Abstract

We propose a new type of noncanonical optical vortex, named “power-exponent-phase vortex (PEPV)”. The spiral focusing of the autofocusing Airy beams carrying PEPVs are experimentally demonstrated, and the physical mechanism is theoretically analyzed by using the energy flow and far field mapping. In addition, the influences of the parameters of PEPVs on the focal fields and orbital angular momenta are also discussed. It is expected that the proposed PEPVs and the corresponding conclusions can be useful for the extension applications of optical vortices, especially for particle trapping and rotating.

© 2014 Optical Society of America

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  1. N. K. Efremidis, D. N. Christodoulides, “Abruptly autofocusing waves,” Opt. Lett. 35(23), 4045–4047 (2010).
    [CrossRef] [PubMed]
  2. I. Chremmos, N. K. Efremidis, D. N. Christodoulides, “Pre-engineered abruptly autofocusing beams,” Opt. Lett. 36(10), 1890–1892 (2011).
    [CrossRef] [PubMed]
  3. D. G. Papazoglou, N. K. Efremidis, D. N. Christodoulides, S. Tzortzakis, “Observation of abruptly autofocusing waves,” Opt. Lett. 36(10), 1842–1844 (2011).
    [CrossRef] [PubMed]
  4. I. Chremmos, P. Zhang, J. Prakash, N. K. Efremidis, D. N. Christodoulides, Z. Chen, “Fourier-space generation of abruptly autofocusing beams and optical bottle beams,” Opt. Lett. 36(18), 3675–3677 (2011).
    [CrossRef] [PubMed]
  5. P. Zhang, J. Prakash, Z. Zhang, M. S. Mills, N. K. Efremidis, D. N. Christodoulides, Z. Chen, “Trapping and guiding microparticles with morphing autofocusing Airy beams,” Opt. Lett. 36(15), 2883–2885 (2011).
    [CrossRef] [PubMed]
  6. Y. Jiang, K. Huang, X. Lu, “Propagation dynamics of abruptly autofocusing Airy beams with optical vortices,” Opt. Express 20(17), 18579–18584 (2012).
    [CrossRef] [PubMed]
  7. S. Liu, P. Li, M. Wang, P. Zhang, and J. Zhao, “Observation of abrupt polarization transitions associated with spin-orbit interaction of vector autofocusing Airy beams,” in Frontiers in Optics (2013).
  8. S. Liu, M. Wang, P. Li, P. Zhang, J. Zhao, “Abrupt polarization transition of vector autofocusing Airy beams,” Opt. Lett. 38(14), 2416–2418 (2013).
    [CrossRef] [PubMed]
  9. J. A. Davis, D. M. Cottrell, D. Sand, “Abruptly autofocusing vortex beams,” Opt. Express 20(12), 13302–13310 (2012).
    [CrossRef] [PubMed]
  10. P. Panagiotopoulos, D. G. Papazoglou, A. Couairon, S. Tzortzakis, “Sharply autofocused ring-Airy beams transforming into non-linear intense light bullets,” Nat. Commun. 4, 2622 (2013).
    [CrossRef] [PubMed]
  11. Y. Jiang, K. Huang, X. Lu, “Radiation force of abruptly autofocusing Airy beams on a Rayleigh particle,” Opt. Express 21(20), 24413–24421 (2013).
    [CrossRef] [PubMed]
  12. L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45(11), 8185–8189 (1992).
    [CrossRef] [PubMed]
  13. A. T. O’Neil, I. MacVicar, L. Allen, M. J. Padgett, “Intrinsic and extrinsic nature of the orbital angular momentum of a light beam,” Phys. Rev. Lett. 88(5), 053601 (2002).
    [CrossRef] [PubMed]
  14. G. Molina-Terriza, J. P. Torres, L. Torner, “Twisted photons,” Nat. Phys. 3(5), 305–310 (2007).
    [CrossRef]
  15. G. Gibson, J. Courtial, M. J. Padgett, M. Vasnetsov, V. Pas’ko, S. M. Barnett, S. Franke-Arnold, “Free-space information transfer using light beams carrying orbital angular momentum,” Opt. Express 12(22), 5448–5456 (2004).
