Abstract

We study the effects of non-Kolmogorov turbulence on the orbital angular momentum (OAM) of Hypergeometric-Gaussian (HyGG) beams in a paraxial atmospheric link. The received power and crosstalk power of OAM states of the HyGG beams are established. It is found that the hollowness parameter of the HyGG beams plays an important role in the received power and crosstalk power. The larger values of hollowness parameter give rise to the higher received power and lower crosstalk power. The results also show that the smaller OAM quantum number and longer wavelength of the launch beam may lead to the higher received power and lower crosstalk power.

© 2015 Optical Society of America

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  1. V. V. Kotlyar, R. V. Skidanov, S. N. Khonina, and V. A. Soifer, “Hypergeometric modes,” Opt. Lett. 32(7), 742–744 (2007).
    [Crossref] [PubMed]
  2. V. V. Kotlyar, A. A. Kovalev, R. V. Skidanov, S. N. Khonina, and J. Turunen, “Generating hypergeometric laser beams with a diffractive optical element,” Appl. Opt. 47(32), 6124–6133 (2008).
    [Crossref] [PubMed]
  3. R. V. Skidanov, S. N. Khonina, and A. A. Morozov, “Optical rotation of microparticles in hypergeometric beams formed by diffraction optical elements with multilevel microrelief,” J. Opt. Technol. 80(10), 585–589 (2013).
    [Crossref]
  4. J. Chen, “Production of confluent hypergeometric beam by computer-generated hologram,” Opt. Eng. 50(2), 024201 (2011).
    [Crossref]
  5. B. de Lima Bernardo and F. Moraes, “Data transmission by hypergeometric modes through a hyperbolic-index medium,” Opt. Express 19(12), 11264–11270 (2011).
    [Crossref] [PubMed]
  6. J. Li and Y. Chen, “Propagation of confluent hypergeometric beam through uniaxial crystals orthogonal to the optical axis,” Opt. Laser Technol. 44(5), 1603–1610 (2012).
    [Crossref]
  7. V. V. Kotlyar, A. A. Kovalev, and A. G. Nalimov, “Propagation of hypergeometric laser beams in a medium with a parabolic refractive index,” J. Opt. 15(12), 125706 (2013).
    [Crossref]
  8. H. T. Eyyuboğlu and Y. Cai, “Hypergeometric Gaussian beam and its propagation in turbulence,” Opt. Commun. 285(21–22), 4194–4199 (2012).
    [Crossref]
  9. H. T. Eyyuboğlu, “Scintillation analysis of hypergeometric Gaussian beam via phase screen method,” Opt. Commun. 309, 103–107 (2013).
    [Crossref]
  10. E. Karimi, G. Zito, B. Piccirillo, L. Marrucci, and E. Santamato, “Hypergeometric-Gaussian modes,” Opt. Lett. 32(21), 3053–3055 (2007).
    [Crossref] [PubMed]
  11. E. Karimi, B. Piccirillo, L. Marrucci, and E. Santamato, “Improved focusing with hypergeometric-gaussian type-II optical modes,” Opt. Express 16(25), 21069–21075 (2008).
    [Crossref] [PubMed]
  12. G. Molina-Terriza, J. P. Torres, and L. Torner, “Management of the angular momentum of light: preparation of photons in multidimensional vector states of angular momentum,” Phys. Rev. Lett. 88(1), 013601 (2001).
    [Crossref] [PubMed]
  13. C. Paterson, “Atmospheric turbulence and orbital angular momentum of single photons for optical communication,” Phys. Rev. Lett. 94(15), 153901 (2005).
    [Crossref] [PubMed]
  14. E. Golbraikh, H. Branover, N. S. Kopeika, and A. Zilberman, “Non-Kolmogorov atmospheric turbulence and optical signal propagation,” Nonlinear Process. Geophys. 13(3), 297–301 (2006).
    [Crossref]
  15. C. Rao, W. Jiang, and N. Ling, “Spatial and temporal characterization of phase fluctuations in non-Kolmogorov atmospheric turbulence,” J. Mod. Opt. 47(6), 1111–1126 (2000).
    [Crossref]
  16. A. Zilberman, E. Golbraikh, and N. S. Kopeika, “Propagation of electromagnetic waves in Kolmogorov and non-Kolmogorov atmospheric turbulence: three-layer altitude model,” Appl. Opt. 47(34), 6385–6391 (2008).
    [Crossref] [PubMed]
  17. A. Zilberman, E. Golbraikh, N. S. Kopeika, A. Virtser, I. Kupershmidt, and Y. Shtemler, “Lidar study of aerosol turbulence characteristics in the troposphere: Kolmogorov and non-Kolmogorov turbulence,” Atmos. Res. 88(1), 66–77 (2008).
    [Crossref]
  18. G. Wu, H. Guo, S. Yu, and B. Luo, “Spreading and direction of Gaussian-Schell model beam through a non-Kolmogorov turbulence,” Opt. Lett. 35(5), 715–717 (2010).
    [Crossref] [PubMed]
  19. I. Toselli, L. C. Andrews, R. L. Phillips, and V. Ferrero, “Angle of arrival fluctuations for free space laser beam propagation through non kolmogorov turbulence,” Proc. SPIE 6551, 65510E (2007).
    [Crossref]
  20. I. Toselli, L. C. Andrews, R. L. Phillips, and V. Ferrero, “Free-space optical system performance for laser beam propagation through non-Kolmogorov turbulence,” Opt. Eng. 47(2), 026001 (2008).
  21. Y. Zhang, Y. Wang, J. Xu, J. Wang, and J. Jia, “Orbital angular momentum crosstalk of single photons propagation in a slant non-Kolmogorov turbulence channel,” Opt. Commun. 284(5), 1132–1138 (2011).
    [Crossref]
  22. L. C. Andrews and R. L. Phillips, Laser Beam Propagation Through Random Media (SPIE, 2005).
  23. L. Torner, J. Torres, and S. Carrasco, “Digital spiral imaging,” Opt. Express 13(3), 873–881 (2005).
    [Crossref] [PubMed]
  24. A. Jeffrey and D. Zwillinger, Table of Integrals, Series, and Products (Academic, 2007).
  25. Y. Liu, C. Gao, M. Gao, and F. Li, “Coherent-mode representation and orbital angular momentum spectrum of partially coherent beam,” Opt. Commun. 281(8), 1968–1975 (2008).
    [Crossref]
  26. G. A. Tyler and R. W. Boyd, “Influence of atmospheric turbulence on the propagation of quantum states of light carrying orbital angular momentum,” Opt. Lett. 34(2), 142–144 (2009).
    [Crossref] [PubMed]
  27. J. Ou, Y. Jiang, J. Zhang, H. Tang, Y. He, S. Wang, and J. Liao, “Spreading of spiral spectrum of Bessel–Gaussian beam in non-Kolmogorov turbulence,” Opt. Commun. 318, 95–99 (2014).
    [Crossref]
  28. B. E. Stribling, B. M. Welsh, and M. C. Roggemann, “Optical propagation in non-Kolmogorov atmospheric turbulence,” Proc. SPIE 2471, 181–196 (1995).
    [Crossref]

