Abstract

It is well known that a light beam with vortex phase or twist phase carries orbital angular momentum (OAM), while twist phase only exists in a partially coherent beam. In this paper, we introduce a new partially coherent beam, named twisted Laguerre-Gaussian Schell-model (TLGSM) beam. This TLGSM beam carries both vortex phase and twist phase. Further, the evolutional properties of the spectral density and spectral degree of coherence (SDOC)] of the TLGSM beam passing through a paraxial ABCD optical system are explored in detail. Our results reveal that the vortex and twist phases’ handedness significantly affects the evolution properties. When the twist phase’s handedness is the same as that of the vortex phase, the beam profile maintains a dark hollow shape during propagation and the side rings in SDOC are suppressed; however, when the handedness of two phases is opposite, then the beam shape evolves into a Gaussian shape and the side rings in SDOC are enhanced. Furthermore, we obtain the analytical expression for the OAM of the TLGSM beam. It is found that the vortex phase’s and twist phase’s contributions to the OAM are interrelated, which greatly increases the amount of OAM. In addition, the OAM variation of the TLGSM beam passing through an anisotropic optical system is also explored in detail. Our results will be useful for information transfer and optical manipulations.

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

Full Article  |  PDF Article
OSA Recommended Articles
Partially coherent fractional vortex beam

Jun Zeng, Xianlong Liu, Fei Wang, Chengliang Zhao, and Yangjian Cai
Opt. Express 26(21) 26830-26844 (2018)

Orbital angular moment of an electromagnetic Gaussian Schell-model beam with a twist phase

Lin Liu, Yusheng Huang, Yahong Chen, Lina Guo, and Yangjian Cai
Opt. Express 23(23) 30283-30296 (2015)

References

  • View by:
  • |
  • |
  • |

  1. D. G. Grier, “A revolution in optical manipulation,” Nature 424(6950), 810–816 (2003).
    [Crossref] [PubMed]
  2. S. Fürhapter, A. Jesacher, S. Bernet, and M. Ritsch-Marte, “Spiral phase contrast imaging in microscopy,” Opt. Express 13(3), 689–694 (2005).
    [Crossref] [PubMed]
  3. J. Wang, J. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6(7), 488–496 (2012).
    [Crossref]
  4. A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, “Entanglement of the orbital angular momentum states of photons,” Nature 412(6844), 313–316 (2001).
    [Crossref] [PubMed]
  5. M. P. J. Lavery, F. C. Speirits, S. M. Barnett, and M. J. Padgett, “Detection of a spinning object using light’s orbital angular momentum,” Science 341(6145), 537–540 (2013).
    [Crossref] [PubMed]
  6. L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and 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]
  7. Y. Izdebskaya, T. Fadeyeva, V. Shvedov, and A. Volyar, “Vortex-bearing array of singular beams with very high orbital angular momentum,” Opt. Lett. 31(17), 2523–2525 (2006).
    [Crossref] [PubMed]
  8. Y. Chen, Z. X. Fang, Y. X. Ren, L. Gong, and R. D. Lu, “Generation and characterization of a perfect vortex beam with a large topological charge through a digital micromirror device,” Appl. Opt. 54(27), 8030–8035 (2015).
    [Crossref] [PubMed]
  9. Y. Shen, G. T. Campbell, B. Hage, H. Zou, B. C. Buchler, and P. K. Lam, “Generation and interferometric analysis of high charge optical vortices,” J. Opt. 15(4), 044005 (2013).
    [Crossref]
  10. J. Courtial, K. Dholakia, L. Allen, and M. J. Padgett, “Gaussian beams with very high orbital angular momentum,” Opt. Commun. 144(4–6), 210–213 (1997).
    [Crossref]
  11. V. V. Kotlyar, A. A. Kovalev, and A. P. Porfirev, “Astigmatic laser beams with a large orbital angular momentum,” Opt. Express 26(1), 141–156 (2018).
    [Crossref] [PubMed]
  12. S. M. Kim and G. Gbur, “Angular momentum conservation in partially coherent wave fields,” Phys. Rev. A 86(4), 043814 (2012).
    [Crossref]
  13. X. Liu, Y. Shen, L. Liu, F. Wang, and Y. Cai, “Experimental demonstration of vortex phase-induced reduction in scintillation of a partially coherent beam,” Opt. Lett. 38(24), 5323–5326 (2013).
    [Crossref] [PubMed]
  14. Y. Huang, Y. Yuan, X. Liu, J. Zeng, F. Wang, J. Yu, L. Liu, and Y. Cai, “Propagation of optical coherence vortex lattices in turbulent atmosphere,” Appl. Sci. (Basel) 8(12), 2476 (2018).
    [Crossref]
  15. X. Liu, X. Peng, L. Liu, G. Wu, C. Zhao, F. Wang, and Y. Cai, “Self-reconstruction of the degree of coherence of a partially coherent vortex beam obstructed by an opaque obstacle,” Appl. Phys. Lett. 110(18), 181104 (2017).
    [Crossref]
  16. X. Liu, L. Liu, X. Peng, L. Liu, F. Wang, Y. Gao, and Y. Cai, “Partially coherent vortex beam with periodical coherence properties,” J. Quant. Spectrosc. Radiat. Transf. 222–223, 138–144 (2019).
    [Crossref]
  17. L. Guo, Y. Chen, X. Liu, L. Liu, and Y. Cai, “Vortex phase-induced changes of the statistical properties of a partially coherent radially polarized beam,” Opt. Express 24(13), 13714–13728 (2016).
    [Crossref] [PubMed]
  18. Y. Huang, F. Wang, Z. Gao, and B. Zhang, “Propagation properties of partially coherent electromagnetic hyperbolic-sine-Gaussian vortex beams through non-Kolmogorov turbulence,” Opt. Express 23(2), 1088–1102 (2015).
    [Crossref] [PubMed]
  19. Y. Huang, B. Zhang, Z. Gao, G. Zhao, and Z. Duan, “Evolution behavior of Gaussian Schell-model vortex beams propagating through oceanic turbulence,” Opt. Express 22(15), 17723–17734 (2014).
    [Crossref] [PubMed]
  20. X. Zhu, K. Wang, F. Wang, C. Zhao, and Y. Cai, “Coupling efficiency of a partially coherent radially vortex beam in single-mode fiber,” Appl. Sci. (Basel) 8(8), 1313 (2018).
    [Crossref]
  21. X. Liu, L. Liu, Y. Chen, and Y. Cai, “Partially Coherent Vortex Beam: From Theory to Experiment,” in Vortex Dynamics and Optical Vortices, H. Perez-de-Tejada, ed. (InTech-open science, 2017), Chap. 11, pp. 275–296.
  22. Y. Cai, Y. Chen, J. Yu, X. Liu, and L. Liu, “Generation of partially coherent beams,” Prog. Opt. 62, 157–223 (2017).
    [Crossref]
  23. B. Perez-Garcia, A. Yepiz, R. I. Hernandez-Aranda, A. Forbes, and G. A. Swartzlander, “Digital generation of partially coherent vortex beams,” Opt. Lett. 41(15), 3471–3474 (2016).
    [Crossref] [PubMed]
  24. T. van Dijk and T. D. Visser, “Evolution of singularities in a partially coherent vortex beam,” J. Opt. Soc. Am. A 26(4), 741–744 (2009).
    [Crossref] [PubMed]
  25. C. Zhao, F. Wang, Y. Dong, Y. Han, and Y. Cai, “Effect of spatial coherence on determining the topological charge of a vortex beam,” Appl. Phys. Lett. 101(26), 261104 (2012).
    [Crossref]
  26. Y. Yang, M. Mazilu, and K. Dholakia, “Measuring the orbital angular momentum of partially coherent optical vortices through singularities in their cross-spectral density functions,” Opt. Lett. 37(23), 4949–4951 (2012).
    [Crossref] [PubMed]
  27. R. Simon and N. Mukunda, “Twisted Gaussian Schell-model beams,” J. Opt. Soc. Am. A 10(1), 95–109 (1993).
    [Crossref]
  28. A. T. Friberg, E. Tervonen, and J. Turunen, “Interpretation and experimental demonstration of twisted Gaussian Schell-model beams,” J. Opt. Soc. Am. A 11(6), 1818–1826 (1994).
    [Crossref]
  29. Y. Cai, Q. Lin, and D. Ge, “Propagation of partially coherent twisted anisotropic Gaussian Schell-model beams in dispersive and absorbing media,” J. Opt. Soc. Am. A 19(10), 2036–2042 (2002).
    [Crossref] [PubMed]
  30. Y. Cai and L. Hu, “Propagation of partially coherent twisted anisotropic Gaussian Schell-model beams through an apertured astigmatic optical system,” Opt. Lett. 31(6), 685–687 (2006).
    [Crossref] [PubMed]
  31. F. Wang and Y. Cai, “Second-order statistics of a twisted gaussian Schell-model beam in turbulent atmosphere,” Opt. Express 18(24), 24661–24672 (2010).
    [Crossref] [PubMed]
  32. G. Wu, “Propagation properties of a radially polarized partially coherent twisted beam in free space,” J. Opt. Soc. Am. A 33(3), 345–350 (2016).
    [Crossref] [PubMed]
  33. X. Peng, L. Liu, J. Yu, X. Liu, Y. Cai, Y. Baykal, and W. Li, “Propagation of a radially polarized twisted Gaussian Schell-model beam in turbulent atmosphere,” J. Opt. 18(12), 125601 (2016).
    [Crossref]
  34. L. Liu, Y. Chen, L. Guo, and Y. Cai, “Twist phase-induced changes of the statistical properties of a stochastic electromagnetic beam propagating in a uniaxial crystal,” Opt. Express 23(9), 12454–12467 (2015).
    [Crossref] [PubMed]
  35. F. Wang, Y. Cai, H. T. Eyyuboğlu, and Y. Baykal, “Twist phase-induced reduction in scintillation of a partially coherent beam in turbulent atmosphere,” Opt. Lett. 37(2), 184–186 (2012).
    [Crossref] [PubMed]
  36. Y. Cai, Q. Lin, and O. Korotkova, “Ghost imaging with twisted Gaussian Schell-model beam,” Opt. Express 17(4), 2453–2464 (2009).
    [Crossref] [PubMed]
  37. C. Zhao, Y. Cai, and O. Korotkova, “Radiation force of scalar and electromagnetic twisted Gaussian Schell-model beams,” Opt. Express 17(24), 21472–21487 (2009).
    [Crossref] [PubMed]
  38. Z. Tong and O. Korotkova, “Beyond the classical Rayleigh limit with twisted light,” Opt. Lett. 37(13), 2595–2597 (2012).
    [Crossref] [PubMed]
  39. F. Gori and M. Santarsiero, “Twisted Gaussian Schell-model beams as series of partially coherent modified Bessel-Gauss beams,” Opt. Lett. 40(7), 1587–1590 (2015).
    [Crossref] [PubMed]
  40. Q. Lin and Y. Cai, “Tensor ABCD law for partially coherent twisted anisotropic Gaussian-Schell model beams,” Opt. Lett. 27(4), 216–218 (2002).
    [Crossref] [PubMed]
  41. J. Chen, E. Zhang, X. Peng, and Y. Cai, “Efficient tensor approach for simulating paraxial propagation of arbitrary partially coherent beams,” Opt. Express 25(20), 24780–24789 (2017).
    [Crossref] [PubMed]
  42. R. Borghi, F. Gori, G. Guattari, and M. Santarsiero, “Twisted Schell-model beams with axial symmetry,” Opt. Lett. 40(19), 4504–4507 (2015).
    [Crossref] [PubMed]
  43. R. Borghi, “Twisting partially coherent light,” Opt. Lett. 43(8), 1627–1630 (2018).
    [Crossref] [PubMed]
  44. Z. Mei and O. Korotkova, “Random sources for rotating spectral densities,” Opt. Lett. 42(2), 255–258 (2017).
    [Crossref] [PubMed]
  45. F. Gori and M. Santarsiero, “Devising genuine twisted cross-spectral densities,” Opt. Lett. 43(3), 595–598 (2018).
    [Crossref] [PubMed]
  46. F. Wang, Y. Cai, and O. Korotkova, “Partially coherent standard and elegant Laguerre-Gaussian beams of all orders,” Opt. Express 17(25), 22366–22379 (2009).
    [Crossref] [PubMed]
  47. J. Serna and J. M. Movilla, “Orbital angular momentum of partially coherent beams,” Opt. Lett. 26(7), 405–407 (2001).
    [Crossref] [PubMed]
  48. Q. Lin and Y. Cai, “Tensor ABCD law for partially coherent twisted anisotropic Gaussian-Schell model beams,” Opt. Lett. 27(4), 216–218 (2002).
    [Crossref] [PubMed]
  49. C. Zhao, Y. Dong, Y. Wang, F. Wang, Y. Zhang, and Y. Cai, “Experimental generation of a partially coherent Laguerre-Gaussian beam,” Appl. Phys. B 109(2), 345–349 (2012).
    [Crossref]
  50. J. Courtial and M. J. Padgett, “Performance of a cylindrical lens mode converter for producing Laguerre-Gaussian laser modes,” Opt. Commun. 159(1–3), 13–18 (1999).
    [Crossref]

