Abstract

The partially coherent elegant Laguerre-Gaussian (ELG) beam is of importance and exhibits extraordinary characteristics in many fields, such as optical communications and optical trapping. Here, we show a method to measure the topological charge of a partially coherent ELG beam. We find that the number of ring dislocations in the far-field complex degree of coherence is equal to the topological charge |l| of a partially coherent ELG beam, and which is confirmed experimentally. Our results will be useful for applications using partially coherent ELG beams.

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

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    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]

2018 (1)

2017 (2)

T. Yang, Y. Xu, H. Tian, D. Die, Q. Du, B. Zhang, and Y. Dan, “Propagation of partially coherent Laguerre Gaussian beams through inhomogeneous turbulent atmosphere,” J. Opt. Soc. Am. A 34(5), 713–720 (2017).
[Crossref] [PubMed]

Y. Yang, G. Thirunavukkarasu, M. Babiker, and J. Yuan, “Orbital-Angular-Momentum Mode Selection by Rotationally Symmetric Superposition of Chiral States with Application to Electron Vortex Beams,” Phys. Rev. Lett. 119(9), 094802 (2017).
[Crossref] [PubMed]

2016 (2)

Y. Yang and Y. D. Liu, “Measuring azimuthal and radial mode indices of a partially coherent vortex field,” J. Opt. 18(1), 015604 (2016).
[Crossref]

T. Yang, Y. Xu, H. Tiana, Q. Du, D. Die, and Y. Dan, “Comparative study of propagation properties of partially coherent standard and elegant Hermite-Gaussian beams in inhomogeneous atmospheric turbulence,” Optik (Stuttg.) 127(22), 10772–10779 (2016).
[Crossref]

2015 (1)

2014 (1)

2013 (6)

W. Nasalski, “Exact elegant Laguerre-Gaussian vector wave packets,” Opt. Lett. 38(6), 809–811 (2013).
[Crossref] [PubMed]

J. Long, R. Liu, F. Wang, Y. Wang, P. Zhang, H. Gao, and F. Li, “Evaluating Laguerre-Gaussian beams with an invariant parameter,” Opt. Lett. 38(16), 3047–3049 (2013).
[Crossref] [PubMed]

Y. Yang, Y. Dong, C. Zhao, and Y. Cai, “Generation and propagation of an anomalous vortex beam,” Opt. Lett. 38(24), 5418–5421 (2013).
[Crossref] [PubMed]

A. Y. Escalante, B. Perez-Garcia, R. I. Hernandez-Aranda, and G. A. Swartzlander, “Determination of angular momentum content in partially coherent beams through cross correlation measurements,” Proc. SPIE 8843, 884302 (2013).
[Crossref]

Y. Yang, M. Chen, M. Mazilu, A. Mourka, Y. Liu, and K. Dholakia, “Effect of the radial and azimuthal mode indices of a partially coherent vortex field upon a spatial correlation singularity,” New J. Phys. 15(11), 113053 (2013).
[Crossref]

Y. Zhang, Y. Dong, W. Wen, F. Wang, and Y. Cai, “Spectral shift of a partially coherent standard or elegant Laguerre–Gaussian beam in turbulent atmosphere,” J. Mod. Opt. 60(5), 422–430 (2013).
[Crossref]

2012 (3)

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]

H. Xu, H. Luo, Z. Cui, and J. Qu, “Polarization characteristics of partially coherent elegant Laguerre-Gaussian beams in non-Kolmogorov turbulence,” Opt. Lasers Eng. 50(5), 760–766 (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]

2011 (3)

2010 (3)

F. Wang and Y. Cai, “Average intensity and spreading of partially coherent standard and elegant Laguerre- Gaussian beams in turbulent atmosphere,” Prog. Electromagn. Res 103, 33–56 (2010).

J. M. Hickmann, E. J. S. Fonseca, W. C. Soares, and S. Chávez-Cerda, “Unveiling a Truncated Optical Lattice Associated with a Triangular Aperture Using Light’s Orbital Angular Momentum,” Phys. Rev. Lett. 105(5), 053904 (2010).
[Crossref] [PubMed]

H. D. L. Pires, J. Woudenberg, and M. P. van Exter, “Measurement of the orbital angular momentum spectrum of partially coherent beams,” Opt. Lett. 35(6), 889–891 (2010).
[Crossref] [PubMed]

2009 (4)

Y. L. Gu and G. Gbur, “Topological reactions of optical correlation vortices,” Opt. Commun. 282(5), 709–716 (2009).
[Crossref]

T. van Dijk, H. F. Schouten, and T. D. Visser, “Coherence singularities in the field generated by partially coherent sources,” Phys. Rev. A 79(3), 033805 (2009).
[Crossref]

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]

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]

2008 (4)

I. D. Maleev and G. A. Swartzlander, “Propagation of spatial correlation vortices,” J. Opt. Soc. Am. B 25(6), 915–922 (2008).
[Crossref]

A. April, “Nonparaxial elegant Laguerre-Gaussian beams,” Opt. Lett. 33(12), 1392–1394 (2008).
[Crossref] [PubMed]

G. Anzolin, F. Tamburini, A. Bianchini, G. Umbriaco, and C. Barbieri, “Optical vortices with starlight,” Astron. Astrophys. 488(3), 1159–1165 (2008).
[Crossref]

