Research On Generation,Propagation,Detection And Application Of Airy Vortex Beam

Airy beam has unique properties such as non-diffraction,self-healing and self-bending.The circular Airy beam,due to its abruptly auto-focusing property,has great application value and has received extensive attention since it was proposed in 2010.The vortex beam is a light field with a phase singularity.It has a spiral structure wavefront,carries orbital angular momentum,and there is a dark area in its light intensity pattern.Based on these characteristics,vortex beams have many applications,such as particle capture and rotation,optical communication,and exploring the relation or conversion between spin angular momentum and orbital angular momentum.The combination of the vortex beam and the Airy beam,that is,the Airy vortex beam especially the circular Airy vortex beam(CAVB),is an interesting research content that has been very hot in recent years and has a wide range of potential application.Based on the above research background,this article takes Airy vortex beam as the research object.Specifically,it will be introduced from the introduction and theoretical methods,experimental methods,circular Airy vortex beams with a single vortex,CAVB carrying a pair of vortices with same or opposite signs and its experiments,elliptical Airy vortex beams(EAVB)and its experiments,detecting the characteristic parameters of the EAVB using deep learning methods,and at last a conclusion.The specific chapters of this paper are arranged as follows:Chapter 1 first introduces the research background and current situation of Airy vortex beams,and points out the research purpose and significance of this thesis.Then introduced the theoretical basis and research methods involved in this thesis,including:Helmholtz equation and paraxial conditions and equations,the diffraction integral method of beam propagation,the angular spectrum theorem of beam propagation,and the introduction of the discretization approximation and matrix multiplication realization of of two-dimensional Fourier transform.Chapter 2 introduces in detail two encoding methods that use a single phase spatial light modulator to generate complex amplitude light fields,namely the diffraction-based encoding method and the checkerboard interference-based encoding method,explains why the phase plate needs an offset phase,deduces the relationship between the added linear offset phase and the order migration distance at the spectrum plane,and at last introduces the corresponding experimental principles.Chapter 3 studies the properties of the CAVB loaded with a single vortex in detail.Optical vortices can be classfied into r-shaped vortices and tanh vortices(including point vortices).First,a comparative study of the CAVB with r-shaped vortex and point vortex in the center of the initial plane is conducted.The validity of the angular spectrum transmission calculation is proved from the comparative study and it is clarified that it is a shortcoming that the topological charge of the r-shaped vortex will affect the distribution of the light intensity at the initial plane.In view of the shortcoming of the r-shaped vortex,it is proposed to study the CAVB with tanh vortex.Then the distribution of light intensity at initial plane is independent of the topological number m,and the CAVBs with a central tanh vortex and a single off-axis tanh vortex in the initial plane are studied separately.It is found that the autofocusing effect of the CAVB loaded with tanh vortices(including point vortices)is controlled by the topological number m and the vortex width factor wv.Chapter 4 studies the properties of CAVBs with a pair of vortices with the same and opposite signs at symmetrical positions on the x-axis of the initial plane.Through a combination of theoretical simulation and experiment,this chapter focuses on the effect of the vortex position on the properties of focal pattern.The experimental results are highly consistent with the theoretical ones,and the application value of controlling the position of a pair of vortices is briefly discussed,such as encoding information for communication or precise adjustment of the position of captured particles in particle manipulation experiments.Chapter 5 studies the properties of the EAVB and verifies the simulation results experimentally.The experimental results are highly consistent with the theoretical ones.The study found that the EAVB still has autofocusing properties,and the ellipse parameter and topological charge m mainly affect the focal spot size and autofocusing performance,and almost have no effect on the autofocusing position.The focal pattern is a plurality of |m|+1 bright spots arranged obliquely,and the oblique direction is related to the sign of m.Finally,the possibility of using the properties of the EAVB to detect the topological charge of the vortex beam and its application in optical communication is proposed and briefly discussed.Chapter 6 first introduces the application and practice of deep learning in the field of optics,and introduces the basic principles of neural networks and convolutional neural networks(CNN),and then constructs and trains a CNN model to detect the ellipse parameter t and the topological charge m of the elliptical Airy vortex beam,it is found in practice that the deep learning method is feasible and effective in detecting the characteristic parameters of the elliptical Airy vortex beam,which has guiding significance for other tasks such as communication using the elliptical Airy vortex beam.Chapter 7 summarizes the main work and innovations of this paper,and puts forward prospects for future work.