Study On Some Nonlinear Phenomenon In Coherent Atomic Medium

Since the invention of laser, nonlinear optics has attracted extensive attention and acquired very wide applications. As is well-known, when the frequency of probe pulse is close to the resonantly frequency of media, even a beam of weak probe pulse, provided the very large optical absorption can be avoided, is powerful enough to produce a strong nonlinearity. However, in the early development stage of nonlinear optics there was lack of applicable system, in which the very large optical absorption can be avoided. So, in order to produce a strong nonlinear optical effect laser with high light intensity was requisite till electromagnetically induced transparency (EIT) and active Raman gain (ARG) was proposed in the atomic coherence resonance media. EIT not only intensify the nonlinear polarizability of active media, but also can sharply reduce the absorption of light, and realize subluminal propagation. ARG can intensify the nonlinear polarizability. Meanwhile, ARG will enhance signal light rather than absorb signal light, and can achieve superluminal propagation as well as subluminal propagation. The novel features of the atomic coherence resonance system attracts extensive attention.In recent years, the research mainly concentrated in the linear phenomenon and nonlinear propagation, etc. But the model which has potential application value and profound physical meaning, is still in a fledging period. The related theory need further exploration and improvement.In this dissertation, we have explored nonlinear effects of weak light in coherent atomic media deeply, using the multiple-scales method combined with numerical simulations developed in resonant nonlinear optics by our research group in recent years. Or to be more exact, we have studied optical bistable state in N-type active Raman gain atomic media and Anderson localization modes and nonlinear solitons of parity-time symmetry complex potential in electromagnetically induced transparent media. Our works include the following aspects:1.We study the optical bistability (OB) in an active Raman gain atomic medium by means of a unidirectional ring cavity. The system considered is a resonant N-type four-level atomic ensemble, which can be realized at room temperature, and not only has a lot of tunable parameters, such as the detuning, the atomic concentration, the pump and control field, but also possesses gain-free (or little gain) transparency windows. We discuss the conditions and the range of these parameters for realizing OB, and even the condition for realizing optical multistability. Our results will provide theoretical basis for experimental realization.2.We propose a scheme to realize linear Anderson localization modes and nonlinear solitons via atomic coherence. The system suggested is a resonant atomic ensemble having N configuration. We show that the envelope of the probe field satisfies a modified nonlinear Schrodinger equation, which includes diffraction, Kerr nonlinearity, parity-time symmetric periodic complex potentials and small dissipation. The PT potential can be generated by an assistant field and an additional far-detuned laser field. In addition, these nonlinear coefficients and PT potential can be easily controlled by adjusting system parameters, such as detuning, field intensity, and so on. In the case of adding random potential into PT model, we not only obtain the linear Anderson localization modes, various solitons, but also find the relationship between Anderson modes and nonlinear modes by adjusting the nonlinear coefficient. The stability of various solitons is also studied by linear stability analysis.