A Theoretical Research For The Breathers And The Solitons Solutions In The Hermite-Gaussian Form Of The Beam Propagating In The Strong Nonlocal Media

In this paper, the evolution of the Hermite-Gaussian(HG) beams, governed by theSnyder-Mitchell model, is discussed in the strong nonlocal media, and exact analyticalsolutions in the HG form of the beam propagating are obtained. For the strongly nonlocalcase, HG solitons can be expressed in terms of the linear superposition of Gaussiansolitons.The paper is organized as follows:Chapter 1, we present an overview of recent advances in the research of optical beampropagating in the strong nonolocal nonlinear media.Chapter 2, based on the Snyder-Mitchell linear model in the rectangular coordinatesystem, we obtain the exact (1+D)-dimensional (D=1 or 2) analytical solutions withthe HG form in the strongly nonlocal nonlinear media. Then, we discuss the solutions,the comparisons of analytical solutions with numerical simulations of the NNLSE aregiven, and we achieve that HG solitons can be expressed With the linear superpositionof Gaussian solitons. Finally, a conclusion is presented.Chapter 3, In summary.The main achievement of the paper is that exact analytical HG solutions are derivedin strongly nonlocal nonlinear media. The evolution of the HG beams in strongly nonlocalnonlinear media is discussed. The comparisons of analytical Solutions with numericalsimulations of the NNLSE show that the analytical HG solutions arein good agreementwith the numerical results in the case of strong nonlocality. Our results show that thecritical power for the HG soliton propagation is independent of the mode number of HGbeams, but the propagation constant increases as the mode number increases. For thestrongly nonlocal case, HG solitons can be expressed in terms of the linear superpositionof Gaussian solitons. Gaussian breathers and Gaussian solitons can be treated as specialcases of HG breathers and HG solitons.