Abstract

We report a novel method to freely transform the modes of a perfect optical vortex (POV). By adjusting the scaling factor of the Bessel–Gauss beam at the object plane, the POV mode transformation can be easily controlled from circle to ellipse with a high mode purity. Combined with the modulation of the cone angle of an axicon, the ellipse mode can be freely adjusted along the two orthogonal directions. The properties of the “perfect vortex” are experimentally verified. Moreover, fractional elliptic POVs with versatile modes are presented, where the number and position of the gaps are controllable. These findings are significant for applications that require the complex structured optical field of the POV.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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2017 (8)

B. Ndagano, B. Perez-Garcia, F. S. Roux, M. McLaren, C. Rosales-Guzman, Y. Zhang, O. Mouane, R. I. Hernandez-Aranda, T. Konrad, and A. Forbes, “Characterizing quantum channels with non-separable states of classical light,” Nat. Phys. 13(4), 397–402 (2017).
[Crossref]

P. Figliozzi, N. Sule, Z. Yan, Y. Bao, S. Burov, S. K. Gray, S. A. Rice, S. Vaikuntanathan, and N. F. Scherer, “Driven optical matter: Dynamics of electrodynamically coupled nanoparticles in an optical ring vortex,” Phys Rev E 95(2), 022604 (2017).
[Crossref] [PubMed]

A. Aleksanyan, N. Kravets, and E. Brasselet, “Multiple-Star System Adaptive Vortex Coronagraphy Using a Liquid Crystal Light Valve,” Phys. Rev. Lett. 118(20), 203902 (2017).
[Crossref] [PubMed]

H. Ma, X. Li, Y. Tai, H. Li, J. Wang, M. Tang, Y. Wang, J. Tang, and Z. Nie, “In situ measurement of the topological charge of a perfect vortex using the phase shift method,” Opt. Lett. 42(1), 135–138 (2017).
[Crossref] [PubMed]

X. Weng, L. Du, P. Shi, and X. Yuan, “Tunable optical cage array generated by Dammann vector beam,” Opt. Express 25(8), 9039–9048 (2017).
[Crossref] [PubMed]

G. Tkachenko, M. Chen, K. Dholakia, and M. Mazilu, “Is it possible to create a perfect fractional vortex beam?” Optica 4(3), 330–333 (2017).
[Crossref]

A. A. Kovalev, V. V. Kotlyar, and A. P. Porfirev, “A highly efficient element for generating elliptic perfect optical vortices,” Appl. Phys. Lett. 110(26), 261102 (2017).
[Crossref]

V. V. Kotlyar, A. A. Kovalev, and A. P. Porfirev, “Asymmetric Gaussian optical vortex,” Opt. Lett. 42(1), 139–142 (2017).
[Crossref] [PubMed]

2016 (8)

A. A. Kovalev, V. V. Kotlyar, and A. P. Porfirev, “Optical trapping and moving of microparticles by using asymmetrical Laguerre-Gaussian beams,” Opt. Lett. 41(11), 2426–2429 (2016).
[Crossref] [PubMed]

D. Deng, Y. Li, Y. Han, X. Su, J. Ye, J. Gao, Q. Sun, and S. Qu, “Perfect vortex in three-dimensional multifocal array,” Opt. Express 24(25), 28270–28278 (2016).
[Crossref] [PubMed]

S. Fu, T. Wang, and C. Gao, “Perfect optical vortex array with controllable diffraction order and topological charge,” J. Opt. Soc. Am. A 33(9), 1836–1842 (2016).
[Crossref] [PubMed]

C. Zhang, C. Min, L. Du, and X. C. Yuan, “Perfect optical vortex enhanced surface plasmon excitation for plasmonic structured illumination microscopy imaging,” Appl. Phys. Lett. 108(20), 201601 (2016).
[Crossref]

S. Fu, T. Wang, Y. Gao, and C. Gao, “Diagnostics of the topological charge of optical vortex by a phase-diffractive element,” Chin. Opt. Lett. 14(8), 080501 (2016).
[Crossref]

J. Xin, X. Lou, Z. Zhou, M. Dong, and L. Zhu, “Generation of polarization vortex beams by segmented quarter-wave plates,” Chin. Opt. Lett. 14(7), 070501 (2016).
[Crossref]

