Trajectory Engineering Of Fractional-order Airy Talbot Effect Modulated By Linear Potential

Airy beam possesses unique properties such as non-diffraction,self-healing,and transverse self-bending,providing extensive prospects in various fields,including optical communication,optical micro-manipulation,and super-resolution imaging.Nonetheless,the effective control of Airy beams under diverse propagation conditions remains a formidable challenge for researchers.Hence,this paper conducts profound theoretical research on the interactive interaction of Airy beams in fractional-order nonlinear media and the Airy-Talbot effect under fractional-order effects.The specific research content is as follows:(1)Researching the impact of fractional-order effects on the interaction of Airy beams in competing nonlinear media:According to the propagation and evolution equation of Airy beams in a fractional-order competitive nonlinear medium,an expression for the incident beam is constructed,and the interaction of Airy beams in a fractional-order competitive nonlinear medium is numerically simulated using the split-step Fourier method.The results show that under a larger beam spacing,two in-phase Airy beams attract or repel each other,while two out-of-phase Airy beams repel each other.For slightly smaller beam spacings,a "funnel-like" transmission structure is formed when the α = 1 reaches the limit condition.Under smaller beam spacings,solitons with single and symmetric breathing modes form in the in-phase and out-of-phase cases,respectively.Reducing α enhances the oscillation of the breathing soliton,increases the peak intensity,and decreases the soliton width;it also makes the width of the symmetrical-breath soliton pair narrower and the beam repulsion stronger.In addition,the defocusing quintic coefficient can effectively adjust the interaction of Airy beams.(2)Researching the effects of fractional-order on the Airy-Talbot effect within a linear potential:We utilized analytical and numerical methods to further control the Airy-Talbot effect under linear potential based on the fractional-order effect.In addition to utilizing the linear potential gradient to propagate the self-imaging along a predefined trajectory,control of the self-imaging can also be achieved through the manipulation of the Lévy index α.The fractional-order effect changes trajectory,period of the self-imaging and Airy-Talbot length.We also extended the results to self-imaging in periodic light fields,demonstrating that the self-imaging period increases with decreasing Lévy index under the influence of fractional-order effects for either periodic or non-periodic incident light fields.The Talbot length and Airy-Talbot length at α = 1 is both twice that of α = 2.The self-imaging trajectory under fractional-order effect is determined by both the linear potential gradient and the Lévy index.