Linear And Nonlinear Localized States Of Light Waves In Coherent Atomic Media

Anderson location(AL)is about the impacts of impurities on electron transport.Non-interaction AL hasn't been observed in laboratory for the interference of the coupling interaction between electrons and the Coulomb interaction of atomic core on electron.Now scientists usually choose light waves to conduct research on AL as light waves aren't confronted with those problems that electrons be.Modeling.Firstly,the dissertation chooses atomic system with special energy configu-ration as the research object,obtaining Maxwell-Schrodinger equation system via electric-dipole approximation,rotating-wave approximation,and slowly varying envelope approx-imation.Secondly,the dissertation achieves 1D and 2D nonlinear Schrodinger equation system through multiple scale method of weak lights of nonlinear optics system.Then,the article obtains 1D and 2D linear Anderson models with various random potentials which includes totally random potential and periodical potential plus random potential,and non-linear models with various potentials and nonlinear effects which includes Kerr nonlinear effects,cubic-quintic nonlinear effests and saturable nonlinear effects.Anderson models' properties.In linear Anderson models,the article obtains local-ized states by utilizing strictly diagonalized numerical method to solve linear Anderson models.Then,the article discusses the localization properties of localized states by taking different dimensionality,potentials and nonlinearities into account,finding that the local-ization property of linear Anderson localized state with periodical potential plus random potential is better than the one with random potential,and the localization property of two-dimensional linear Anderson localized state is also better than one-dimensional situation.Solitons and their stability.Firstly,the article obtains soliton solutions by using Fourier collocation method,Accelerated imaginary-time evolution method and Newton-preconditioned-conjugate-gradient method to solve nonlinear models.Then,the disser-tation analyzes the stability of solitons via Linear stability method and Stepping Fourier transformation method,finding that the stability of nonlinear solions with periodical poten-tial plus random potential is globally best than purely random and non-potential situations,however,the stability of one-dimensional cubic-quintic nonlinear soliton with purely ran-dom potentical when g11 = 1,g12 =-1 is best than the stability of solitons with periodical potential plus random potential and null-potential at the same dimensionality and equa-tions.The coherent atom selected by the dissertation can be realized at room temperature,simply and easily controlled the potential parameters,therefore it is a feasible experimen-tal scheme to carry out the AL and solions and modulate them.