V. V. Kotlyar, A. A. Kovalev, and A. P. Porfirev, “Optimal phase element for generating a perfect optical vortex,” J. Opt. Soc. Am. A 33(12), 2376–2384 (2016).
[Crossref] [PubMed]

P. Li, Y. Zhang, S. Liu, C. Ma, L. Han, H. Cheng, and J. Zhao, “Generation of perfect vectorial vortex beams,” Opt. Lett. 41(10), 2205–2208 (2016).
[Crossref] [PubMed]

2015 (2)

2014 (5)

2013 (5)

N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, “Terabit-Scale Orbital Angular Momentum Mode Division Multiplexing in Fibers,” Science 340(6140), 1545–1548 (2013).
[Crossref] [PubMed]

S. Li and J. Wang, “Multi-orbital-angular-momentum multi-ring fiber for high-density space-division multiplexing,” IEEE Photonics J. 5(5), 7101007 (2013).
[Crossref]

A. S. Ostrovsky, C. Rickenstorff-Parrao, and V. Arrizón, “Generation of the “perfect” optical vortex using a liquid-crystal spatial light modulator,” Opt. Lett. 38(4), 534–536 (2013).
[Crossref] [PubMed]

M. Woerdemann, C. Alpmann, M. Esseling, and C. Denz, “Advanced optical trapping by complex beam shaping,” Laser Photonics Rev. 7(6), 839–854 (2013).
[Crossref]

M. Chen, M. Mazilu, Y. Arita, E. M. Wright, and K. Dholakia, “Dynamics of microparticles trapped in a perfect vortex beam,” Opt. Lett. 38(22), 4919–4922 (2013).
[Crossref] [PubMed]

2012 (2)

2011 (1)

M. Padgett and R. Bowman, “Tweezers with a twist,” Nat. Photonics 5(6), 343–348 (2011).
[Crossref]

2010 (2)

2009 (1)

2008 (1)

2007 (2)

2006 (1)

2004 (1)

M. V. Berry, “Optical vortices evolving from helicoidal integer and fractional phase steps,” J. Opt. A, Pure Appl. Opt. 6(2), 259–268 (2004).
[Crossref]

2003 (1)

M. P. MacDonald, G. C. Spalding, and K. Dholakia, “Microfluidic sorting in an optical lattice,” Nature 426(6965), 421–424 (2003).
[Crossref] [PubMed]

Aleksanyan, A.

A. Aleksanyan, N. Kravets, and E. Brasselet, “Multiple-Star System Adaptive Vortex Coronagraphy Using a Liquid Crystal Light Valve,” Phys. Rev. Lett. 118(20), 203902 (2017).
[Crossref] [PubMed]

Alpmann, C.

M. Woerdemann, C. Alpmann, M. Esseling, and C. Denz, “Advanced optical trapping by complex beam shaping,” Laser Photonics Rev. 7(6), 839–854 (2013).
[Crossref]

Ando, T.

Arita, Y.

Arrizón, V.

Bao, Y.

P. Figliozzi, N. Sule, Z. Yan, Y. Bao, S. Burov, S. K. Gray, S. A. Rice, S. Vaikuntanathan, and N. F. Scherer, “Driven optical matter: Dynamics of electrodynamically coupled nanoparticles in an optical ring vortex,” Phys Rev E 95(2), 022604 (2017).
[Crossref] [PubMed]

Berry, M. V.

M. V. Berry, “Optical vortices evolving from helicoidal integer and fractional phase steps,” J. Opt. A, Pure Appl. Opt. 6(2), 259–268 (2004).
[Crossref]

Bowman, R.

M. Padgett and R. Bowman, “Tweezers with a twist,” Nat. Photonics 5(6), 343–348 (2011).
[Crossref]

Bozinovic, N.

N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, “Terabit-Scale Orbital Angular Momentum Mode Division Multiplexing in Fibers,” Science 340(6140), 1545–1548 (2013).
[Crossref] [PubMed]

Brasselet, E.