G. C. G. Berkhout and M. W. Beijersbergen, “Method for Probing the Orbital Angular Momentum of Optical Vortices in Electromagnetic Waves from Astronomical Objects,” Phys. Rev. Lett. 101(10), 100801 (2008).
[Crossref] [PubMed]

2007 (1)

2004 (3)

D. G. Fischer and T. D. Visser, “Spatial correlation properties of focused partially coherent light,” J. Opt. Soc. Am. A 21(11), 2097–2102 (2004).
[Crossref] [PubMed]

D. M. Palacios, I. D. Maleev, A. S. Marathay, and G. A. Swartzlander, “Spatial Correlation Singularity of a Vortex Field,” Phys. Rev. Lett. 92(14), 143905 (2004).
[Crossref] [PubMed]

G. Gbur, T. D. Visser, and E. Wolf, “‘Hidden’ singularities in partially coherent wavefields,” J. Opt. A, Pure Appl. Opt. 6(5), S239–S242 (2004).
[Crossref]

2003 (4)

G. Gbur and T. D. Visser, “Coherence vortices in partially coherent beams,” Opt. Commun. 222(1), 117–125 (2003).
[Crossref]

A. Vaziri, J. W. Pan, T. Jennewein, G. Weihs, and A. Zeilinger, “Concentration of Higher Dimensional Entanglement: Qutrits of Photon Orbital Angular Momentum,” Phys. Rev. Lett. 91(22), 227902 (2003).
[Crossref] [PubMed]

G. V. Bogatyryova, C. V. Fel’de, P. V. Polyanskii, S. A. Ponomarenko, M. S. Soskin, and E. Wolf, “Partially coherent vortex beams with a separable phase,” Opt. Lett. 28(11), 878–880 (2003).
[Crossref] [PubMed]

H. F. Schouten, G. Gbur, T. D. Visser, and E. Wolf, “Phase singularities of the coherence functions in Young’s interference pattern,” Opt. Lett. 28(12), 968–970 (2003).
[Crossref] [PubMed]

2001 (1)

1998 (1)

F. Gori, M. Santarsiero, R. Borghi, and S. Vicalvi, “Partially coherent sources with helicoidal modes,” J. Mod. Opt. 45(3), 539–554 (1998).
[Crossref]

1996 (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]

1986 (1)

1985 (1)

1973 (1)

Allen, L.

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]

Anzolin, G.

G. Anzolin, F. Tamburini, A. Bianchini, G. Umbriaco, and C. Barbieri, “Optical vortices with starlight,” Astron. Astrophys. 488(3), 1159–1165 (2008).
[Crossref]

April, A.

Babiker, M.

Y. Yang, G. Thirunavukkarasu, M. Babiker, and J. Yuan, “Orbital-Angular-Momentum Mode Selection by Rotationally Symmetric Superposition of Chiral States with Application to Electron Vortex Beams,” Phys. Rev. Lett. 119(9), 094802 (2017).
[Crossref] [PubMed]

Barbieri, C.

G. Anzolin, F. Tamburini, A. Bianchini, G. Umbriaco, and C. Barbieri, “Optical vortices with starlight,” Astron. Astrophys. 488(3), 1159–1165 (2008).
[Crossref]

Beijersbergen, M. W.

G. C. G. Berkhout and M. W. Beijersbergen, “Method for Probing the Orbital Angular Momentum of Optical Vortices in Electromagnetic Waves from Astronomical Objects,” Phys. Rev. Lett. 101(10), 100801 (2008).
[Crossref] [PubMed]

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]

Berkhout, G. C. G.

G. C. G. Berkhout and M. W. Beijersbergen, “Method for Probing the Orbital Angular Momentum of Optical Vortices in Electromagnetic Waves from Astronomical Objects,” Phys. Rev. Lett. 101(10), 100801 (2008).
[Crossref] [PubMed]

Bianchini, A.

G. Anzolin, F. Tamburini, A. Bianchini, G. Umbriaco, and C. Barbieri, “Optical vortices with starlight,” Astron. Astrophys. 488(3), 1159–1165 (2008).
[Crossref]

Bogatyryova, G. V.

Borghi, R.

M. A. Porras, R. Borghi, and M. Santarsiero, “Relationship between elegant Laguerre-Gauss and Bessel-Gauss beams,” J. Opt. Soc. Am. A 18(1), 177–184 (2001).
[Crossref] [PubMed]

F. Gori, M. Santarsiero, R. Borghi, and S. Vicalvi, “Partially coherent sources with helicoidal modes,” J. Mod. Opt. 45(3), 539–554 (1998).
[Crossref]

Cai, Y.

Y. Shao, X. Lu, S. Konijnenberg, C. Zhao, Y. Cai, and H. P. Urbach, “Spatial coherence measurement and partially coherent diffractive imaging using self-referencing holography,” Opt. Express 26(4), 4479–4490 (2018).
[Crossref] [PubMed]

Y. Zhang, Y. Dong, W. Wen, F. Wang, and Y. Cai, “Spectral shift of a partially coherent standard or elegant Laguerre–Gaussian beam in turbulent atmosphere,” J. Mod. Opt. 60(5), 422–430 (2013).
[Crossref]

Y. Yang, Y. Dong, C. Zhao, and Y. Cai, “Generation and propagation of an anomalous vortex beam,” Opt. Lett. 38(24), 5418–5421 (2013).
[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 and Y. Cai, “Trapping two types of particles using a focused partially coherent elegant Laguerre-Gaussian beam,” Opt. Lett. 36(12), 2251–2253 (2011).
[Crossref] [PubMed]

F. Wang and Y. Cai, “Average intensity and spreading of partially coherent standard and elegant Laguerre- Gaussian beams in turbulent atmosphere,” Prog. Electromagn. Res 103, 33–56 (2010).

