Design of accelerating beams based on caustic method

Wen Yuan-Hui; Chen Yu-Jie; Yu Si-Yuan

doi:10.7498/aps.66.144210

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:

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).

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Cited By

[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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Vol. 66, Issue 14 - 2017-07-20

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