Theoretical Research Of High-order Spatial Optical Soliton Propagation In Nonlocal Media

In this paper,we focus on studying the propagation transformation characteristics of beams with more complicated transverse structures in strongly nonlocal nonlinear media.When a light beam is propagated in a nonlocal nonlinear medium,spatial optical soliton and breather can be formed due to the balance of self-focusing and diffraction effects.In this paper,based on the nonlocal nonlinear Schr¨odinger equation,the evolution equation of the parameters of the beam with complicated light field structure is derived in theory,and the propagation transformation characteristics and control methods of higher-order spatial solitons in the strong nonlocal nonlinear media are studied.The main research contents are as follows:In chapter 1,the research background and significance of spatial solitons are described,the concept and classification of nonlocal media are introduced,and the application value of nonlocal spatial solitons is expounded.In chapter 2,the propagation characteristics of astigmatic hyperbolic sinusoidal Gaussian beams in nonlocal nonlinear media are discussed.The propagation expression is derived theoretically,and the evolution of light intensity distribution,beam width,and curvature are analyzed in detail.We find that the parameters of the hyperbolic sinusoidal function,the initial power,and the initial position are important factors that influence the propagation behavior of the beam.The beam can form fundamental soliton and generalized breather during propagation.By adjusting the incident power,the beam width in the two transverse directions can be expanded or compressed at the same time,or the beam width can be unchanged in one direction and compressed or expanded in the other direction.In chapter 3,the propagation transformation characteristics of complex-valued hyperboliccosine-Gaussian beams in strongly nonlocal nonlinear media are studied based on the nonlocal nonlinear Schr¨odinger equation.By adjusting the complex-valued parameters,this beam can propagate with different forms,including Gaussian-like,nearly flat-topped,multi-peak,and fourpeak forms.This beam can form shape-invariant solitons and breathers under certain incident parameters.In addition,this beam can also form generalized shape-variant high-order spatial solitons and breathers.The beam exhibits some unique propagation properties.A complete theoretical model was constructed,and the expressions of the propagation,light intensity,and second-order moment beam width were obtained analytically.The expressions of the maximum and minimum of the beam width are obtained,and the locations of the extremes of the beam width along the propagation direction are given.In chapter 4,the complex-valued astigmatic cosine-Gaussian beams model is created and its propagation characteristics in strongly nonlocal media are studied.In the strongly nonlocal nonlinear media,the transverse pattern of this beam is diversified and controllable.By adjusting the parameters,higher-order solitons and breathers with special light intensity distribution can be realized.The propagation characteristics of the light intensity pattern and the beam width of this beam in the strongly nonlocal nonlinear media have been systematically discussed.The two-dimensional transverse equivalent opposite evolution of the beam width can be formed.The position,number,and shape of the wave crest can be controlled by parameters.According to the different parameter values,the transverse pattern propagation and transformation characteristics of the beam are classified and discussed.The difference between this beam and other beams with relatively simple field distribution is summarized.In chapter 5,the propagation characteristics of tripolar breather trial solution in nonlocal nonlinear media with loss are studied.The approximate equations of parameters of the tripolar breather trial solution are obtained analytically by the variational method.The analytical solution is verified according to the numerical simulation.The results show that the analytical solution and the numerical solution are in good agreement at a certain propagation distance.Especially when the degree of nonlocality is large,the analytical solution and the numerical solution are very close.Tripolar loss soliton and tripolar loss breather can be formed under suitable incident conditions.By analogy with Newton’s laws of motion in classical mechanics,we regard the evolution of the triple breather as a particle with a mass equal to 1.By studying the evolution law of the equivalent force and the equivalent potential energy,the in-depth physical reasons for the periodic evolution of the tripolar breather are analyzed.In Chapter 6,the research results of this paper are summarized,the shortcomings of this work and the prospect of future research are given.