基于焦散线方法的自加速光束设计

闻远辉; 陈钰杰; 余思远

doi:10.7498/aps.66.144210

摘要

以艾里光束为代表的自加速光束是一类在自由空间中具有弯曲传播特性的新型特殊光束.这类光束因其具有无衍射、自加速和自修复等奇异特性引起了人们的广泛关注，有望应用于光学微粒操控、激光微加工、全光路由和超分辨成像等诸多领域.由于艾里光束只能沿着抛物线的轨迹传播，限制了其在实际应用中的灵活性，因而设计出能够沿着不同轨迹传播的自加速光束是这一研究领域的关键问题，而基于焦散线方法的自加速光束设计是解决该问题的有效途径之一.这一方法是将设计的传播轨迹与光学焦散线联系起来，通过分析形成该焦散线所需的光线簇构造出对应的初始场分布.基于该原理并经过不断发展，不同类型的自加速光束相继得以实现，并且借助维格纳函数还可以同时实现实空间和傅里叶空间的自加速光束设计，为自加速光束的应用提供了更多的可能性.本文对基于焦散线方法的自加速光束设计原理和进展进行全面介绍.

关键词:

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:

作者及机构信息

1.
中山大学电子与信息工程学院, 光电材料与技术国家重点实验室, 广州 510275;

2.
布里斯托大学电气与电子工程系, 布里斯托 BS81TR, 英国

通信作者: 陈钰杰, chenyj69@mail.sysu.edu.cn

基金项目: 国家重点基础研究发展计划（批准号：2014CB340000）、国家自然科学基金（批准号：11690031，61323001，61490715，51403244）、广州市科技计划科学研究一般项目（批准号：2018）和中山大学高校基本科研业务费青年教师重点培育项目（批准号：17lgzd06，16lgjc16，15lgpy04，15lgzs095，15lgjc25）资助的课题.

Authors and contacts

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

Corresponding author: Chen Yu-Jie, chenyj69@mail.sysu.edu.cn

Funds: 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).