2019 (1)

X. Liu, L. Liu, X. Peng, L. Liu, F. Wang, Y. Gao, and Y. Cai, “Partially coherent vortex beam with periodical coherence properties,” J. Quant. Spectrosc. Radiat. Transf. 222–223, 138–144 (2019).
[Crossref]

2018 (5)

V. V. Kotlyar, A. A. Kovalev, and A. P. Porfirev, “Astigmatic laser beams with a large orbital angular momentum,” Opt. Express 26(1), 141–156 (2018).
[Crossref] [PubMed]

X. Zhu, K. Wang, F. Wang, C. Zhao, and Y. Cai, “Coupling efficiency of a partially coherent radially vortex beam in single-mode fiber,” Appl. Sci. (Basel) 8(8), 1313 (2018).
[Crossref]

Y. Huang, Y. Yuan, X. Liu, J. Zeng, F. Wang, J. Yu, L. Liu, and Y. Cai, “Propagation of optical coherence vortex lattices in turbulent atmosphere,” Appl. Sci. (Basel) 8(12), 2476 (2018).
[Crossref]

R. Borghi, “Twisting partially coherent light,” Opt. Lett. 43(8), 1627–1630 (2018).
[Crossref] [PubMed]

F. Gori and M. Santarsiero, “Devising genuine twisted cross-spectral densities,” Opt. Lett. 43(3), 595–598 (2018).
[Crossref] [PubMed]

2017 (4)

Z. Mei and O. Korotkova, “Random sources for rotating spectral densities,” Opt. Lett. 42(2), 255–258 (2017).
[Crossref] [PubMed]

J. Chen, E. Zhang, X. Peng, and Y. Cai, “Efficient tensor approach for simulating paraxial propagation of arbitrary partially coherent beams,” Opt. Express 25(20), 24780–24789 (2017).
[Crossref] [PubMed]

X. Liu, X. Peng, L. Liu, G. Wu, C. Zhao, F. Wang, and Y. Cai, “Self-reconstruction of the degree of coherence of a partially coherent vortex beam obstructed by an opaque obstacle,” Appl. Phys. Lett. 110(18), 181104 (2017).
[Crossref]

Y. Cai, Y. Chen, J. Yu, X. Liu, and L. Liu, “Generation of partially coherent beams,” Prog. Opt. 62, 157–223 (2017).
[Crossref]

2016 (4)

2015 (5)

2014 (1)

2013 (3)

X. Liu, Y. Shen, L. Liu, F. Wang, and Y. Cai, “Experimental demonstration of vortex phase-induced reduction in scintillation of a partially coherent beam,” Opt. Lett. 38(24), 5323–5326 (2013).
[Crossref] [PubMed]

