Study On Generation And Diffraction Properties Of Airy Accelerating Beams And Abruptly Autofocusing Beams

Airy accelerating beams have attracted a great deal of interest because of their non-diffractingand self-accelerating properties. Recently, it is found that the radially symmetric Airy beamsexhibit interesting focusing characteristics, since they undergo an abrupt increase in theirintensity as the focus is approached. Airy accelerating beams with these special propertieshave been widely used in nonlinear optics, optical micromanipulations and medicalapplications. In order to generate Airy accelerating beams, a lot of methods are proposed,such as, using the spatial light modulator, using phase mask and using Airy laser. But there isa lack of low energy efficiency with the methods above mentioned to generate Airy beams. Inorder to generate Airy beams effectively, this article introduce a simple algorithm for findingthe pure-phase expression of an acceleration beam from its given accelerating trajectory,based on the relationship between the local spatial frequency and the accelerating trajectoryof the beam, and we design the phase-only diffractive optical element according to thepure-phase expression of an acceleration beam to demonstrate the algorithm. As the new wayin this article avoids the use of Fourier lens, it is helpful to generate this specific beam withhigh energy efficiency. According to the methods above mentioned, we generate abruptlyautofocusing beams following circular trajectory for the first time, and give the optimizationdesign parameters for the intensity of the focus spot by the computer simulation of itsself-focusing property. Main contents in this paper are as follows:1. We introduce the background and status of Airy beams and abruptly autofocusing beams indetail. We also give the fundamental theory and the derivation of Airy accelerating beams.With the computer simulations of finite-energy Airy beams, we demonstrate self-accelerating,non-diffracting and self-healing properties experimentally.2. The way to generate Airy accelerating beams with phase-only pattern is proposed. Thisapproach mainly uses the zero-points coordinates of the Airy function to calculate the localspatial frequency of a general accelerating beam and an analytical formula accuratelydescribing the local spatial frequency distribution is given. Based on the relationship betweenthe local spatial frequency and the accelerating trajectory of the beam, we give a simplealgorithm for finding the pure-phase expression of an acceleration beam from its givenaccelerating trajectory. As a calculation example, we obtain the pure phase function of beamswith several typical accelerating trajectories. Finally a pure-phase diffractive optical element is designed and demonstrated successfully.3. A method for determining the phase function of abruptly autofocusing beams followingarbitrary trajectories is proposed, and the approach is based on the relationship between thelocal spatial frequency and the accelerating trajectory of the beam to calculate the pure phasefunction. We can design the phase-only diffraction elements to generate abruptlyautofocusing beams with arbitrary trajectories. We theoretically and experimentally studyabruptly autofocusing beams following circular trajectory. The computer simulation resultsshow the variation of the intensity at the focus spot, and we find the dependence of thefocused intensity and initial radius through the theoretical analysis and experimental results,and we give the optimal initial radius which can make the intensity of the focus spot to itsmaximum in different conditions.