2014 (1)

J. Ou, Y. Jiang, J. Zhang, H. Tang, Y. He, S. Wang, and J. Liao, “Spreading of spiral spectrum of Bessel–Gaussian beam in non-Kolmogorov turbulence,” Opt. Commun. 318, 95–99 (2014).
[Crossref]

2013 (3)

V. V. Kotlyar, A. A. Kovalev, and A. G. Nalimov, “Propagation of hypergeometric laser beams in a medium with a parabolic refractive index,” J. Opt. 15(12), 125706 (2013).
[Crossref]

H. T. Eyyuboğlu, “Scintillation analysis of hypergeometric Gaussian beam via phase screen method,” Opt. Commun. 309, 103–107 (2013).
[Crossref]

R. V. Skidanov, S. N. Khonina, and A. A. Morozov, “Optical rotation of microparticles in hypergeometric beams formed by diffraction optical elements with multilevel microrelief,” J. Opt. Technol. 80(10), 585–589 (2013).
[Crossref]

2012 (2)

H. T. Eyyuboğlu and Y. Cai, “Hypergeometric Gaussian beam and its propagation in turbulence,” Opt. Commun. 285(21–22), 4194–4199 (2012).
[Crossref]

J. Li and Y. Chen, “Propagation of confluent hypergeometric beam through uniaxial crystals orthogonal to the optical axis,” Opt. Laser Technol. 44(5), 1603–1610 (2012).
[Crossref]

2011 (3)

J. Chen, “Production of confluent hypergeometric beam by computer-generated hologram,” Opt. Eng. 50(2), 024201 (2011).
[Crossref]

Y. Zhang, Y. Wang, J. Xu, J. Wang, and J. Jia, “Orbital angular momentum crosstalk of single photons propagation in a slant non-Kolmogorov turbulence channel,” Opt. Commun. 284(5), 1132–1138 (2011).
[Crossref]

B. de Lima Bernardo and F. Moraes, “Data transmission by hypergeometric modes through a hyperbolic-index medium,” Opt. Express 19(12), 11264–11270 (2011).
[Crossref] [PubMed]

2010 (1)

2009 (1)

2008 (6)

V. V. Kotlyar, A. A. Kovalev, R. V. Skidanov, S. N. Khonina, and J. Turunen, “Generating hypergeometric laser beams with a diffractive optical element,” Appl. Opt. 47(32), 6124–6133 (2008).
[Crossref] [PubMed]

A. Zilberman, E. Golbraikh, and N. S. Kopeika, “Propagation of electromagnetic waves in Kolmogorov and non-Kolmogorov atmospheric turbulence: three-layer altitude model,” Appl. Opt. 47(34), 6385–6391 (2008).
[Crossref] [PubMed]