Y. Shen, G. T. Campbell, B. Hage, H. Zou, B. C. Buchler, and P. K. Lam, “Generation and interferometric analysis of high charge optical vortices,” J. Opt. 15(4), 044005 (2013).
[Crossref]

M. P. J. Lavery, F. C. Speirits, S. M. Barnett, and M. J. Padgett, “Detection of a spinning object using light’s orbital angular momentum,” Science 341(6145), 537–540 (2013).
[Crossref] [PubMed]

2012 (7)

J. Wang, J. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6(7), 488–496 (2012).
[Crossref]

S. M. Kim and G. Gbur, “Angular momentum conservation in partially coherent wave fields,” Phys. Rev. A 86(4), 043814 (2012).
[Crossref]

F. Wang, Y. Cai, H. T. Eyyuboğlu, and Y. Baykal, “Twist phase-induced reduction in scintillation of a partially coherent beam in turbulent atmosphere,” Opt. Lett. 37(2), 184–186 (2012).
[Crossref] [PubMed]

C. Zhao, F. Wang, Y. Dong, Y. Han, and Y. Cai, “Effect of spatial coherence on determining the topological charge of a vortex beam,” Appl. Phys. Lett. 101(26), 261104 (2012).
[Crossref]

Y. Yang, M. Mazilu, and K. Dholakia, “Measuring the orbital angular momentum of partially coherent optical vortices through singularities in their cross-spectral density functions,” Opt. Lett. 37(23), 4949–4951 (2012).
[Crossref] [PubMed]

Z. Tong and O. Korotkova, “Beyond the classical Rayleigh limit with twisted light,” Opt. Lett. 37(13), 2595–2597 (2012).
[Crossref] [PubMed]

C. Zhao, Y. Dong, Y. Wang, F. Wang, Y. Zhang, and Y. Cai, “Experimental generation of a partially coherent Laguerre-Gaussian beam,” Appl. Phys. B 109(2), 345–349 (2012).
[Crossref]

2010 (1)

2009 (4)

2006 (2)

2005 (1)

2003 (1)

D. G. Grier, “A revolution in optical manipulation,” Nature 424(6950), 810–816 (2003).
[Crossref] [PubMed]

2002 (3)

2001 (2)

J. Serna and J. M. Movilla, “Orbital angular momentum of partially coherent beams,” Opt. Lett. 26(7), 405–407 (2001).
[Crossref] [PubMed]

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, “Entanglement of the orbital angular momentum states of photons,” Nature 412(6844), 313–316 (2001).
[Crossref] [PubMed]

1999 (1)

J. Courtial and M. J. Padgett, “Performance of a cylindrical lens mode converter for producing Laguerre-Gaussian laser modes,” Opt. Commun. 159(1–3), 13–18 (1999).
[Crossref]

1997 (1)

J. Courtial, K. Dholakia, L. Allen, and M. J. Padgett, “Gaussian beams with very high orbital angular momentum,” Opt. Commun. 144(4–6), 210–213 (1997).
[Crossref]

1994 (1)

1993 (1)

1992 (1)

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and 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]

Ahmed, N.

J. Wang, J. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6(7), 488–496 (2012).
[Crossref]

Allen, L.

J. Courtial, K. Dholakia, L. Allen, and M. J. Padgett, “Gaussian beams with very high orbital angular momentum,” Opt. Commun. 144(4–6), 210–213 (1997).
[Crossref]

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and 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]

Barnett, S. M.

M. P. J. Lavery, F. C. Speirits, S. M. Barnett, and M. J. Padgett, “Detection of a spinning object using light’s orbital angular momentum,” Science 341(6145), 537–540 (2013).
[Crossref] [PubMed]

Baykal, Y.

X. Peng, L. Liu, J. Yu, X. Liu, Y. Cai, Y. Baykal, and W. Li, “Propagation of a radially polarized twisted Gaussian Schell-model beam in turbulent atmosphere,” J. Opt. 18(12), 125601 (2016).
[Crossref]

F. Wang, Y. Cai, H. T. Eyyuboğlu, and Y. Baykal, “Twist phase-induced reduction in scintillation of a partially coherent beam in turbulent atmosphere,” Opt. Lett. 37(2), 184–186 (2012).
[Crossref] [PubMed]

Beijersbergen, M. W.

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and 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]

Bernet, S.

Borghi, R.

Buchler, B. C.

Y. Shen, G. T. Campbell, B. Hage, H. Zou, B. C. Buchler, and P. K. Lam, “Generation and interferometric analysis of high charge optical vortices,” J. Opt. 15(4), 044005 (2013).
[Crossref]

Cai, Y.

X. Liu, L. Liu, X. Peng, L. Liu, F. Wang, Y. Gao, and Y. Cai, “Partially coherent vortex beam with periodical coherence properties,” J. Quant. Spectrosc. Radiat. Transf. 222–223, 138–144 (2019).
[Crossref]

X. Zhu, K. Wang, F. Wang, C. Zhao, and Y. Cai, “Coupling efficiency of a partially coherent radially vortex beam in single-mode fiber,” Appl. Sci. (Basel) 8(8), 1313 (2018).
[Crossref]

Y. Huang, Y. Yuan, X. Liu, J. Zeng, F. Wang, J. Yu, L. Liu, and Y. Cai, “Propagation of optical coherence vortex lattices in turbulent atmosphere,” Appl. Sci. (Basel) 8(12), 2476 (2018).
[Crossref]

X. Liu, X. Peng, L. Liu, G. Wu, C. Zhao, F. Wang, and Y. Cai, “Self-reconstruction of the degree of coherence of a partially coherent vortex beam obstructed by an opaque obstacle,” Appl. Phys. Lett. 110(18), 181104 (2017).
[Crossref]

Y. Cai, Y. Chen, J. Yu, X. Liu, and L. Liu, “Generation of partially coherent beams,” Prog. Opt. 62, 157–223 (2017).
[Crossref]

J. Chen, E. Zhang, X. Peng, and Y. Cai, “Efficient tensor approach for simulating paraxial propagation of arbitrary partially coherent beams,” Opt. Express 25(20), 24780–24789 (2017).
[Crossref] [PubMed]

L. Guo, Y. Chen, X. Liu, L. Liu, and Y. Cai, “Vortex phase-induced changes of the statistical properties of a partially coherent radially polarized beam,” Opt. Express 24(13), 13714–13728 (2016).
[Crossref] [PubMed]

X. Peng, L. Liu, J. Yu, X. Liu, Y. Cai, Y. Baykal, and W. Li, “Propagation of a radially polarized twisted Gaussian Schell-model beam in turbulent atmosphere,” J. Opt. 18(12), 125601 (2016).
[Crossref]

L. Liu, Y. Chen, L. Guo, and Y. Cai, “Twist phase-induced changes of the statistical properties of a stochastic electromagnetic beam propagating in a uniaxial crystal,” Opt. Express 23(9), 12454–12467 (2015).
[Crossref] [PubMed]

X. Liu, Y. Shen, L. Liu, F. Wang, and Y. Cai, “Experimental demonstration of vortex phase-induced reduction in scintillation of a partially coherent beam,” Opt. Lett. 38(24), 5323–5326 (2013).
[Crossref] [PubMed]

F. Wang, Y. Cai, H. T. Eyyuboğlu, and Y. Baykal, “Twist phase-induced reduction in scintillation of a partially coherent beam in turbulent atmosphere,” Opt. Lett. 37(2), 184–186 (2012).
[Crossref] [PubMed]

C. Zhao, F. Wang, Y. Dong, Y. Han, and Y. Cai, “Effect of spatial coherence on determining the topological charge of a vortex beam,” Appl. Phys. Lett. 101(26), 261104 (2012).
[Crossref]

C. Zhao, Y. Dong, Y. Wang, F. Wang, Y. Zhang, and Y. Cai, “Experimental generation of a partially coherent Laguerre-Gaussian beam,” Appl. Phys. B 109(2), 345–349 (2012).
[Crossref]

F. Wang and Y. Cai, “Second-order statistics of a twisted gaussian Schell-model beam in turbulent atmosphere,” Opt. Express 18(24), 24661–24672 (2010).
[Crossref] [PubMed]

