Studies Of Linear Localization And Nonlinear Localization Of Light In Coherent Atomic Media

By means of observing, analyzing, and summarizing the phenomena appear during or after the process of the interaction between light and medium, we can investigate the properties of light and medium. In certain circumstances, such as the one in which large refractive index is necessary, we prefer to the system in which light and medium interact resonantly. However, it was well known that light would be absorbed strongly by the medi-um at resonance. Fortunately, electromagnetically induced transparency (EIT) and active Raman gain (ARG) were proposed. EIT system is able to suppress the strong absorbtion of light while light and medium are interacting resonantly. Unlike EIT system, ARG system is able to offset the strong absorbtion of light. These two system are arousing a boom in the field about resonance interaction between week light and media.In this paper, the concept ’coherent atomic media’is identical to the concept ’EIT system’ or ’ARG system’. We focus primarily on the properties of light field, especially the transverse localization of light in coherent atomic media.(1) We propose an EIT system, which is a cold, resonant atomic gas system with N-type levels configuration. In this system, we realize (2+1)D Aubry-Andre model (AA model) in which quasi-periodic potential is introduced. By this model, we achieve vari-ous linear ground states, including extended modes and localized modes. In addition, we display the nonlinearity and dimensionality effects on AA localization, and show how the quasi-periodic potentials affect the propagation of light. Especially, we can modulate the strength and type of the quasi-periodic potential at will.(2) Based on ARG, we propose a scheme to construct a (1+1)D Anderson model in coherent atomic gas under room temperature. By this model, we study various localized states, include linear modes and nonlinear modes. And we display the nonlinearity effects on Anderson localization. We also research the stability for solitons, using the linear stability analysis and the propagation under random noise perturbations.In order to accomplish this work, we have employed the method of multiple scales and some numerical methods, such as Accelerated imaginary-time evolution method, Split-step Fourier transform method, Newton-preconditioned-conjugate-gradient method.