Propagation Properties Of Spatial Optical Solitons In Optical Lattices With PT-symmetric Complex Potentials

When light propagates in the nonlinear medium with complex potentials,the balance between diffraction,nonlinearity,and gain-loss lead to the formation of spatial optical solitons.It has been shown that the optical solitons have important potential applications in all-optical communications and all-optical devices.In particular,the vortex optical solitons carrying the angular momentum have potentical applications in optical micro-manipilation,partical capture,information transmission and so on.Moreover,studying on the optical solitons has great academic significance in the complete understanding of neighboring disciplines.The dynamics of beam in nonlinear media with complex potentials are described by the nonlinear Schr?dinger equation.The evolution of spatial optical solitons is investigated by numerical calculation,numerical analysis,and numerical simulation.And our findings are as follows:1.The existence and stability of in-phase quadrupole and vortex solitons in PT-symmetric optical lattices are investigated.It is found that both in-phase quadrupole and vortex solitons exist in the first gap,and they can be stable in a certain range of parameters.However,the in-phase quadrupole solitons formed by ring beam are more stable than the vortex solitons.The stable region of vortex solitons shrinks by decreasing the PT-symmetric optical depth or increasing the gain-loss component.It is also found that the power of unstable vortex soliton oscillates irregularly along with the propagation distance,and this phenomenon is very different from the case in the real optical lattices.Moreover,it is found that the vortex soliton undergo phase transiton if the gain-loss component is near to the PT-symmetry critical threshold.2.The evolution of single-charged vortex solitons in the PT-symmetric optical lattices with focusing saturable nonlinearity is investigated.It is found that the singled-charged vortex solitons exist in the semi-infite gap,and the saturable parameter has a great effect on the existence and stablility of single-charged vortex solitons.There exists a threshold value for saturable parameter,belowe which the vortex solitons are unstable in their whole existence regions;while above this threshold the vortex solitons can be stable in some higher power regions.Increasing the saturable parameter will lead that the existence region of single-charged vortex solitons shrinks and their stable region first expands and then shrinks.If the saturable parameter is large enough,the nonlinear term in the model is approximated as a linear term and the single-charged vortex soliton will not exist.In addition,for a fixed saturable parameter,both existence and stability regions of single-charged vortex soliton shrink with the increase of gain-loss component of lattice.The vortex solitons can exist even the gain-loss component of PT-symmetric complex potential is at its phase transition point.However,the vortex solitons diffuse quickly during propagation.Dramatically,the stable regions of out-of-phase quadrupole solitons are broador than the single-charged vortex solitons?,while the stable regions of in-phase quadrupole solitons are narrower than the single-charged vortex solitons?.3.The PT-symmetric triangular optical lattices with a single-site defect can support stable defect modes.The defect depth has a significance effect on the existence and stability of these defect modes.The positive defect fundamental solitons exist in both first and semi-infinite gaps,while the fundamental and negative defect solitons only exist in the first gap.Their stability is in accordance with the anti-Vakhitov-Kolokolov(anti-VK)criterion.For defect vortex solitons,the negative vortex solitons are unstable in their whole existence regions.However,the positive defect plays a stabilizing role on vortex solitons.In addition,taking the positive defect fundamental soliton as example,the gain-loss component on these defect modes is also discussed.4.It is found that two-dimensional mixed linear-nonlinear PT-symmetric optical lattices can support stable spatial optical solitons.The nonlinearity-modulation depth has a great effect on the properties of optical solitons.And the solitons undergo shape transition in a certain range of nonlinearity-modulation depth.The influence of nonlinear-modulation depth and the relative intensity of the imaginary part of nonlinear lattice on the soliton shape transition are discussed in detail.For different nonlinear-modulation depth,the system can present self-focusing or defocusing nonlinearity.In the both first and semi-infinite gaps,the stable regions of optical solitons first expand and then shrink with the increase of nonlinearity-modulation depth for fixed relative intensity of the imaginary part of nonlinear lattice.However,the stable regions of optical solitons shrink with the increase of relative intensity of the imaginary part of nonlinear lattice for a fixed nonlinearity-modulation depth.Moreover,the period of nonlinear lattice can influence the properties of solitons dramatically.In addition,the mobility of optical solitons is also investigated.It indicates that the optical soliton will maintain its original shape while the mass center of soliton oscillates periodically for a small tilt angle.If the tilt angle is large enough,the soliton will be distorted and its mass center oscillates irregularly.5.We investigate the existence and stability of PT-asymmetric multi-peak solitons in the parity-time-symmetric potentials with quasi-one-dimensional imaginary part.It is found that the in-phase PT-asymmetric multipeak solitons with both even and odd number of peaks can stably exist in some regions of the first gap,but these regions are piecewise for some multi-peak solitons.The imaginary part of the potential can dramatically affect the existence and stability of these PT-asymmetric solitons.The asymmetric of these solitons is investigated in detail.The out-of-phase PT-asymmetric multipeak solitons are unstable in their whole existence regions.The properties of PT-symmetric one-,two-,rhombic four-and five-peak solitons are also analysed.The one-,two-and rhombic five-peak solitons can be stable in a wide region,while the rhombic four-peak solitons are unstable in their whole existence region.