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]

Chávez-Cerda, S.

J. M. Hickmann, E. J. S. Fonseca, W. C. Soares, and S. Chávez-Cerda, “Unveiling a Truncated Optical Lattice Associated with a Triangular Aperture Using Light’s Orbital Angular Momentum,” Phys. Rev. Lett. 105(5), 053904 (2010).
[Crossref] [PubMed]

Chen, M.

Y. Yang, M. Chen, M. Mazilu, A. Mourka, Y. Liu, and K. Dholakia, “Effect of the radial and azimuthal mode indices of a partially coherent vortex field upon a spatial correlation singularity,” New J. Phys. 15(11), 113053 (2013).
[Crossref]

Cheng, D.

Cui, Z.

H. Xu, H. Luo, Z. Cui, and J. Qu, “Polarization characteristics of partially coherent elegant Laguerre-Gaussian beams in non-Kolmogorov turbulence,” Opt. Lasers Eng. 50(5), 760–766 (2012).
[Crossref]

Dan, Y.

T. Yang, Y. Xu, H. Tian, D. Die, Q. Du, B. Zhang, and Y. Dan, “Propagation of partially coherent Laguerre Gaussian beams through inhomogeneous turbulent atmosphere,” J. Opt. Soc. Am. A 34(5), 713–720 (2017).
[Crossref] [PubMed]

T. Yang, Y. Xu, H. Tiana, Q. Du, D. Die, and Y. Dan, “Comparative study of propagation properties of partially coherent standard and elegant Hermite-Gaussian beams in inhomogeneous atmospheric turbulence,” Optik (Stuttg.) 127(22), 10772–10779 (2016).
[Crossref]

Dholakia, K.

Y. Yang, M. Chen, M. Mazilu, A. Mourka, Y. Liu, and K. Dholakia, “Effect of the radial and azimuthal mode indices of a partially coherent vortex field upon a spatial correlation singularity,” New J. Phys. 15(11), 113053 (2013).
[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]

Die, D.

T. Yang, Y. Xu, H. Tian, D. Die, Q. Du, B. Zhang, and Y. Dan, “Propagation of partially coherent Laguerre Gaussian beams through inhomogeneous turbulent atmosphere,” J. Opt. Soc. Am. A 34(5), 713–720 (2017).
[Crossref] [PubMed]

T. Yang, Y. Xu, H. Tiana, Q. Du, D. Die, and Y. Dan, “Comparative study of propagation properties of partially coherent standard and elegant Hermite-Gaussian beams in inhomogeneous atmospheric turbulence,” Optik (Stuttg.) 127(22), 10772–10779 (2016).
[Crossref]

Djordjevic, I. B.

Dong, Y.

Y. Yang, Y. Dong, C. Zhao, and Y. Cai, “Generation and propagation of an anomalous vortex beam,” Opt. Lett. 38(24), 5418–5421 (2013).
[Crossref] [PubMed]

Y. Zhang, Y. Dong, W. Wen, F. Wang, and Y. Cai, “Spectral shift of a partially coherent standard or elegant Laguerre–Gaussian beam in turbulent atmosphere,” J. Mod. Opt. 60(5), 422–430 (2013).
[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]

Du, Q.

T. Yang, Y. Xu, H. Tian, D. Die, Q. Du, B. Zhang, and Y. Dan, “Propagation of partially coherent Laguerre Gaussian beams through inhomogeneous turbulent atmosphere,” J. Opt. Soc. Am. A 34(5), 713–720 (2017).
[Crossref] [PubMed]

T. Yang, Y. Xu, H. Tiana, Q. Du, D. Die, and Y. Dan, “Comparative study of propagation properties of partially coherent standard and elegant Hermite-Gaussian beams in inhomogeneous atmospheric turbulence,” Optik (Stuttg.) 127(22), 10772–10779 (2016).
[Crossref]

Escalante, A. Y.

A. Y. Escalante, B. Perez-Garcia, R. I. Hernandez-Aranda, and G. A. Swartzlander, “Determination of angular momentum content in partially coherent beams through cross correlation measurements,” Proc. SPIE 8843, 884302 (2013).
[Crossref]

Fel’de, C. V.

Fischer, D. G.

Fonseca, E. J. S.

J. M. Hickmann, E. J. S. Fonseca, W. C. Soares, and S. Chávez-Cerda, “Unveiling a Truncated Optical Lattice Associated with a Triangular Aperture Using Light’s Orbital Angular Momentum,” Phys. Rev. Lett. 105(5), 053904 (2010).
[Crossref] [PubMed]

Fukumitsu, O.

Gahagan, K. T.

Gao, H.

Gbur, G.

Y. L. Gu and G. Gbur, “Topological reactions of optical correlation vortices,” Opt. Commun. 282(5), 709–716 (2009).
[Crossref]

G. Gbur, T. D. Visser, and E. Wolf, “‘Hidden’ singularities in partially coherent wavefields,” J. Opt. A, Pure Appl. Opt. 6(5), S239–S242 (2004).
[Crossref]

G. Gbur and T. D. Visser, “Coherence vortices in partially coherent beams,” Opt. Commun. 222(1), 117–125 (2003).
[Crossref]

H. F. Schouten, G. Gbur, T. D. Visser, and E. Wolf, “Phase singularities of the coherence functions in Young’s interference pattern,” Opt. Lett. 28(12), 968–970 (2003).
[Crossref] [PubMed]

Gori, F.

