Discrete Multipole Dark Solitons In Saturable Nonlinearity Media With Parity-time Symmetric Lattices

Soliton is a new concept proposed in the 1970 s.The discrete spatial soliton,formed by the balance of the self-focusing or self-defocusing effect produced by the discrete nonlinear waveguide and the natural diffraction effect,will also make the transmitted beam locate in the original direction and the transverse dimension does not change.It is found that discrete solitons can exist in nonlinear media such as Kerr medium,photorefractive and liquid crystal cell.This property with constant envelope width makes it has high application value and is involved in many optical devices.Along with the new theory of parity-time(PT)symmetry,PT soliton has become a new research hot spot in recent years.The achievements of discrete PT soliton are mainly concentrated in Kerr medium,ring structure,alternating coupling coefficient Kerr media and other topics,and research direction is limited to bright soliton.While the multipole dark solitons in the saturated nonlinear medium have not been reported.Therefore,this paper mainly studies the existence and stability of discrete PT multipole dark solitons in saturated nonlinear media.The main methods and research contents are as follows:This paper starts from the historical background and the research results of soliton in recent years.On the basis of expounding the concept,the formation mechanism of soliton is described in detail by means of evidence,and the spatial dark soliton of this paper is introduced from the point of view of different classification.Then we briefly deduce the nonlinear Schr(o)dinger equation model which describes the propagation of the beam in the fiber,and then introduce the numerical method,the squared-operator iteration method(SOM)and the modified squared-operator method(MSOM),as well as soliton steady-state solution analysis method and simulation propagation method to verify the stability analysis.Simultaneously,the center topic-Prity-time(PT)symmetric theory is proposed.We briefly describes the PT symmetry model in optical and discuss the continuous and discrete systems of the PT soliton,respectively.For the discrete PT equations with saturable nonlinear terms corresponding to this subject,the effects of propagation constants,saturable parameters and lattice constants on multipole dark solitons are studied.Therefore,the soliton solution is obtained by the advantages of high precision and fast convergence of MSOM,and the characteristic polynomial and stability parameter of judgment stability are deduced by linear stability analysis of soliton solution.In this paper,we use the wide-angle finite difference beam propagation method because of the advantages of accuracy and logic simulation,so asto verify the stability of the stability analysis.In this paper,we study the influence of propagation constants,nonlinear saturation coefficients and lattice constants on the existence and stability of discrete PT multipole dark solitons.As a case of multipole dark soliton,we take dipole and triple soliton for example.It is found that the steady-state solutions of dipole soliton and triple soliton exist in the same parameter interval,.In the effective region of the soliton solution,the total energy flow of the soliton increases with the propagation constant,and the total power of the dipole dark soliton is smaller than that of the triple soliton.For the saturation coefficient,the soliton power is the same increasing tendency.In the same way,the power of dipole soliton is still less than that of the triple dark soliton.In the effective region,the stable interval of the dipole soliton is slightly longer than the triple,namely it is more stable.However,for the lattice constant,the overall power show a decreasing tendency and the deceleration is not obvious,it is indicating that the effect of lattice parameters on the PT dark soliton is not too big.