Abstract
Over the past several years, spatially shaped self-accelerating beams along different trajectories have been studied extensively. Due to their useful properties such as resistance to diffraction, self-healing, and self-bending even in free space, these beams have attracted great attention with many proposed applications. Interestingly, some of these beams could be designed with controllable spatial profiles and thus propagate along various desired trajectories such as parabolic, snake-like, hyperbolic, hyperbolic secant, three-dimensional spiraling, and even self-propelling trajectories. Experimentally, such beams are realized typically by using a spatial light modulator so as to imprint a desired phase distribution on a Gaussian-like input wave front propagating under paraxial or nonparaxial conditions. In this paper, we provide a brief overview of our recent work on specially shaped self-accelerating beams, including Bessel-like, breathing Bessel-like, and vortex Bessel-like beams. In addition, we propose and demonstrate a new type of dynamical Bessel-like beams that can exhibit not only self-accelerating but also self-propelling during propagation. Both theoretical and experimental results are presented along with a brief discussion of potential applications.
摘要
本文综述了多种特殊设计的自加速类贝塞尔光束。这些光束在理论上通过相位调制或叠加等方法产生,并经过实验装置得以验证。其范围覆盖傍轴和大角度自弯曲非傍轴情况,具体包括类贝塞尔光束、自呼吸型类贝塞尔光束、涡旋型类贝塞尔光束、自螺旋型类贝塞尔光束,以及非傍轴类贝塞尔光束。基于这些光束具有无衍射、自加速、自修复、光场中心对称及光束传输轨迹可调控等特点,它们不仅具有重要的基础研究价值, 而且在微粒操控、等离子体、大气科学、生物操控等诸多领域都具有重要的应用前景。
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References
Berry MV, Balazs NL (1979) Nonspreading wave packets. Am J Phys 47:264–267
Greenberger DM (1980) Comment on “Nonspreading wave packets”. Am J Phys 48:256
Siviloglou GA, Christodoulides DN (2007) Accelerating finite energy Airy beams. Opt Lett 32:979–981
Siviloglou GA, Broky J, Dogariu A et al (2007) Observation of accelerating Airy beams. Phys Rev Lett 99:213901
Hu Y, Siviloglou GA, Zhang P et al (2012) Self-accelerating Airy beams: generation, control, and applications. In: Chen Z, Morandotti R (eds) Nonlinear photonics and novel optical phenomena. Springer, New York, pp 1–46
Bandres MA, Kaminer I, Mills M et al (2013) Accelerating optical beams. Opt Photonics News 24:30–37
Zhang Z, Hu Y, Zhao JY et al (2013) Research progress and application prospect of Airy beams. Chin Sci Bull 58:3513–3520 (in Chinese)
Baumgartl J, Mazilu M, Dholakia K (2008) Optically mediated particle clearing using Airy wavepackets. Nat Photonics 2:675–678
Zhang P, Zhang Z, Prakash J et al (2011) Trap** and guiding microparticles with morphing autofocusing Airy beams. Opt Lett 36:2883–2885
Polynkin P, Kolesik M, Moloney JV et al (2009) Curved plasma channel generation using ultraintense Airy beams. Science 324:229–232
Zhang P, Wang S, Liu Y et al (2011) Plasmonic Airy beams with dynamically controlled trajectories. Opt Lett 36:3191–3193
Minovich A, Klein AE, Janunts N et al (2011) Generation and near-field imaging of Airy surface plasmons. Phys Rev Lett 107:116802
Li L, Li T, Wang SM et al (2011) Plasmonic Airy beam generated by in-plane diffraction. Phys Rev Lett 107:126804
Voloch-Bloch N, Lereah Y, Lilach Y et al (2013) Generation of electron Airy beams. Nature 494:331–335
Jia S, Vaughan JC, Zhuang X (2014) Isotropic three-dimensional super-resolution imaging with a self-bending point spread function. Nat Photon 8:302–306
Vettenburg T, Dalgarno HI, Nylk J et al (2014) Light-sheet microscopy using an Airy beam. Nat Methods 5:541–544