F. Wang, Y. Cai, and O. Korotkova, “Partially coherent standard and elegant Laguerre-Gaussian beams of all orders,” Opt. Express 17(25), 22366–22379 (2009).
[Crossref] [PubMed]

Y. Cai, Q. Lin, and O. Korotkova, “Ghost imaging with twisted Gaussian Schell-model beam,” Opt. Express 17(4), 2453–2464 (2009).
[Crossref] [PubMed]

C. Zhao, Y. Cai, and O. Korotkova, “Radiation force of scalar and electromagnetic twisted Gaussian Schell-model beams,” Opt. Express 17(24), 21472–21487 (2009).
[Crossref] [PubMed]

Y. Cai and L. Hu, “Propagation of partially coherent twisted anisotropic Gaussian Schell-model beams through an apertured astigmatic optical system,” Opt. Lett. 31(6), 685–687 (2006).
[Crossref] [PubMed]

Q. Lin and Y. Cai, “Tensor ABCD law for partially coherent twisted anisotropic Gaussian-Schell model beams,” Opt. Lett. 27(4), 216–218 (2002).
[Crossref] [PubMed]

Y. Cai, Q. Lin, and D. Ge, “Propagation of partially coherent twisted anisotropic Gaussian Schell-model beams in dispersive and absorbing media,” J. Opt. Soc. Am. A 19(10), 2036–2042 (2002).
[Crossref] [PubMed]

Q. Lin and Y. Cai, “Tensor ABCD law for partially coherent twisted anisotropic Gaussian-Schell model beams,” Opt. Lett. 27(4), 216–218 (2002).
[Crossref] [PubMed]

Campbell, G. T.

Y. Shen, G. T. Campbell, B. Hage, H. Zou, B. C. Buchler, and P. K. Lam, “Generation and interferometric analysis of high charge optical vortices,” J. Opt. 15(4), 044005 (2013).
[Crossref]

Chen, J.

Chen, Y.

Courtial, J.

J. Courtial and M. J. Padgett, “Performance of a cylindrical lens mode converter for producing Laguerre-Gaussian laser modes,” Opt. Commun. 159(1–3), 13–18 (1999).
[Crossref]

J. Courtial, K. Dholakia, L. Allen, and M. J. Padgett, “Gaussian beams with very high orbital angular momentum,” Opt. Commun. 144(4–6), 210–213 (1997).
[Crossref]

Dholakia, K.

Dolinar, S.

J. Wang, J. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6(7), 488–496 (2012).
[Crossref]

Dong, Y.

C. Zhao, Y. Dong, Y. Wang, F. Wang, Y. Zhang, and Y. Cai, “Experimental generation of a partially coherent Laguerre-Gaussian beam,” Appl. Phys. B 109(2), 345–349 (2012).
[Crossref]

C. Zhao, F. Wang, Y. Dong, Y. Han, and Y. Cai, “Effect of spatial coherence on determining the topological charge of a vortex beam,” Appl. Phys. Lett. 101(26), 261104 (2012).
[Crossref]

Duan, Z.

Eyyuboglu, H. T.

Fadeyeva, T.

Fang, Z. X.

Fazal, I. M.

J. Wang, J. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6(7), 488–496 (2012).
[Crossref]

Forbes, A.

Friberg, A. T.

Fürhapter, S.

Gao, Y.

X. Liu, L. Liu, X. Peng, L. Liu, F. Wang, Y. Gao, and Y. Cai, “Partially coherent vortex beam with periodical coherence properties,” J. Quant. Spectrosc. Radiat. Transf. 222–223, 138–144 (2019).
[Crossref]

Gao, Z.

Gbur, G.

S. M. Kim and G. Gbur, “Angular momentum conservation in partially coherent wave fields,” Phys. Rev. A 86(4), 043814 (2012).
[Crossref]

Ge, D.

Gong, L.

Gori, F.

Grier, D. G.

D. G. Grier, “A revolution in optical manipulation,” Nature 424(6950), 810–816 (2003).
[Crossref] [PubMed]

Guattari, G.

Guo, L.

Hage, B.

Y. Shen, G. T. Campbell, B. Hage, H. Zou, B. C. Buchler, and P. K. Lam, “Generation and interferometric analysis of high charge optical vortices,” J. Opt. 15(4), 044005 (2013).
[Crossref]

Han, Y.

C. Zhao, F. Wang, Y. Dong, Y. Han, and Y. Cai, “Effect of spatial coherence on determining the topological charge of a vortex beam,” Appl. Phys. Lett. 101(26), 261104 (2012).
[Crossref]

Hernandez-Aranda, R. I.

Hu, L.

Huang, H.

J. Wang, J. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6(7), 488–496 (2012).
[Crossref]

Huang, Y.

Izdebskaya, Y.

Jesacher, A.

Kim, S. M.

S. M. Kim and G. Gbur, “Angular momentum conservation in partially coherent wave fields,” Phys. Rev. A 86(4), 043814 (2012).
[Crossref]

Korotkova, O.

Kotlyar, V. V.

Kovalev, A. A.

Lam, P. K.

Y. Shen, G. T. Campbell, B. Hage, H. Zou, B. C. Buchler, and P. K. Lam, “Generation and interferometric analysis of high charge optical vortices,” J. Opt. 15(4), 044005 (2013).
[Crossref]

Lavery, M. P. J.

M. P. J. Lavery, F. C. Speirits, S. M. Barnett, and M. J. Padgett, “Detection of a spinning object using light’s orbital angular momentum,” Science 341(6145), 537–540 (2013).
[Crossref] [PubMed]

Li, W.

X. Peng, L. Liu, J. Yu, X. Liu, Y. Cai, Y. Baykal, and W. Li, “Propagation of a radially polarized twisted Gaussian Schell-model beam in turbulent atmosphere,” J. Opt. 18(12), 125601 (2016).
[Crossref]

Lin, Q.

Liu, L.

X. Liu, L. Liu, X. Peng, L. Liu, F. Wang, Y. Gao, and Y. Cai, “Partially coherent vortex beam with periodical coherence properties,” J. Quant. Spectrosc. Radiat. Transf. 222–223, 138–144 (2019).
[Crossref]

X. Liu, L. Liu, X. Peng, L. Liu, F. Wang, Y. Gao, and Y. Cai, “Partially coherent vortex beam with periodical coherence properties,” J. Quant. Spectrosc. Radiat. Transf. 222–223, 138–144 (2019).
[Crossref]

Y. Huang, Y. Yuan, X. Liu, J. Zeng, F. Wang, J. Yu, L. Liu, and Y. Cai, “Propagation of optical coherence vortex lattices in turbulent atmosphere,” Appl. Sci. (Basel) 8(12), 2476 (2018).
[Crossref]

X. Liu, X. Peng, L. Liu, G. Wu, C. Zhao, F. Wang, and Y. Cai, “Self-reconstruction of the degree of coherence of a partially coherent vortex beam obstructed by an opaque obstacle,” Appl. Phys. Lett. 110(18), 181104 (2017).
[Crossref]

Y. Cai, Y. Chen, J. Yu, X. Liu, and L. Liu, “Generation of partially coherent beams,” Prog. Opt. 62, 157–223 (2017).
[Crossref]

X. Peng, L. Liu, J. Yu, X. Liu, Y. Cai, Y. Baykal, and W. Li, “Propagation of a radially polarized twisted Gaussian Schell-model beam in turbulent atmosphere,” J. Opt. 18(12), 125601 (2016).
[Crossref]

L. Guo, Y. Chen, X. Liu, L. Liu, and Y. Cai, “Vortex phase-induced changes of the statistical properties of a partially coherent radially polarized beam,” Opt. Express 24(13), 13714–13728 (2016).
[Crossref] [PubMed]

L. Liu, Y. Chen, L. Guo, and Y. Cai, “Twist phase-induced changes of the statistical properties of a stochastic electromagnetic beam propagating in a uniaxial crystal,” Opt. Express 23(9), 12454–12467 (2015).
[Crossref] [PubMed]

X. Liu, Y. Shen, L. Liu, F. Wang, and Y. Cai, “Experimental demonstration of vortex phase-induced reduction in scintillation of a partially coherent beam,” Opt. Lett. 38(24), 5323–5326 (2013).
[Crossref] [PubMed]

Liu, X.