F. Gori, M. Santarsiero, R. Borghi, and S. Vicalvi, “Partially coherent sources with helicoidal modes,” J. Mod. Opt. 45(3), 539–554 (1998).
[Crossref]

Gu, Y. L.

Y. L. Gu and G. Gbur, “Topological reactions of optical correlation vortices,” Opt. Commun. 282(5), 709–716 (2009).
[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]

Y. Han and G. Zhao, “Measuring the topological charge of optical vortices with an axicon,” Opt. Lett. 36(11), 2017–2019 (2011).
[Crossref] [PubMed]

Hernandez-Aranda, R. I.

A. Y. Escalante, B. Perez-Garcia, R. I. Hernandez-Aranda, and G. A. Swartzlander, “Determination of angular momentum content in partially coherent beams through cross correlation measurements,” Proc. SPIE 8843, 884302 (2013).
[Crossref]

Hickmann, J. M.

J. M. Hickmann, E. J. S. Fonseca, W. C. Soares, and S. Chávez-Cerda, “Unveiling a Truncated Optical Lattice Associated with a Triangular Aperture Using Light’s Orbital Angular Momentum,” Phys. Rev. Lett. 105(5), 053904 (2010).
[Crossref] [PubMed]

Huang, Z.

Jennewein, T.

A. Vaziri, J. W. Pan, T. Jennewein, G. Weihs, and A. Zeilinger, “Concentration of Higher Dimensional Entanglement: Qutrits of Photon Orbital Angular Momentum,” Phys. Rev. Lett. 91(22), 227902 (2003).
[Crossref] [PubMed]

Konijnenberg, S.

Korotkova, O.

Li, F.

Li, Y.

Liu, R.

Liu, Y.

Y. Yang, M. Chen, M. Mazilu, A. Mourka, Y. Liu, and K. Dholakia, “Effect of the radial and azimuthal mode indices of a partially coherent vortex field upon a spatial correlation singularity,” New J. Phys. 15(11), 113053 (2013).
[Crossref]

Liu, Y. D.

Y. Yang and Y. D. Liu, “Measuring azimuthal and radial mode indices of a partially coherent vortex field,” J. Opt. 18(1), 015604 (2016).
[Crossref]

Long, J.

Lu, X.

Luo, H.

H. Xu, H. Luo, Z. Cui, and J. Qu, “Polarization characteristics of partially coherent elegant Laguerre-Gaussian beams in non-Kolmogorov turbulence,” Opt. Lasers Eng. 50(5), 760–766 (2012).
[Crossref]

Maleev, I. D.

I. D. Maleev and G. A. Swartzlander, “Propagation of spatial correlation vortices,” J. Opt. Soc. Am. B 25(6), 915–922 (2008).
[Crossref]

D. M. Palacios, I. D. Maleev, A. S. Marathay, and G. A. Swartzlander, “Spatial Correlation Singularity of a Vortex Field,” Phys. Rev. Lett. 92(14), 143905 (2004).
[Crossref] [PubMed]

Marathay, A. S.

D. M. Palacios, I. D. Maleev, A. S. Marathay, and G. A. Swartzlander, “Spatial Correlation Singularity of a Vortex Field,” Phys. Rev. Lett. 92(14), 143905 (2004).
[Crossref] [PubMed]

Mazilu, M.

Y. Yang, M. Chen, M. Mazilu, A. Mourka, Y. Liu, and K. Dholakia, “Effect of the radial and azimuthal mode indices of a partially coherent vortex field upon a spatial correlation singularity,” New J. Phys. 15(11), 113053 (2013).
[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]

Mourka, A.

Y. Yang, M. Chen, M. Mazilu, A. Mourka, Y. Liu, and K. Dholakia, “Effect of the radial and azimuthal mode indices of a partially coherent vortex field upon a spatial correlation singularity,” New J. Phys. 15(11), 113053 (2013).
[Crossref]

Nasalski, W.

Palacios, D. M.

D. M. Palacios, I. D. Maleev, A. S. Marathay, and G. A. Swartzlander, “Spatial Correlation Singularity of a Vortex Field,” Phys. Rev. Lett. 92(14), 143905 (2004).
[Crossref] [PubMed]

Pan, J. W.

A. Vaziri, J. W. Pan, T. Jennewein, G. Weihs, and A. Zeilinger, “Concentration of Higher Dimensional Entanglement: Qutrits of Photon Orbital Angular Momentum,” Phys. Rev. Lett. 91(22), 227902 (2003).
[Crossref] [PubMed]

Perez-Garcia, B.

A. Y. Escalante, B. Perez-Garcia, R. I. Hernandez-Aranda, and G. A. Swartzlander, “Determination of angular momentum content in partially coherent beams through cross correlation measurements,” Proc. SPIE 8843, 884302 (2013).
[Crossref]

Pires, H. D. L.

Polyanskii, P. V.

Ponomarenko, S. A.

Porras, M. A.

Pu, J.

Qu, J.

H. Xu, H. Luo, Z. Cui, and J. Qu, “Polarization characteristics of partially coherent elegant Laguerre-Gaussian beams in non-Kolmogorov turbulence,” Opt. Lasers Eng. 50(5), 760–766 (2012).
[Crossref]

Rao, L.