Kaminer I, Bekenstein R, Nemirovsky J et al (2012) Nondiffracting accelerating wave packets of Maxwell’s equations. Phys Rev Lett 108:163901
Courvoisier F, Mathis A, Froehly L et al (2012) Sending femtosecond pulses in circles: highly nonparaxial accelerating beams. Opt Lett 37:1736–1738
Zhang P, Hu Y, Cannan D et al (2012) Generation of linear and nonlinear nonparaxial accelerating beams. Opt Lett 37:2820–2822
Aleahmad P, Miri MA, Mills MS et al (2012) Fully vectorial accelerating diffraction-free Helmholtz beams. Phys Rev Lett 109:203902
Zhang P, Hu Y, Li T et al (2012) Nonparaxial Mathieu and Weber accelerating beams. Phys Rev Lett 109:193901
Bandres MA, Rodriguez-Lara BM (2013) Nondiffracting accelerating waves: weber waves and parabolic momentum. New J Phys 15:013054
Libster-Hershko A, Epstein I, Arie A (2014) Rapidly accelerating Mathieu and Weber surface plasmon beams. Phys Rev Lett 113:123902
Mathis A, Courvoisier F, Giust R et al (2013) Arbitrary nonparaxial accelerating periodic beams and spherical sha** of light. Opt Lett 38:2218–2220
Morris JE, Cizmár T, Dalgarno HIC et al (2010) Realization of curved Bessel beams: propagation around obstructions. J Opt 12:124002
Jarutis V, Matijosius A, Trapani PD et al (2009) Spiraling zero-order Bessel beam. Opt Lett 34:2129–2131
Rosen J, Yariv A (1995) Snake beam: a paraxial arbitrary focal line. Opt Lett 20:2042–2044
Chremmos ID, Chen Z, Christodoulides DN et al (2012) Bessel-like optical beams with arbitrary trajectories. Opt Lett 37:5003–5005
Zhao J, Zhang P, Deng D et al (2013) Observation of self-accelerating Bessel-like optical beams along arbitrary trajectories. Opt Lett 38:498–500
Chremmos ID, Zhao JY, Christodoulides DN et al (2014) Diffraction-resisting vortex Bessel beams with arbitrary trajectories. In: Conference on lasers and electro-optics: quantum electronics and laser science (QELS_fundamental science), Optical Society of America Technical Digest (online), San Jose, CA USA, p FM3D.1
Zhao JY, Zhang P, Liu JJ et al (2013) Trap** and guiding microparticles with self-accelerating vortex beams. In: Conference on lasers and electro-optics: science and innovations, Optical Society of America Technical Digest (online), San Jose, CA USA, p CM1 M.6
Zhao JY, Zhang P, Deng D et al (2013) Self-accelerating and self-breathing Bessel-like beams along arbitrary trajectories. Chin Opt Lett 11:110701
Deng HC, Yuan LB (2013) Two-dimensional Airy-like beam generation by coupling waveguides. J Opt Soc Am A: 30:1404–1408
Jiang YF, Huang KK, Lu XH (2012) Airy-related beam generated from flat-topped Gaussian beams. J Opt Soc Am A: 29:1412–1416
Zhang YQ, Belić MR, Zheng HB et al (2013) Fresnel diffraction patterns as accelerating beams. Europhys Lett 104:34007
Zhang YQ, Belić MR, Zheng HB et al (2014) Three-dimensional nonparaxial accelerating beams from the transverse Whittaker integral. Europhys Lett 107:34001
Chremmos ID, Efremidis NK (2013) Nonparaxial accelerating Bessel-like beams. Phys Rev A 88:063816
Ren ZJ, Wu Q, Shi YL et al (2014) Production of accelerating quad Airy beams and their optical characteristics. Opt Express 22:15154–15164
Hu Y, Bongiovanni D, Chen ZG et al (2013) Periodic self-accelerating beams by combined phase and amplitude modulation in the Fourier space. Opt Lett 38:3387–3389
Efremidis NK, Christodoulides DN (2010) Abruptly autofocusing waves. Opt Lett 35:4045–4047
Chremmos I, Efremidis NK, Christodoulides DN (2011) Pre-engineered abruptly autofocusing beams. Opt Lett 36:1890–1892
Allen L, Beijersbergen MW, Spreeuw RJC et al (1992) Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes. Phys Rev A 45:8185–8189
