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In this paper, the self-reconstruction property of astigmatic Bessel beam is studied experimentally and theoretically. Based on the Fresnel diffraction integral theory and Babinet principle, the general expression of the intensity distribution of astigmatic Bessel beams passing through a circular obstacle is derived. The cross-section light intensity at transmission distance of, 10, 30, and 80 mm after astigmatism of the astigmatic Bessel beam are occluded by circular obstacles. The self-reconstruction process of the light field is observed and verified by using an specially designed experimental setup. In the experiment, we choose He-Ne laser as a light source, collimate and expand the beam through a telescope system, and a zero-order astigmatic Bessel beam is generated by a beam vertically incident on the tilted axicon after the diaphragm. A circular obstacle with a radius of 0.2 mm is placed at a distance of 200 mm behind the axicon. Finally, the cross-section intensities at different distances are observed and recorded by a microscope. The experimental phenomena are in good agreement with the theoretical prediction. The results show that the reconstruction of the zero-order astigmatic Bessel beams will occur after passing through the on-axis and off-axis obstacles. And as the transmission distance increases, the outer contour size of the astigmatic Bessel beam becomes larger, and the number of central spot arrays increases, and the complete beam is gradually reconstructed. Particularly, this feature is different from the behavior of the non-diffracting Bessel beam, which maintains the light field unchanged during transmission and has a single central spot. It is expected to be applied to multi-layer multi-particle control. And a new optical property is discovered in the experiments: the reconstruction speed of the beam in the horizontal and vertical direction are not consistent in the reconstruction process, and there is a certain speed difference. Further, we add a spiral phase plate between the diaphragm and the axicon to produce a high-order astigmatic Bessel beam. And it is verified that the high-order astigmatism Bessel beam has the same self-reconstruction characteristics after being shielded by obstacles. Compared with the zero-order aperture system, the high-order beam can not only expand the operating range, but also use the orbital angular momentum carried by the beam to achieve light rotation, which makes the particle manipulation more flexible. The research proves the self-reconstruction characteristics of astigmatic Bessel beams theoretically and experimentally, and broadens the research range of astigmatic Bessel beams. The research results have practical significance and application value in the field of optical micro-manipulation.
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[1] Durnin J, Miceli J J, Eberly J H 1987 Phys. Rev. Lett. 58 1499
[2] Gecevičius M, Drevinskas R, Beresna M, Kazansky P G 2014 Appl. Phys. Lett. 104 288
[3] Ambrosio L A, Zamboni-Rached M 2015 J. Opt. Soc. Am. B 32 B37
[4] Fickler R, Lapkiewicz R, Plick W N, Krenn M, Schaeff C, Ramelow S, Zeilinger A 2012 Science 338 640
[5] Planchon T A, Liang G, Milkie D E, Davidson M W, Galbraith J A, Galbraith C G, Betzig E 2011 Nat. Methods 8 417
[6] Luo H, Zhou J, Wen S, et al. 2015 Opt. Lett. 40 5506
[7] Liu Y, Ke Y, Zhou J, et al. 2017 Sci. Rep. 7 44096
[8] Chen H, Ling X H, He W G, Li Q G, Yi X N 2017 Acta Phys. Sin. 66 044203 (in Chinese) [陈欢, 凌晓辉, 何武光, 李钱光, 易煦农 2017 物理学报 66 044203]
[9] Rao A S, Samanta G K 2018 Opt. Lett. 43 3029
[10] Zhao B, Zhu L 1998 Appl. Opt. 37 2563
[11] Thaning A, Jaroszewicz Z, Friberg A T 2003 Appl. Opt. 42 9
[12] Liu S, Li Y F, Cai X Y, Zhang N 2016 Acta Phys. Sin. 65 194210 (in Chinese) [刘莎, 李亚飞, 蔡先勇, 张楠 2016 物理学报 65 194210]
[13] Jiang X G, Wu F T 2008 Acta Phys. Sin. 57 4207 (in Chinese) [江新光, 吴逢铁 2008 物理学报 57 4207]
[14] Hu R, Wu F T, Zhu Q Z, Yang Y F 2017 Acta Opt. Sin. 37 0826002 (in Chinese) [胡润, 吴逢铁, 朱清智, 杨艳飞 2017 光学学报 37 0826002]
[15] Yang Y F, Wu F T, Zhu Q Z, Hu R 2018 Acta Opt. Sin. 38 0505004 (in Chinese) [杨艳飞, 吴逢铁, 朱清智, 胡润 2018 光学学报 38 0505004]
[16] Garcés-Chávez V, Mcgloin D, Melville H, Sibbett W, Dholakia K 2002 Nature 419 145
[17] Lee K S, Rolland J P 2008 Opt. Lett. 33 1696
[18] Weber N, Spether D, Seifert A, Zappe H 2012 J. Opt. Soc. Am. A 29 808
[19] Broky J, Siviloglou G A, Dogariu A, Christodoulides D N 2008 Opt. Express 16 12880
[20] Zhang Q A, Wu F T, Zheng W T, Pu J X 2011 Sci. China: Phys. Mech. Astron. 41 1131 (in Chinese) [张前安, 吴逢铁, 郑维涛, 蒲继雄 2011 中国科学: 物理学 力学 天文学 41 1131]
[21] Li D, Wu F T, Xie X X, Sun C 2015 Acta Phys. Sin. 64 014201 (in Chinese) [李冬, 吴逢铁, 谢晓霞, 孙川 2015 物理学报 64 014201]
[22] Anguianomorales M, Martínez A, Iturbecastillo M D, Chávez-Cerda S, Alcalá-Ochoa N 2007 Appl. Opt. 46 8284
[23] Yang G G, Song F J 2008 Higher Physical Optics (2nd Edition) (Hefei: China University of Science and Technology Press) pp81-82 (in Chinese) [羊国光, 宋菲君 2008 高等物理光学(第2版) (合肥: 中国科学技术大学出版社) 第81–82页]
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