A. Aleksanyan, N. Kravets, and E. Brasselet, “Multiple-Star System Adaptive Vortex Coronagraphy Using a Liquid Crystal Light Valve,” Phys. Rev. Lett. 118(20), 203902 (2017).
[Crossref] [PubMed]

Burov, S.

P. Figliozzi, N. Sule, Z. Yan, Y. Bao, S. Burov, S. K. Gray, S. A. Rice, S. Vaikuntanathan, and N. F. Scherer, “Driven optical matter: Dynamics of electrodynamically coupled nanoparticles in an optical ring vortex,” Phys Rev E 95(2), 022604 (2017).
[Crossref] [PubMed]

Cai, Y.

Chan, C. T.

J. Ng, Z. Lin, and C. T. Chan, “Theory of optical trapping by an optical vortex beam,” Phys. Rev. Lett. 104(10), 103601 (2010).
[Crossref] [PubMed]

Chen, M.

Chen, Y.

Cheng, H.

Cottrell, D. M.

Davis, J. A.

Deng, D.

Denz, C.

M. Woerdemann, C. Alpmann, M. Esseling, and C. Denz, “Advanced optical trapping by complex beam shaping,” Laser Photonics Rev. 7(6), 839–854 (2013).
[Crossref]

Dholakia, K.

Dong, M.

Du, L.

X. Weng, L. Du, P. Shi, and X. Yuan, “Tunable optical cage array generated by Dammann vector beam,” Opt. Express 25(8), 9039–9048 (2017).
[Crossref] [PubMed]

C. Zhang, C. Min, L. Du, and X. C. Yuan, “Perfect optical vortex enhanced surface plasmon excitation for plasmonic structured illumination microscopy imaging,” Appl. Phys. Lett. 108(20), 201601 (2016).
[Crossref]

Duan, K.

Esseling, M.

M. Woerdemann, C. Alpmann, M. Esseling, and C. Denz, “Advanced optical trapping by complex beam shaping,” Laser Photonics Rev. 7(6), 839–854 (2013).
[Crossref]

Figliozzi, P.

P. Figliozzi, N. Sule, Z. Yan, Y. Bao, S. Burov, S. K. Gray, S. A. Rice, S. Vaikuntanathan, and N. F. Scherer, “Driven optical matter: Dynamics of electrodynamically coupled nanoparticles in an optical ring vortex,” Phys Rev E 95(2), 022604 (2017).
[Crossref] [PubMed]

Forbes, A.

B. Ndagano, B. Perez-Garcia, F. S. Roux, M. McLaren, C. Rosales-Guzman, Y. Zhang, O. Mouane, R. I. Hernandez-Aranda, T. Konrad, and A. Forbes, “Characterizing quantum channels with non-separable states of classical light,” Nat. Phys. 13(4), 397–402 (2017).
[Crossref]

Fu, S.

Fukuchi, N.

Gao, C.

Gao, J.

Gao, Y.

García-García, J.

Gray, S. K.

P. Figliozzi, N. Sule, Z. Yan, Y. Bao, S. Burov, S. K. Gray, S. A. Rice, S. Vaikuntanathan, and N. F. Scherer, “Driven optical matter: Dynamics of electrodynamically coupled nanoparticles in an optical ring vortex,” Phys Rev E 95(2), 022604 (2017).
[Crossref] [PubMed]

Gutiérrez-Vega, J. C.

Han, L.

Han, Y.

Hara, T.

Hernandez-Aranda, R. I.

B. Ndagano, B. Perez-Garcia, F. S. Roux, M. McLaren, C. Rosales-Guzman, Y. Zhang, O. Mouane, R. I. Hernandez-Aranda, T. Konrad, and A. Forbes, “Characterizing quantum channels with non-separable states of classical light,” Nat. Phys. 13(4), 397–402 (2017).
[Crossref]

Huang, H.

N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, “Terabit-Scale Orbital Angular Momentum Mode Division Multiplexing in Fibers,” Science 340(6140), 1545–1548 (2013).
[Crossref] [PubMed]

Inoue, T.

Ito, H.

Jia, W.

Konrad, T.

