Propagation Dynamics Of Multipole Breathers In Nonlinear Media

The propagation process of a laser beam in strongly nonlocal nonlinear medium(SNNM)is described by the nonlocal nonlinear Schr?dinger equation(NNLSE).When the propagation satisfies the strong nonlocality condition,the NNLSE can be simplified to Snyder-Mitchell model.In strongly nonlocal nonlinear media,the beam propagation can exist in different forms,such as optical solitons and breathers.When the beam propagates in the nonlocal media,it will show many special properties,which are very different froms that in the local media.Multipolar soliton,optical breather,vortex soliton,Laguerre Gaussian soliton and so on,they can not stable propagation or even do not exist in local media,but they can exist and stable propagation in nonlocal media,some different characteristics can be obtained.Due to its potential applications in all-optical switching,photon information transmission and processing,optical logic and other related fields,the propagation of spatial optical solitons and breathers has attracted extensive research interest.In this paper,based on NNLSE,we used variational method to solve the problem of the propagation of breathers in lossless and lossy SNNM,respectively.In this paper,the propagation dynamics of multipole breathers in nonlocal media are studied theoretically.The research contents and structure are as follows:In chapter 1,the basic concepts of optical soliton,breather and SNNM are briefly introduced,the research progress and significance of nonlocal optical solitons and breathers are summarized and the basic principle and process of the variational method are simply introduced.In chapter 2,we demonstrate the propagation dynamics of tripole breathers in nonlinear media with a spatial nonlocality by employing the variational method.Taking a tripole breather as an example,the approximate analytical solution and the physical propagation properties is obtained,such as the evolution of the critical power,the spot size,the wavefront curvature,and the intensity distribution of the breather have been discussed in detail.The physical reasons for the evolution of the tripole breathers are analyzed by borrowing the ideas from Newtonian mechanics.It is found that the analytical results obtained by the variational approach agree well with the numerical simulations of the NNLSE in the physical settings of strongly nonlocality,especially when the input power approaches the critical power.In chapter 3,we investigate the propagation properties of quadrupole breathers in nonlinear media with a nonlocal exponential-decay response by using the variational method and the equivalent particle method.The analytical solution of the quadrupole breather is obtained.The breather beam width,the wavefront curvature,the intensity pattern,and the comparisons between the analytical quadrupole breathers solution and the numerical simulations of the NNLSE in the case of highly nonlocal nonlinearity are analyzed.The results show that the analytical solution is in good agreement with the numerical simulations at near-critical power incidence.Furthermore,we find that the envelope of the difference value curve between the analytical solution and the numerical simulation can be described as a logarithmic function under different input powers.It is useful for further understanding the propagation properties of optical breathers in nonlocal nonlinear media and might be of interest to the applications in error analysis and precision measurements.In chapter 4,the propagation characteristics of the dipolar breathers in lossy SNNM(for example,nematic liquid crystals)are studied by using the variational method.The approximate analytical solution of the dipolar breathers is obtained.In the analytical theory,we predicted the evolution of the propagation process of the breathers and obtained the approximate solutions of the breathers at different losses.The results show that in the case of high degree of nonlocality and within a certain range of loss,the analytical results are in good agreement with the numerical simulation results.In chapter 5,we summarize the main results and shortcomings and make a research prospect with respect to the research directions and potential applications.