E. Karimi, B. Piccirillo, L. Marrucci, and E. Santamato, “Improved focusing with hypergeometric-gaussian type-II optical modes,” Opt. Express 16(25), 21069–21075 (2008).
[Crossref] [PubMed]

A. Zilberman, E. Golbraikh, N. S. Kopeika, A. Virtser, I. Kupershmidt, and Y. Shtemler, “Lidar study of aerosol turbulence characteristics in the troposphere: Kolmogorov and non-Kolmogorov turbulence,” Atmos. Res. 88(1), 66–77 (2008).
[Crossref]

Y. Liu, C. Gao, M. Gao, and F. Li, “Coherent-mode representation and orbital angular momentum spectrum of partially coherent beam,” Opt. Commun. 281(8), 1968–1975 (2008).
[Crossref]

I. Toselli, L. C. Andrews, R. L. Phillips, and V. Ferrero, “Free-space optical system performance for laser beam propagation through non-Kolmogorov turbulence,” Opt. Eng. 47(2), 026001 (2008).

2007 (3)

2006 (1)

E. Golbraikh, H. Branover, N. S. Kopeika, and A. Zilberman, “Non-Kolmogorov atmospheric turbulence and optical signal propagation,” Nonlinear Process. Geophys. 13(3), 297–301 (2006).
[Crossref]

2005 (2)

C. Paterson, “Atmospheric turbulence and orbital angular momentum of single photons for optical communication,” Phys. Rev. Lett. 94(15), 153901 (2005).
[Crossref] [PubMed]

L. Torner, J. Torres, and S. Carrasco, “Digital spiral imaging,” Opt. Express 13(3), 873–881 (2005).
[Crossref] [PubMed]

2001 (1)

G. Molina-Terriza, J. P. Torres, and L. Torner, “Management of the angular momentum of light: preparation of photons in multidimensional vector states of angular momentum,” Phys. Rev. Lett. 88(1), 013601 (2001).
[Crossref] [PubMed]

2000 (1)

C. Rao, W. Jiang, and N. Ling, “Spatial and temporal characterization of phase fluctuations in non-Kolmogorov atmospheric turbulence,” J. Mod. Opt. 47(6), 1111–1126 (2000).
[Crossref]

1995 (1)

B. E. Stribling, B. M. Welsh, and M. C. Roggemann, “Optical propagation in non-Kolmogorov atmospheric turbulence,” Proc. SPIE 2471, 181–196 (1995).
[Crossref]

Andrews, L. C.

I. Toselli, L. C. Andrews, R. L. Phillips, and V. Ferrero, “Free-space optical system performance for laser beam propagation through non-Kolmogorov turbulence,” Opt. Eng. 47(2), 026001 (2008).

I. Toselli, L. C. Andrews, R. L. Phillips, and V. Ferrero, “Angle of arrival fluctuations for free space laser beam propagation through non kolmogorov turbulence,” Proc. SPIE 6551, 65510E (2007).
[Crossref]

Boyd, R. W.

Branover, H.

E. Golbraikh, H. Branover, N. S. Kopeika, and A. Zilberman, “Non-Kolmogorov atmospheric turbulence and optical signal propagation,” Nonlinear Process. Geophys. 13(3), 297–301 (2006).
[Crossref]

Cai, Y.

H. T. Eyyuboğlu and Y. Cai, “Hypergeometric Gaussian beam and its propagation in turbulence,” Opt. Commun. 285(21–22), 4194–4199 (2012).
[Crossref]

Carrasco, S.

Chen, J.

J. Chen, “Production of confluent hypergeometric beam by computer-generated hologram,” Opt. Eng. 50(2), 024201 (2011).
[Crossref]

Chen, Y.

J. Li and Y. Chen, “Propagation of confluent hypergeometric beam through uniaxial crystals orthogonal to the optical axis,” Opt. Laser Technol. 44(5), 1603–1610 (2012).
[Crossref]

de Lima Bernardo, B.

Eyyuboglu, H. T.

H. T. Eyyuboğlu, “Scintillation analysis of hypergeometric Gaussian beam via phase screen method,” Opt. Commun. 309, 103–107 (2013).
[Crossref]

H. T. Eyyuboğlu and Y. Cai, “Hypergeometric Gaussian beam and its propagation in turbulence,” Opt. Commun. 285(21–22), 4194–4199 (2012).
[Crossref]

Ferrero, V.

I. Toselli, L. C. Andrews, R. L. Phillips, and V. Ferrero, “Free-space optical system performance for laser beam propagation through non-Kolmogorov turbulence,” Opt. Eng. 47(2), 026001 (2008).

I. Toselli, L. C. Andrews, R. L. Phillips, and V. Ferrero, “Angle of arrival fluctuations for free space laser beam propagation through non kolmogorov turbulence,” Proc. SPIE 6551, 65510E (2007).
[Crossref]

Gao, C.

Y. Liu, C. Gao, M. Gao, and F. Li, “Coherent-mode representation and orbital angular momentum spectrum of partially coherent beam,” Opt. Commun. 281(8), 1968–1975 (2008).
[Crossref]

Gao, M.

