附加球面相位引致Airy光束在单轴晶体传输时的两次镜像演化

朱开成; 梁瑞生; 易亚军; 刘伟慈; 朱洁

doi:10.7498/aps.69.20191592

摘要

利用单轴晶体光束传输理论, 求得了具有附加球面相位Airy光束在单轴晶体中的传输公式. 数值模拟计算结果表明, 线偏振附加球面相位Airy光束在晶体中传输时仍为线偏振, 但不是传输不变的. 粗略地讲, 具有附加球面相位的Airy光束在晶体中传输时, 近场是传输不变的; 而在由晶体寻常与非寻常折射率和球面半径共同确定的两个特定传输距离处, 传输光束转换成了取向不同的Gaussian-Airy光束, 且高斯依赖的束宽度敏感地与截断因子相关; 而当光束依次穿过此两位置时光斑花样先后相对于两横向轴平面做镜像演化, 且镜像演化顺序也与晶体寻常和非寻常折射率相对大小密切相关, 其总的效果是远场强度花样能恢复原样但花样取向产生了关于对过横平面二、四象限平分平面的镜像演化. 这些结果表明, 通过恰当选择晶体材料(即折射率)和附加球面相位的半径R, 可以调控光束花样的形状、取向及表征各向异性材料的相关性质.

关键词:

Abstract

Airy beams have received considerable attention due to their unique features on propagation, including non-spreading, self-healing, self-accelerating, and parabolic trajectories. Here in this work we study the propagation of linearly polarized Airy beams with an added spherical phase in uniaxial crystal orthogonal to the optical axis. Based on the beam transmission theory in uniaxial crystals, the analytical expressions for the intensity distribution of the beams in different view planes are derived. Numerical calculations are performed and some novel propagation features are presented graphically. It is shown that the Airy beam with an added spherical phase remains linearly polarized but cannot keep other properties unchanged during propagation in uniaxial crystal. Such a beam maintains its intensity profile in the near-field, then with the propagation distance increasing, converts into the Gaussian-Airy beams with different orientations at two specified distances which are codetermined by the extraordinary and ordinary refractive index of the crystal (namely n_e and n_o) and the radius of the spherical phase, and most impressively, forms a mirror-like reflection profile in the far field, i.e., the intensity pattern in the far field returns to the initial Airy beam profile while its orientation on the transversal plane is reversed along the bisector line of the second and fourth quadrant. Note that the intensity pattern successively experiences two mirror transformations along the x and y coordinate axis when passing through these two critical positions, which can give rise to the mirror reflection effect for the whole Airy beam. Moreover, we further demonstrate that the sequences of these two mirror transformations are in close relation with the relative size between n_e and n_o. Therefore, the results obtained in this paper reveal new propagation features in anisotropic medium of Airy beams with added spherical phase and provide a novel route to controlling propagation properties like the pattern profile and orientation of the Airy beams through choosing appropriate anisotropic materials and the radius of the spherical phase factor. Considering that it is easy to obtain an Airy beam with an added spherical phase which can be realized with an Airy beam through an ideal lens, our investigation may lead to potential applications in many fields where the ability to change profile and orientation of the intensity pattern and the ability to determine the refractive index of anisotropic medium are both required.

Keywords:

Airy beam /
uniaxial anisotropic crystal /
added spherical phase /
mirror inversion /
ordinary and extraordinary refractive index

作者及机构信息

1.
广州工商学院电子信息工程系, 广州　510850

2.
中南大学物理与电子学院, 长沙　410083

3.
贵州理工学院理学院, 贵阳　550003

通信作者: 朱洁, jiezh_16@163.com

Authors and contacts

1.
Department of Electronics and Information Engineering, Guangzhou College of Technology and Business, Guangzhou 510850, China

2.
School of Physics and Electronics, Central South University, Changsha 410083, China

3.
College of Science, Guizhou Institute of Technology, Guiyang 550003, China

Corresponding author: Zhu Jie, jiezh_16@163.com

文章全文 : translate this paragraph

参考文献

[1]	Berry M V, Balazs N L 1979 Am. J. Phys. 47 264 Google Scholar
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[44]	Xiao Z Y, Xia H, Yu T, et al. 2018 Opt. Rev. 25 323 Google Scholar
[45]	Valloee O, Soares M 2004 Airy Functions and Applications to Physics (London: Imperial College Press) p10, 87
[46]	Grossman J G, Casperson L W, Stafsudd O M, Sutter Jr L V 1984 Appl. Opt. 23 48 Google Scholar
[47]	Zhang J, Pang Z, Feng L, Zhong T, Wang L, Deng D M 2017 Chin. Opt. Lett. 15 060501 Google Scholar
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施引文献