参考文献

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施引文献

[1]	Siviloglou G A, Broky J, Dogariu A, Christodoulides D N 2007 Phys. Rev. Lett. 99 213901
[2]	Baumgartl J, Mazilu M, Dholakia K 2008 Nat. Photon. 2 675
[3]	Zhao J, Chremmos I D, Song D, Christodoulides D N, Efremidis N K, Chen Z 2015 Sci. Rep. 5 12086
[4]	Polynkin P, Kolesik M, Moloney J V, Siviloglou G A, Christodoulides D N 2009 Science 324 229
[5]	Chong A, Renninger W H, Christodoulides D N, Wise F W 2010 Nat. Photon. 4 103
[6]	Abdollahpour D, Suntsov S, Papazoglou D G, Tzortzakis S 2010 Phys. Rev. Lett. 105 253901
[7]	Mathis A, Courvoisier F, Froehly L, Furfaro L, Jacquot M, Lacourt P A, Dudley J M 2012 Appl. Phys. Lett. 101 071110
[8]	Rose P, Diebel F, Boguslawski M, Denz C 2013 Appl. Phys. Lett. 102 101101
[9]	Jia S, Vaughan J C, Zhuang X 2014 Nat. Photon. 8 302
[10]	Vettenburg T, Dalgarno H I C, Nylk J, Coll-Llad C, Ferrier D E K, Čizr T, Gunn-Moore F J, Dholakia K 2014 Nat. Method 11 541
[11]	Clerici M, Hu Y, Lassonde P, Milin C, Couairon A, Christodoulides D N, Chen Z, Razzari L, Vidal F, Lgar F, Faccio D, Morandotti R 2015 Sci. Adv. 1 e1400111
[12]	Minovich A, Klein A E, Janunts N, Pertsch T, Neshev D N, Kivshar Y S 2011 Phys. Rev. Lett. 107 116802
[13]	Li L, Li T, Wang S M, Zhang C, Zhu S N 2011 Phys. Rev. Lett. 107 126804
[14]	Zhang P, Wang S, Liu Y, Yin X, Lu C, Chen Z, Zhang X 2011 Opt. Lett. 36 3191
[15]	Epstein I, Arie A 2014 Phys. Rev. Lett. 112 023903
[16]	Voloch-Bloch N, Lereah Y, Lilach Y, Gover A, Arie A 2013 Nature 494 331
[17]	Efremidis N K, Paltoglou V, von Klizing W 2013 Phys. Rev. A 87 043637
[18]	Zhang P, Li T, Zhu J, Zhu X, Yang S, Wang Y, Yin X, Zhang, X 2014 Nat. Commun. 5 4316
[19]	Zhao S, Hu Y, Lu J, Qiu X, Cheng J, Burnett I 2014 Sci. Rep. 4 6628
[20]	Fu S, Tsur Y, Zhou J, Shemer L, Arie A 2015 Phys. Rev. Lett. 115 034501
[21]	Chen Z G, Xu J J, Hu Y, Song D H, Zhang Z, Zhao J Y, Liang Y 2016 Acta Opt. Sin. 36 1026009 (in Chinese) [陈志刚, 许京军, 胡毅, 宋道红, 张泽, 赵娟莹, 梁毅 2016 光学学报 36 1026009]
[22]	Wen W, Cai Y J 2017 Laser Optoelectr. Prog. 54 020002 (in Chinese) [文伟, 蔡阳健 2017 激光与光电子学进展 54 020002]
[23]	Kaminer I, Bekenstein R, Nemirovsky J, Segev M 2012 Phys. Rev. Lett. 108 163901
[24]	Zhang P, Hu Y, Li T, Cannan D, Yin X, Morandotti R, Chen Z, Zhang X 2012 Phys. Rev. Lett. 109 193901
[25]	Aleahmad P, Miri M, Mills M S, Kaminer I, Segev M, Christodoulides D N 2012 Phys. Rev. Lett. 109 203902
[26]	Kravtsov Y A, Orlov Y I 1983 Sov. Phys. Usp. 26 1038
[27]	Vaveliuk P, Lencina A, Rodrigo J A, Matos O M 2015 Phys. Rev. A 92 033850
[28]	Greenfield E, Segev M, Walasik W, Raz O 2011 Phys. Rev. Lett. 106 213902
[29]	Froehly L, Courvoisier F, Mathis A, Jacquot M, Furfaro L, Giust R, Lacourt P A, Dudley J M 2011 Opt. Express 19 16455
[30]	Wen Y, Chen Y, Zhang Y, Chen H, Yu S 2016 Phys. Rev. A 94 013829
[31]	Wen Y, Chen Y, Zhang Y, Chen H, Yu S 2017 Phys. Rev. A 95 023825
[32]	Wen Y, Chen Y, Zhang Y, Yu S 2017 Chin. Opt. Lett. 15 030011
[33]	Wong R 2001 Asymptotic Approximations of Integrals. (Society for Industrial and Applied Mathematics) p76
[34]	Li Z, Cheng H, Liu Z, Chen S, Tan J 2016 Adv. Opt. Mater. 4 1230
[35]	Pu M, Li X, Ma X, Wang Y, Zhao Z, Wang C, Hu C, Gao P, Huang C, Ren H, Li X, Qin F, Yang J, Gu M, Hong M, Luo X 2015 Sci. Adv. 1 e1500396
[36]	Li X, Pu M, Zhao Z, Ma X, Jin J, Wang Y, Gao P, Luo X 2016 Sci. Rep. 6 20524
[37]	Lin J, Wang Q, Yuan G, Du L, Kou S S, Yuan X C 2015 Sci. Rep. 5 10529
[38]	Dolev I, Epstein I, Arie A 2012 Phys. Rev. Lett. 109 203903
[39]	Jarutis V, Matijoius A, Trapani P D, Piskarskas A 2009 Opt. Lett. 34 2129
[40]	Zhao J, Zhang P, Deng D, Liu J, Gao Y, Chremmos I D, Efremidis N K, Christodoulides D N, Chen Z 2013 Opt. Lett. 38 498

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