关键词: 物理光学/
自加速光束/
焦散线/
维格纳函数
English Abstract
Design of accelerating beams based on caustic method
Wen Yuan-Hui1,Chen Yu-Jie1,
Yu Si-Yuan1,2
1.State Key Laboratory of Optoelectronic Materials and Technologies, School of Electronics and Information Technology, Sun Yat-sen University, Guangzhou 510275, China;
2.Photonics Group, Merchant Venturers School of Engineering, University of Bristol, Bristol BS8 1UB, United Kingdom
Fund Project:Project supported by the National Basic Research Program of China (Grant No. 2014CB340000), the National Natural Science Foundation of China (Grant Nos. 11690031, 61323001, 61490715, 51403244), the Science and Technology Program of Guangzhou, China (Grant No. 2018), and Sun Yat-sen University Fundamental Research Funds for the Central Universities of China (Grant Nos. 17lgzd06, 16lgjc16, 15lgpy04, 15lgzs095, 15lgjc25).Received Date:16 June 2017
Accepted Date:17 July 2017
Published Online:05 July 2017
Abstract:Self-accelerating beam is a kind of light beam capable of self-bending in free space without any external potential, of which a typical one is the well-known Airy beam. Such a beam has gained great attention for its extraordinary properties, including nondiffracting, self-accelerating and self-healing, which may have versatile applications in the delivery and guiding of energy, information and objects using light, such as particle manipulation, micro-machining, optical routing, super-resolution imaging, etc. However, since Airy beam can only propagate along parabolic trajectory, which reduces the flexibility in practical applications, thus how to design accelerating beams propagating along arbitrary trajectory is still a crucial problem in this area. One scheme is to keep on finding other analytical solutions of the wave equation besides Airy beam, such as semi-Bessel accelerating beams, Mathius beams, and Weber beams, moving along circular, elliptical, or parabolic trajectories, but it becomes increasingly difficult to find out any more solutions. A more effective solution to this problem is based on the caustic method, which associates the predesigned trajectory with an optical caustics and then obtains the necessary initial field distribution by performing a light-ray analysis of the caustics. This method has been implemented in real space and Fourier space based on Fresnel diffraction integral and angular-spectrum integral, respectively. It has been found recently that they can be unified by constructing Wigner distribution function in phase space. Based on the caustic method, accelerating beams were constructed to propagate along arbitrary convex trajectories in two-dimensional space at first. With continuous development of this method, the types of accelerating beams available have been extending from convex trajectories to nonconvex trajectories, from two-dimensional trajectories to three-dimensional trajectories, and from one main lobe to multiple main lobes, which opens up more possibilities for emerging applications based on accelerating beams. In future, previous researches and applications based on Airy beams will certainly be generalized to all these new types of accelerating beams, and owing to the great flexibility in designing accelerating beams, more application scenarios may emerge in this process with huge development potential. Thus in this paper, we review the principle and progress of the caustic method in designing accelerating beams.
Keywords: physical optics/
self-accelerating beams/
caustic/
Wigner distribution function