X. Liu, L. Liu, X. Peng, L. Liu, F. Wang, Y. Gao, and Y. Cai, “Partially coherent vortex beam with periodical coherence properties,” J. Quant. Spectrosc. Radiat. Transf. 222–223, 138–144 (2019).
[Crossref]

Y. Huang, Y. Yuan, X. Liu, J. Zeng, F. Wang, J. Yu, L. Liu, and Y. Cai, “Propagation of optical coherence vortex lattices in turbulent atmosphere,” Appl. Sci. (Basel) 8(12), 2476 (2018).
[Crossref]

X. Liu, X. Peng, L. Liu, G. Wu, C. Zhao, F. Wang, and Y. Cai, “Self-reconstruction of the degree of coherence of a partially coherent vortex beam obstructed by an opaque obstacle,” Appl. Phys. Lett. 110(18), 181104 (2017).
[Crossref]

Y. Cai, Y. Chen, J. Yu, X. Liu, and L. Liu, “Generation of partially coherent beams,” Prog. Opt. 62, 157–223 (2017).
[Crossref]

X. Peng, L. Liu, J. Yu, X. Liu, Y. Cai, Y. Baykal, and W. Li, “Propagation of a radially polarized twisted Gaussian Schell-model beam in turbulent atmosphere,” J. Opt. 18(12), 125601 (2016).
[Crossref]

L. Guo, Y. Chen, X. Liu, L. Liu, and Y. Cai, “Vortex phase-induced changes of the statistical properties of a partially coherent radially polarized beam,” Opt. Express 24(13), 13714–13728 (2016).
[Crossref] [PubMed]

X. Liu, Y. Shen, L. Liu, F. Wang, and Y. Cai, “Experimental demonstration of vortex phase-induced reduction in scintillation of a partially coherent beam,” Opt. Lett. 38(24), 5323–5326 (2013).
[Crossref] [PubMed]

Lu, R. D.

Mair, A.

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, “Entanglement of the orbital angular momentum states of photons,” Nature 412(6844), 313–316 (2001).
[Crossref] [PubMed]

Mazilu, M.

Mei, Z.

Movilla, J. M.

Mukunda, N.

Padgett, M. J.

M. P. J. Lavery, F. C. Speirits, S. M. Barnett, and M. J. Padgett, “Detection of a spinning object using light’s orbital angular momentum,” Science 341(6145), 537–540 (2013).
[Crossref] [PubMed]

J. Courtial and M. J. Padgett, “Performance of a cylindrical lens mode converter for producing Laguerre-Gaussian laser modes,” Opt. Commun. 159(1–3), 13–18 (1999).
[Crossref]

J. Courtial, K. Dholakia, L. Allen, and M. J. Padgett, “Gaussian beams with very high orbital angular momentum,” Opt. Commun. 144(4–6), 210–213 (1997).
[Crossref]

Peng, X.

X. Liu, L. Liu, X. Peng, L. Liu, F. Wang, Y. Gao, and Y. Cai, “Partially coherent vortex beam with periodical coherence properties,” J. Quant. Spectrosc. Radiat. Transf. 222–223, 138–144 (2019).
[Crossref]

X. Liu, X. Peng, L. Liu, G. Wu, C. Zhao, F. Wang, and Y. Cai, “Self-reconstruction of the degree of coherence of a partially coherent vortex beam obstructed by an opaque obstacle,” Appl. Phys. Lett. 110(18), 181104 (2017).
[Crossref]

J. Chen, E. Zhang, X. Peng, and Y. Cai, “Efficient tensor approach for simulating paraxial propagation of arbitrary partially coherent beams,” Opt. Express 25(20), 24780–24789 (2017).
[Crossref] [PubMed]

X. Peng, L. Liu, J. Yu, X. Liu, Y. Cai, Y. Baykal, and W. Li, “Propagation of a radially polarized twisted Gaussian Schell-model beam in turbulent atmosphere,” J. Opt. 18(12), 125601 (2016).
[Crossref]

Perez-Garcia, B.

Porfirev, A. P.

Ren, Y.

J. Wang, J. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6(7), 488–496 (2012).
[Crossref]

Ren, Y. X.

Ritsch-Marte, M.

Santarsiero, M.

Serna, J.

Shen, Y.

X. Liu, Y. Shen, L. Liu, F. Wang, and Y. Cai, “Experimental demonstration of vortex phase-induced reduction in scintillation of a partially coherent beam,” Opt. Lett. 38(24), 5323–5326 (2013).
[Crossref] [PubMed]

Y. Shen, G. T. Campbell, B. Hage, H. Zou, B. C. Buchler, and P. K. Lam, “Generation and interferometric analysis of high charge optical vortices,” J. Opt. 15(4), 044005 (2013).
[Crossref]

Shvedov, V.

Simon, R.

Speirits, F. C.

M. P. J. Lavery, F. C. Speirits, S. M. Barnett, and M. J. Padgett, “Detection of a spinning object using light’s orbital angular momentum,” Science 341(6145), 537–540 (2013).
[Crossref] [PubMed]

Spreeuw, R. J. C.

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and 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]

Swartzlander, G. A.

Tervonen, E.

Tong, Z.

Tur, M.

J. Wang, J. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6(7), 488–496 (2012).
[Crossref]

Turunen, J.

van Dijk, T.

Vaziri, A.

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, “Entanglement of the orbital angular momentum states of photons,” Nature 412(6844), 313–316 (2001).
[Crossref] [PubMed]

Visser, T. D.

Volyar, A.

Wang, F.

X. Liu, L. Liu, X. Peng, L. Liu, F. Wang, Y. Gao, and Y. Cai, “Partially coherent vortex beam with periodical coherence properties,” J. Quant. Spectrosc. Radiat. Transf. 222–223, 138–144 (2019).
[Crossref]

X. Zhu, K. Wang, F. Wang, C. Zhao, and Y. Cai, “Coupling efficiency of a partially coherent radially vortex beam in single-mode fiber,” Appl. Sci. (Basel) 8(8), 1313 (2018).
[Crossref]

Y. Huang, Y. Yuan, X. Liu, J. Zeng, F. Wang, J. Yu, L. Liu, and Y. Cai, “Propagation of optical coherence vortex lattices in turbulent atmosphere,” Appl. Sci. (Basel) 8(12), 2476 (2018).
[Crossref]

X. Liu, X. Peng, L. Liu, G. Wu, C. Zhao, F. Wang, and Y. Cai, “Self-reconstruction of the degree of coherence of a partially coherent vortex beam obstructed by an opaque obstacle,” Appl. Phys. Lett. 110(18), 181104 (2017).
[Crossref]

Y. Huang, F. Wang, Z. Gao, and B. Zhang, “Propagation properties of partially coherent electromagnetic hyperbolic-sine-Gaussian vortex beams through non-Kolmogorov turbulence,” Opt. Express 23(2), 1088–1102 (2015).
[Crossref] [PubMed]

X. Liu, Y. Shen, L. Liu, F. Wang, and Y. Cai, “Experimental demonstration of vortex phase-induced reduction in scintillation of a partially coherent beam,” Opt. Lett. 38(24), 5323–5326 (2013).
[Crossref] [PubMed]

F. Wang, Y. Cai, H. T. Eyyuboğlu, and Y. Baykal, “Twist phase-induced reduction in scintillation of a partially coherent beam in turbulent atmosphere,” Opt. Lett. 37(2), 184–186 (2012).
[Crossref] [PubMed]

C. Zhao, Y. Dong, Y. Wang, F. Wang, Y. Zhang, and Y. Cai, “Experimental generation of a partially coherent Laguerre-Gaussian beam,” Appl. Phys. B 109(2), 345–349 (2012).
[Crossref]

C. Zhao, F. Wang, Y. Dong, Y. Han, and Y. Cai, “Effect of spatial coherence on determining the topological charge of a vortex beam,” Appl. Phys. Lett. 101(26), 261104 (2012).
[Crossref]

F. Wang and Y. Cai, “Second-order statistics of a twisted gaussian Schell-model beam in turbulent atmosphere,” Opt. Express 18(24), 24661–24672 (2010).
[Crossref] [PubMed]

F. Wang, Y. Cai, and O. Korotkova, “Partially coherent standard and elegant Laguerre-Gaussian beams of all orders,” Opt. Express 17(25), 22366–22379 (2009).
[Crossref] [PubMed]

Wang, J.

