(1+2)-dimensional Perturbated Solutions Of The Nonlocal Spatial Optical Solitons

In this paper, with the perturbation method, we analyze the propagation of the(1+2)-dimensional[(1+2)-D] solitons in the sub-strongly nonlocal case and in the nematicliquid crystals (NLC). The perturbation method can deal with not only the nonlocal casewith a regular response function, such as a Gaussian-type rensponse function, but alsothe nonlocal case with a singular response function, such as the response function in theNLC.The paper is organized as follows:Chapter 1, we present an overview of recent advances in the research of solitonspropagating in nonlocal nonlinear media.Chapter 2, by extending the (1+1)-D perturbation method to the (1+2)-D case, weobtain the fundamental soliton solutions to the (1+2)-D nonlocal nonlinear Schrodingerequation (NNLSE) with a Gaussian-type response function for the sub-strongly nonlocalcase. Numerical simulations verify our soliton solution. The soliton solution can beapplied to not only the sub-strongly nonlocal case but also the strongly nonlocal case.Making the comparison with the strongly nonlocal soliton solution obtained by Guo etal., we find the soliton solution obtained with the perturbation method is more accurate.The critical power of the strongly nonlocal soliton is proportion to the 4th power of thecharacteristic length of the response function and in inverse proportion to the 4th powerof beam width.Chapter 3, with the perturbation method, we deal with the nonlocal case with asingular response function and present a (1+2)-D fundamental soliton solution in theNLC. Numerical simulations show this analytical soliton solution can describe the exact(1+2)-D soliton state in the NLC for the strongly nonlocal case. The critical power ofthe strongly nonlocal soliton is proportion to the 2th power of the characteristic lengthof the response function and in inverse proportion to the 2th power of beam width. The critical power in the NLC cell accords with the numerical simulation in Ref [35] greatly.Chapter 4, in summary.The main acievement of the paper is that, with the perturbation method method,we have obtained the (1+2)-D fundamental soliton solution in the sub-strongly nonlcoalnonlinear media and in the NLC. The perturbation method can be applied to not only thecase with a regular response function, but also the case with a singular response function.