| Nowadays, more and more people are attracted to research the optical soliton in the nonlocal nonlinear medium. The results from experiment and theory studies show that:compared with local soliton, nonlocal spatial soliton has more research contents and wider potential application value.First of all, the evolution equations and rules of each beam parameter and critical power are obtained, when analyzing the 1+2D Sech-type beams'propagation in the weak nonlocal nonlinear medium with small loss and e index response. Furthermore, if the medium's loss is small enough,1+2D Sech-type lossy spatial solitons which has a phase shift and remains almost the same beam width.And then, based on the detailed analysis of the 1+1D Gaussian type single beam loss spatial soliton, the evolution equations of each parameter and the evolution rules of the light beam width are obtained. When the light beam incidents at the light beam waist in the medium with small enough loss, and the initial power equals the critical power, the 1+1D Gaussian type single light beam's beam width shows a very slow getting-wide process. When the 1+1D Gaussian type single light beam propagates in a short distance, the quasi-spatial-optical-solition which is a lossy optical soliton whose beam width gets wide slowly is obtained approximately. When the initial power is smaller than critical power, the broadening change of the beam width will satisfy the quasi-periodic cosine function. When the initial power is bigger than critical power, beam width will be quasi-periodic cosine function first and then over-compression to make periodic changes of broadening change.Thirdly, the evolution equations of each beam parameter and the evolution rules of the beam width are gained, when researching the paraxial elliptical Gaussian type beams'propagation in elliptical symmetry strong nonlocal nonlinear medium with small loss. The results show that:the beam width gets wide continuously and slowly, when initial power equals critical power and the paraxial elliptical Gaussian beam propagates in medium with small enough loss, that is, the elliptical Gaussian type lossy spatial soliton is obtained in a way.Last,1+1D Gaussian type double beam propagation model is set up, when studying the mutual interaction of the 1+1D Gaussian type double beam in the nonlocal nonlinear medium with small loss. Using analytical method to study the evolution rules of two-beam transmission, quasi-soliton solution is obtained. Further analysis manifests that the center track of the two beams attracts each other in the form of AiryAi function during the transmission process. When the loss increases gradually, the transmission distance becomes gradually longer, and the two tracks are farther and farther away from the center beam transmission shaft, and the distance between the centers of two beams gets grower and grower as well. |