Y. Liu, C. Gao, M. Gao, and F. Li, “Coherent-mode representation and orbital angular momentum spectrum of partially coherent beam,” Opt. Commun. 281(8), 1968–1975 (2008).
[Crossref]

Golbraikh, E.

A. Zilberman, E. Golbraikh, and N. S. Kopeika, “Propagation of electromagnetic waves in Kolmogorov and non-Kolmogorov atmospheric turbulence: three-layer altitude model,” Appl. Opt. 47(34), 6385–6391 (2008).
[Crossref] [PubMed]

A. Zilberman, E. Golbraikh, N. S. Kopeika, A. Virtser, I. Kupershmidt, and Y. Shtemler, “Lidar study of aerosol turbulence characteristics in the troposphere: Kolmogorov and non-Kolmogorov turbulence,” Atmos. Res. 88(1), 66–77 (2008).
[Crossref]

E. Golbraikh, H. Branover, N. S. Kopeika, and A. Zilberman, “Non-Kolmogorov atmospheric turbulence and optical signal propagation,” Nonlinear Process. Geophys. 13(3), 297–301 (2006).
[Crossref]

Guo, H.

He, Y.

J. Ou, Y. Jiang, J. Zhang, H. Tang, Y. He, S. Wang, and J. Liao, “Spreading of spiral spectrum of Bessel–Gaussian beam in non-Kolmogorov turbulence,” Opt. Commun. 318, 95–99 (2014).
[Crossref]

Jia, J.

Y. Zhang, Y. Wang, J. Xu, J. Wang, and J. Jia, “Orbital angular momentum crosstalk of single photons propagation in a slant non-Kolmogorov turbulence channel,” Opt. Commun. 284(5), 1132–1138 (2011).
[Crossref]

Jiang, W.

C. Rao, W. Jiang, and N. Ling, “Spatial and temporal characterization of phase fluctuations in non-Kolmogorov atmospheric turbulence,” J. Mod. Opt. 47(6), 1111–1126 (2000).
[Crossref]

Jiang, Y.

J. Ou, Y. Jiang, J. Zhang, H. Tang, Y. He, S. Wang, and J. Liao, “Spreading of spiral spectrum of Bessel–Gaussian beam in non-Kolmogorov turbulence,” Opt. Commun. 318, 95–99 (2014).
[Crossref]

Karimi, E.

Khonina, S. N.

Kopeika, N. S.

A. Zilberman, E. Golbraikh, and N. S. Kopeika, “Propagation of electromagnetic waves in Kolmogorov and non-Kolmogorov atmospheric turbulence: three-layer altitude model,” Appl. Opt. 47(34), 6385–6391 (2008).
[Crossref] [PubMed]

A. Zilberman, E. Golbraikh, N. S. Kopeika, A. Virtser, I. Kupershmidt, and Y. Shtemler, “Lidar study of aerosol turbulence characteristics in the troposphere: Kolmogorov and non-Kolmogorov turbulence,” Atmos. Res. 88(1), 66–77 (2008).
[Crossref]

E. Golbraikh, H. Branover, N. S. Kopeika, and A. Zilberman, “Non-Kolmogorov atmospheric turbulence and optical signal propagation,” Nonlinear Process. Geophys. 13(3), 297–301 (2006).
[Crossref]

Kotlyar, V. V.

Kovalev, A. A.

V. V. Kotlyar, A. A. Kovalev, and A. G. Nalimov, “Propagation of hypergeometric laser beams in a medium with a parabolic refractive index,” J. Opt. 15(12), 125706 (2013).
[Crossref]

V. V. Kotlyar, A. A. Kovalev, R. V. Skidanov, S. N. Khonina, and J. Turunen, “Generating hypergeometric laser beams with a diffractive optical element,” Appl. Opt. 47(32), 6124–6133 (2008).
[Crossref] [PubMed]

Kupershmidt, I.

A. Zilberman, E. Golbraikh, N. S. Kopeika, A. Virtser, I. Kupershmidt, and Y. Shtemler, “Lidar study of aerosol turbulence characteristics in the troposphere: Kolmogorov and non-Kolmogorov turbulence,” Atmos. Res. 88(1), 66–77 (2008).
[Crossref]

Li, F.

Y. Liu, C. Gao, M. Gao, and F. Li, “Coherent-mode representation and orbital angular momentum spectrum of partially coherent beam,” Opt. Commun. 281(8), 1968–1975 (2008).
[Crossref]

Li, J.

J. Li and Y. Chen, “Propagation of confluent hypergeometric beam through uniaxial crystals orthogonal to the optical axis,” Opt. Laser Technol. 44(5), 1603–1610 (2012).
[Crossref]

Liao, J.

J. Ou, Y. Jiang, J. Zhang, H. Tang, Y. He, S. Wang, and J. Liao, “Spreading of spiral spectrum of Bessel–Gaussian beam in non-Kolmogorov turbulence,” Opt. Commun. 318, 95–99 (2014).
[Crossref]

Ling, N.

