## Investigation on the scintillation reduction of elliptical vortex beams propagating in atmospheric turbulence |

Optics Express, Vol. 19, Issue 27, pp. 26444-26450 (2011)

http://dx.doi.org/10.1364/OE.19.026444

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### Abstract

We numerically investigate the scintillation index of an elliptical vortex beam in both modest turbulence and strong turbulence. Numerical simulations are realized with random phase screen scheme. It is shown that the on-axis scintillation index can be effectively reduced by an elliptical vortex beam if crucial parameters are properly chosen. The mechanisms of scintillation reduction in turbulence of different strengths are different. We find that the topological charge and the ratio of minor axis to major axis of an elliptical vortex beam are important in determining the on-axis scintillation index. Our simulation results indicate that using an elliptical vortex beam is a promising strategy to alleviate atmospheric influence on free space optical communication link.

© 2011 OSA

## 1. Introduction

9. L. Allen, M. W. Beijersbergen, R. J. 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]

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

11. R. Čelechovský and Z. Bouchal, “Optical implementation of the vortex information channel,” New J. Phys. **9**(9), 328 (2007). [CrossRef]

12. G. Gbur and R. K. Tyson, “Vortex beam propagation through atmospheric turbulence and topological charge conservation,” J. Opt. Soc. Am. A **25**(1), 225–230 (2008). [CrossRef] [PubMed]

13. H. T. Eyyuboğlu, Y. Baykal, and X. Ji, “Scintillations of Laguerre Gaussian beams,” Appl. Phys. B **98**(4), 857–863 (2010). [CrossRef]

14. W. Cheng, J. W. Haus, and Q. Zhan, “Propagation of vector vortex beams through a turbulent atmosphere,” Opt. Express **17**(20), 17829–17836 (2009). [CrossRef] [PubMed]

15. J. M. Martin and S. M. Flatté, “Intensity images and statistics from numerical simulation of wave propagation in 3-D random media,” Appl. Opt. **27**(11), 2111–2126 (1988). [CrossRef] [PubMed]

16. Y. Tian, J. Guo, R. Wang, and T. Wang, “Mathematic model analysis of Gaussian beam propagation through an arbitrary thickness random phase screen,” Opt. Express **19**(19), 18216–18228 (2011). [CrossRef] [PubMed]

## 2. Numerical simulation method

*N × N*points in the x-y plane and is described by an

*N × N*matrix. The sampling interval is

*N*always increases after propagating between two adjacent phase screens. The newly-added elements of the matrix are assigned to zero.

*L*is 10m and the inner scale

_{0}*l*is 2mm.The spectrum of random phase can be expressed as [15

_{0}15. J. M. Martin and S. M. Flatté, “Intensity images and statistics from numerical simulation of wave propagation in 3-D random media,” Appl. Opt. **27**(11), 2111–2126 (1988). [CrossRef] [PubMed]

15. J. M. Martin and S. M. Flatté, “Intensity images and statistics from numerical simulation of wave propagation in 3-D random media,” Appl. Opt. **27**(11), 2111–2126 (1988). [CrossRef] [PubMed]

*i*b is generated, a and b obeying normal distribution

*N*(0,1). Multiplying the gained matrix by

18. V. V. Kotlyar, S. N. Khonina, A. A. Almazov, V. A. Soifer, K. Jefimovs, and J. Turunen, “Elliptic Laguerre-Gaussian beams,” J. Opt. Soc. Am. A **23**(1), 43–56 (2006). [CrossRef] [PubMed]

*m*indicates the topological charge of an optical vortex. If

*I*and

*I*.

^{2}## 3. Performances of elliptical vortex beams with different topological charges

### 3.1 Scintillation in modest turbulence

*w*is not adjusted. This is because one axis keeps the original length while the perpendicular axis is stretched, rendering the area of the source larger. Therefore, the value of

*w*should be multiplied by

19. G. P. Berman, V. N. Gorshkov, and S. V. Torous, “Scintillation reduction for laser beams propagating through turbulent atmosphere,” J. Phys. At. Mol. Opt. Phys. **44**(5), 055402 (2011). [CrossRef]

### 3.2 Scintillation in strong turbulence

## 4. Dependence of scintillation index on the ratio of minor axis to major axis

## 5. Conclusion

## Acknowledgments

## References and links

1. | O. Korotkova and E. Wolf, “Beam criterion for atmospheric propagation,” Opt. Lett. |

2. | O. Korotkova and E. Shchepakina, “Color changes in stochastic light fields propagating in non-Kolmogorov turbulence,” Opt. Lett. |