    [CrossRef] [PubMed]
  16. M. J. Padgett, R. Bowman, “Tweezers with a twist,” Nat. Photonics 5(6), 343–348 (2011).
    [CrossRef]
  17. H. He, M. E. J. Friese, N. R. Heckenberg, H. Rubinsztein-Dunlop, “Direct observation of transfer of angular momentum to absorptive particles from a laser beam with a phase singularity,” Phys. Rev. Lett. 75(5), 826–829 (1995).
    [CrossRef] [PubMed]
  18. K. T. Gahagan, G. A. Swartzlander., “Optical vortex trapping of particles,” Opt. Lett. 21(11), 827–829 (1996).
    [CrossRef] [PubMed]
  19. X. Gan, J. Zhao, S. Liu, L. Fang, “Generation and motion control of optical multi-vortex,” Chin. Opt. Lett. 7(12), 1142–1145 (2009).
    [CrossRef]
  20. W. Zhang, S. Liu, P. Li, X. Jiao, J. Zhao, “Controlling the polarization singularities of the focused azimuthally polarized beams,” Opt. Express 21(1), 974–983 (2013).
    [CrossRef] [PubMed]
  21. isX. Gan, P. Zhang, S. Liu, F. Xiao, J. Zhao, “Beam steering and topological transformations driven by interactions between a discrete vortex soliton and a discrete fundamental soliton,” Phys. Rev. A 89(1), 013844 (2014).
    [CrossRef]
  22. G. Molina-Terriza, E. M. Wright, L. Torner, “Propagation and control of noncanonical optical vortices,” Opt. Lett. 26(3), 163–165 (2001).
    [CrossRef] [PubMed]
  23. G.-H. Kim, H. J. Lee, J.-U. Kim, H. Suk, “Propagation dynamics of optical vortices with anisotropic phase profiles,” J. Opt. Soc. Am. B 20(2), 351–360 (2003).
    [CrossRef]
  24. N. Hermosa, C. Rosales-Guzmán, J. P. Torres, “Helico-conical optical beams self-heal,” Opt. Lett. 38(3), 383–385 (2013).
    [CrossRef] [PubMed]
  25. C.-A. Alonzo, P. J. Rodrigo, J. Glückstad, “Helico-conical optical beams: a product of helical and conical phase fronts,” Opt. Express 13(5), 1749–1760 (2005).
    [CrossRef] [PubMed]
  26. N. P. Hermosa, C. O. Manaois, “Phase structure of helicon-conical optical beams,” Opt. Commun. 271(1), 178–183 (2007).
    [CrossRef]
  27. J. B. Götte, K. O’Holleran, D. Preece, F. Flossmann, S. Franke-Arnold, S. M. Barnett, M. J. Padgett, “Light beams with fractional orbital angular momentum and their vortex structure,” Opt. Express 16(2), 993–1006 (2008).
    [CrossRef] [PubMed]
  28. S. H. Tao, X.-C. Yuan, J. Lin, X. Peng, H. B. Niu, “Fractional optical vortex beam induced rotation of particles,” Opt. Express 13(20), 7726–7731 (2005).
    [CrossRef] [PubMed]
  29. H. Li, J. Yin, “Generation of a vectorial Mathieu-like hollow beam with a periodically rotated polarization property,” Opt. Lett. 36(10), 1755–1757 (2011).
    [CrossRef] [PubMed]
  30. J. E. Curtis, D. G. Grier, “Modulated optical vortices,” Opt. Lett. 28(11), 872–874 (2003).
    [CrossRef] [PubMed]
  31. J. Broky, G. A. Siviloglou, A. Dogariu, D. N. Christodoulides, “Self-healing properties of optical Airy beams,” Opt. Express 16(17), 12880–12891 (2008).
    [CrossRef] [PubMed]
  32. H. I. Sztul, R. R. Alfano, “The Poynting vector and angular momentum of Airy beams,” Opt. Express 16(13), 9411–9416 (2008).
    [CrossRef] [PubMed]
  33. J. E. Curtis, D. G. Grier, “Structure of optical vortices,” Phys. Rev. Lett. 90(13), 133901 (2003).
    [CrossRef] [PubMed]
  34. S. A. C. Baluyot, N. P. Hermosa, “Intensity profiles and propagation of optical beams with bored helical phase,” Opt. Express 17(18), 16244–16254 (2009).
    [CrossRef] [PubMed]

