Properties Research Of Surface Gap Solitons In A Nonlinear Fractional Schr(?)dinger Equation

The formation of spatial solitons can be explained by the self-trapping effect of optical field in nonlinear medium,has potential application value in optical switches,all-optical photonic devices and all-optical communications.A lot of research work has been carried out on the traditional spatial solitons,and many novel characteristics have been found.The fractional nonlinear Schrodinger equation proposed by Nick Laskin describes the evolution behavior of fractional spin particles.In 2015,S.Longhi considered that the Schrodinger equation and the paraxial wave equation had the same mathematical form.For the first time,the fractional Schrodinger equation was introduced into optics,which opened up a new research direction for the optical field--the fractional light field dynamics.However,the research on the spatial solitons supported by fractional nonlinear Schrodinger equation is still in its infancy.We have carried out some research work on this issue.This thesis,stable solitons solution of surface gap solitons in nonlinear fractional Schrodinger equation,we use a series of numerical methods such as Newton Conjugate-gradient method,Square-Operator Iteration methods;The eigenvalues of the solitons are calculated by adding the perturbation to the solitons.Then determine the parameter window for the soliton stability;The propagation characteristics of the solitons by using Split-Step Fourier Methods analysis and Pesudospectral method.This article includes the following core content:1.We study the propagation dynamics of the surface bandgap soliton supported by the periodic fractional nonlinear Schrodinger equation in the interface separating a defocusing uniform medium and a semi-infinite optical lattice imprinted in it.Interestingly;in the fractional order system,by analyzing the dispersion relation and the band gap energy spectrum,we find that with the increase of the band gap of the soliton in the variation of the Levy coefficient,the existence scope of the soliton is constantly expanding.The existence of solitons will shift.As the Levy coefficient decreases,the soliton becomes increasingly localized,and the power of the soliton becomes larger,which effectively suppresses the diffraction in the propagation process of the linear light field.The width,amplitude,and power of the nonlinear eigenstate-soliton are analyzed,and the dependence of the surface soliton correlation on the Levy coefficient is obtained,and the conclusion that the Levy index can be used to expand the parameter space of the soliton stability is given.2.We have also found a multi-peak surface-gap soliton in this system,and with the increase of the peak,the stability interval has also expanded.The reduction of the stable region of the multi-peak surface-gap soliton is due to the decrease of the Levy coefficient or the increase in the number of soliton peak.Our group is the first to propose a nonlinear fractional surface gap soliton research.The results of the paper have implications for other forms of spatial soliton research in fractional order systems.