Theory Of Multi-soliton Interactions In Nonlocal Nonlinear Media

The generation and development of the theoretical model of soliton are more than a significant event in the study of nonlinear science.Optical soliton is one of the crucial nonlinear optical phenomena and has been widely investigated in both space and time.An important class of nonlinearities in optics is associated with the nonlocal process.Nonlocal nonlinearity means that the nonlinear response of a medium at a certain spatial point is determined not only by the optical wave at that point but also by the wave in its vicinity,which has a great difference from traditional local nonlinearity.Spatial optical solitons can be formed when the self-focusing of the beam induced by the nonlocal nonlinearity of the medium cancels out with its diffraction nature.Nonlocal effects can support quite a few novel forms of solitons and bring about numerous unique phenomena.The research results of nonlocal nonlinear optical system can provide references for the optical fractional Fourier transform system,the quadratic nonlinear system,the Fresnel diffraction system,the gravitational system,free space,and the linear system with external harmonic potentials,and have potential application prospects in optical communication,optical switch,particle manipulation,and other related fields.In this paper,the propagation dynamics of multiple spatial solitons in nonlinear media with strong spatial nonlocality are studied theoretically by taking advantage of approximate analytical methods.The research contents and structure are listed as follows.In chapter 1,the basic concepts and classification of optical solitons and nonlocal nonlinear media are briefly introduced,the research progress and significance of nonlocal optical solitons are summarized.In chapter 2,we focus on the evolution of the Gaussian-shaped soliton clusters in strongly nonlocal nonlinear media,which is modeled by the nonlocal nonlinear Schr¨odinger equation.The influences of the three initial incident parameters(the initial transverse velocity,the initial position,and the input power)on the propagation dynamics of the soliton clusters are all discussed in detail.The results show that the optical intensity distribution,the propagation trajectory,the center distance,the angular velocity,and the phase shift of the clusters can be controlled by adjusting the initial incident parameters.A series of analytical solutions on the propagation dynamics of the clusters are derived by borrowing ideas from classical physics,and the conservation of angular momentum of soliton motion has been proved.In chapter 3,we theoretically investigate the evolution of the soliton pairs in strongly nonlocal nonlinear media,which is modeled by the nonlocal nonlinear Schr¨odinger equation.Taking two pairs of Gaussian-shaped solitons as an example,which initial incident directions have mirror symmetry,a set of mathematical expressions are derived to describe the soliton pairs' propagation,the soliton spacing,the area of the optical field.The results demonstrate that the motion state of the soliton pairs is mirror-symmetry and satisfies the conservation of mechanical energy.Numerical simulations are carried out to illustrate the quintessential propagation properties.In chapter 4,we introduce a novel class of the generalized spiraling anomalous vortex soliton arrays in strongly nonlocal nonlinear media.The general analytical formula for the arrays is derived,and its propagation properties are analyzed.It is shown that the spiraling anomalous vortex soliton arrays can present three different propagation states(shrink,expansion,and the dynamical bound state)depending on the absolute value of the introduced transverse velocity parameter.Accordingly,we proposed the concept of array breathers and array solitons.The topological charge of the vortex and the number of the constituent anomalous vortex beams also play important roles in the evolution of the anomalous vortex soliton arrays.It is found that the light intensity of the central region of the array's field under in-phase incident condition is not zero during propagation if and only if the ratio between the two parameters is an integer.A series of numerical simulations are exhibited to illustrate these typical propagation properties.Besides,we have given a variety of array forms of multi-soliton interactions.In chapter 5,we investigate the propagation dynamics of Laguerre-Gaussian soliton arrays in nonlinear media with a strong nonlocality and introduce two parameters,which we refer to as initial transverse velocity and displacement,to control the propagation path.The general analytical expression for the evolution of the soliton array is derived and the propagation properties,such as the intensity distribution,the propagation trajectory,the center distance,and the angular velocity are analyzed.The concept of array similarity is proposed and the types of soliton arrays are extended to multiple modes.It is found that the initial transverse velocity and displacement make the solitons sinusoidally oscillate in the x and y directions,each constituent soliton undergoes elliptically or circularly spiral trajectory during propagation.A series of numerical examples are exhibited to graphically illustrate these typical propagation properties.In chapter 6,we summarize the main results and shortcomings and make a research prospect with respect to the research directions and potential applications.