2014

isX. Gan, P. Zhang, S. Liu, F. Xiao, J. Zhao, “Beam steering and topological transformations driven by interactions between a discrete vortex soliton and a discrete fundamental soliton,” Phys. Rev. A 89(1), 013844 (2014).
[CrossRef]

2013

2012

2011

2010

2009

2008

2007

N. P. Hermosa, C. O. Manaois, “Phase structure of helicon-conical optical beams,” Opt. Commun. 271(1), 178–183 (2007).
[CrossRef]

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

2005

2004

2003

2002

A. T. O’Neil, I. MacVicar, L. Allen, M. J. Padgett, “Intrinsic and extrinsic nature of the orbital angular momentum of a light beam,” Phys. Rev. Lett. 88(5), 053601 (2002).
[CrossRef] [PubMed]

2001

1996

1995

H. He, M. E. J. Friese, N. R. Heckenberg, H. Rubinsztein-Dunlop, “Direct observation of transfer of angular momentum to absorptive particles from a laser beam with a phase singularity,” Phys. Rev. Lett. 75(5), 826–829 (1995).
[CrossRef] [PubMed]

1992

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45(11), 8185–8189 (1992).
[CrossRef] [PubMed]

Alfano, R. R.

Allen, L.

A. T. O’Neil, I. MacVicar, L. Allen, M. J. Padgett, “Intrinsic and extrinsic nature of the orbital angular momentum of a light beam,” Phys. Rev. Lett. 88(5), 053601 (2002).
[CrossRef] [PubMed]

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45(11), 8185–8189 (1992).
[CrossRef] [PubMed]

Alonzo, C.-A.

Baluyot, S. A. C.

Barnett, S. M.

Beijersbergen, M. W.

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45(11), 8185–8189 (1992).
[CrossRef] [PubMed]

Bowman, R.

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

Broky, J.

Chen, Z.

Chremmos, I.

Christodoulides, D. N.

Cottrell, D. M.

Couairon, A.

P. Panagiotopoulos, D. G. Papazoglou, A. Couairon, S. Tzortzakis, “Sharply autofocused ring-Airy beams transforming into non-linear intense light bullets,” Nat. Commun. 4, 2622 (2013).
[CrossRef] [PubMed]

Courtial, J.

Curtis, J. E.

J. E. Curtis, D. G. Grier, “Structure of optical vortices,” Phys. Rev. Lett. 90(13), 133901 (2003).
[CrossRef] [PubMed]

J. E. Curtis, D. G. Grier, “Modulated optical vortices,” Opt. Lett. 28(11), 872–874 (2003).
[CrossRef] [PubMed]

Davis, J. A.

Dogariu, A.

Efremidis, N. K.

Fang, L.

Flossmann, F.

Franke-Arnold, S.

Friese, M. E. J.

H. He, M. E. J. Friese, N. R. Heckenberg, H. Rubinsztein-Dunlop, “Direct observation of transfer of angular momentum to absorptive particles from a laser beam with a phase singularity,” Phys. Rev. Lett. 75(5), 826–829 (1995).
[CrossRef] [PubMed]

Gahagan, K. T.

Gan, X.

isX. Gan, P. Zhang, S. Liu, F. Xiao, J. Zhao, “Beam steering and topological transformations driven by interactions between a discrete vortex soliton and a discrete fundamental soliton,” Phys. Rev. A 89(1), 013844 (2014).
[CrossRef]

X. Gan, J. Zhao, S. Liu, L. Fang, “Generation and motion control of optical multi-vortex,” Chin. Opt. Lett. 7(12), 1142–1145 (2009).
[CrossRef]

Gibson, G.

Glückstad, J.

Götte, J. B.

Grier, D. G.

J. E. Curtis, D. G. Grier, “Structure of optical vortices,” Phys. Rev. Lett. 90(13), 133901 (2003).
[CrossRef] [PubMed]

J. E. Curtis, D. G. Grier, “Modulated optical vortices,” Opt. Lett. 28(11), 872–874 (2003).
[CrossRef] [PubMed]

He, H.

H. He, M. E. J. Friese, N. R. Heckenberg, H. Rubinsztein-Dunlop, “Direct observation of transfer of angular momentum to absorptive particles from a laser beam with a phase singularity,” Phys. Rev. Lett. 75(5), 826–829 (1995).
[CrossRef] [PubMed]

Heckenberg, N. R.

H. He, M. E. J. Friese, N. R. Heckenberg, H. Rubinsztein-Dunlop, “Direct observation of transfer of angular momentum to absorptive particles from a laser beam with a phase singularity,” Phys. Rev. Lett. 75(5), 826–829 (1995).
[CrossRef] [PubMed]

Hermosa, N.

Hermosa, N. P.

S. A. C. Baluyot, N. P. Hermosa, “Intensity profiles and propagation of optical beams with bored helical phase,” Opt. Express 17(18), 16244–16254 (2009).
[CrossRef] [PubMed]

N. P. Hermosa, C. O. Manaois, “Phase structure of helicon-conical optical beams,” Opt. Commun. 271(1), 178–183 (2007).
[CrossRef]

Huang, K.

Jiang, Y.

Jiao, X.

Kim, G.-H.

Kim, J.-U.

Lee, H. J.

Li, H.

Li, P.

Lin, J.

Liu, S.

Lu, X.

MacVicar, I.

A. T. O’Neil, I. MacVicar, L. Allen, M. J. Padgett, “Intrinsic and extrinsic nature of the orbital angular momentum of a light beam,” Phys. Rev. Lett. 88(5), 053601 (2002).
[CrossRef] [PubMed]

Manaois, C. O.

N. P. Hermosa, C. O. Manaois, “Phase structure of helicon-conical optical beams,” Opt. Commun. 271(1), 178–183 (2007).
[CrossRef]

Mills, M. S.

Molina-Terriza, G.

Niu, H. B.

O’Holleran, K.

O’Neil, A. T.

A. T. O’Neil, I. MacVicar, L. Allen, M. J. Padgett, “Intrinsic and extrinsic nature of the orbital angular momentum of a light beam,” Phys. Rev. Lett. 88(5), 053601 (2002).
[CrossRef] [PubMed]

Padgett, M. J.

Panagiotopoulos, P.

P. Panagiotopoulos, D. G. Papazoglou, A. Couairon, S. Tzortzakis, “Sharply autofocused ring-Airy beams transforming into non-linear intense light bullets,” Nat. Commun. 4, 2622 (2013).
[CrossRef] [PubMed]

Papazoglou, D. G.

P. Panagiotopoulos, D. G. Papazoglou, A. Couairon, S. Tzortzakis, “Sharply autofocused ring-Airy beams transforming into non-linear intense light bullets,” Nat. Commun. 4, 2622 (2013).
[CrossRef] [PubMed]

D. G. Papazoglou, N. K. Efremidis, D. N. Christodoulides, S. Tzortzakis, “Observation of abruptly autofocusing waves,” Opt. Lett. 36(10), 1842–1844 (2011).
[CrossRef] [PubMed]

Pas’ko, V.

Peng, X.

Prakash, J.

Preece, D.

Rodrigo, P. J.

Rosales-Guzmán, C.

Rubinsztein-Dunlop, H.

H. He, M. E. J. Friese, N. R. Heckenberg, H. Rubinsztein-Dunlop, “Direct observation of transfer of angular momentum to absorptive particles from a laser beam with a phase singularity,” Phys. Rev. Lett. 75(5), 826–829 (1995).
[CrossRef] [PubMed]

Sand, D.

Siviloglou, G. A.

Spreeuw, R. J. C.

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45(11), 8185–8189 (1992).
[CrossRef] [PubMed]

Suk, H.

Swartzlander, G. A.

Sztul, H. I.

Tao, S. H.

Torner, L.

Torres, J. P.

Tzortzakis, S.

P. Panagiotopoulos, D. G. Papazoglou, A. Couairon, S. Tzortzakis, “Sharply autofocused ring-Airy beams transforming into non-linear intense light bullets,” Nat. Commun. 4, 2622 (2013).
[CrossRef] [PubMed]

D. G. Papazoglou, N. K. Efremidis, D. N. Christodoulides, S. Tzortzakis, “Observation of abruptly autofocusing waves,” Opt. Lett. 36(10), 1842–1844 (2011).
[CrossRef] [PubMed]

Vasnetsov, M.

Wang, M.

Woerdman, J. P.

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45(11), 8185–8189 (1992).
[CrossRef] [PubMed]

Wright, E. M.

Xiao, F.

isX. Gan, P. Zhang, S. Liu, F. Xiao, J. Zhao, “Beam steering and topological transformations driven by interactions between a discrete vortex soliton and a discrete fundamental soliton,” Phys. Rev. A 89(1), 013844 (2014).
[CrossRef]

Yin, J.

Yuan, X.-C.

Zhang, P.

Zhang, W.

Zhang, Z.

Zhao, J.

Chin. Opt. Lett.

J. Opt. Soc. Am. B

Nat. Commun.

P. Panagiotopoulos, D. G. Papazoglou, A. Couairon, S. Tzortzakis, “Sharply autofocused ring-Airy beams transforming into non-linear intense light bullets,” Nat. Commun. 4, 2622 (2013).
[CrossRef] [PubMed]

Nat. Photonics

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

Nat. Phys.

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

Opt. Commun.

N. P. Hermosa, C. O. Manaois, “Phase structure of helicon-conical optical beams,” Opt. Commun. 271(1), 178–183 (2007).
[CrossRef]

Opt. Express

J. B. Götte, K. O’Holleran, D. Preece, F. Flossmann, S. Franke-Arnold, S. M. Barnett, M. J. Padgett, “Light beams with fractional orbital angular momentum and their vortex structure,” Opt. Express 16(2), 993–1006 (2008).
[CrossRef] [PubMed]

S. H. Tao, X.-C. Yuan, J. Lin, X. Peng, H. B. Niu, “Fractional optical vortex beam induced rotation of particles,” Opt. Express 13(20), 7726–7731 (2005).
[CrossRef] [PubMed]

W. Zhang, S. Liu, P. Li, X. Jiao, J. Zhao, “Controlling the polarization singularities of the focused azimuthally polarized beams,” Opt. Express 21(1), 974–983 (2013).
[CrossRef] [PubMed]

J. Broky, G. A. Siviloglou, A. Dogariu, D. N. Christodoulides, “Self-healing properties of optical Airy beams,” Opt. Express 16(17), 12880–12891 (2008).
[CrossRef] [PubMed]

H. I. Sztul, R. R. Alfano, “The Poynting vector and angular momentum of Airy beams,” Opt. Express 16(13), 9411–9416 (2008).
[CrossRef] [PubMed]

C.-A. Alonzo, P. J. Rodrigo, J. Glückstad, “Helico-conical optical beams: a product of helical and conical phase fronts,” Opt. Express 13(5), 1749–1760 (2005).
[CrossRef] [PubMed]

S. A. C. Baluyot, N. P. Hermosa, “Intensity profiles and propagation of optical beams with bored helical phase,” Opt. Express 17(18), 16244–16254 (2009).
[CrossRef] [PubMed]

G. Gibson, J. Courtial, M. J. Padgett, M. Vasnetsov, V. Pas’ko, S. M. Barnett, S. Franke-Arnold, “Free-space information transfer using light beams carrying orbital angular momentum,” Opt. Express 12(22), 5448–5456 (2004).
[CrossRef] [PubMed]

Y. Jiang, K. Huang, X. Lu, “Radiation force of abruptly autofocusing Airy beams on a Rayleigh particle,” Opt. Express 21(20), 24413–24421 (2013).
[CrossRef] [PubMed]

Y. Jiang, K. Huang, X. Lu, “Propagation dynamics of abruptly autofocusing Airy beams with optical vortices,” Opt. Express 20(17), 18579–18584 (2012).
[CrossRef] [PubMed]

J. A. Davis, D. M. Cottrell, D. Sand, “Abruptly autofocusing vortex beams,” Opt. Express 20(12), 13302–13310 (2012).
[CrossRef] [PubMed]

Opt. Lett.

S. Liu, M. Wang, P. Li, P. Zhang, J. Zhao, “Abrupt polarization transition of vector autofocusing Airy beams,” Opt. Lett. 38(14), 2416–2418 (2013).
[CrossRef] [PubMed]

N. K. Efremidis, D. N. Christodoulides, “Abruptly autofocusing waves,” Opt. Lett. 35(23), 4045–4047 (2010).
[CrossRef] [PubMed]

I. Chremmos, N. K. Efremidis, D. N. Christodoulides, “Pre-engineered abruptly autofocusing beams,” Opt. Lett. 36(10), 1890–1892 (2011).
[CrossRef] [PubMed]

D. G. Papazoglou, N. K. Efremidis, D. N. Christodoulides, S. Tzortzakis, “Observation of abruptly autofocusing waves,” Opt. Lett. 36(10), 1842–1844 (2011).
[CrossRef] [PubMed]

I. Chremmos, P. Zhang, J. Prakash, N. K. Efremidis, D. N. Christodoulides, Z. Chen, “Fourier-space generation of abruptly autofocusing beams and optical bottle beams,” Opt. Lett. 36(18), 3675–3677 (2011).
[CrossRef] [PubMed]

P. Zhang, J. Prakash, Z. Zhang, M. S. Mills, N. K. Efremidis, D. N. Christodoulides, Z. Chen, “Trapping and guiding microparticles with morphing autofocusing Airy beams,” Opt. Lett. 36(15), 2883–2885 (2011).
[CrossRef] [PubMed]

N. Hermosa, C. Rosales-Guzmán, J. P. Torres, “Helico-conical optical beams self-heal,” Opt. Lett. 38(3), 383–385 (2013).
[CrossRef] [PubMed]

K. T. Gahagan, G. A. Swartzlander., “Optical vortex trapping of particles,” Opt. Lett. 21(11), 827–829 (1996).
[CrossRef] [PubMed]

G. Molina-Terriza, E. M. Wright, L. Torner, “Propagation and control of noncanonical optical vortices,” Opt. Lett. 26(3), 163–165 (2001).
[CrossRef] [PubMed]

H. Li, J. Yin, “Generation of a vectorial Mathieu-like hollow beam with a periodically rotated polarization property,” Opt. Lett. 36(10), 1755–1757 (2011).
[CrossRef] [PubMed]

J. E. Curtis, D. G. Grier, “Modulated optical vortices,” Opt. Lett. 28(11), 872–874 (2003).
[CrossRef] [PubMed]

Phys. Rev. A

isX. Gan, P. Zhang, S. Liu, F. Xiao, J. Zhao, “Beam steering and topological transformations driven by interactions between a discrete vortex soliton and a discrete fundamental soliton,” Phys. Rev. A 89(1), 013844 (2014).
[CrossRef]

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45(11), 8185–8189 (1992).
[CrossRef] [PubMed]

Phys. Rev. Lett.

A. T. O’Neil, I. MacVicar, L. Allen, M. J. Padgett, “Intrinsic and extrinsic nature of the orbital angular momentum of a light beam,” Phys. Rev. Lett. 88(5), 053601 (2002).
[CrossRef] [PubMed]

H. He, M. E. J. Friese, N. R. Heckenberg, H. Rubinsztein-Dunlop, “Direct observation of transfer of angular momentum to absorptive particles from a laser beam with a phase singularity,” Phys. Rev. Lett. 75(5), 826–829 (1995).
[CrossRef] [PubMed]

J. E. Curtis, D. G. Grier, “Structure of optical vortices,” Phys. Rev. Lett. 90(13), 133901 (2003).
[CrossRef] [PubMed]

Other

S. Liu, P. Li, M. Wang, P. Zhang, and J. Zhao, “Observation of abrupt polarization transitions associated with spin-orbit interaction of vector autofocusing Airy beams,” in Frontiers in Optics (2013).