C. Rao, W. Jiang, and N. Ling, “Spatial and temporal characterization of phase fluctuations in non-Kolmogorov atmospheric turbulence,” J. Mod. Opt. 47(6), 1111–1126 (2000).
[Crossref]

Liu, Y.

Y. Liu, C. Gao, M. Gao, and F. Li, “Coherent-mode representation and orbital angular momentum spectrum of partially coherent beam,” Opt. Commun. 281(8), 1968–1975 (2008).
[Crossref]

Luo, B.

Marrucci, L.

Molina-Terriza, G.

G. Molina-Terriza, J. P. Torres, and L. Torner, “Management of the angular momentum of light: preparation of photons in multidimensional vector states of angular momentum,” Phys. Rev. Lett. 88(1), 013601 (2001).
[Crossref] [PubMed]

Moraes, F.

Morozov, A. A.

Nalimov, A. G.

V. V. Kotlyar, A. A. Kovalev, and A. G. Nalimov, “Propagation of hypergeometric laser beams in a medium with a parabolic refractive index,” J. Opt. 15(12), 125706 (2013).
[Crossref]

Ou, J.

J. Ou, Y. Jiang, J. Zhang, H. Tang, Y. He, S. Wang, and J. Liao, “Spreading of spiral spectrum of Bessel–Gaussian beam in non-Kolmogorov turbulence,” Opt. Commun. 318, 95–99 (2014).
[Crossref]

Paterson, C.

C. Paterson, “Atmospheric turbulence and orbital angular momentum of single photons for optical communication,” Phys. Rev. Lett. 94(15), 153901 (2005).
[Crossref] [PubMed]

Phillips, R. L.

I. Toselli, L. C. Andrews, R. L. Phillips, and V. Ferrero, “Free-space optical system performance for laser beam propagation through non-Kolmogorov turbulence,” Opt. Eng. 47(2), 026001 (2008).

I. Toselli, L. C. Andrews, R. L. Phillips, and V. Ferrero, “Angle of arrival fluctuations for free space laser beam propagation through non kolmogorov turbulence,” Proc. SPIE 6551, 65510E (2007).
[Crossref]

Piccirillo, B.

Rao, C.

C. Rao, W. Jiang, and N. Ling, “Spatial and temporal characterization of phase fluctuations in non-Kolmogorov atmospheric turbulence,” J. Mod. Opt. 47(6), 1111–1126 (2000).
[Crossref]

Roggemann, M. C.

B. E. Stribling, B. M. Welsh, and M. C. Roggemann, “Optical propagation in non-Kolmogorov atmospheric turbulence,” Proc. SPIE 2471, 181–196 (1995).
[Crossref]

Santamato, E.

Shtemler, Y.

A. Zilberman, E. Golbraikh, N. S. Kopeika, A. Virtser, I. Kupershmidt, and Y. Shtemler, “Lidar study of aerosol turbulence characteristics in the troposphere: Kolmogorov and non-Kolmogorov turbulence,” Atmos. Res. 88(1), 66–77 (2008).
[Crossref]

Skidanov, R. V.

Soifer, V. A.

Stribling, B. E.

B. E. Stribling, B. M. Welsh, and M. C. Roggemann, “Optical propagation in non-Kolmogorov atmospheric turbulence,” Proc. SPIE 2471, 181–196 (1995).
[Crossref]

Tang, H.

J. Ou, Y. Jiang, J. Zhang, H. Tang, Y. He, S. Wang, and J. Liao, “Spreading of spiral spectrum of Bessel–Gaussian beam in non-Kolmogorov turbulence,” Opt. Commun. 318, 95–99 (2014).
[Crossref]

Torner, L.

L. Torner, J. Torres, and S. Carrasco, “Digital spiral imaging,” Opt. Express 13(3), 873–881 (2005).
[Crossref] [PubMed]

G. Molina-Terriza, J. P. Torres, and L. Torner, “Management of the angular momentum of light: preparation of photons in multidimensional vector states of angular momentum,” Phys. Rev. Lett. 88(1), 013601 (2001).
[Crossref] [PubMed]

Torres, J.

Torres, J. P.

G. Molina-Terriza, J. P. Torres, and L. Torner, “Management of the angular momentum of light: preparation of photons in multidimensional vector states of angular momentum,” Phys. Rev. Lett. 88(1), 013601 (2001).
[Crossref] [PubMed]

Toselli, I.

I. Toselli, L. C. Andrews, R. L. Phillips, and V. Ferrero, “Free-space optical system performance for laser beam propagation through non-Kolmogorov turbulence,” Opt. Eng. 47(2), 026001 (2008).

I. Toselli, L. C. Andrews, R. L. Phillips, and V. Ferrero, “Angle of arrival fluctuations for free space laser beam propagation through non kolmogorov turbulence,” Proc. SPIE 6551, 65510E (2007).
[Crossref]

Turunen, J.

Tyler, G. A.

Virtser, A.

A. Zilberman, E. Golbraikh, N. S. Kopeika, A. Virtser, I. Kupershmidt, and Y. Shtemler, “Lidar study of aerosol turbulence characteristics in the troposphere: Kolmogorov and non-Kolmogorov turbulence,” Atmos. Res. 88(1), 66–77 (2008).
[Crossref]

Wang, J.

Y. Zhang, Y. Wang, J. Xu, J. Wang, and J. Jia, “Orbital angular momentum crosstalk of single photons propagation in a slant non-Kolmogorov turbulence channel,” Opt. Commun. 284(5), 1132–1138 (2011).
[Crossref]

Wang, S.

J. Ou, Y. Jiang, J. Zhang, H. Tang, Y. He, S. Wang, and J. Liao, “Spreading of spiral spectrum of Bessel–Gaussian beam in non-Kolmogorov turbulence,” Opt. Commun. 318, 95–99 (2014).
[Crossref]

Wang, Y.

Y. Zhang, Y. Wang, J. Xu, J. Wang, and J. Jia, “Orbital angular momentum crosstalk of single photons propagation in a slant non-Kolmogorov turbulence channel,” Opt. Commun. 284(5), 1132–1138 (2011).
[Crossref]

Welsh, B. M.

B. E. Stribling, B. M. Welsh, and M. C. Roggemann, “Optical propagation in non-Kolmogorov atmospheric turbulence,” Proc. SPIE 2471, 181–196 (1995).
[Crossref]

Wu, G.

Xu, J.

Y. Zhang, Y. Wang, J. Xu, J. Wang, and J. Jia, “Orbital angular momentum crosstalk of single photons propagation in a slant non-Kolmogorov turbulence channel,” Opt. Commun. 284(5), 1132–1138 (2011).
[Crossref]

Yu, S.

Zhang, J.

J. Ou, Y. Jiang, J. Zhang, H. Tang, Y. He, S. Wang, and J. Liao, “Spreading of spiral spectrum of Bessel–Gaussian beam in non-Kolmogorov turbulence,” Opt. Commun. 318, 95–99 (2014).
[Crossref]

Zhang, Y.

Y. Zhang, Y. Wang, J. Xu, J. Wang, and J. Jia, “Orbital angular momentum crosstalk of single photons propagation in a slant non-Kolmogorov turbulence channel,” Opt. Commun. 284(5), 1132–1138 (2011).
[Crossref]

Zilberman, A.

A. Zilberman, E. Golbraikh, N. S. Kopeika, A. Virtser, I. Kupershmidt, and Y. Shtemler, “Lidar study of aerosol turbulence characteristics in the troposphere: Kolmogorov and non-Kolmogorov turbulence,” Atmos. Res. 88(1), 66–77 (2008).
[Crossref]

A. Zilberman, E. Golbraikh, and N. S. Kopeika, “Propagation of electromagnetic waves in Kolmogorov and non-Kolmogorov atmospheric turbulence: three-layer altitude model,” Appl. Opt. 47(34), 6385–6391 (2008).
[Crossref] [PubMed]

E. Golbraikh, H. Branover, N. S. Kopeika, and A. Zilberman, “Non-Kolmogorov atmospheric turbulence and optical signal propagation,” Nonlinear Process. Geophys. 13(3), 297–301 (2006).
[Crossref]

Zito, G.

Appl. Opt. (2)

Atmos. Res. (1)

A. Zilberman, E. Golbraikh, N. S. Kopeika, A. Virtser, I. Kupershmidt, and Y. Shtemler, “Lidar study of aerosol turbulence characteristics in the troposphere: Kolmogorov and non-Kolmogorov turbulence,” Atmos. Res. 88(1), 66–77 (2008).
[Crossref]

J. Mod. Opt. (1)

C. Rao, W. Jiang, and N. Ling, “Spatial and temporal characterization of phase fluctuations in non-Kolmogorov atmospheric turbulence,” J. Mod. Opt. 47(6), 1111–1126 (2000).
[Crossref]

J. Opt. (1)

V. V. Kotlyar, A. A. Kovalev, and A. G. Nalimov, “Propagation of hypergeometric laser beams in a medium with a parabolic refractive index,” J. Opt. 15(12), 125706 (2013).
[Crossref]

J. Opt. Technol. (1)

Nonlinear Process. Geophys. (1)

E. Golbraikh, H. Branover, N. S. Kopeika, and A. Zilberman, “Non-Kolmogorov atmospheric turbulence and optical signal propagation,” Nonlinear Process. Geophys. 13(3), 297–301 (2006).
[Crossref]

Opt. Commun. (5)

Y. Zhang, Y. Wang, J. Xu, J. Wang, and J. Jia, “Orbital angular momentum crosstalk of single photons propagation in a slant non-Kolmogorov turbulence channel,” Opt. Commun. 284(5), 1132–1138 (2011).
[Crossref]