Zhou GQ, Wang XG, Dai CQ et al (2014) Angular momentum density of a Gaussian vortex beam. Sci China Phys Mech Astron 57:619–627
Zhou GQ, Cai YJ, Dai CQ (2013) Hollow vortex Gaussian beams. Sci China Phys Mech Astron 56:896–903
Zhou GQ, Wang XG, Chu XX (2013) Fractional Fourier transform of Lorentz–Gauss vortex beams. Sci China Phys Mech Astron 56:1487–1494
Dai HT, Liu YJ, Luo D et al (2010) Propagation dynamics of an optical vortex imposed on an Airy beam. Opt Lett 35:4075–4077
O’Neil AT, Padgett MJ (2002) Rotational control within optical tweezers by use of a rotating aperture. Opt Lett 27:743–745
Madison KW, Chevy F, Wohlleben W et al (2000) Vortex formation in a stirred Bose–Einstein condensate. Phys Rev Lett 84:806–809
Sasaki K, Koshioka M, Misawa H et al (1992) Optical trap** of a metal particle and a water droplet by a scanning laser beam. Appl Phys Lett 60:807–809
Paterson L, MacDonald MP, Arlt J et al (2001) Controlled rotation of optically trapped microscopic particles. Science 292:912–914
Rotschild C, Saraf M, Barak A et al (2008) Complex nonlinear opto-fluidity. In: Frontiers in optics, Optical Society of America Technical Digest (CD), Rochester, USA, p FME2
Anastassiou C, Pigier C, Segev MC et al (2001) Self-trap** of bright rings. Opt Lett 26:911–913
Zhang P, Huang S, Hu Y et al (2010) Generation and nonlinear self-trap** of optical propelling beams. Opt Lett 35:3129–3131
Zhang P, Hernandez D, Cannan D et al (2012) Trap** and rotating microparticles and bacteria with moiré-based optical propelling beams. Biomed Opt Express 3:1891–1897
Deng D, Gao Y, Zhao J et al (2013) Three-dimensional nonparaxial beams in parabolic rotational coordinates. Opt Lett 38:3934–3936
Gong L, Ren YX, Xue GS et al (2013) Generation of nondiffracting Bessel beam using digital micromirror device. Appl Opt 52:4566–4575
Ornigotti M, Aiello A (2014) Generalized Bessel beams with two indices. Opt Lett 39:5618–5621
Wang F, Zhao C, Dong Y et al (2014) Generation and tight-focusing properties of cylindrical vector circular Airy beams. Appl Phys B 117:905–913
Zhu WG, She WL (2014) Improved nonparaxial accelerating beams due to additional off-axis spiral phases. J Opt Soc Am A 31:2365–2369
Liu ZH, Zhang YX, Zhang Y et al (2014) All-fiber self-accelerating Bessel-like beam generator and its application. Opt Lett 39:6185–6188
Huang C, Lu H (2014) Accelerating propagation properties of misplaced Hermite–Gaussian beams. J Opt Soc Am A 31:1762–1765
Liu X, Zhao D (2014) Optical trap** Rayleigh particles by using focused multi-Gaussian Schell-model beams. Appl Opt 53:3976–3981
Vetter C, Eichelkraut T, Ornigotti M et al (2014) Generalized radially self-accelerating Helicon beams. Phys Rev Lett 113:183901
Schley R, Kaminer I, Greenfield E et al (2014) Loss-proof self-accelerating beams and their use in non-paraxial manipulation of particles’ trajectories. Nat Commun 5:5189
Acknowledgments
This work was supported by the National Natural Science Foundation of China (61475161 and 11304165), China Scholarship Council, and Natural Science Foundation (NSF) and Air Force Office of Scientific Research (AFOSR) in USA.
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The authors declare that they have no conflict of interest.
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Zhao, J., Chremmos, I.D., Zhang, Z. et al. Specially shaped Bessel-like self-accelerating beams along predesigned trajectories. Sci. Bull. 60, 1157–1169 (2015). https://doi.org/10.1007/s11434-015-0792-1
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DOI: https://doi.org/10.1007/s11434-015-0792-1