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Figures (11)

Fig. 1
Fig. 1

Spiral phase distributions of (a) OV (l = 7) and (b) PEPV with l = 7, n = 4.

Fig. 2
Fig. 2

Experimental setup for generation of AABs carrying PEPV. RT = reversed telescope (5x, NA = 0.1); PSLM = phase spatial light modulator (Holoeye pluto, effective area: 15.36 mm × 8.64 mm); L = lens (focal length = 10 cm). A spatial filter and 4f system are used for generation desired AABs and AABs carrying PEPV. The insets depict the computer-generated hologram (CGH, top right) and the corresponding output intensity distribution at the focal region (bottom left).

Fig. 3
Fig. 3

Propagation characteristics of AABs with different phase distributions. (a) Intensity profile of the generated AAB (10 cm away from the L2), where the top-right inset depicts the CGH used to generate AAB; (b),(c),(e) Intensity distributions near the focal points, where the top-right insets depict the corresponding initial phase distributions of AABs (30 cm away from the L2); (d) side view of the beam propagation from numerical simulation corresponding to (e). (b) l = n = 0; (c) l = n = 1; (e) l = 8, n = 2.

Fig. 4
Fig. 4

Numerical results of the intensity profiles of the AABs with a PEPV (l = 12, n = 2) at different propagation distances near the focal point. (a)-(d) Corresponding to z = 19.52 cm, 20.50 cm, 21.48 cm, 22.45 cm, respectively. The white arrow head denotes the rotating direction.

Fig. 5
Fig. 5

Numerical simulation results of energy flow of the AABs at the input planes (top, z = 0 cm) and before the focal points (bottom, z = 20 cm). (a) l = n = 0; (b) l = n = 1; (c) l = 12, n = 2; (d) l = 12, n = 3.

Fig. 6
Fig. 6

Numerical results of the phase distributions near the focal point (z = 20 cm). (a) l = n = 0; (b) l = n = 1; (c) l = 12, n = 2; (d) l = 12, n = 3.

Fig. 7
Fig. 7

(a) Spatial frequency mapping to the focal field; (b) focal field (30 cm away from L2) of the AAB with a PEPV.

Fig. 8
Fig. 8

Focal fields of AABs carrying PEPVs (l = 8, 30 cm away from L2). (a)-(h) Corresponding to n = 2, 3, 4, …, 9, respectively. The inserted white lines depict the corresponding spatial frequency mappings.

Fig. 9
Fig. 9

Focal fields of AABs carrying PEPVs (n = 2, 30 cm away from L2). (a)-(h) Corresponding to l = 3, 4, 5, …, 10, respectively. The inserted white lines depict the corresponding spatial frequency mappings.

Fig. 10
Fig. 10

Numerical results of the OAM density distributions of AABs with different phases at the focal points (z = 20 cm). (a) l = n = 0; (b) l = n = 1; (c) l = 12, n = 2; (d) l = 12, n = 3.

Fig. 11
Fig. 11

Influence of l and n on the OAM of AABs carrying PEPVs.

Equations (7)

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ψ=lθ,
ψ=2πl ( θ 2π ) n ,
u( r,θ,z=0 )=Ai( r 0 r ω )exp( r 0 r ω )exp( iψ ),
E( x,y ) u( x , y )exp[ i k z ( x x +y y ) ]d x d y ,
f x = 1 2π x ψ( r,θ ), f y = 1 2π y ψ( r,θ ),
f x = nl θ n1 sinθ ( ) n r , f y nl θ n1 cosθ ( ) n r .
J z = ( r× E×H ) z =x S y y S x ,

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