Dynamics Of Solitons With Complex Structure In Nonlocal Nonlinear Media With Parity-Time Symmetry

The precise balance between linear(diffraction)and nonlinear effects in a nonlinear medium can keep the initial state of input light unchanged.That is,a spatial soliton is formed.For the applications,spatial solitons have been used in signal processing,all-optical devices,addressing and optical control and so on.In order to achieve more applications of spatial optical solitons,it is very meaningful to study the propagation characteristics of spatial optical solitons and reveal their internal interaction mechanism.The nonlocal nonlinear model(Snyder-Mitchell model)allows the study of optical solitons extended from local media to non-local media with more abundant materials.The discovery of Parity-Time(PT)symmetric structure extends the study of optical solitons from conservative to dissipative systems.In recent ten years,a lot of research has been done in nonlocal nonlinear media and PT symmetric nonlinear media.In recent years,new structures of nonlocal nonlinear media with PT symmetric structure have emerged,but researches on these new structures are still open.Most recent researches focus on the existence and stability of multi-dimensional soliton solutions and one-dimensional solitons.The internal physical mechanism of stable or unstable transmission of optical solitons has not been analyzed.Based on the above,a new nonlocal nonlinear model of two-dimensional PT symmetric structure is established,and the dynamic characteristics of complex optical solitons in this model are studied for the first time.The internal physical mechanism of optical soliton transmission process is analyzed from the angle of energy flow inside complex optical soliton.The effects of different degrees of nonlocal,gain-loss coefficient,phase and propagation constant on the existence range and transmission stability of optical soliton are revealed.The propagation characteristics of dipole solitons in self-defocusing Kerr media with partially PT symmetric structure are also studied.The main innovative research results are as follows:1.A non-local non-linear dissipative system model with PT symmetric structure is established.The band structures of quadrilateral and triangular optical lattices in the model are numerically calculated.The improved SOM(square operator method)is used to solve the numerical solutions of optical solitons and the step-by-step Fourier method is used to study the transmission characteristics.Random interference signal is added to the initial solution to further verify its transmission stability.The range of existence and stability of optical solitons are obtained,and the energy interaction in optical solitons is analyzed,which provides a theoretical basis for the application of optical solitons.2.For the first time,multi-peak optical solitons(dipole,four-peak,six-peak and eight-peak solitons)and vortex optical solitons with angular momentum are found in nonlocal selfdefocusing nonlinear square optical lattices and triangular lattices with PT symmetry,and their existence is analyzed.It is found that either the vertical or adjacent dipolar solitons with the same or different phases or other multi-hump solitons can only exist in the first bandgap.Vortex solitons can exist in the semi-infinite bandgap and the first bandgap.One of the novel phenomena is that the six-peak optical soliton in the nonlocal self-defocusing nonlinear triangular lattice with PT symmetry.In the strong nonlocal region,the refractive index difference between peaks decreases due to the strong nonlocal feature,while in the center region of the six-peak gravity center,a new peak appears and changes to a seven-peak optical soliton.3.By comparing the stability of multimodal solitons in different models,it is found that the threshold of PT symmetry breaking for triangular optical lattices(W0=3)is much higher than that for square lattices(W0=0.5).The stability range of in-phase dipole solitons is larger than that of out-of-phase dipole solitons in either PT-symmetric nonlocal nonlinear optical lattices or partial PT-symmetric self-defocusing Kerr nonlinear optical lattices.In PT symmetric nonlocal nonlinear quadrilateral lattices,in-phase dipole solitons can propagate stably in weak nonlocal and immediate nonlocal regions,while non-phase dipole solitons can only propagate in weak nonlocal stability.In partially PT symmetric self-defocusing Kerr nonlinear optical lattices,the stability range of diagonal dipole solitons is larger than that of dipole solitons.The stability range of multi-hump solitons decreases with the increase of the number of peaks.The stable transmission distance of multi-hump optical solitons in triangular lattices is shorter than that in square lattices.4.The power variation characteristics of optical solitons during transmission are studied.The power of multi-hump soliton and vortex soliton decreases with the increase of propagation constant.The power of in-phase dipole solitons is higher than that of out-of-phase dipole solitons at the same degrees of nonlocal and propagation constants.5.The oscillation of optical soliton's center of gravity in PT symmetric nonlocal nonlinear medium is analyzed.The propagation of multi-hump optical solitons is analyzed by using the energy flow inside the optical soliton.Because of the combined action of linear diffraction effect and nonlinear effect,the energy in soliton peak will flow with each other,and the refractive index will be affected differently in different degrees of nonlocality,which leads to different phenomena of soliton in different degrees of nonlocality,such as the phenomenon of "breathing-like" in the weak nonlocal medium and the phenomenon of in-phase dipole in the square lattices.Solitons compete in strong nonlocal regions,and the center of gravity of out-ofphase dipole solitons oscillates more violently than that of in-phase dipole solitons.The higher the peak value is,the more difficult it is to balance the energy inside the soliton and the more violent the center of gravity oscillation is.6.The solutions of vortex solitons with different topological charges in PT symmetric selfdefocusing nonlocal triangular lattices are studied.Because of the angular momentum of the soliton,the solutions of the soliton with different topological charges are also different.With the same nonlocal response,the closer the vortex soliton is to the energy band,the more difficult it is to maintain its original shape.In the strong nonlocal region,the change of refractive index leads to the change of energy distribution.Vortex soliton even breaks its own shape and redistributes its energy to form a new multimodal shape,but it can maintain the stable transmission of the shape.In summary,this paper studies the nonlocal nonlinear model of two-dimensional PT symmetric structure,the propagation dynamics of complex optical solitons in partially PT symmetric self-defocusing Kerr nonlinear optical lattices,and provides theoretical basis for the design of optical logic gates,photodiodes,optical devices,optical control and optical information storage in all-optical communication.