Study On Generation And Propagation Characteristics Of Spatial Solitons

As a result of a balance between diffraction and nonlinear effects in nonlinear media,spatial solitons can maintain their shape and phase as they propagate.Solitons still keep each constant shape and velotity like particles after their interactions.Solitons have been extensively studied in many branches of physics such as optics,biophysics,plasma physics,condensed matter physics,fluid mechanics,particle physics and even astrophysics because of their specific properties.Therefore the research on spatial solitons has important academic and realistic significance.In this thesis,we briefly review the historical origins of solitons,the background and developments of spatial solitons,and then discuss the associated theory foundation and research methods,including the plane-wave expansion method,Newton iterative method,square-operator iterative method,modified square-operator iterative method,relaxation method,homogenizing methods,finite difference methods,variational method and split-step Fourier method.We mainly study the existence,stability and propagation properties of spatial solitons in one-dimensional composite optical lattices and two-dimensional optical lattices with a line defect,the generation and propagation characteristics of spatial solitons in the two-dimensional complex Ginzburg-Landau equation and the nonlinear dynamics of spatiotemporal necklace-ring solitons in the three-dimensional complex Ginzburg-Landau equation.The research results are as follows:1.Defect solitons in one-dimensional composite optical latticesWe have numerically and analytically investigated the existence,stability and propagation dynamics of defect solitons at interfaces in one-dimensional composite optical lattices with focusing saturable nonlinearity.With the change of defect intensity,solitons show unique properties.For a positive defect,the defect solitons only exist in the semi-infinite gap,which is stable at low power and unstable at high power.For a negative defect,the defect solitons exist not only in the semi-infinite gap,but also in the first gap.The surface solitons show rich characteristics of stability and instability in the entire semi-infinite gap and the first gap.2.Defect solitons at interfaces between dual-frequency and simple latticesWe have studied the existence,stability and propagation properties of defect solitons at interfaces between dual-frequency and simple lattices with focusing saturable nonlinearity.Solitons with some unique properties exist in such composite structures with the change of defect intensity.For zero defect or positive defect,the defect solitons exist in the semi-infinite gap but not exist in the first gap,and solitons are stable at lower power but unstable at high power.With increasing of the intensity of positive defect depth,the stable region of surface solitons becomes narrower in the semi-infinite gap.For the case of negative defect,the defect solitons exist not only in the semi-infinite gap,but also in the first gap.With increasing of the intensity of negative defect depth,the stable region of defect solitons becomes narrower in the semi-infinite gap.And these solitons are stable within a moderate power region in the first gap and unstable in the entire semi-infinite gap.3.Defect solitons in two-dimensional optical lattices with a line defectWe have studied the existence,stability and propagation properties of defect solitons in two-dimensional optical lattices with a line defect.With the change of defect intensity,solitons have different existing and stable region in different gaps.When line defects with various defect intensities are introduced into two-dimensional optical lattices,defect solitons can exist in different bandgaps.Some unique characteristics show that the line defect embedded into two-dimensional optical lattices can profoundly influence the shape,stability and propagation of solitons.For zero or positive defect,the solitons only exist in the semi-infinite gap and cannot be stable in the high power region.For a negative defect,the solitons can exist not only in the semi-infinite gap,but also in the first gap.And the solitons are stable in the moderate power region in the first gap.4.Continuous generation of dissipative spatial solitons in two-dimensional Ginzburg–Landau models with elliptical shaped potentialsWe have studied the rich dynamics of two-dimensional fundamental solitons coupled and interacting on the top of an elliptical shaped potential in a two-dimensional Ginzburg-Landau model.Under the elliptical shaped potential,the solitons display unique dynamic properties,such as the generation of straight-line arrays,emission of either one elliptical shaped soliton or several elliptical ring soliton arrays,and soliton decay.For the soliton with fixing other parameters of the potential,various scenarios of soliton dynamics are also revealed with changing the depth and sharpness of the external potential.5.Spatiotemporal necklace-ring solitons induced umbrella-shaped potential: emission of vorticesWe have studied the generation and propagation properties of the spatiotemporal necklace-ring solitons.Under the action of umbrella-shaped potential,the vortex forms necklace-ring solitons.Emissions of spatiotemporal necklace-ring solitons from vortex with the topological charges S=1 and 2 are researched and analyzed.It is found that an appropriate umbrella-shaped potential forces the vortices gradually to form the spatiotemporal necklace-ring solitons.For given topological charges,the change of the potential intensity is in favor of the generation of spatiotemporal necklace-ring solitons with the changing number of folding umbrella.For given topological charges and potential intensity,the increasing number of folding umbrella emits more pearls.However,a strong potential will destroy the vortices.