Evolution And Interaction Of Pearcey-Gaussian Beams In Different Media

Compared with traditional communication methods,fiber optic communication is one of the most important components of modern communication methods because it uses optical fibers as transmission medium during long-distance transmission,and this change allows the transmission quality of light waves to be maintained at a high level with minimal environmental pollution.In order to further improve its transmission efficiency,the search for new diffraction-free light beams has become one of the main research priorities in the field of optics.Earlier,many new diffraction-free wave packets,such as Airy wave packets and Bessel wave packets,have been discovered,and the unique properties of these beams have attracted much attention from researchers and started a new wave of nonlinear optics.When people continued to search for special beams,the emergence of Pearcey beams successfully caught people’s attention.Pearcey beams are special diffractive beams that have a wide range of applications in the fields of optical transmission of particles,particle confinement,and optical tweezers technology due to their self-focusing,self-healing,and structure-invariant properties,and further exploration of new transmission properties of Pearcey beams has become a meaningful topic.In this paper,the kinetic transport properties of the Pearcey-Gaussian beam in different media are numerically calculated using a stepwise Fourier transform algorithm.The content is organized as follows: Chapter 1introduces several common special beams.Chapter 2 introduces several transmission media starting from Schr(?)dinger equation.The numerical methods and analytical solutions involved in this paper are also described.Chapters 3 and 4 are the core of this paper.In the Chapter 3,the evolution and interaction of the Pearcey-Gaussian beam in nonlinear Kerr medium are numerically studied.The results show that the self-focusing effect can suppress the inversion of the Pearcey-Gaussian beam and cause the main lobe and side lobes of Pearcey-Gaussian beam to separate,forming solitons during propagation,while the defocusing effect can retain partially the beam inversion and accelerate its spatial expansion after the inversion.As for the interaction between the Pearcey-Gaussian beams,in self-focusing medium,except for the elastic interaction between the main lobes,the inphase between them can result in the pattern of periodic collision around the center of coordinate caused by the side lobes,while the out-of-phase can suppress its occurrence.In defocusing medium,the interactions of the in-phase and out-of-phase Pearcey-Gaussian beams show the constructive and destructive interference,respectively.Finally,the influence of the width of Gaussian function in Pearcey-Gaussian beam on the interaction of the two Pearcey-Gaussian beams is studied.In Chapter 4,the transmission properties of a Pearcey-Gaussian beam are studied in a competing triple-quintic nonlinear medium.For a single beam,solitons are easily generated when the strength of the triple focusing nonlinearity is large.And when the quintuple scattering nonlinearity dominates,it suppresses the beam inversion and accelerates its spatial diffusion.For two beams,when we set the cubic focusing nonlinearity parameter to a fixed value,the change of the intensity of the quintuple scattering nonlinearity will accelerate the self-accelerating behavior of the beams,making them more capable of fusing with each other in the in-phase case,while in the out-of-phase case,the phenomenon of elastic collision and then repulsion of the beams advances,and the inter-soliton repulsion becomes larger.It is worth noting that when the intensity of the five times scattering is large enough,the interacting beams bifurcate in both the same and opposite phases,generating new soliton pairs.And when the five times scattering nonlinear intensity is a fixed value,the diffraction effect of the beam can gradually be canceled by the nonlinear effect of the medium as the three times focusing intensity becomes larger in the same phase case,forming breathing solitons.In the out-of-phase case,as the three times focusing takes on larger values,the beam becomes farther away from the location of the elastic touch that occurs during transmission and the repulsive force is weakened.