图 1 金红石晶体中不同传输距离处的光场强度分布, 其他参数分别为N_w = 100, a = b = 0.1, δ = 1

Fig. 1. Intensity distributions of the Airy beams in rutile crystal at several propagation distances with N_w = 100, a = b = 0.1, δ = 1

下载: 全尺寸图片幻灯片

图 2 金红石晶体时不同传输距离处的光束强度分布, 其他参数分别为N_w = 1, a = b = 0.1, δ = 1

Fig. 2. Intensity distributions of the Airy beams in rutile crystal at several propagation distances with N_w = 1, a = b = 0.1, δ = 1.

下载: 全尺寸图片幻灯片

图 3 淡红银矿晶体时不同传输距离处的光束强度分布, 其他参数分别为N_w = 100, a = b = 0.1, δ = 1

Fig. 3. Intensity distributions of the Airy beams in proustite crystal at several propagation distances with N_w = 100, a = b = 0.1, δ = 1.

下载: 全尺寸图片幻灯片

map

[1]	Berry M V, Balazs N L 1979 Am. J. Phys. 47 264 Google Scholar
[2]	Siviloglou G A, Broky J, Dogariu A, Christodoulides D N 2007 Phys. Rev. Lett. 99 213901 Google Scholar
[3]	Siviloglou G A, Broky J, Dogariu A, Christodoulides D N 2008 Opt. Lett. 33 207 Google Scholar
[4]	Siviloglou G A, Christodoulides D N 2007 Opt. Lett. 32 979 Google Scholar
[5]	Broky J, Siviloglou G A, Dogariu A, Christodoulides D N 2008 Opt. Express 16 12880 Google Scholar
[6]	Christodoulides D N 2008 Nat. Photonics 2 652 Google Scholar
[7]	Chong A, Renninger W H, Christodoulides D N, Wise F W 2010 Nat. Photonics 4 103 Google Scholar
[8]	Zhang Y Q, Zhong H, Belic M R, Zhang Y P 2017 Appl. Sci. 7 341 Google Scholar
[9]	Efremidis N, Chen Z G, Segev M, Christodoulides D N 2019 Optica 6 686 Google Scholar
[10]	Polynkin P, Kolesik M, Moloney J V, Siviloglou G A, Christodoulides D N 2009 Science 324 229 Google Scholar
[11]	Rose P, Diebel F, Boguslawski M, Denz C 2013 Appl. Phys. Lett. 102 101101 Google Scholar
[12]	Wiersma N, Marsal N, Sciamanna M, Wolfersberger D 2014 Opt. Lett. 39 5997 Google Scholar
[13]	Liang Y, Hu Y, Song D, Lou C, Zhang X, Chen Z, Xu J 2015 Opt. Lett. 40 5686 Google Scholar
[14]	Deng D M, Guo Q 2009 New J. Phys. 11 103029 Google Scholar
[15]	Deng D M, Du S L, Guo Q 2013 Opt. Commun. 289 6 Google Scholar
[16]	Chu X X 2011 Opt. Lett. 36 2701 Google Scholar
[17]	Wen W, Chu X X 2014 J. Mod. Opt. 61 379 Google Scholar
[18]	Wen W, Chu X X, Ma H T 2015 Opt. Commun. 336 326 Google Scholar
[19]	Zhou G Q, Chen R P, Ru G Y 2014 Laser Phys. Lett. 11 105001 Google Scholar
[20]	Ruiz-Jimenez C, Nobrega K Z, Porras M A 2015 Opt. Express 23 8918 Google Scholar
[21]	Zhuang F, Du X Y, Ye Y Q, Zhao D M 2012 Opt. Lett. 37 1871 Google Scholar
[22]	Shen M, Li W, Lee R K 2016 Opt. Express 24 8501 Google Scholar
[23]	Chen R P, Chew K H, Zhao T Y, Li P G, Li C R 2014 Laser Phys. 24 115402
[24]	Xiao F, Li B, Wang M, Zhu W, Zhang P, Liu S, Premaratne M, Zhao J 2014 Opt. Express 22 22763 Google Scholar
[25]	Zhou G Q, Chen R P, Chu X X 2012 Appl. Phys. B 109 549 Google Scholar