J. Wang, J. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6(7), 488–496 (2012).
[Crossref]

Wang, K.

X. Zhu, K. Wang, F. Wang, C. Zhao, and Y. Cai, “Coupling efficiency of a partially coherent radially vortex beam in single-mode fiber,” Appl. Sci. (Basel) 8(8), 1313 (2018).
[Crossref]

Wang, Y.

C. Zhao, Y. Dong, Y. Wang, F. Wang, Y. Zhang, and Y. Cai, “Experimental generation of a partially coherent Laguerre-Gaussian beam,” Appl. Phys. B 109(2), 345–349 (2012).
[Crossref]

Weihs, G.

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, “Entanglement of the orbital angular momentum states of photons,” Nature 412(6844), 313–316 (2001).
[Crossref] [PubMed]

Willner, A. E.

J. Wang, J. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6(7), 488–496 (2012).
[Crossref]

Woerdman, J. P.

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and 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]

Wu, G.

X. Liu, X. Peng, L. Liu, G. Wu, C. Zhao, F. Wang, and Y. Cai, “Self-reconstruction of the degree of coherence of a partially coherent vortex beam obstructed by an opaque obstacle,” Appl. Phys. Lett. 110(18), 181104 (2017).
[Crossref]

G. Wu, “Propagation properties of a radially polarized partially coherent twisted beam in free space,” J. Opt. Soc. Am. A 33(3), 345–350 (2016).
[Crossref] [PubMed]

Yan, Y.

J. Wang, J. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6(7), 488–496 (2012).
[Crossref]

Yang, J.

J. Wang, J. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6(7), 488–496 (2012).
[Crossref]

Yang, Y.

Yepiz, A.

Yu, J.

Y. Huang, Y. Yuan, X. Liu, J. Zeng, F. Wang, J. Yu, L. Liu, and Y. Cai, “Propagation of optical coherence vortex lattices in turbulent atmosphere,” Appl. Sci. (Basel) 8(12), 2476 (2018).
[Crossref]

Y. Cai, Y. Chen, J. Yu, X. Liu, and L. Liu, “Generation of partially coherent beams,” Prog. Opt. 62, 157–223 (2017).
[Crossref]

X. Peng, L. Liu, J. Yu, X. Liu, Y. Cai, Y. Baykal, and W. Li, “Propagation of a radially polarized twisted Gaussian Schell-model beam in turbulent atmosphere,” J. Opt. 18(12), 125601 (2016).
[Crossref]

Yuan, Y.

Y. Huang, Y. Yuan, X. Liu, J. Zeng, F. Wang, J. Yu, L. Liu, and Y. Cai, “Propagation of optical coherence vortex lattices in turbulent atmosphere,” Appl. Sci. (Basel) 8(12), 2476 (2018).
[Crossref]

Yue, Y.

J. Wang, J. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6(7), 488–496 (2012).
[Crossref]

Zeilinger, A.

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, “Entanglement of the orbital angular momentum states of photons,” Nature 412(6844), 313–316 (2001).
[Crossref] [PubMed]

Zeng, J.

Y. Huang, Y. Yuan, X. Liu, J. Zeng, F. Wang, J. Yu, L. Liu, and Y. Cai, “Propagation of optical coherence vortex lattices in turbulent atmosphere,” Appl. Sci. (Basel) 8(12), 2476 (2018).
[Crossref]

Zhang, B.

Zhang, E.

Zhang, Y.

C. Zhao, Y. Dong, Y. Wang, F. Wang, Y. Zhang, and Y. Cai, “Experimental generation of a partially coherent Laguerre-Gaussian beam,” Appl. Phys. B 109(2), 345–349 (2012).
[Crossref]

Zhao, C.

X. Zhu, K. Wang, F. Wang, C. Zhao, and Y. Cai, “Coupling efficiency of a partially coherent radially vortex beam in single-mode fiber,” Appl. Sci. (Basel) 8(8), 1313 (2018).
[Crossref]

X. Liu, X. Peng, L. Liu, G. Wu, C. Zhao, F. Wang, and Y. Cai, “Self-reconstruction of the degree of coherence of a partially coherent vortex beam obstructed by an opaque obstacle,” Appl. Phys. Lett. 110(18), 181104 (2017).
[Crossref]

C. Zhao, F. Wang, Y. Dong, Y. Han, and Y. Cai, “Effect of spatial coherence on determining the topological charge of a vortex beam,” Appl. Phys. Lett. 101(26), 261104 (2012).
[Crossref]

C. Zhao, Y. Dong, Y. Wang, F. Wang, Y. Zhang, and Y. Cai, “Experimental generation of a partially coherent Laguerre-Gaussian beam,” Appl. Phys. B 109(2), 345–349 (2012).
[Crossref]

C. Zhao, Y. Cai, and O. Korotkova, “Radiation force of scalar and electromagnetic twisted Gaussian Schell-model beams,” Opt. Express 17(24), 21472–21487 (2009).
[Crossref] [PubMed]

Zhao, G.

Zhu, X.

X. Zhu, K. Wang, F. Wang, C. Zhao, and Y. Cai, “Coupling efficiency of a partially coherent radially vortex beam in single-mode fiber,” Appl. Sci. (Basel) 8(8), 1313 (2018).
[Crossref]

Zou, H.

Y. Shen, G. T. Campbell, B. Hage, H. Zou, B. C. Buchler, and P. K. Lam, “Generation and interferometric analysis of high charge optical vortices,” J. Opt. 15(4), 044005 (2013).
[Crossref]

Appl. Opt. (1)

Appl. Phys. B (1)

C. Zhao, Y. Dong, Y. Wang, F. Wang, Y. Zhang, and Y. Cai, “Experimental generation of a partially coherent Laguerre-Gaussian beam,” Appl. Phys. B 109(2), 345–349 (2012).
[Crossref]

Appl. Phys. Lett. (2)

X. Liu, X. Peng, L. Liu, G. Wu, C. Zhao, F. Wang, and Y. Cai, “Self-reconstruction of the degree of coherence of a partially coherent vortex beam obstructed by an opaque obstacle,” Appl. Phys. Lett. 110(18), 181104 (2017).
[Crossref]

C. Zhao, F. Wang, Y. Dong, Y. Han, and Y. Cai, “Effect of spatial coherence on determining the topological charge of a vortex beam,” Appl. Phys. Lett. 101(26), 261104 (2012).
[Crossref]

Appl. Sci. (Basel) (2)

X. Zhu, K. Wang, F. Wang, C. Zhao, and Y. Cai, “Coupling efficiency of a partially coherent radially vortex beam in single-mode fiber,” Appl. Sci. (Basel) 8(8), 1313 (2018).
[Crossref]

Y. Huang, Y. Yuan, X. Liu, J. Zeng, F. Wang, J. Yu, L. Liu, and Y. Cai, “Propagation of optical coherence vortex lattices in turbulent atmosphere,” Appl. Sci. (Basel) 8(12), 2476 (2018).
[Crossref]

J. Opt. (2)

Y. Shen, G. T. Campbell, B. Hage, H. Zou, B. C. Buchler, and P. K. Lam, “Generation and interferometric analysis of high charge optical vortices,” J. Opt. 15(4), 044005 (2013).
[Crossref]

X. Peng, L. Liu, J. Yu, X. Liu, Y. Cai, Y. Baykal, and W. Li, “Propagation of a radially polarized twisted Gaussian Schell-model beam in turbulent atmosphere,” J. Opt. 18(12), 125601 (2016).
[Crossref]

