Propagation Of The Airy Beams Class In Two Different Reflective Index Potentials

In recent years,the Airy beam which possess three interesting properties like self-acceleration,no diffraction and self-healing,has a lot of potential applications in many field.Such as plasma channel,optical particle manipulation,inducing surface plasmon polariton,electron acceleration,optical bullet and so on.So the Airy beam has become a hot topic in optical transmission field.Especially the study on the propagation of quasi-Airy beam in different medium has caught a number of attention.However,the achievements are mainly concentrated in the propagation properties of the(quasi-)Airy beam in homogeneous nonlinear medium and free space,while the propagation and the interaction of the(quasi-)Airy beam in PT potential and in defected lattices has not been reported yet.Therefore,this paper studies the propagation of an Airy beam in PT potential and the propagation of an Airy-Gaussian vortex beam in defected lattices,finds out how different potential affect the propagation properties of the quasi-Airy beams.This article reviews the nearly research results of the(quasi-)Airy beams.We will introduce the mathematical theoretical model of the(quasi-)Airy beams and analysis the implementation method and mathematical model of(quasi-)Airy beams propagating in the defected lattices and PT potential.After that,we use the finite difference beam propagation method to simulate the propagation the(quasi-)Airy beam in two different mediums.Two main topics have been studied in this article:1)The propagation and interaction of an Airy beam in PT potential.We first study the propagation of the Airy beam in the PT potential,by comparing the propagation of the Airy beam in the free space and the PT potential,and investigating how the change of the imaginary part of PT potential affect the propagation of the Airy beam,we find that the Airy will divide into a quasi-soliton part and a self-accelerating part due to the PT potential.And the bigger imaginary part of PT symmetric potential,the smaller oscillation amplitude of the quasi-soliton part.Then we study the interaction of the Airy beam and PT soliton in the PT potential.By investigating the relative location,the imaginary part of PT potential and the amplitude of the Airy beam,we know that the interaction of the Airy beam and PT soliton will divide into three parts: a quasi-soliton part,a reflected wave part and a self-accelerating part.The increment of initial separation and the amplitude of the beam will result in the oscillation amplitude of the quasi-soliton part become bigger,but nothing to do with the oscillation period of the quasi-soliton part.2)The propagation of an Airy-Gaussian vortex beam in the defected lattices.We investigate the influence of the nonlinear coefficient,the lattice modulation depth,the defect depth,the defect coefficient,the distribution factor and the location of vortex on the propagation of an Airy-Gaussian vortex beam by changing these parameters.It is found that unlike the case in free space,the main lobe which destroyed by the vortex will not be formed when an Airy-Gaussian vortex beam propagates in the defected lattices.And,the positive defected lattices can constrain the energy of the beam in the position of the positive defect and make the beam form a lattices soliton.On the contrary,the negative one can diffuse the beam.Furthermore,with the higher defect depth,the more energy can be constrained and the shorter transmission distance for the beam form a lattices soliton.Also,so long as the defect depth is high enough,the beam will always form a lattice soliton at the location of the defected lattices no matter where the position of vortex is.Besides,we find that the effect of self-focusing nonlinear can compress the beam while the self-defocusing one has a diffused effect.Additionally,the effect of defects is bigger than the effect of nonlinear.In conclusion,this article investigates the propagation of the(quasi-)Airy beam in the PT potential or defected lattices which has not been reported yet.It is beneficial to study the potential application value.And it will be the foundation for the(quasi-)Airy beam were applied in practical application.Besides,the study on the(quasi-)Airy beam propagation in the new medium or on the interaction between other beam is worth to investigate.