[26]	Zhang Y Q, Belic M R, Zhang L, Zhong W P, Zhu D, Wang R, Zhang R P 2015 Opt. Express 23 10467 Google Scholar
[27]	Besieris I M, Shaarawi A M, Ramboni-Rached M 2016 Opt. Commun. 369 56 Google Scholar
[28]	Li H H, Wang J G, Tang M M, Cao J X, Li X Z 2017 Optik 149 144 Google Scholar
[29]	Xie W K, Zhang P, Wang H, Chu X X 2018 Opt. Commun. 427 288 Google Scholar
[30]	Zhou G Q, Chen R P, Chu X X 2012 Opt. Express 20 2196 Google Scholar
[31]	Deng D M, Chen C D, Zhao X, Li H G 2013 Appl. Phys. B 110 433
[32]	Zhou M L, Chen C D, Chen B, Peng X, Peng Y L, Deng D M 2015 Chin. Phys. B 24 124102 Google Scholar
[33]	Deng F, Deng D M 2016 Opt. Commun. 380 280 Google Scholar
[34]	Yu W, Zhao R, Deng F, Huang J, Chen C, Yang X, Zhao Y, Deng D M 2016 Chin. Phys. B 25 044201 Google Scholar
[35]	Li D D, Peng X, Peng Y L, Zhang L P, Deng D M 2017 J. Opt. Soc. Am. B 34 891 Google Scholar
[36]	Zheng G L, Deng X Q, Xu S X, Wu Q Y 2017 Appl. Opt. 56 2444 Google Scholar
[37]	Zheng G L, Xu S X, Wu Q Y, Wang Q, Ouyang Z B 2017 Opt. Express 25 14654 Google Scholar
[38]	Zhang J B, Zhou K Z, Liang J H, Lai Z Y, Yang X L, Deng D M 2018 Opt. Express 26 1290 Google Scholar
[39]	Chen Y Z, Zhao G W, Ye F, Xu C J, Deng D M 2018 Chin. Phys. B 27 104201 Google Scholar
[40]	Wu X L, Xie J T, Deng D M 2019 Appl. Phys. B 125 87
[41]	Tang H Q, Zhu K C 2013 Opt. Laser Technol. 54 68 Google Scholar
[42]	朱开成, 唐慧琴, 郑小娟, 唐英 2014 63 104210 Google Scholar Zhu K C, Tang H Q, Zheng X J, Tang Y 2014 Acta Phys. Sin. 63 104210 Google Scholar
[43]	朱洁, 朱开成 2016 65 204204 Google Scholar Zhu J, Zhu K C 2016 Acta Phys. Sin. 65 204204 Google Scholar
[44]	Xiao Z Y, Xia H, Yu T, et al. 2018 Opt. Rev. 25 323 Google Scholar
[45]	Valloee O, Soares M 2004 Airy Functions and Applications to Physics (London: Imperial College Press) p10, 87
[46]	Grossman J G, Casperson L W, Stafsudd O M, Sutter Jr L V 1984 Appl. Opt. 23 48 Google Scholar
[47]	Zhang J, Pang Z, Feng L, Zhong T, Wang L, Deng D M 2017 Chin. Opt. Lett. 15 060501 Google Scholar
[48]	Feng L, Zhang J, Pang Z, Wang L, Zhong T, Yang X, Deng D M 2017 Opt. Commun. 402 60 Google Scholar
[49]	Zhang L P, Deng F, Peng Y L 2017 Laser Phys. 27 015404 Google Scholar
[50]	Xie J T, Zhang J B, Ye J R, Liu H W, Liang Z Y, Long S J, Zhou K Z, Deng D M 2018 Opt. Express 26 5845 Google Scholar
[51]	Zhang J G, Tian Z W, Li Y F 2018 Optik 158 64 Google Scholar
[52]	Bai X Q, Wang Y H, Zhang J, Xiao Y 2019 Appl. Phys. B 125 188
[53]	Zhu J, Tang H Q, Su Q, Zhu K C 2017 Europhys. Lett. 118 14001 Google Scholar
[54]	朱洁, 唐慧琴, 李晓利, 刘小钦 2017 66 164202 Google Scholar Zhu J, Tang H Q, Li X L, Liu X Q 2017 Acta Phys. Sin. 66 164202 Google Scholar

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附加球面相位引致Airy光束在单轴晶体传输时的两次镜像演化