Propagation Dynamics Of Special Beams In Nonlocal Nonlinear Media

Since the invention of ruby laser,the propagation dynamics of beam in various nonlinear systems have developed rapidly.When a beam propagates in nonlinear medium,the balance between diffraction effect and self-focusing nonlinear effect will produce a stable propagation soliton.Because spatial optical soliton has important practical value in the optical fiber communication,optical information processing,all-optical switches and other fields,it is very necessary to explore the transmission characteristics of optical beams(optical solitons)in different nonlinear systems.In the past,many studies on nonlinear response in media were local,such as Kerr nonlinearity,saturation nonlinearity and photorefractive nonlinearity.Compared with local response,nonlocal response can not only support more soliton types,but also has more complicated physical mechanism.The discovery of nonlocal response also provides a broader platform for the propagation dynamics of special beams.Taking the linear or nonlinear Schr(?)dinger equation as the theoretical model,this paper explores the evolution behavior of two special beams in nonlocal nonlinear media,which is divided into the following three research contents,corresponding to the second,third and fourth chapters of the paper respectively.(1)Taking the linear Schr(?)dinger equation with parabolic potential as the theoretical model,the dynamics of one-dimensional chirped cosh-Gaussian beams are discussed analytically and numerically.The results show that the beam propagation in this system is similar to the process of self-Fourier transform,showing a periodic self-focusing behavior.The depth of parabolic potential can control the characteristic parameters of beam evolution,such as period and peak intensity.Chirp parameters also have an influence on the beam trajectory and energy localization modulation.(2)Taking the SNNLSE(strongly nonlocal nonlinear Schr(?)dinger equation)as the theoretical model,the characteristics of two-dimensional chirped cosh-Gaussian beams are studied analytically.The results show that the evolution is still periodic,and the values of initial parameters and input power largely determine the evolution mode of beam and soliton.Under certain conditions,the beam will form solitons or breathing solitons during transmission,and the influence brought by chirp parameters is basically the same as that in chapter 2.(3)Taking the competing CQNNLSE(cubic-quintic nonlocal nonlinear Schr(?)dinger equation)as the theoretical model,the transmission behavior of Pearcey-Gaussian beam under the influence of nonlinear and nonlocal response is numerically studied by performing the split-step Fourier method.Under the nonlinear action,the beam will form solitons in bound state or breathing state.The respiratory period and peak intensity of solitons can be regulated by the balance between nonlinear strength and the degree of nonlocal response.In addition,the complex interaction between two beams is also explored.