Research On Propagation Modulation And Imaging Characteristics Of Airy Beams Under Fractional Effect

Non-diffracting finite energy Airy beams have attracted great interest from researchers all over the world.Under the influence of nonlinear effect,the energy of the main lobe of Airy beam falls off during propagation and forms breathing solitons,for instance,Airy beam will form breathing oscillating solitons during propagation in anomalous dispersion and self-phase modulated single-mode fibers.When two Airy beams interact in Kerr or saturated nonlinear media,solitons or soliton pairs with different modes can be formed.The nonlinear modulation of Airy beams is limited to nonlinear media and its theoretical and experimental worka have been widely reported.The existence of external potential field in nonlinear medium also plays an important role in regulating the evolution of light field.In addition,the research on the propagation regulation of light field under the fractional Schr(?)dinger equation and the Airy-Talbot effect is still less of it,which is expected to become one of the hot topics in the field of light field regulation.In this paper,the interaction between Airy beams and solitons in nonlinear media,the influence of fractional effect on interactive beam and the exploration of The Airy-Talbot effect are studied.The specific contents of the study are organized as follows:(1)Establishing the evolution equation of light wave propagation and using the external potential field to control the propagation of Airy beam:This article establishes the theoretical model and consider the one-dimensional case for convenience.The propagation of light wave in saturated nonlinear medium satisfies the nonlinear Schr(?)dinger equation and we set the expression of different initial incident beams.Then,the split-step Fourier method is employed to simulate the beam evolution in saturated nonlinear medium.In addition,the dynamic characteristics of FEABs and soliton are discussed by changing the parameters: initial amplitude ratio,initial interval,phase shift and saturable nonlinear strength,respectively.(2)Studying the influence of fractional effect on Airy beams interaction and discussing the method of light field regulation:In this paper,the dynamic characteristics of interaction between two Airy beams in linear potential field are studied by using fractional effect with analytical and numerical evolution methods,and a new regulation theory of interaction between Airy beams is proposed.The results show that in the absence of an applied potential field,the two Airy beams continue to diffract after the collision when the Levy index α = 2,while in the limit case,a symmetric split discrete non-diffractive beam is formed when α = 1.If the external linear potential field is considered,the interacting Airy beams exhibit periodic modulation oscillations with zigzag trajectories during propagation.The propagation period is proportional to the absolute value of the potential field depth coefficient.(3)Studying the generation conditions of Airy-Talbot effect and its self-imaging effect manipulation method:In this paper,the Airy-Talbot effect is realized by adjusting the circular Airy beam(CAi),which can provide a theoretical basis for image reproduction.By adjusting the system parameters of CAi beam propagating in the transversely linear index potential with gradient,the self-imaging effect of CAi beam under different system parameters is realized.