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随着激光技术的发展, 无衍射光束的应用领域不断拓展. 具有自加速特性的类贝塞尔光束, 能够在保持贝塞尔光束的无衍射性下实现主瓣沿着弯曲轨迹传播. 本文研究基于磁液变形镜来生成弯曲轨迹可控的自加速类贝塞尔光束. 磁液变形镜具有镜面变形幅值大、制造成本低、镜面连续光滑、驱动器易于拓展等优点, 并且克服了传统变形镜驱动器间相对行程较小的缺点, 从而有利于生成理想的锥形面. 首先, 本文通过数学几何分析来预测类贝塞尔光束的弯曲轨迹; 然后再利用磁液变形镜拟合相应面形; 最后, 搭建基于磁液变形镜的自适应光学实验平台来生成沿抛物线轨迹的自加速类贝塞尔光束, 实验结果验证了所建模型以及类贝塞尔光束沿预定抛物线轨迹传播的准确性, 并且通过快速修改参数实现对光束轨迹的微调.
With the development of laser technology, the application scope of nondiffracting beams, such as Bessel beams, Mathieu beams, cosine beams, and parabolic beams, which remain invariant along their propagation, continues to expand. During its propagation, the main lobes of these beams tend to bend towards off-axis position, which is called self-accelerating (or self-bending) property. A Bessel-like beam with self-acceleration can realize the propagation of the main lobe along a curved trajectory while maintaining the non-diffraction. Because of the above property, Bessel-like beams have been utilized in various areas such as guiding particles along arbitrarily curved trajectories, self-accelerating beams in nonlinear medium, plasma guidance, and laser-assisted guiding of electric discharges around objects. In this paper, we propose a method of bending the trajectory of Bessel-like beams by using a magnetic fluid deformable mirror (MFDM) instead of traditional spatial light modulator (SLM) and Pancharatnam-Berry (PB) phase manipulation. The MFDM provides a method without pixelation, where all parameters can be rapidly modified for fine-tuning. Furthermore, compared with the conventional deformable mirror, the MFDM has the advantages of a continuous and smooth mirror surface, large shape deformation, low manufacture cost, easy extension, and large inter-actuator stroke. Therefore, it is easy for the MFDM to generate the ideal shape of an axicon. Firstly, according to geometric analysis, the asymmetrical mirror profile to produce a self-accelerating Bessel-like optical beam is proposed. The proposed mirror profile can be used to compensate for the difference in optical path length for each annular slice of the axicon. If a collimated Gaussian beam is incident on the mirror combining the axicon and the asymmetrical mirror profiles, which can obtain Bessel-like beams with arbitrarily curved trajectories. Secondly, the resultant of the self-accelerating Bessel-like beams along parabolic trajectories is validated by the simulation in MATLAB. Finally, a prototype of MFDM consisting of the dual-layer arrays of miniature electromagnetic coils, a Maxwell coil and the magnetic fluid filled in a circular container is fabricated for the experiment. The experimental results show that the Bessel-like beams propagate along the parabolic trajectories, with the MFDM used, and the accuracy of the curved trajectories is verified. The proposed method in this paper opens a new experimental way to the study of Bessel-like beam; the theoretical approach can also be generalized mathematically for other non-paraxial beam propagation. -
Keywords:
- magnetic fluid /
- deformable mirror /
- nondiffracting beam /
- Bessel beam
[1] Durnin J 1987 J. Opt. Soc. 4 651Google Scholar
[2] Hu Y, Nie J, Sun K, Ye Q, Wang L 2017 Opt. Commun. 394 108Google Scholar
[3] Nadgaran H, Fallah R 2015 Opt. Commun. 341 160Google Scholar
[4] Dolev I, Libster A, Arie A 2012 Appl. Phys. Lett. 101 101109Google Scholar
[5] Siviloglou G A, Christodoulides D N 2007 Opt. Lett. 32 979Google Scholar
[6] 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 498Google Scholar
[7] Chremmos I D, Chen Z, Christodoulides D N, Efremidis N K 2012 Opt. Lett. 37 5003Google Scholar
[8] Jarutis V, Matijošius A, Di Trapani P, Piskarskas A 2009 Opt. Lett. 34 2129Google Scholar
[9] Zhao Z, Zang W, Tian J 2016 J. Optics-UK 18 025607Google Scholar
[10] Dolev I, Kaminer I, Shapira A, Segev M, Arie A 2012 Phys. Rev. Lett. 108 113903Google Scholar
[11] Polynkin P, Kolesik M, Moloney J V, Siviloglou G A, Christodoulides D N 2009 Science 324 229Google Scholar
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[14] Vieira T A, Zamboni-Rached M, Gesualdi M R 2014 Opt. Commun. 315 374Google Scholar
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[19] 赵娟莹, 邓冬梅, 张泽, 刘京郊, 姜东升 2014 物理学报 63 044204
Zhao J Y, Deng D M, Zhang Z, Liu J J, Jiang D S 2014 Acta Phys. Sin. 63 044204
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[21] 陈欢, 凌晓辉, 何武光, 李钱光, 易煦农 2017 物理学报 66 044203
Chen H, Ling X H, He W G, Li Q G, Yi X N 2017 Acta Phys. Sin. 66 044203
[22] Wu Z, Iqbal A, Amara F B 2012 Modeling and Control of Magnetic Fluid Deformable Mirrors for Adaptive Optics Systems (Springer Science & Business Media)
[23] Allen L, Beijersbergen M W, Spreeuw R J C, Woerdman J P 1992 Phys. Rev. A 45 8185Google Scholar
[24] He Y, Liu Z, Liu Y, Zhou J, Ke Y, Luo H, Wen S 2015 Opt. Lett. 40 5506Google Scholar
[25] Zhou J, Liu Y, Ke Y, Luo H, Wen S 2015 Opt. Lett. 40 3193Google Scholar
[26] Liu Y, Ke Y, Zhou J, Liu Y, Luo H, Wen S, Fan D 2017 Sci. Rep. 7 44096Google Scholar
[27] Pampaloni F, Enderlein J 2004 arXiv: physics/0410021
[28] Kamilov U S, Papadopoulos I N, Shoreh M H, Goy A, Vonesch C, Unser M, Psaltis D 2015 Optica 2 517Google Scholar
[29] Brousseau D, Drapeau J, Piché M, Borra E F 2011 Appl. Opt. 50 4005Google Scholar
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[31] Yen Y T, Lu T Y, Lee Y C, Yu C C, Tsai Y C, Tseng Y C, Chen H L 2014 ACS Appl. Mater. Inter. 6 4292Google Scholar
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图 4 沿抛物线轨迹的自加速类贝塞尔光束仿真 (a) 数值模拟类贝塞尔光束传输的侧面图; (b) 弯曲轨迹类贝塞尔光束在传播距离
$z = 4{\rm{0 \;cm}}$ 处的光强; (c)—(f) 图(a)中不同传播距离处光强的横截面分布Fig. 4. The simulation of self-accelerating Bessel-like beam along a parabolic trajectory: (a) Numerically simulated side-view propagation of the generated beam; (b) intensity of a bended Bessel-like beam when propagation distance
$z = 4{\rm{0 \;cm}}$ ; (c)−(f) cross-sectional images of Bessel-like beam along different distance. -
[1] Durnin J 1987 J. Opt. Soc. 4 651Google Scholar
[2] Hu Y, Nie J, Sun K, Ye Q, Wang L 2017 Opt. Commun. 394 108Google Scholar
[3] Nadgaran H, Fallah R 2015 Opt. Commun. 341 160Google Scholar
[4] Dolev I, Libster A, Arie A 2012 Appl. Phys. Lett. 101 101109Google Scholar
[5] Siviloglou G A, Christodoulides D N 2007 Opt. Lett. 32 979Google Scholar
[6] 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 498Google Scholar
[7] Chremmos I D, Chen Z, Christodoulides D N, Efremidis N K 2012 Opt. Lett. 37 5003Google Scholar
[8] Jarutis V, Matijošius A, Di Trapani P, Piskarskas A 2009 Opt. Lett. 34 2129Google Scholar
[9] Zhao Z, Zang W, Tian J 2016 J. Optics-UK 18 025607Google Scholar
[10] Dolev I, Kaminer I, Shapira A, Segev M, Arie A 2012 Phys. Rev. Lett. 108 113903Google Scholar
[11] Polynkin P, Kolesik M, Moloney J V, Siviloglou G A, Christodoulides D N 2009 Science 324 229Google Scholar
[12] Clerici M, Hu Y, Lassonde P, Milián C, Couairon A, Christodoulides D N, Chen Z, Razzari L, Vidal F, Légaré F, Faccio D, Morandotti R 2015 Sci. Adv. 1 e1400111
[13] Durnin J, Miceli Jr J J, Eberly J H 1987 Phys. Rev. Lett. 58 1499Google Scholar
[14] Vieira T A, Zamboni-Rached M, Gesualdi M R 2014 Opt. Commun. 315 374Google Scholar
[15] Herman R M, Wiggins T A 1991 J. Opt. Soc. Am. A 8 932Google Scholar
[16] Cox A J, Dibble D C 1992 J. Opt. Soc. Am. A 9 282Google Scholar
[17] Dudutis J, GeČys P, RaČiukaitis G 2016 Opt. Express 24 28433Google Scholar
[18] Wu G, Wang F, Cai Y 2014 Phys. Rev. A 89 043807Google Scholar
[19] 赵娟莹, 邓冬梅, 张泽, 刘京郊, 姜东升 2014 物理学报 63 044204
Zhao J Y, Deng D M, Zhang Z, Liu J J, Jiang D S 2014 Acta Phys. Sin. 63 044204
[20] Chen J S, Jia J, Chu D 2017 Chin. Opt. Lett. 15 100901Google Scholar
[21] 陈欢, 凌晓辉, 何武光, 李钱光, 易煦农 2017 物理学报 66 044203
Chen H, Ling X H, He W G, Li Q G, Yi X N 2017 Acta Phys. Sin. 66 044203
[22] Wu Z, Iqbal A, Amara F B 2012 Modeling and Control of Magnetic Fluid Deformable Mirrors for Adaptive Optics Systems (Springer Science & Business Media)
[23] Allen L, Beijersbergen M W, Spreeuw R J C, Woerdman J P 1992 Phys. Rev. A 45 8185Google Scholar
[24] He Y, Liu Z, Liu Y, Zhou J, Ke Y, Luo H, Wen S 2015 Opt. Lett. 40 5506Google Scholar
[25] Zhou J, Liu Y, Ke Y, Luo H, Wen S 2015 Opt. Lett. 40 3193Google Scholar
[26] Liu Y, Ke Y, Zhou J, Liu Y, Luo H, Wen S, Fan D 2017 Sci. Rep. 7 44096Google Scholar
[27] Pampaloni F, Enderlein J 2004 arXiv: physics/0410021
[28] Kamilov U S, Papadopoulos I N, Shoreh M H, Goy A, Vonesch C, Unser M, Psaltis D 2015 Optica 2 517Google Scholar
[29] Brousseau D, Drapeau J, Piché M, Borra E F 2011 Appl. Opt. 50 4005Google Scholar
[30] Wu Z, Kong X, Zhang Z, Wu J, Wang T, Liu M 2017 Micromachines 8 72Google Scholar
[31] Yen Y T, Lu T Y, Lee Y C, Yu C C, Tsai Y C, Tseng Y C, Chen H L 2014 ACS Appl. Mater. Inter. 6 4292Google Scholar
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