B. Ndagano, B. Perez-Garcia, F. S. Roux, M. McLaren, C. Rosales-Guzman, Y. Zhang, O. Mouane, R. I. Hernandez-Aranda, T. Konrad, and A. Forbes, “Characterizing quantum channels with non-separable states of classical light,” Nat. Phys. 13(4), 397–402 (2017).
[Crossref]

Kotlyar, V. V.

Kovalev, A. A.

Kravets, N.

A. Aleksanyan, N. Kravets, and E. Brasselet, “Multiple-Star System Adaptive Vortex Coronagraphy Using a Liquid Crystal Light Valve,” Phys. Rev. Lett. 118(20), 203902 (2017).
[Crossref] [PubMed]

Kristensen, P.

N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, “Terabit-Scale Orbital Angular Momentum Mode Division Multiplexing in Fibers,” Science 340(6140), 1545–1548 (2013).
[Crossref] [PubMed]

Li, H.

H. Ma, X. Li, Y. Tai, H. Li, J. Wang, M. Tang, Y. Wang, J. Tang, and Z. Nie, “In situ measurement of the topological charge of a perfect vortex using the phase shift method,” Opt. Lett. 42(1), 135–138 (2017).
[Crossref] [PubMed]

X. Li, Y. Tai, L. Zhang, H. Li, and L. Li, “Characterization of dynamic random process using optical vortex metrology,” Appl. Phys. B 116(4), 901–909 (2014).
[Crossref]

Li, L.

X. Li, Y. Tai, L. Zhang, H. Li, and L. Li, “Characterization of dynamic random process using optical vortex metrology,” Appl. Phys. B 116(4), 901–909 (2014).
[Crossref]

Li, P.

Li, S.

S. Li and J. Wang, “Multi-orbital-angular-momentum multi-ring fiber for high-density space-division multiplexing,” IEEE Photonics J. 5(5), 7101007 (2013).
[Crossref]

Li, T.

P. Zhang, T. Li, J. Zhu, X. Zhu, S. Yang, Y. Wang, X. Yin, and X. Zhang, “Generation of acoustic self-bending and bottle beams by phase engineering,” Nat. Commun. 5, 4316 (2014).
[PubMed]

Li, X.

H. Ma, X. Li, Y. Tai, H. Li, J. Wang, M. Tang, Y. Wang, J. Tang, and Z. Nie, “In situ measurement of the topological charge of a perfect vortex using the phase shift method,” Opt. Lett. 42(1), 135–138 (2017).
[Crossref] [PubMed]

X. Li, Y. Tai, L. Zhang, H. Li, and L. Li, “Characterization of dynamic random process using optical vortex metrology,” Appl. Phys. B 116(4), 901–909 (2014).
[Crossref]

X. Li, Y. Tai, and Z. Nie, “Digital speckle correlation method based on phase vortices,” Opt. Eng. 51(7), 077004 (2012).
[Crossref]

Li, Y.

Lin, J.

Lin, Z.

J. Ng, Z. Lin, and C. T. Chan, “Theory of optical trapping by an optical vortex beam,” Phys. Rev. Lett. 104(10), 103601 (2010).
[Crossref] [PubMed]

Liu, L.

Liu, S.

López-Mariscal, C.

Lou, X.

Lu, Y.

Ma, C.

Ma, H.

MacDonald, M. P.

M. P. MacDonald, G. C. Spalding, and K. Dholakia, “Microfluidic sorting in an optical lattice,” Nature 426(6965), 421–424 (2003).
[Crossref] [PubMed]

Matsumoto, N.

Mazilu, M.

McLaren, M.

B. Ndagano, B. Perez-Garcia, F. S. Roux, M. McLaren, C. Rosales-Guzman, Y. Zhang, O. Mouane, R. I. Hernandez-Aranda, T. Konrad, and A. Forbes, “Characterizing quantum channels with non-separable states of classical light,” Nat. Phys. 13(4), 397–402 (2017).
[Crossref]

Milne, G.

Min, C.

C. Zhang, C. Min, L. Du, and X. C. Yuan, “Perfect optical vortex enhanced surface plasmon excitation for plasmonic structured illumination microscopy imaging,” Appl. Phys. Lett. 108(20), 201601 (2016).
[Crossref]

Moh, K. J.

Molina-Terriza, G.