Santarsiero, M.

M. A. Porras, R. Borghi, and M. Santarsiero, “Relationship between elegant Laguerre-Gauss and Bessel-Gauss beams,” J. Opt. Soc. Am. A 18(1), 177–184 (2001).
[Crossref] [PubMed]

F. Gori, M. Santarsiero, R. Borghi, and S. Vicalvi, “Partially coherent sources with helicoidal modes,” J. Mod. Opt. 45(3), 539–554 (1998).
[Crossref]

Schouten, H. F.

T. van Dijk, H. F. Schouten, and T. D. Visser, “Coherence singularities in the field generated by partially coherent sources,” Phys. Rev. A 79(3), 033805 (2009).
[Crossref]

H. F. Schouten, G. Gbur, T. D. Visser, and E. Wolf, “Phase singularities of the coherence functions in Young’s interference pattern,” Opt. Lett. 28(12), 968–970 (2003).
[Crossref] [PubMed]

Shao, Y.

Siegman, A. E.

Soares, W. C.

J. M. Hickmann, E. J. S. Fonseca, W. C. Soares, and S. Chávez-Cerda, “Unveiling a Truncated Optical Lattice Associated with a Triangular Aperture Using Light’s Orbital Angular Momentum,” Phys. Rev. Lett. 105(5), 053904 (2010).
[Crossref] [PubMed]

Soskin, M. S.

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.

A. Y. Escalante, B. Perez-Garcia, R. I. Hernandez-Aranda, and G. A. Swartzlander, “Determination of angular momentum content in partially coherent beams through cross correlation measurements,” Proc. SPIE 8843, 884302 (2013).
[Crossref]

I. D. Maleev and G. A. Swartzlander, “Propagation of spatial correlation vortices,” J. Opt. Soc. Am. B 25(6), 915–922 (2008).
[Crossref]

D. M. Palacios, I. D. Maleev, A. S. Marathay, and G. A. Swartzlander, “Spatial Correlation Singularity of a Vortex Field,” Phys. Rev. Lett. 92(14), 143905 (2004).
[Crossref] [PubMed]

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

Takenaka, T.

Tamburini, F.

G. Anzolin, F. Tamburini, A. Bianchini, G. Umbriaco, and C. Barbieri, “Optical vortices with starlight,” Astron. Astrophys. 488(3), 1159–1165 (2008).
[Crossref]

Thirunavukkarasu, G.

Y. Yang, G. Thirunavukkarasu, M. Babiker, and J. Yuan, “Orbital-Angular-Momentum Mode Selection by Rotationally Symmetric Superposition of Chiral States with Application to Electron Vortex Beams,” Phys. Rev. Lett. 119(9), 094802 (2017).
[Crossref] [PubMed]

Tian, H.

Tiana, H.

T. Yang, Y. Xu, H. Tiana, Q. Du, D. Die, and Y. Dan, “Comparative study of propagation properties of partially coherent standard and elegant Hermite-Gaussian beams in inhomogeneous atmospheric turbulence,” Optik (Stuttg.) 127(22), 10772–10779 (2016).
[Crossref]

Umbriaco, G.

G. Anzolin, F. Tamburini, A. Bianchini, G. Umbriaco, and C. Barbieri, “Optical vortices with starlight,” Astron. Astrophys. 488(3), 1159–1165 (2008).
[Crossref]

Urbach, H. P.

van Dijk, T.

T. van Dijk, H. F. Schouten, and T. D. Visser, “Coherence singularities in the field generated by partially coherent sources,” Phys. Rev. A 79(3), 033805 (2009).
[Crossref]

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]

van Exter, M. P.

Vaziri, A.

A. Vaziri, J. W. Pan, T. Jennewein, G. Weihs, and A. Zeilinger, “Concentration of Higher Dimensional Entanglement: Qutrits of Photon Orbital Angular Momentum,” Phys. Rev. Lett. 91(22), 227902 (2003).
[Crossref] [PubMed]

Vicalvi, S.

F. Gori, M. Santarsiero, R. Borghi, and S. Vicalvi, “Partially coherent sources with helicoidal modes,” J. Mod. Opt. 45(3), 539–554 (1998).
[Crossref]

Visser, T. D.

T. van Dijk, H. F. Schouten, and T. D. Visser, “Coherence singularities in the field generated by partially coherent sources,” Phys. Rev. A 79(3), 033805 (2009).
[Crossref]

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]

D. G. Fischer and T. D. Visser, “Spatial correlation properties of focused partially coherent light,” J. Opt. Soc. Am. A 21(11), 2097–2102 (2004).
[Crossref] [PubMed]

G. Gbur, T. D. Visser, and E. Wolf, “‘Hidden’ singularities in partially coherent wavefields,” J. Opt. A, Pure Appl. Opt. 6(5), S239–S242 (2004).
[Crossref]

G. Gbur and T. D. Visser, “Coherence vortices in partially coherent beams,” Opt. Commun. 222(1), 117–125 (2003).
[Crossref]

H. F. Schouten, G. Gbur, T. D. Visser, and E. Wolf, “Phase singularities of the coherence functions in Young’s interference pattern,” Opt. Lett. 28(12), 968–970 (2003).
[Crossref] [PubMed]

Wang, F.

