Interactions Between (3+1)D Spatiotemporal Optical Solitons In Dispersive Optical Media With The Cubic-quintic Nonlinearity

Solitons have attracted a great deal of attention for many decades because of their resilient, robust behavior. They arise in many areas of physics such as hydrodynamics, nonlinear optics and plasma physics etc. In spite of their diversity, interactions between solitons, through which many particle-like features of solitons are exhibited, all follow the same principles. Recently, interactions between solitons in nonlinear optics have been the main area for studying solitons collisions due to the convection of the experiments and their applications with cheerful prospect.In this thesis, we investigate the interactions between (3+1)D spatiotemporal optical solitons in dispersive cubic-quintic nonlinear media by numerical simulations using the split-step Fourier method. First, We investigate energy exchange between (3+1)D colliding spatiotemporal solitons (STSs) in this media. Energy exchange between two (3+1)D head on colliding STSs, caused by their phase difference, is observed, just as occurred in other optical media. Moreover, energy exchange between two head on colliding STSs with different speeds is firstly shown in the cubic-quintic and saturable media. Second, we compare the interactions between (3+1)D spatiotemporal optical solitons in the cubic-quintic media, such as repulsion, fusion, scattering, spiraling, with the counterparts in saturable media. These corresponding interactions in the two media behave the same. There is similarity in their interactions. These phenomena, we believe, may arise some interests in the future studies of soliton collision in optical media.The thesis consists of five chapters, which are organized as follow.Chapter one is a brief introduction of the nonlinear phenomenon, especially the history of solitons. Some typical character and properties of solitons as well as the corresponding nonlinear equations are also introduced.The chapter two is mainly devote to depicting the basic concept of solitons in nonlinear optics, including temporal solitons , optical spatial solitons, spatiotemporal optical solitons. Meanwhile, the split-step Fourier method is introduced. The interactions between optical spatial solitons and spatiotemporal optical solitons are present.In chapter three, We investigate energy exchange between (3+1)D colliding spatiotemporal solitons (STSs) in media with the cubic-quintic nonlinearity. The clear picture of energy exchange process is shown.In chapter four, through extensive numerical simulations, we compare the interactions between (3+1)D spatiotemporal optical solitons in the cubic-quintic media, such as repulsion, fusion, scattering, spiraling, with the counterparts in saturable media.Finally, we present a conclusion for our work and some prospects for future works in this field.