G. Molina-Terriza, J. P. Torres, and L. Torner, “Twisted photons,” Nat. Phys. 3(5), 305–310 (2007).
[Crossref]

Moreno, I.

Mouane, O.

B. Ndagano, B. Perez-Garcia, F. S. Roux, M. McLaren, C. Rosales-Guzman, Y. Zhang, O. Mouane, R. I. Hernandez-Aranda, T. Konrad, and A. Forbes, “Characterizing quantum channels with non-separable states of classical light,” Nat. Phys. 13(4), 397–402 (2017).
[Crossref]

Ndagano, B.

B. Ndagano, B. Perez-Garcia, F. S. Roux, M. McLaren, C. Rosales-Guzman, Y. Zhang, O. Mouane, R. I. Hernandez-Aranda, T. Konrad, and A. Forbes, “Characterizing quantum channels with non-separable states of classical light,” Nat. Phys. 13(4), 397–402 (2017).
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J. Ng, Z. Lin, and C. T. Chan, “Theory of optical trapping by an optical vortex beam,” Phys. Rev. Lett. 104(10), 103601 (2010).
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Ohtake, Y.

Ostrovsky, A. S.

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M. Padgett and R. Bowman, “Tweezers with a twist,” Nat. Photonics 5(6), 343–348 (2011).
[Crossref]

Perez-Garcia, B.

B. Ndagano, B. Perez-Garcia, F. S. Roux, M. McLaren, C. Rosales-Guzman, Y. Zhang, O. Mouane, R. I. Hernandez-Aranda, T. Konrad, and A. Forbes, “Characterizing quantum channels with non-separable states of classical light,” Nat. Phys. 13(4), 397–402 (2017).
[Crossref]

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Qu, S.

Ramachandran, S.

N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, “Terabit-Scale Orbital Angular Momentum Mode Division Multiplexing in Fibers,” Science 340(6140), 1545–1548 (2013).
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Ren, Y.

N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, “Terabit-Scale Orbital Angular Momentum Mode Division Multiplexing in Fibers,” Science 340(6140), 1545–1548 (2013).
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P. Figliozzi, N. Sule, Z. Yan, Y. Bao, S. Burov, S. K. Gray, S. A. Rice, S. Vaikuntanathan, and N. F. Scherer, “Driven optical matter: Dynamics of electrodynamically coupled nanoparticles in an optical ring vortex,” Phys Rev E 95(2), 022604 (2017).
[Crossref] [PubMed]

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Rosales-Guzman, C.

B. Ndagano, B. Perez-Garcia, F. S. Roux, M. McLaren, C. Rosales-Guzman, Y. Zhang, O. Mouane, R. I. Hernandez-Aranda, T. Konrad, and A. Forbes, “Characterizing quantum channels with non-separable states of classical light,” Nat. Phys. 13(4), 397–402 (2017).
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B. Ndagano, B. Perez-Garcia, F. S. Roux, M. McLaren, C. Rosales-Guzman, Y. Zhang, O. Mouane, R. I. Hernandez-Aranda, T. Konrad, and A. Forbes, “Characterizing quantum channels with non-separable states of classical light,” Nat. Phys. 13(4), 397–402 (2017).
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Rusch, L.

Scherer, N. F.

P. Figliozzi, N. Sule, Z. Yan, Y. Bao, S. Burov, S. K. Gray, S. A. Rice, S. Vaikuntanathan, and N. F. Scherer, “Driven optical matter: Dynamics of electrodynamically coupled nanoparticles in an optical ring vortex,” Phys Rev E 95(2), 022604 (2017).
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Spalding, G. C.

M. P. MacDonald, G. C. Spalding, and K. Dholakia, “Microfluidic sorting in an optical lattice,” Nature 426(6965), 421–424 (2003).
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Sule, N.

P. Figliozzi, N. Sule, Z. Yan, Y. Bao, S. Burov, S. K. Gray, S. A. Rice, S. Vaikuntanathan, and N. F. Scherer, “Driven optical matter: Dynamics of electrodynamically coupled nanoparticles in an optical ring vortex,” Phys Rev E 95(2), 022604 (2017).
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Tai, Y.

H. Ma, X. Li, Y. Tai, H. Li, J. Wang, M. Tang, Y. Wang, J. Tang, and Z. Nie, “In situ measurement of the topological charge of a perfect vortex using the phase shift method,” Opt. Lett. 42(1), 135–138 (2017).
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X. Li, Y. Tai, and Z. Nie, “Digital speckle correlation method based on phase vortices,” Opt. Eng. 51(7), 077004 (2012).
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Tang, M.

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G. Molina-Terriza, J. P. Torres, and L. Torner, “Twisted photons,” Nat. Phys. 3(5), 305–310 (2007).
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N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, “Terabit-Scale Orbital Angular Momentum Mode Division Multiplexing in Fibers,” Science 340(6140), 1545–1548 (2013).
[Crossref] [PubMed]

Vaikuntanathan, S.

P. Figliozzi, N. Sule, Z. Yan, Y. Bao, S. Burov, S. K. Gray, S. A. Rice, S. Vaikuntanathan, and N. F. Scherer, “Driven optical matter: Dynamics of electrodynamically coupled nanoparticles in an optical ring vortex,” Phys Rev E 95(2), 022604 (2017).
[Crossref] [PubMed]

Vaity, P.

Wang, F.

Wang, J.

Wang, T.

Wang, Y.

H. Ma, X. Li, Y. Tai, H. Li, J. Wang, M. Tang, Y. Wang, J. Tang, and Z. Nie, “In situ measurement of the topological charge of a perfect vortex using the phase shift method,” Opt. Lett. 42(1), 135–138 (2017).
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P. Zhang, T. Li, J. Zhu, X. Zhu, S. Yang, Y. Wang, X. Yin, and X. Zhang, “Generation of acoustic self-bending and bottle beams by phase engineering,” Nat. Commun. 5, 4316 (2014).
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Weng, X.

Willner, A. E.

N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, “Terabit-Scale Orbital Angular Momentum Mode Division Multiplexing in Fibers,” Science 340(6140), 1545–1548 (2013).
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M. Woerdemann, C. Alpmann, M. Esseling, and C. Denz, “Advanced optical trapping by complex beam shaping,” Laser Photonics Rev. 7(6), 839–854 (2013).
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P. Figliozzi, N. Sule, Z. Yan, Y. Bao, S. Burov, S. K. Gray, S. A. Rice, S. Vaikuntanathan, and N. F. Scherer, “Driven optical matter: Dynamics of electrodynamically coupled nanoparticles in an optical ring vortex,” Phys Rev E 95(2), 022604 (2017).
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Yang, S.

P. Zhang, T. Li, J. Zhu, X. Zhu, S. Yang, Y. Wang, X. Yin, and X. Zhang, “Generation of acoustic self-bending and bottle beams by phase engineering,” Nat. Commun. 5, 4316 (2014).
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Yin, X.

P. Zhang, T. Li, J. Zhu, X. Zhu, S. Yang, Y. Wang, X. Yin, and X. Zhang, “Generation of acoustic self-bending and bottle beams by phase engineering,” Nat. Commun. 5, 4316 (2014).
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Yuan, X.

Yuan, X. C.

C. Zhang, C. Min, L. Du, and X. C. Yuan, “Perfect optical vortex enhanced surface plasmon excitation for plasmonic structured illumination microscopy imaging,” Appl. Phys. Lett. 108(20), 201601 (2016).
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N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, “Terabit-Scale Orbital Angular Momentum Mode Division Multiplexing in Fibers,” Science 340(6140), 1545–1548 (2013).
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Zhang, C.

C. Zhang, C. Min, L. Du, and X. C. Yuan, “Perfect optical vortex enhanced surface plasmon excitation for plasmonic structured illumination microscopy imaging,” Appl. Phys. Lett. 108(20), 201601 (2016).
[Crossref]

Zhang, E.

Zhang, L.

X. Li, Y. Tai, L. Zhang, H. Li, and L. Li, “Characterization of dynamic random process using optical vortex metrology,” Appl. Phys. B 116(4), 901–909 (2014).
[Crossref]

Zhang, N.

Zhang, P.

