapter.In the 2nd chapter, we present the concept of chaos, some famous models, and methods in studying chaos. Besides, we introduce the Lorenz-Haken equation which was derived by Haken for the description of two-level single-photon laser.In the 3rd chapter, we derive equations and study nonlinear dynamics of cascade two-photon laser, in which the electromagnetic field in the cavity is driven by coherently prepared three-level atoms and classical field injected into the cavity. The dynamic equations of such a system are derived by using the technique of quantum Langevin operators, and then are studied numerically under different driving conditions. The results show that under certain conditions the cascade two-photon laser can generate chaotic, period doubling, periodic, stable and bistable states. Chaos can be inhibited by atomic populations, atomic coherences, and injected classical field. In addition, no chaos occurs in optical bistability.In the 4th chapter, We derived the dynamic equations for effective two-photon lasers by using quantum Langevin equation theory with considerations of the atomic coherence and the injected classical field. The dynamics of the effective two-photon lasers and the effects of time-delayed feedback, atomic coherence, and the injected field on the dynamics are numerically studied. The results show that stable state and quasi-periodic attractor exist in effective two-photon lasers, and the time-delayed feedback can induce chaotic states in the presence of the injected classical field. The bifurcation diagrams show the transition to chaos via Hopf...