3. | X. Ji, H. T. Eyyuboğlu, and Y. Baykal, “Influence of turbulence on the effective radius of curvature of radial Gaussian array beams,” Opt. Express |

4. | Y. Cai, Y. Chen, H. T. Eyyuboğlu, and Y. Baykal, “Scintillation index of elliptical Gaussian beam in turbulent atmosphere,” Opt. Lett. |

5. | Y. Chen, Y. Cai, H. T. Eyyuboğlu, and Y. Baykal, “Scintillation properties of dark hollow beams in a weak turbulent atmosphere,” Appl. Phys. B |

6. | X. Qian, W. Zhu, and R. Rao, “Numerical investigation on propagation effects of pseudo-partially coherent Gaussian Schell-model beams in atmospheric turbulence,” Opt. Express |

7. | Y. Gu, O. Korotkova, and G. Gbur, “Scintillation of nonuniformly polarized beams in atmospheric turbulence,” Opt. Lett. |

8. | P. Polynkin, A. Peleg, L. Klein, T. Rhoadarmer, and J. V. Moloney, “Optimized multiemitter beams for free-space optical communications through turbulent atmosphere,” Opt. Lett. |

9. | L. Allen, M. W. Beijersbergen, R. J. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A |

10. | G. Gibson, J. Courtial, M. J. Padgett, M. Vasnetsov, V. Pas’ko, S. Barnett, and S. Franke-Arnold, “Free-space information transfer using light beams carrying orbital angular momentum,” Opt. Express |

11. | R. Čelechovský and Z. Bouchal, “Optical implementation of the vortex information channel,” New J. Phys. |

12. | G. Gbur and R. K. Tyson, “Vortex beam propagation through atmospheric turbulence and topological charge conservation,” J. Opt. Soc. Am. A |

13. | H. T. Eyyuboğlu, Y. Baykal, and X. Ji, “Scintillations of Laguerre Gaussian beams,” Appl. Phys. B |

14. | W. Cheng, J. W. Haus, and Q. Zhan, “Propagation of vector vortex beams through a turbulent atmosphere,” Opt. Express |

15. | J. M. Martin and S. M. Flatté, “Intensity images and statistics from numerical simulation of wave propagation in 3-D random media,” Appl. Opt. |

16. | Y. Tian, J. Guo, R. Wang, and T. Wang, “Mathematic model analysis of Gaussian beam propagation through an arbitrary thickness random phase screen,” Opt. Express |

17. | L. C. Andrews and R. L. Phillips, |

18. | V. V. Kotlyar, S. N. Khonina, A. A. Almazov, V. A. Soifer, K. Jefimovs, and J. Turunen, “Elliptic Laguerre-Gaussian beams,” J. Opt. Soc. Am. A |

19. | G. P. Berman, V. N. Gorshkov, and S. V. Torous, “Scintillation reduction for laser beams propagating through turbulent atmosphere,” J. Phys. At. Mol. Opt. Phys. |

**OCIS Codes**

(010.1290) Atmospheric and oceanic optics : Atmospheric optics

(060.2605) Fiber optics and optical communications : Free-space optical communication

**ToC Category:**

Atmospheric and Oceanic Optics

**History**

Original Manuscript: September 19, 2011

Revised Manuscript: October 26, 2011

Manuscript Accepted: November 21, 2011

Published: December 12, 2011

**Citation**

Xianhe Liu and Jixiong Pu, "Investigation on the scintillation reduction of elliptical vortex beams propagating in atmospheric turbulence," Opt. Express **19**, 26444-26450 (2011)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-27-26444

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### References

- O. Korotkova and E. Wolf, “Beam criterion for atmospheric propagation,” Opt. Lett.32(15), 2137–2139 (2007). [CrossRef] [PubMed]
- O. Korotkova and E. Shchepakina, “Color changes in stochastic light fields propagating in non-Kolmogorov turbulence,” Opt. Lett.35(22), 3772–3774 (2010). [CrossRef] [PubMed]
- X. Ji, H. T. Eyyuboğlu, and Y. Baykal, “Influence of turbulence on the effective radius of curvature of radial Gaussian array beams,” Opt. Express18(7), 6922–6928 (2010). [CrossRef] [PubMed]
- Y. Cai, Y. Chen, H. T. Eyyuboğlu, and Y. Baykal, “Scintillation index of elliptical Gaussian beam in turbulent atmosphere,” Opt. Lett.32(16), 2405–2407 (2007). [CrossRef] [PubMed]
- Y. Chen, Y. Cai, H. T. Eyyuboğlu, and Y. Baykal, “Scintillation properties of dark hollow beams in a weak turbulent atmosphere,” Appl. