Study On The Propagation And Interaction Of(2+1) Dimensional Nonlocal Spatial Solitons

Spatial optical soliton is essentially the result of continuous light wave under the balance of its spontaneous diffraction and the nonlinearity.By virtue of the nonlocal nonlinearity,(2 + 1)dimensional((2+1)D in short)nonlocal spatial optical soliton can not only stabilize its profile and the phase structure,but also interact with other optical solitons nonlocally.On the one hand,the study of(2+1)D nonlocal spatial solitons reveals the nature of the interaction between matter and strong light,which is of great academic value.On the other hand,the investigation of the propagation and the interaction of(2+1)D nonlocal spatial solitons leads the research and development of new-type all-optical devices,which is with important application prospect.Based on the coupled nonlinear Schr?dinger equations that describes the propagation of(2+1)D nonlocal spatial solitons,this paper applies the numerical calculation and analysis and studies the propagation and the interaction of(2+1)D nonlocal spatial solitons under the influence of the PT symmetric and periodic linear potential,the Gauss-type local linear potential or the nonlocal nonlinearity with longitudinal modulation.The specific results are as follows:(1)The existence and stability of local fundamental solitons,local vortex solitons and nonlocal solitons in the PT symmetric lattices with competing cubic-quantic nonlinearity are studied.In the case of the self-focusing cubic and self-defocusing quintic nonlinearity,the fundamental solitons and vortex solitons can exist in a wide range of parameters,but only a few of them are stable.Moreover,the power curve of vortex soliton has a shape of "double fork" with the upper and lower branches.In the case of the self-defocusing cubic and self-focusing quintic nonlinearity,the fundamental solitons and vortex solitons exist in a relatively narrow range but most are stable.In the case that the cubic nonlinearity is nonlocal,the self-focusing cubic and self-defocusing quintic nonlinearity can support and stabilize solitons in the first Bloch bandgap,while the self-defocusing cubic and self-focusing quintic nonlinearity can support solitons in the semi-infinite Bloch bandgap but cannot stabilize them.(2)The propagation of vector solitons in nonlocal nonlinear optical lattice with PT symmetry is studied.The gravity center and the power of vector solitons oscillates,which is of beat patterns.According to the analysis of beat patterns,PT symmetry is demonstrated to be the necessary condition for beat patterns.The degree of nonlocality affects the stability of propagation and the shape of beat patterns.And the general nonlocal nonlinearity is most suitable for stable propagation and distinct beat patterns.The propagation constants of the two components of vector solitons also influence the beat patterns.When their propagation constants are equal,the beat patterns are most distinct.When the difference between propagation constants is large,the beat patterns degenerate into equal-amplitude oscillations.(3)The influences of the Gauss barrier or the Gauss trap on the propagation of vector solitons in a nonlocal nonlinear bulk medium is studied.In homogeneous nonlocal nonlinear bulk media,the two components of vector soliton will spontaneously separate or fuse during propagation.The Gauss barrier can suppress the spontaneous separation of the out-of-phase solitons,while the Gauss trap can suppress the spontaneous fusion of the in-phase solitons.But only the Gauss barrier(or trap)with appropriate height(or depth)and width performs well.(4)The asymmetric propagation of scalar spatial solitons in a bulk medium with nonlocal nonlinearity whose nonlocality is longitudinally and gradually changed.In a bulk medium whose nonlinear nonlocality changes from strong nonlocality to weak nonlocality along the longitudinal direction,the solitons with sufficient input power can stably propagate from the strongly nonlocal end to the weakly nonlocal end.However,these solitons will diffract rapidly along the opposite direction,which means they cannot propagate through the media stably.Moreover,the asymmetric propagation of solitons under the gradually nonlocal nonlinearity with different forms are similar.Based on the quantitative analysis of the relationship between the input power and the width magnification of the soliton,the optimal input power of the unidirectional transmission of solitons is found.(5)A series of new-type all-optical logic gates are designed based on the interaction between the components of vector solitons in nonlocal nonlinear bulk media.The logic gate uses only two input beams,without any additional detection beams.Moreover,these logic gates are(2+1)dimensional,which means they are flexible in operation.The input logical states are determined by tilting the input beams or not,and the output logical states are decided by the power received by the back end.Six types of logical operation operations are realized,including AND,NAND,OR,NOR,XOR and NXOR.