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Airy accelerating beams have aroused a great deal of interest because of their non-diffracting and self-accelerating properties, which have many potential applications such as in optical micromanipulations, nonlinear optics and vacuum electron acceleration. A key issue in research of the acceleration beam and its applications is how to generate this specific type of beams with high energy efficiency. In this paper, the spatial oscillation properties of the complex amplitude of an accelerating beam are analyzed and a theory describing the accelerating properties of the beam based on its local spatial frequency is proposed. The local spatial frequency of a general Airy beam is calculated through the zero-point coordinates of the Airy function, and an analytical formula accurately describing the local spatial frequency distribution is given. The relationship between the local spatial frequency and the accelerating trajectory of the beam is also given, based on which a simple algorithm for finding the pure-phase expression of an acceleration beam from its given accelerating trajectory is presented. Finally an analytical expression of the pure-phase function of an acceleration beam for generating a circle-arced trajectory is found out, based on which a pure-phase diffractive optical element is designed and demonstrated successfully.
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Keywords:
- diffractive optics /
- accelerating beam /
- local spatial frequency
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[1] Siviloglou G A, Christodoulides D N 2007 Opt. Lett. 32 979
[2] Xu J, Liu J, Xie J H, Wang Y T 2010 Laser & Optoelectron. Prog. 47 070501 (in Chinese) [徐佳, 刘娟, 谢敬辉, 王涌天 2010 激光与光电子学进展 47 070501]
[3] Wu F T, Jiang X G, Liu B, Qiu Z X 2009 Acta Phys. Sin. 58 3125 (in Chinese) [吴逢铁, 江新光, 刘彬, 邱振兴 2009 物理学报 58 3125]
[4] Zheng W T, Wu F T, Zhang Q A, Cheng Z M 2012 Acta Phys. Sin. 61 144201 (in Chinese) [郑维涛, 吴逢铁, 张前安, 程治明 2012 物理学报 61 144201]
[5] Zhang P, Prakash J, Zhang Z, Mills M S, Efremidis N K, Christodoulides D N, Chen Z 2011 Opt. Lett. 36 2883
[6] Cao R, Yang Y, Wang J, Bu J, Wang M, Yuan X C 2011 Appl. Phys. Lett. 99 261106
[7] Kaminer I, Segev M, Christodoulides D N 2011 Phys. Rev. Lett. 106 213903
[8] Dolev I, Kaminer I, Shapira A, Segev M, Arie A 2012 Phys. Rev. Lett. 108 113903
[9] Ren Z J, Fan C J, Zhou W D 2011 Chin. J. Lasers 38 1202005 (in Chinese) [任志君, 范长江, 周卫东2011 中国激光 38 1202005]
[10] Ren Z J, Wu Q, Zhou W D, Wu G Z, Shi Y L 2012 Acta Phys. Sin. 61 174207 (in Chinese) [任志君, 吴琼, 周卫东, 吴根柱, 施逸乐 2012 物理学报 61 174207 ]
[11] Li J, Zang W, Tian J 2010 Opt. Express 18 7300
[12] Wang G H, Wang X F, Dong K G 2012 Acta Phys. Sin. 61 165201 (in Chinese) [王广辉, 王晓方, 董克攻 2012 物理学报 61 165201]
[13] Siviloglou G A, Broky J, Dogariu A, Christodoulides D N 2007 Phys. Rev. Lett. 99 213901
[14] Dai H T, Sun X W, Luo D, Liu Y J 2009 Opt. Express 17 19365
[15] Ellenbogen T, Voloch N, Ganany-Padowicz A, Arie A 2009 Nat. Photon. 3 395
[16] Davis J A, Mitry M J, Bandres M A, Ruiz I 2009 Appl. Opt. 48 3170
[17] Hu Y, Zhang P, Lou C, Huang S, Xu J, Chen Z 2010 Opt. Lett. 35 2260
[18] Cottrell D M, Davis J A, Hazard T M 2009 Opt. Lett. 34 2634
[19] Wang J, Bu J, Wang M, Yang Y, Yuan X C 2011 Appl. Opt. 50 6627
[20] Froehly L, Courvoisier F, Mathis A, Jacquot M, Furfaro L, Giust R, Lacourt P A, Dudley J M 2011 Opt. Express 19 16455
[21] Greenfield E, Segev M, Walasik W, Raz O 2011 Phys. Rev. Lett. 106 213902
[22] Qi X Q, Gao C Q, Liu Y D 2010 Acta Phys. Sin. 59 264 (in Chinese) [齐晓庆, 高春清, 刘义东 2010 物理学报 59 264]
[23] Kaminer I, Bekenstein R, Nemirovsky J, Segev M 2012 Phys. Rev. Lett. 108 163901
[24] Zhang P, Hu Y, Cannan D, Salandrino A, Li T, Morandotti R, Zhang X, Chen Z 2012 Opt. Lett. 37 2820
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