Research On The Property Of Spatial Optical Soliton In Fractional-Order Optical Lattice

In the transmission process of the light beam in the nonlinear medium,when the nonlinear effect of the medium and the diffraction effect of the beam reach a balance,a self-stable transmission state which always keeps the waveform unchanged is called spatial optical soliton.With the rapid development of nonlinear disciplines,more and more scholars have devoted themselves to the research of spatial optical soliton.In theory,exploring the transmission characteristics of spatial optical soliton and the physical mechanism of its internal interaction is convenient for perfecting the theoretical basis of optical soliton,and can guide and promote the development of related disciplines.In terms of application,spatial optical soliton has important practical development prospects in optical control,all-optical devices,all-optical computing,and optical storage.Subsequently,the concepts of parity-time(PT)symmetric complex potential and fractional Schr?dinger equation(FSE)were successively proposed.These concepts are introduced into optics,which opens up a new direction for the study of the propagation properties of spatial optical solitons.In this paper,the Schr?dinger equation describing the propagation of spatial optical soliton based on the fractional-order diffraction effect is expanded.Using the methods of numerical calculation,numerical simulation and numerical analysis,the transmission dynamics of vector surface soliton and superlattice gap soliton with PT symmetry are studied.We study the band gap structure of the optical soliton by using the plane wave-expansion method to solve it,and the optical soliton solution can be calculated by using the Modified Squared-Operator Iteration Method(MSOM).Add perturbation to the soliton solution,and use the Fourier collocation method to further study the stability of the optical soliton,and obtain a linear stability spectrum,and the propagation properties of the optical soliton can be numerically simulated by using the split-step Fourier method.The main research contents of this paper are as follows:1.We report on the existence and stability of mixed-gap vector surface solitons at the interface between a uniform medium and an optical lattice with fractional-order diffraction.Two components of these vector surface soliton: arise from the semi-infinite and the first finite gaps of the optical lattices,respectively.Itis found that the mixed-gap vector surface solitons can be stable in the nonlinear fractional Schr?dinger equations.For some propagation constants of the first component,the stability domain of these vector surface solitons can also be widened by decreasing the Lévy index.Moreover,we also perform stability analysis on the vector surface solitons,and it is corroborated by the propagations of the perturbed vector surface solitons.2.We report on the existence and stability of gap solitons supported by one-dimensional(1D)PT-symmetric superlattices in nonlinear fractional Schr?dinger equation.Two modes of nonlinear states,i.e.,fundamental solitons and out-of-phase dipole solitons can be found in the semi-infinite gap.The combination of fractional effects and PT-symmetric superlattices features the unique properties of gap solitons.We perform stability analysis on the fundamental solitons and out-of-phase dipole solitons.From the obtained results,we can see that the stability region of these solitons becomes wider with the increase of the Lévy index,which can effectively suppress the propagation instability phenomenon of solitons.Moreover,the propagation constant on the soliton propagation properties are also investigated.With the increase of the propagation constant,the stable range of the Lévy index corresponding to the fundamental solitons becomes narrower,while the stable range of the Lévy index corresponding to the outof-phase dipole solitons becomes wider.