Y. Zhang, Y. Dong, W. Wen, F. Wang, and Y. Cai, “Spectral shift of a partially coherent standard or elegant Laguerre–Gaussian beam in turbulent atmosphere,” J. Mod. Opt. 60(5), 422–430 (2013).
[Crossref]

J. Long, R. Liu, F. Wang, Y. Wang, P. Zhang, H. Gao, and F. Li, “Evaluating Laguerre-Gaussian beams with an invariant parameter,” Opt. Lett. 38(16), 3047–3049 (2013).
[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]

F. Wang and Y. Cai, “Average intensity and spreading of partially coherent standard and elegant Laguerre- Gaussian beams in turbulent atmosphere,” Prog. Electromagn. Res 103, 33–56 (2010).

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, Y.

Weihs, G.

A. Vaziri, J. W. Pan, T. Jennewein, G. Weihs, and A. Zeilinger, “Concentration of Higher Dimensional Entanglement: Qutrits of Photon Orbital Angular Momentum,” Phys. Rev. Lett. 91(22), 227902 (2003).
[Crossref] [PubMed]

Wen, W.

Y. Zhang, Y. Dong, W. Wen, F. Wang, and Y. Cai, “Spectral shift of a partially coherent standard or elegant Laguerre–Gaussian beam in turbulent atmosphere,” J. Mod. Opt. 60(5), 422–430 (2013).
[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]

Wolf, E.

Woudenberg, J.

Xu, H.

H. Xu, H. Luo, Z. Cui, and J. Qu, “Polarization characteristics of partially coherent elegant Laguerre-Gaussian beams in non-Kolmogorov turbulence,” Opt. Lasers Eng. 50(5), 760–766 (2012).
[Crossref]

Xu, Y.

Xu, Z.

Yang, T.

T. Yang, Y. Xu, H. Tian, D. Die, Q. Du, B. Zhang, and Y. Dan, “Propagation of partially coherent Laguerre Gaussian beams through inhomogeneous turbulent atmosphere,” J. Opt. Soc. Am. A 34(5), 713–720 (2017).
[Crossref] [PubMed]

T. Yang, Y. Xu, H. Tiana, Q. Du, D. Die, and Y. Dan, “Comparative study of propagation properties of partially coherent standard and elegant Hermite-Gaussian beams in inhomogeneous atmospheric turbulence,” Optik (Stuttg.) 127(22), 10772–10779 (2016).
[Crossref]

Yang, Y.

Y. Yang, G. Thirunavukkarasu, M. Babiker, and J. Yuan, “Orbital-Angular-Momentum Mode Selection by Rotationally Symmetric Superposition of Chiral States with Application to Electron Vortex Beams,” Phys. Rev. Lett. 119(9), 094802 (2017).
[Crossref] [PubMed]

Y. Yang and Y. D. Liu, “Measuring azimuthal and radial mode indices of a partially coherent vortex field,” J. Opt. 18(1), 015604 (2016).
[Crossref]

Y. Yang, M. Chen, M. Mazilu, A. Mourka, Y. Liu, and K. Dholakia, “Effect of the radial and azimuthal mode indices of a partially coherent vortex field upon a spatial correlation singularity,” New J. Phys. 15(11), 113053 (2013).
[Crossref]

Y. Yang, Y. Dong, C. Zhao, and Y. Cai, “Generation and propagation of an anomalous vortex beam,” Opt. Lett. 38(24), 5418–5421 (2013).
[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]

Yokota, M.

Yuan, J.

Y. Yang, G. Thirunavukkarasu, M. Babiker, and J. Yuan, “Orbital-Angular-Momentum Mode Selection by Rotationally Symmetric Superposition of Chiral States with Application to Electron Vortex Beams,” Phys. Rev. Lett. 119(9), 094802 (2017).
[Crossref] [PubMed]

Zauderer, E.

Zeilinger, A.

A. Vaziri, J. W. Pan, T. Jennewein, G. Weihs, and A. Zeilinger, “Concentration of Higher Dimensional Entanglement: Qutrits of Photon Orbital Angular Momentum,” Phys. Rev. Lett. 91(22), 227902 (2003).
[Crossref] [PubMed]

Zhang, B.

Zhang, P.

Zhang, Y.

Y. Zhang, Y. Dong, W. Wen, F. Wang, and Y. Cai, “Spectral shift of a partially coherent standard or elegant Laguerre–Gaussian beam in turbulent atmosphere,” J. Mod. Opt. 60(5), 422–430 (2013).
[Crossref]

Zhao, C.

Zhao, G.

Zhao, X.

Zhu, T.

Appl. Opt. (1)

Appl. Phys. Lett. (1)

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]

Astron. Astrophys. (1)

G. Anzolin, F. Tamburini, A. Bianchini, G. Umbriaco, and C. Barbieri, “Optical vortices with starlight,” Astron. Astrophys. 488(3), 1159–1165 (2008).
[Crossref]

J. Mod. Opt. (2)

F. Gori, M. Santarsiero, R. Borghi, and S. Vicalvi, “Partially coherent sources with helicoidal modes,” J. Mod. Opt. 45(3), 539–554 (1998).
[Crossref]

Y. Zhang, Y. Dong, W. Wen, F. Wang, and Y. Cai, “Spectral shift of a partially coherent standard or elegant Laguerre–Gaussian beam in turbulent atmosphere,” J. Mod. Opt. 60(5), 422–430 (2013).
[Crossref]

J. Opt. (1)

Y. Yang and Y. D. Liu, “Measuring azimuthal and radial mode indices of a partially coherent vortex field,” J. Opt. 18(1), 015604 (2016).
[Crossref]