Y. Liu, C. Gao, M. Gao, and F. Li, “Coherent-mode representation and orbital angular momentum spectrum of partially coherent beam,” Opt. Commun. 281(8), 1968–1975 (2008).
[Crossref]

J. Ou, Y. Jiang, J. Zhang, H. Tang, Y. He, S. Wang, and J. Liao, “Spreading of spiral spectrum of Bessel–Gaussian beam in non-Kolmogorov turbulence,” Opt. Commun. 318, 95–99 (2014).
[Crossref]

H. T. Eyyuboğlu and Y. Cai, “Hypergeometric Gaussian beam and its propagation in turbulence,” Opt. Commun. 285(21–22), 4194–4199 (2012).
[Crossref]

H. T. Eyyuboğlu, “Scintillation analysis of hypergeometric Gaussian beam via phase screen method,” Opt. Commun. 309, 103–107 (2013).
[Crossref]

Opt. Eng. (2)

J. Chen, “Production of confluent hypergeometric beam by computer-generated hologram,” Opt. Eng. 50(2), 024201 (2011).
[Crossref]

I. Toselli, L. C. Andrews, R. L. Phillips, and V. Ferrero, “Free-space optical system performance for laser beam propagation through non-Kolmogorov turbulence,” Opt. Eng. 47(2), 026001 (2008).

Opt. Express (3)

Opt. Laser Technol. (1)

J. Li and Y. Chen, “Propagation of confluent hypergeometric beam through uniaxial crystals orthogonal to the optical axis,” Opt. Laser Technol. 44(5), 1603–1610 (2012).
[Crossref]

Opt. Lett. (4)

Phys. Rev. Lett. (2)

G. Molina-Terriza, J. P. Torres, and L. Torner, “Management of the angular momentum of light: preparation of photons in multidimensional vector states of angular momentum,” Phys. Rev. Lett. 88(1), 013601 (2001).
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C. Paterson, “Atmospheric turbulence and orbital angular momentum of single photons for optical communication,” Phys. Rev. Lett. 94(15), 153901 (2005).
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Proc. SPIE (2)

I. Toselli, L. C. Andrews, R. L. Phillips, and V. Ferrero, “Angle of arrival fluctuations for free space laser beam propagation through non kolmogorov turbulence,” Proc. SPIE 6551, 65510E (2007).
[Crossref]

B. E. Stribling, B. M. Welsh, and M. C. Roggemann, “Optical propagation in non-Kolmogorov atmospheric turbulence,” Proc. SPIE 2471, 181–196 (1995).
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Other (2)

A. Jeffrey and D. Zwillinger, Table of Integrals, Series, and Products (Academic, 2007).

L. C. Andrews and R. L. Phillips, Laser Beam Propagation Through Random Media (SPIE, 2005).

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Figures (6)

Fig. 1
Fig. 1 The spiral spectrum of the HyGG beams propagating in non-Kolmogorov turbulence for different hollowness parameters p. (a) The received power p l 0 observed on OAM mode l= l 0 . (b) The crosstalk power p Δl observed on OAM mode l= l 0 +Δl with OAM number l 0 =1 . The bars of Δl=0 correspond to the original signals. The crosstalk power is symmetric with the OAM mode l= l 0 .

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Fig. 2
Fig. 2 (a) The received power p l 0 of the HyGG beams in non-Kolmogorov turbulence as a function of the propagation distance z for the OAM numbers l= l 0 =0,1,2 and 3. The lower OAM number gives the higher received power. (b) The crosstalk power p Δl versus the propagation distance z for Δl=1,2,3, and 4 with l 0 =1 . The crosstalk power occurs mainly between two adjacent OAM states under the weak turbulence.

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Fig. 3
Fig. 3 (a) The received power p l 0 of the HyGG beams in non-Kolmogorov turbulence as a function of the propagation distance z with the different hollowness parameters p. (b) The crosstalk power p Δl calculated for l 0 =1,Δl=1 versus the propagation distance z when the hollowness parameter p changes from −1 to 3.

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Fig. 4
Fig. 4 The received power p l 0 (a) and the crosstalk power p Δl calculated for l 0 =1,Δl=1 (b) of the HyGG beams propagating in non-Kolmogorov turbulence versus the propagation distance z for the different wavelengths λ=532,632.8,850 and 1550 nm. The longer wavelength is benefit to the propagation of optical signal with OAM.

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Fig. 5
Fig. 5 The received power p l 0 (a) and the crosstalk power p Δl calculated for l 0 =1,Δl=1 (b) of the HyGG beams propagating in non-Kolmogorov turbulence versus the propagation distance z for the different non-Kolmogorov turbulence parameters α=3.07 , 3.37, 3.67 and 3.97. The curves associated with α=3.67 correspond to Kolmogorov turbulence. The smaller α comes with the larger p l 0 .