P. Zhang, T. Li, J. Zhu, X. Zhu, S. Yang, Y. Wang, X. Yin, and X. Zhang, “Generation of acoustic self-bending and bottle beams by phase engineering,” Nat. Commun. 5, 4316 (2014).
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Zhang, X.

P. Zhang, T. Li, J. Zhu, X. Zhu, S. Yang, Y. Wang, X. Yin, and X. Zhang, “Generation of acoustic self-bending and bottle beams by phase engineering,” Nat. Commun. 5, 4316 (2014).
[PubMed]

Zhang, Y.

B. Ndagano, B. Perez-Garcia, F. S. Roux, M. McLaren, C. Rosales-Guzman, Y. Zhang, O. Mouane, R. I. Hernandez-Aranda, T. Konrad, and A. Forbes, “Characterizing quantum channels with non-separable states of classical light,” Nat. Phys. 13(4), 397–402 (2017).
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P. Li, Y. Zhang, S. Liu, C. Ma, L. Han, H. Cheng, and J. Zhao, “Generation of perfect vectorial vortex beams,” Opt. Lett. 41(10), 2205–2208 (2016).
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Zhao, B.

Zhao, C.

Zhao, J.

Zhou, C.

Zhou, Z.

Zhu, J.

P. Zhang, T. Li, J. Zhu, X. Zhu, S. Yang, Y. Wang, X. Yin, and X. Zhang, “Generation of acoustic self-bending and bottle beams by phase engineering,” Nat. Commun. 5, 4316 (2014).
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Zhu, L.

Zhu, X.

P. Zhang, T. Li, J. Zhu, X. Zhu, S. Yang, Y. Wang, X. Yin, and X. Zhang, “Generation of acoustic self-bending and bottle beams by phase engineering,” Nat. Commun. 5, 4316 (2014).
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Appl. Opt. (1)

Appl. Phys. B (1)

X. Li, Y. Tai, L. Zhang, H. Li, and L. Li, “Characterization of dynamic random process using optical vortex metrology,” Appl. Phys. B 116(4), 901–909 (2014).
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C. Zhang, C. Min, L. Du, and X. C. Yuan, “Perfect optical vortex enhanced surface plasmon excitation for plasmonic structured illumination microscopy imaging,” Appl. Phys. Lett. 108(20), 201601 (2016).
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A. A. Kovalev, V. V. Kotlyar, and A. P. Porfirev, “A highly efficient element for generating elliptic perfect optical vortices,” Appl. Phys. Lett. 110(26), 261102 (2017).
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M. Woerdemann, C. Alpmann, M. Esseling, and C. Denz, “Advanced optical trapping by complex beam shaping,” Laser Photonics Rev. 7(6), 839–854 (2013).
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Nat. Commun. (1)

P. Zhang, T. Li, J. Zhu, X. Zhu, S. Yang, Y. Wang, X. Yin, and X. Zhang, “Generation of acoustic self-bending and bottle beams by phase engineering,” Nat. Commun. 5, 4316 (2014).
[PubMed]

Nat. Photonics (1)

M. Padgett and R. Bowman, “Tweezers with a twist,” Nat. Photonics 5(6), 343–348 (2011).
[Crossref]

Nat. Phys. (2)

G. Molina-Terriza, J. P. Torres, and L. Torner, “Twisted photons,” Nat. Phys. 3(5), 305–310 (2007).
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B. Ndagano, B. Perez-Garcia, F. S. Roux, M. McLaren, C. Rosales-Guzman, Y. Zhang, O. Mouane, R. I. Hernandez-Aranda, T. Konrad, and A. Forbes, “Characterizing quantum channels with non-separable states of classical light,” Nat. Phys. 13(4), 397–402 (2017).
[Crossref]

Nature (1)

M. P. MacDonald, G. C. Spalding, and K. Dholakia, “Microfluidic sorting in an optical lattice,” Nature 426(6965), 421–424 (2003).
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Opt. Eng. (1)

X. Li, Y. Tai, and Z. Nie, “Digital speckle correlation method based on phase vortices,” Opt. Eng. 51(7), 077004 (2012).
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Opt. Express (5)

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J. Yu, C. Zhou, Y. Lu, J. Wu, L. Zhu, and W. Jia, “Square lattices of quasi-perfect optical vortices generated by two-dimensional encoding continuous-phase gratings,” Opt. Lett. 40(11), 2513–2516 (2015).
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Optica (1)