J. Opt. Soc. Am. A (5)

J. Quant. Spectrosc. Radiat. Transf. (1)

X. Liu, L. Liu, X. Peng, L. Liu, F. Wang, Y. Gao, and Y. Cai, “Partially coherent vortex beam with periodical coherence properties,” J. Quant. Spectrosc. Radiat. Transf. 222–223, 138–144 (2019).
[Crossref]

Nat. Photonics (1)

J. Wang, J. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6(7), 488–496 (2012).
[Crossref]

Nature (2)

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, “Entanglement of the orbital angular momentum states of photons,” Nature 412(6844), 313–316 (2001).
[Crossref] [PubMed]

D. G. Grier, “A revolution in optical manipulation,” Nature 424(6950), 810–816 (2003).
[Crossref] [PubMed]

Opt. Commun. (2)

J. Courtial, K. Dholakia, L. Allen, and M. J. Padgett, “Gaussian beams with very high orbital angular momentum,” Opt. Commun. 144(4–6), 210–213 (1997).
[Crossref]

J. Courtial and M. J. Padgett, “Performance of a cylindrical lens mode converter for producing Laguerre-Gaussian laser modes,” Opt. Commun. 159(1–3), 13–18 (1999).
[Crossref]

Opt. Express (11)

L. Liu, Y. Chen, L. Guo, and Y. Cai, “Twist phase-induced changes of the statistical properties of a stochastic electromagnetic beam propagating in a uniaxial crystal,” Opt. Express 23(9), 12454–12467 (2015).
[Crossref] [PubMed]

F. Wang, Y. Cai, and O. Korotkova, “Partially coherent standard and elegant Laguerre-Gaussian beams of all orders,” Opt. Express 17(25), 22366–22379 (2009).
[Crossref] [PubMed]

J. Chen, E. Zhang, X. Peng, and Y. Cai, “Efficient tensor approach for simulating paraxial propagation of arbitrary partially coherent beams,” Opt. Express 25(20), 24780–24789 (2017).
[Crossref] [PubMed]

V. V. Kotlyar, A. A. Kovalev, and A. P. Porfirev, “Astigmatic laser beams with a large orbital angular momentum,” Opt. Express 26(1), 141–156 (2018).
[Crossref] [PubMed]

S. Fürhapter, A. Jesacher, S. Bernet, and M. Ritsch-Marte, “Spiral phase contrast imaging in microscopy,” Opt. Express 13(3), 689–694 (2005).
[Crossref] [PubMed]

L. Guo, Y. Chen, X. Liu, L. Liu, and Y. Cai, “Vortex phase-induced changes of the statistical properties of a partially coherent radially polarized beam,” Opt. Express 24(13), 13714–13728 (2016).
[Crossref] [PubMed]

Y. Huang, F. Wang, Z. Gao, and B. Zhang, “Propagation properties of partially coherent electromagnetic hyperbolic-sine-Gaussian vortex beams through non-Kolmogorov turbulence,” Opt. Express 23(2), 1088–1102 (2015).
[Crossref] [PubMed]

Y. Huang, B. Zhang, Z. Gao, G. Zhao, and Z. Duan, “Evolution behavior of Gaussian Schell-model vortex beams propagating through oceanic turbulence,” Opt. Express 22(15), 17723–17734 (2014).
[Crossref] [PubMed]

F. Wang and Y. Cai, “Second-order statistics of a twisted gaussian Schell-model beam in turbulent atmosphere,” Opt. Express 18(24), 24661–24672 (2010).
[Crossref] [PubMed]

Y. Cai, Q. Lin, and O. Korotkova, “Ghost imaging with twisted Gaussian Schell-model beam,” Opt. Express 17(4), 2453–2464 (2009).
[Crossref] [PubMed]

C. Zhao, Y. Cai, and O. Korotkova, “Radiation force of scalar and electromagnetic twisted Gaussian Schell-model beams,” Opt. Express 17(24), 21472–21487 (2009).
[Crossref] [PubMed]

Opt. Lett. (15)

Z. Tong and O. Korotkova, “Beyond the classical Rayleigh limit with twisted light,” Opt. Lett. 37(13), 2595–2597 (2012).
[Crossref] [PubMed]

F. Gori and M. Santarsiero, “Twisted Gaussian Schell-model beams as series of partially coherent modified Bessel-Gauss beams,” Opt. Lett. 40(7), 1587–1590 (2015).
[Crossref] [PubMed]

Q. Lin and Y. Cai, “Tensor ABCD law for partially coherent twisted anisotropic Gaussian-Schell model beams,” Opt. Lett. 27(4), 216–218 (2002).
[Crossref] [PubMed]

Y. Yang, M. Mazilu, and K. Dholakia, “Measuring the orbital angular momentum of partially coherent optical vortices through singularities in their cross-spectral density functions,” Opt. Lett. 37(23), 4949–4951 (2012).
[Crossref] [PubMed]

Y. Cai and L. Hu, “Propagation of partially coherent twisted anisotropic Gaussian Schell-model beams through an apertured astigmatic optical system,” Opt. Lett. 31(6), 685–687 (2006).
[Crossref] [PubMed]

B. Perez-Garcia, A. Yepiz, R. I. Hernandez-Aranda, A. Forbes, and G. A. Swartzlander, “Digital generation of partially coherent vortex beams,” Opt. Lett. 41(15), 3471–3474 (2016).
[Crossref] [PubMed]

X. Liu, Y. Shen, L. Liu, F. Wang, and Y. Cai, “Experimental demonstration of vortex phase-induced reduction in scintillation of a partially coherent beam,” Opt. Lett. 38(24), 5323–5326 (2013).
[Crossref] [PubMed]

Y. Izdebskaya, T. Fadeyeva, V. Shvedov, and A. Volyar, “Vortex-bearing array of singular beams with very high orbital angular momentum,” Opt. Lett. 31(17), 2523–2525 (2006).
[Crossref] [PubMed]

R. Borghi, F. Gori, G. Guattari, and M. Santarsiero, “Twisted Schell-model beams with axial symmetry,” Opt. Lett. 40(19), 4504–4507 (2015).
[Crossref] [PubMed]

R. Borghi, “Twisting partially coherent light,” Opt. Lett. 43(8), 1627–1630 (2018).
[Crossref] [PubMed]

Z. Mei and O. Korotkova, “Random sources for rotating spectral densities,” Opt. Lett. 42(2), 255–258 (2017).
[Crossref] [PubMed]

F. Gori and M. Santarsiero, “Devising genuine twisted cross-spectral densities,” Opt. Lett. 43(3), 595–598 (2018).
[Crossref] [PubMed]

J. Serna and J. M. Movilla, “Orbital angular momentum of partially coherent beams,” Opt. Lett. 26(7), 405–407 (2001).
[Crossref] [PubMed]

Q. Lin and Y. Cai, “Tensor ABCD law for partially coherent twisted anisotropic Gaussian-Schell model beams,” Opt. Lett. 27(4), 216–218 (2002).
[Crossref] [PubMed]

F. Wang, Y. Cai, H. T. Eyyuboğlu, and Y. Baykal, “Twist phase-induced reduction in scintillation of a partially coherent beam in turbulent atmosphere,” Opt. Lett. 37(2), 184–186 (2012).
[Crossref] [PubMed]

Phys. Rev. A (2)

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and 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]

S. M. Kim and G. Gbur, “Angular momentum conservation in partially coherent wave fields,” Phys. Rev. A 86(4), 043814 (2012).
[Crossref]

Prog. Opt. (1)

Y. Cai, Y. Chen, J. Yu, X. Liu, and L. Liu, “Generation of partially coherent beams,” Prog. Opt. 62, 157–223 (2017).
[Crossref]

Science (1)

M. P. J. Lavery, F. C. Speirits, S. M. Barnett, and M. J. Padgett, “Detection of a spinning object using light’s orbital angular momentum,” Science 341(6145), 537–540 (2013).
[Crossref] [PubMed]

Other (1)

X. Liu, L. Liu, Y. Chen, and Y. Cai, “Partially Coherent Vortex Beam: From Theory to Experiment,” in Vortex Dynamics and Optical Vortices, H. Perez-de-Tejada, ed. (InTech-open science, 2017), Chap. 11, pp. 275–296.