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Fig. 6
Fig. 6 The received power p l 0 (a) and the crosstalk power p Δl calculated for l 0 =1,Δl=1 (b) of the HyGG beams in non-Kolmogorov turbulence as a function of z under different turbulent conditions ( C n 2 = 10 −17 , 10 −16 , 10 −15 and 10 −14 m 3−α ) with α=11/3 . The p l 0 almost remains unchanged in the weak turbulence ( C n 2 = 10 −17 m 3−α ), descends gradually in the intermediate turbulence ( C n 2 = 10 −16 and 10 −15 m 3−α ) and in the strong turbulence ( C n 2 = 10 −14 m 3−α ) drops quickly with the increasing propagation distance z.

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Equations (13)

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E p, l 0 ( r,φ,0 )= C p l 0 ( r ω 0 ) p+| l 0 | exp( − r 2 ω 0 2 +i l 0 φ ),
E p ( r,φ,z )= E p, l 0 ( r,φ,z )exp[ ψ 1 ( r,φ,z ) ],
E p, l 0 ( r,φ,z )= C p l 0 ( z z R +i ) −[ 1+| l 0 |+ p 2 ] i | l 0 |+1 ( r ω 0 ) | l 0 | exp( i l 0 φ ) × ( z z R ) p 2 exp[ − i z R r 2 ω 0 2 ( z+i z R ) ] F 1 1 ( − p 2 ,| l 0 |+1; z R 2 r 2 ω 0 2 ( z 2 +iz z R ) ),
E p ( r,φ,z )= 1 2π ∑ l β l ( r,z )exp( −ilφ ) ,
β l ( r,z )= 1 2π ∫ 0 2π E p ( r,φ,z ) exp( ilφ )dφ.
〈 | β l (r,z) | 2 〉= 1 2π ∫ 0 2π ∫ 0 2π 〈 E p ( r,φ,z ) E p * ( r, φ ′ ,z ) 〉 exp[ −il( φ− φ ′ ) ]d φ ′ dφ = 1 2π ∫ 0 2π ∫ 0 2π E p, l 0 ( r,φ,z ) E p, l 0 * ( r, φ ′ ,z ) ×〈 exp[ ψ 1 ( r,φ,z )+ ψ 1 * ( r, φ ′ ,z ) ] 〉exp[ −il( φ− φ ′ ) ]d φ ′ dφ,
〈 exp[ ψ 1 ( r,φ,z )+ ψ 1 * ( r, φ ′ ,z ) ] 〉=exp[ − 2 r 2 −2 r 2 cos( φ− φ ′ ) ρ 0 2 ],
ρ 0 = { 2( α−1 )Γ( 3−α 2 ) [ 8 α−2 Γ( 2 α−2 ) ] ( α−2 ) 2 π 1 2 Γ( 2−α 2 ) k 2 C n 2 z } 1 ( α−2 ) 3<α<4,
〈 | β l (r,z) | 2 〉= 1 2π ∫ 0 2π ∫ 0 2π E p, l 0 ( r,φ,z ) E p, l 0 * ( r, φ ′ ,z ) ×exp[ −il( φ− φ ′ ) ]exp[ − 2 r 2 −2 r 2 cos( φ ′ −φ ) ρ 0 2 ]d φ ′ dφ.
〈 | β l (r,z) | 2 〉= 2 p+| l 0 |+1 2 π 2 Γ(p+| l 0 |+1) Γ 2 (p/2+| l 0 |+1) Γ 2 (| l 0 |+1) [ 1+ ( z z R ) 2 ] −( p/2+| l 0 |+1 ) × ( r ω 0 ) 2| l 0 | ( z z R ) p exp[ − 2 r 2 z R 2 ω 0 2 ( z R 2 + z 2 ) ] | F 1 1 ( − p 2 ,| l 0 |+1; z R 2 r 2 ω 0 2 ( z 2 +iz z R ) ) | 2 ×exp( − 2 r 2 ρ 0 2 ) ∫ 0 2π ∫ 0 2π exp[ −i( l− l 0 )( φ− φ ′ )+ 2 r 2 cos( φ ′ −φ ) ρ 0 2 ]d φ ′ dφ .
∫ 0 2π exp[−in φ 1 +ηcos( φ 1 − φ 2 )] d φ 1 =2πexp(−in φ 2 ) I n (η),
〈 | β l (r,z) | 2 〉= 2 p+| l 0 |+2 Γ(p+| l 0 |+1) Γ 2 ( p 2 +| l 0 |+1) Γ 2 (| l 0 |+1) [ 1+ ( z z R ) 2 ] −( p 2 +| l 0 |+1 ) ( r ω 0 ) 2| l 0 | ( z z R ) p ×exp[ − 2 r 2 z R 2 ω 0 2 ( z R 2 + z 2 ) ] | F 1 1 ( − p 2 ,| l 0 |+1; z R 2 r 2 ω 0 2 z( z+i z R ) ) | 2 exp( − 2 r 2 ρ 0 2 ) I l− l 0 ( 2 r 2 ρ 0 2 ).
p l = ∫ 0 ∞ 〈 | β l (r,z) | 2 〉rdr ∑ l=−∞ ∞ ∫ 0 ∞ 〈 | β l (r,z) | 2 〉rdr .

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