Phys Rev E (1)

P. Figliozzi, N. Sule, Z. Yan, Y. Bao, S. Burov, S. K. Gray, S. A. Rice, S. Vaikuntanathan, and N. F. Scherer, “Driven optical matter: Dynamics of electrodynamically coupled nanoparticles in an optical ring vortex,” Phys Rev E 95(2), 022604 (2017).
[Crossref] [PubMed]

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J. Ng, Z. Lin, and C. T. Chan, “Theory of optical trapping by an optical vortex beam,” Phys. Rev. Lett. 104(10), 103601 (2010).
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Science (1)

N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, “Terabit-Scale Orbital Angular Momentum Mode Division Multiplexing in Fibers,” Science 340(6140), 1545–1548 (2013).
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K. O’Holleran, “Fractality and topology of optical singularities,” (University of Glasgow, 2008).

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Supplementary Material (2)

NameDescription
» Visualization 1       Modes transformation of the EPOV modulated by the scaling factor m.
» Visualization 2       Multi-modes transformation of a fractional EPOV.

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Figures (10)

Fig. 1
Fig. 1 Schematic of the experimental setup.
Fig. 2
Fig. 2 Generation of the phase mask. (a) Spiral phase, (b) phase pattern of the axicon, (c) blazed grating, (d) elliptic aperture, (e) phase mask pattern, and (f) checkerboard pattern.
Fig. 3
Fig. 3 Modes transformation of the EPOV modulated by the scaling factor m. For the detailed transformation process see Visualization 1.
Fig. 4
Fig. 4 Cross-sections of the mode patterns (dots) of Fig. 3 and their fitting curves (solid curves).
Fig. 5
Fig. 5 Intensity patterns of an EPOV for different TCs. In the upper and lower panels, m = 0.5 and m = 2, respectively.
Fig. 6
Fig. 6 Interference patterns between the EPOV in Fig. 5 and their conjugate beams, which verify the existence of a vortex.
Fig. 7
Fig. 7 Fixing axis modulation of the EPOV by adjusting the cone angle of the axicon.
Fig. 8
Fig. 8 Fractional EPOV modes with different gap positions.
Fig. 9
Fig. 9 Multi-modes transformation of a fractional EPOV. Upper two panels: modulation of gap locations and corresponding spiral phase patterns (See Visualization 2). Lower two panels: multi-gaps and their spiral phase design.
Fig. 10
Fig. 10 Fourier spectrum components of the fractional optical vortices with different multi-gaps. (a). l = 1; (b). l' = 1.5, N = 1; (c). l' = 1.5, N = 2; (d). l' = 1.5, N = 3; (e). l' = 1.5, N = 4; (f). l' = 1.5, N = 5.

Tables (1)

Tables Icon

Table 1 Properties of four types of fractional EPOV under different coordinate transformations.

Equations (10)

Equations on this page are rendered with MathJax. Learn more.

F(ρ,φ)= J l ( k ρ ρ)exp(ilφ)exp( ρ 2 ω g 2 )
E(r,θ)= ω g i l1 ω 0 exp(ilθ)exp( (rR) 2 ω 0 2 )
E(u,v)= k i2πf + F(x,y)exp( i k f (ux+vy) ) dxdy
E(r,θ)= k i2πf F(ρ,φ) exp( i k f ρr m cos(θφ) ) ρ m dρdφ
E(r,θ)= ω g i l1 ω m exp(ilθ)exp( (rR) 2 ω m 2 ), ω m =m ω 0
u 2 r 2 + v 2 r 2 / m 2 =1
t(ρ,φ)=circ(ρ)exp[ ik(n1)αρ+ilφ+ i2πρcosφ mD ]
F v = n =1 N { step[ φ 2π( N1 ) N ]exp( i l φ ) }
φ =rem[ φ+ 2π( n 1 ) N ,2π ]
F v = l= + c l exp[ il( φ+ φ 0 ) ] = l= + exp[ 2πi( l l )/N ]1 2πi( l l ) n =1 N exp{ il[ φ+ 2π( n 1 ) N ] }

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