Dynamics Of The Airy-like Beam

The Airy beam is a phase-modulated light beam that has emerged in recent years.Due to their intriguing properties in the transmission process,including non-diffraction,self-healing and self-acceleration,Airy beams have attracted a lot of attention and have tremendous potential applications in quite a few fields,such as routing surface plasmons,light bullets,three-dimensional super resolution imaging,and image signal transmission.With the wide application of the Airy beam,a series of different Airy-like beams derived from the Airy beam have emerged.Compared to the original Airy beam,the Airy-like beams,which have been special modulated,have some advantages in certain characteristics to satisfy the special needs in the application.Through slightly changing the angle between two wings or adding a spiral phase based on the Airy function,this paper main focuses on the transmission dynamics of non-paraxial 2D Airy beams and deformed 2D vortex Airy beams,and systematically summed up with the paraxial 2D Airy beams and standard 2D vortex Airy beams which have been studied before.The specific research content of the paper is as follows:(1)Based on the catastrophe theory,the propagation characteristics of two-dimensional Airy beams with different angles between two wings and different incident angles are derived from the light field distribution equation of two-dimensional Airy beams.We find that the paraxial Airy beam with 90 between two wings propagate along one parabolic trajectory,and the non-paraxial Airy beam with 900° between two wings propagates along two different parabolic trajectories,one is the main lobe and other is the peak point,as a result of the "hyperbolic umbilical" catastrophe;the deformed paraxial or non-paraxial Airy beams propagates along two different parabolic trajectory,as a result of the "hyperbolic umbilical" catastrophe.We also numerical simulate the trajectory of the two-dimensional Paraxial-Airy beam with different angles between two wings,and summarize the regular pattern of its propagation trajectory with the change of the angle between two wings.(2)Combining the numerical simulation results and the experimentally recorded images,we analyzed the transmission dynamics of two-dimensional vortex Airy beams with different topological loadings and arbitrary angles between two wings.We have found that due to the additional helical phase,the main lobe of the 2D vortex Airy beam has a self-healing half-ring gap at the initial position.The self-healing distance is related to the angle between the two wings and the topological charge.Moreover,because the optical vortex has the orbital angular momentum,the beam will be laterally offset to the left.Therefore,the trajectory of the beam main lobe and peak point can be controlled by changing the topological number and the angles between two wings.In addition,considering the change of the energy distribution of the two-dimensional vortex Airy beam,we can control the light intensity ratio of the beam at any position in the cross-sectional profile by changing the angle between two wings and the topological charge number.