J. Opt. A, Pure Appl. Opt. (1)

G. Gbur, T. D. Visser, and E. Wolf, “‘Hidden’ singularities in partially coherent wavefields,” J. Opt. A, Pure Appl. Opt. 6(5), S239–S242 (2004).
[Crossref]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (8)

J. Opt. Soc. Am. B (1)

New J. Phys. (1)

Y. Yang, M. Chen, M. Mazilu, A. Mourka, Y. Liu, and K. Dholakia, “Effect of the radial and azimuthal mode indices of a partially coherent vortex field upon a spatial correlation singularity,” New J. Phys. 15(11), 113053 (2013).
[Crossref]

Opt. Commun. (2)

Y. L. Gu and G. Gbur, “Topological reactions of optical correlation vortices,” Opt. Commun. 282(5), 709–716 (2009).
[Crossref]

G. Gbur and T. D. Visser, “Coherence vortices in partially coherent beams,” Opt. Commun. 222(1), 117–125 (2003).
[Crossref]

Opt. Express (3)

Opt. Lasers Eng. (1)

H. Xu, H. Luo, Z. Cui, and J. Qu, “Polarization characteristics of partially coherent elegant Laguerre-Gaussian beams in non-Kolmogorov turbulence,” Opt. Lasers Eng. 50(5), 760–766 (2012).
[Crossref]

Opt. Lett. (11)

A. April, “Nonparaxial elegant Laguerre-Gaussian beams,” Opt. Lett. 33(12), 1392–1394 (2008).
[Crossref] [PubMed]

W. Nasalski, “Exact elegant Laguerre-Gaussian vector wave packets,” Opt. Lett. 38(6), 809–811 (2013).
[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]

H. D. L. Pires, J. Woudenberg, and M. P. van Exter, “Measurement of the orbital angular momentum spectrum of partially coherent beams,” Opt. Lett. 35(6), 889–891 (2010).
[Crossref] [PubMed]

J. Long, R. Liu, F. Wang, Y. Wang, P. Zhang, H. Gao, and F. Li, “Evaluating Laguerre-Gaussian beams with an invariant parameter,” Opt. Lett. 38(16), 3047–3049 (2013).
[Crossref] [PubMed]

H. F. Schouten, G. Gbur, T. D. Visser, and E. Wolf, “Phase singularities of the coherence functions in Young’s interference pattern,” Opt. Lett. 28(12), 968–970 (2003).
[Crossref] [PubMed]

G. V. Bogatyryova, C. V. Fel’de, P. V. Polyanskii, S. A. Ponomarenko, M. S. Soskin, and E. Wolf, “Partially coherent vortex beams with a separable phase,” Opt. Lett. 28(11), 878–880 (2003).
[Crossref] [PubMed]

Y. Han and G. Zhao, “Measuring the topological charge of optical vortices with an axicon,” Opt. Lett. 36(11), 2017–2019 (2011).
[Crossref] [PubMed]

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

C. Zhao and Y. Cai, “Trapping two types of particles using a focused partially coherent elegant Laguerre-Gaussian beam,” Opt. Lett. 36(12), 2251–2253 (2011).
[Crossref] [PubMed]

Y. Yang, Y. Dong, C. Zhao, and Y. Cai, “Generation and propagation of an anomalous vortex beam,” Opt. Lett. 38(24), 5418–5421 (2013).
[Crossref] [PubMed]

Optik (Stuttg.) (1)

T. Yang, Y. Xu, H. Tiana, Q. Du, D. Die, and Y. Dan, “Comparative study of propagation properties of partially coherent standard and elegant Hermite-Gaussian beams in inhomogeneous atmospheric turbulence,” Optik (Stuttg.) 127(22), 10772–10779 (2016).
[Crossref]

Phys. Rev. A (2)

T. van Dijk, H. F. Schouten, and T. D. Visser, “Coherence singularities in the field generated by partially coherent sources,” Phys. Rev. A 79(3), 033805 (2009).
[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]

Phys. Rev. Lett. (5)

Y. Yang, G. Thirunavukkarasu, M. Babiker, and J. Yuan, “Orbital-Angular-Momentum Mode Selection by Rotationally Symmetric Superposition of Chiral States with Application to Electron Vortex Beams,” Phys. Rev. Lett. 119(9), 094802 (2017).
[Crossref] [PubMed]

A. Vaziri, J. W. Pan, T. Jennewein, G. Weihs, and A. Zeilinger, “Concentration of Higher Dimensional Entanglement: Qutrits of Photon Orbital Angular Momentum,” Phys. Rev. Lett. 91(22), 227902 (2003).
[Crossref] [PubMed]

G. C. G. Berkhout and M. W. Beijersbergen, “Method for Probing the Orbital Angular Momentum of Optical Vortices in Electromagnetic Waves from Astronomical Objects,” Phys. Rev. Lett. 101(10), 100801 (2008).
[Crossref] [PubMed]

J. M. Hickmann, E. J. S. Fonseca, W. C. Soares, and S. Chávez-Cerda, “Unveiling a Truncated Optical Lattice Associated with a Triangular Aperture Using Light’s Orbital Angular Momentum,” Phys. Rev. Lett. 105(5), 053904 (2010).
[Crossref] [PubMed]

D. M. Palacios, I. D. Maleev, A. S. Marathay, and G. A. Swartzlander, “Spatial Correlation Singularity of a Vortex Field,” Phys. Rev. Lett. 92(14), 143905 (2004).
[Crossref] [PubMed]

Proc. SPIE (1)

A. Y. Escalante, B. Perez-Garcia, R. I. Hernandez-Aranda, and G. A. Swartzlander, “Determination of angular momentum content in partially coherent beams through cross correlation measurements,” Proc. SPIE 8843, 884302 (2013).
[Crossref]

Prog. Electromagn. Res (1)

F. Wang and Y. Cai, “Average intensity and spreading of partially coherent standard and elegant Laguerre- Gaussian beams in turbulent atmosphere,” Prog. Electromagn. Res 103, 33–56 (2010).