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (5)

Fig. 1
Fig. 1 Density plot of the normalized spectral density of TLGSM beams for different values of the twist factor μ 0 at several propagation distances after passing through a thin lens. The green solid curve denotes the cross line of spectral density at y = 0.
Fig. 2
Fig. 2 (a) Variation of the degree of hollowness D with (a) the propagation distance z after the lens for different twist factors, (b) the value of twist factor at z = 380mm.
Fig. 3
Fig. 3 Density plot of the spectral degree of coherence of the TLGSM beam with different topological charges l in the focal plane of the lens for three different values of twist factor.
Fig. 4
Fig. 4 Variation of the quantity of the OAM flux of the partially coherent LG beam with twist factor against (a) the normalized twist factor μ 0 k δ 0 2 with different topological charge l; (b) the coherence width with different l for μ 0 k δ 0 2 =1.
Fig. 5
Fig. 5 The dependence of the OAM of the output beam through two cylindrical lenses system on (a) the distance d between two lenses with three different angles of the second lens, (b) the angle of the second lens for different values of d.

Equations (29)

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

W 0 ( r 1 , r 2 )= r 1 | l | r 2 | l | exp( r 1 2 + r 2 2 4 σ 0 2 )exp( ( r 1 r 2 ) 2 2 δ 0 2 )exp[il( φ 1 φ 2 )]exp( ik μ 0 x 1 y 2 +ik μ 0 x 2 y 1 ),
W( ρ 1 , ρ 2 )= 1 ( λB ) 2 exp[ ikD 2B ( ρ 1 2 ρ 2 2 ) ] W 0 ( r 1 , r 2 )exp[ ikA 2B ( r 1 2 r 2 2 ) ] ×exp[ ik B ( r 1 ρ 1 r 2 ρ 2 ) ] d 2 r 1 d 2 r 2 ,
e ilφ ρ l = 1 2 l c=0 l i c ( l n ) H lc ( x ) H c ( y ).
W 0 ( r 1 , r 2 )= 1 2 2l c 1 =0 l c 2 =0 l ( i c 1 ) i c 2 ( l c 1 )( l c 2 ) H l c 1 ( x 1 ) H c 1 ( y 1 ) H l c 2 ( x 2 ) H c 2 ( y 2 ) ×exp( r 1 2 + r 2 2 4 σ 0 2 )exp( ( r 1 r 2 ) 2 2 δ 0 2 )exp( ik μ 0 x 1 y 2 +ik μ 0 x 2 y 1 ).
W( ρ 1 , ρ 2 ,z )= π 2 N 1 l/21 ( λB ) 2 exp[ ikD 2B ( ρ 1 2 ρ 2 2 ) ]exp( k 2 ρ 1 2 4 N 1 B 2 )exp( β 1 2 + β 2 2 ) × c 1 =0 l c 2 =0 l p 1 =0 l c 1 p 2 =0 l c 1 p 1 p 3 =0 c 1 p 4 =0 c 1 p 3 m 1 =0 [ p 1 /2 ] m 2 =0 [ p 2 /2 ] m 3 =0 [ p 3 /2 ] m 4 =0 [ p 4 /2 ] ( 2i ) l α 1 α 2 ( 1 ) p 4 + m 1 + m 2 + m 3 m 4 N 2 1( α 1 + α 2 )/2 × 1 2 l( p 1 + p 3 )/2 ( c 1 p 3 )( c 1 p 3 p 4 )( l c 1 p 1 )( l c 1 p 1 p 2 ) l! ( i ) c 1 c 1 !( l c 1 )! l! i c 2 c 2 !( l c 2 )! × p 1 ! m 1 !( p 1 2 m 1 )! p 2 ! m 2 !( p 2 2 m 2 )! p 3 ! m 3 !( p 3 2 m 3 )! p 4 ! m 4 !( p 4 2 m 4 )! H α 1 ( i β 1 ) H α 2 ( i β 2 ) × ( 2 i N 1 δ 0 2 ) p 1 + p 3 2 m 1 2 m 3 ( 2k μ 0 N 1 ) p 2 + p 4 2 m 2 2 m 4 H c 1 p 3 p 4 ( k ρ 1y N 1 B ) H l c 1 p 1 p 2 ( k ρ 1x N 1 B ),
N 1 = 1 4 σ 0 2 + 1 2 δ 0 2 + ikA 2B , N 2 = N 1 1 4 N 1 δ 0 4 + k 2 μ 0 2 4 N 10 ,
α 1 =l+ p 1 + p 4 c 2 2 m 1 2 m 4 , α 2 = p 2 + p 3 + c 2 2 m 2 2 m 3 ,
β 1 = 1 2 N 2 ( ik ρ 2x B + ik ρ 1x 2 N 1 B δ 0 2 k 2 ρ 1y μ 0 2 N 10 B ), β 2 = 1 2 N 2 ( ik ρ 2y B + k 2 ρ 1x μ 0 2 N 1 B + ik ρ 1y 2 N 1 B δ 0 2 ).
S( ρ,z )=W( ρ,ρ,z ),
γ( ρ 1 , ρ 2 ,z )= W( ρ 1 , ρ 2 ,z ) W( ρ 1 , ρ 1 ,z )W( ρ 2 , ρ 2 ,z ) .
D= S(0,z) [S(ρ,z)] max ,
J z =( I c )( x θ y y θ x ),
h in (r,θ)= k 2 4 π 2 d 2 r d W(r, r d ) exp(ikθ r d ),
W( r s , r d )= [ r 2 r d 2 /4i( x d yx y d ) ] l ×exp( r 2 2 σ 0 2 )exp[ ( 1 8 σ 0 2 + 1 2 δ 0 2 ) r d 2 ] ×exp[ ik μ 0 ( x d yx y d ) ],
ξ a ξ b = 1 I ξ a ξ b h in ( r,θ ) d 2 r d 2 θ d 2 r d = k 2 4 π 2 I ξ a ξ b d 2 r d 2 θ d 2 r d W( r s , r d )exp(ikθ r d ),
x ^ :W(r, r d )xW(r, r d ), θ ^ x :W(r, r d ) 1 ik W(r, r d ) x d , y ^ :W(r, r d )yW(r, r d ), θ ^ y :W(r, r d ) 1 ik W(r, r d ) y d .
ξ a ξ b = 1 I d 2 r ξ ^ a ξ ^ b W(r, r d )| r d =0 .
x 2 = y 2 =( | l |+1 ) σ 0 2 ,
θ x 2 = θ y 2 = | l |+1 4 k 2 σ 0 2 + 1 k 2 δ 0 2 + μ 0 2 ( | l |+1 ) σ 0 2 - l μ 0 k ,
x θ y = y θ x = l 2k μ 0 σ 0 2 k(| l |+1) k ,
xy = θ x θ y = x θ x = y θ y =0.
J z =n[ l2 μ 0 k σ 0 2 2 μ 0 k σ 0 2 | l | ].
S=[ A B C D ],
V out = ξ out ξ out T = 1 I out ξ out ξ out T h out ( ξ out ) d 2 ρ d 2 ϕ,
V out =det(S)S[ ξ ξ T h in ( ξ in ) d 2 r d 2 θ ] S T =SV S T .
J z out = I c ( V 14 out V 23 out ).
A=[ 1 d sin 2 α f dsin2α 2f dsin2α 2f 1 d cos 2 α f ], B=[ d 0 0 d ], C=[ sin 2 α f sin2α 2f ( 1 d f ) sin2α 2f 1 f ( 1 d f ) cos 2 α f ], D=[ 1 0 0 1 d f ].
J z out =( 1 d 2 cos2α 2 f 2 ) J z in + J z g ,
J z g =n( 2 d f ) kd(l+1) σ 0 2 sin2α 2 f 2 .

Metrics