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Figures (4)

Fig. 1
Fig. 1 Distribution (contour graph) of CDOC of a partially coherent ELG beam for different values of l and δ.
Fig. 2
Fig. 2 Distribution (contour graph) of CDOC of partially coherent ELG beams with δ = w0 for different values of l and p.
Fig. 3
Fig. 3 Experimental set up for measuring the mutual correlation function of the focused partially coherent elegant Laguerre-Gaussian beam. BE, beam expander; L1, L2, L3 and L4, lenses; RGGD, rotating ground glass disk; GAF, Gaussian amplitude filter; SLM1 and SLM2, spatial light modulators; SPP, spiral phase plate; BS, beam splitter; CCD, charge coupled device.
Fig. 4
Fig. 4 Experimental results of complex degree of coherence for the partially coherent elegant Laguerre-Gaussian beam with w0 = 0.62mm, δ = 0.35mm, p = 1 and: (a) l = 1; (b) l = 2; (c) l = 3, and the corresponding theoretical results (d),(e),(f).

Equations (13)

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

E ( ρ , θ ; 0 ) = ( ρ w 0 ) | l | L p | l | ( ρ 2 w 0 2 ) exp ( ρ 2 w 0 2 ) exp ( i l θ ) ,
Γ ( ρ 1 , ρ 2 ) = E ( ρ 1 ) E ( ρ 2 ) ,
C ( ρ 1 , ρ 2 ) = C ( | ρ 1 ρ 2 | ) = exp [ | ρ 1 ρ 2 | 2 δ 2 ] ,
Γ ( ρ 1 , ρ 2 ; 0 ) = ( ρ 1 ρ 2 w 0 2 ) | l | L p | l | ( ρ 1 2 w 0 2 ) L p | l | ( ρ 2 2 w 0 2 ) exp ( ρ 1 2 + ρ 2 2 w 0 2 ) × exp [ | ρ 1 ρ 2 | 2 δ 2 ] exp [ i l ( θ 2 θ 1 ) ] .
Γ ( ρ 1 ' , ρ 2 ' ;z ) = ( 1 λ z ) 2 Γ ( ρ 1 , ρ 2 , 0 ) exp [ i 2 π λ z ( ρ 1 ' ρ 1 ρ 2 ' ρ 2 ) ] d ρ 1 d ρ 2 ,
Γ ( x 1 , y 1 , x 2 , y 2 ) = ( 1 z w 0 | l | λ ) 2 L p | l | [ ( x 10 + i y 10 ) ( x 10 i y 10 ) w 0 2 ] L p | l | [ ( x 20 + i y 20 ) ( x 20 i y 20 ) w 0 2 ] × ( x 10 + i y 10 ) | l | ( x 20 i y 20 ) | l | F x 0 F y 0 d x 10 d x 20 d y 10 d y 20 ,
Fx 0 = exp [ g ( x 10 2 + x 20 2 ) + 2 x 10 x 20 δ 2 + i k ( x 1 x 10 - x 2 x 20 ) z ] ,
Fy 0 = exp [ g ( y 10 2 + y 20 2 ) + 2 y 10 y 20 δ 2 + i k ( y 1 y 10 - y 2 y 20 ) z ] ,
g = 1 δ 2 1 w 0 2 .
μ ( x 1 , y 1 , 0 , 0 , z ) = Γ ( x 1 , y 1 , 0 , 0 , z ) I ( x 1 , y 1 , z ) I ( 0 , 0 , z ) ,
I ( x 1 , y 1 , z ) = Γ ( x 1 , y 1 , x 1 , y 1 , z ) .
I ( k ) = [ T ( ρ 1 ) + γ δ ( ρ 1 0 ) ] [ T ( ρ 2 ) + γ δ ( ρ 2 0 ) ] * × Γ ( ρ 1 , ρ 2 ) exp [ i 2 π k ( ρ 1 ρ 2 ) ] d 2 ρ 1 d 2 ρ 2 = I 0 ( k ) + γ γ * Γ ( ρ 0 , ρ 0 ) + γ [ T ( ( ρ ρ 0 ) ) Γ ( ( ρ ρ 0 ) , ρ 0 ) ] * exp [ i 2 π k ρ ] d ρ + γ * T ( ρ + ρ 0 ) Γ ( ρ + ρ 0 , ρ 0 ) exp [ i 2 π k ρ ] d ρ .
F T 1 [ I ( k ) ] ( k ) = F T 1 [ I 0 ( k ) ] ( k ) + γ γ * Γ ( ρ 0 , ρ 0 ) δ ( ρ ) + γ [ Γ ( ( ρ ρ 0 ) , ρ 0 ) T ( ( ρ ρ 0 ) ) ] * . + γ * [ Γ ( ρ + ρ 0 , ρ 0 ) T ( ρ + ρ 0 ) ]

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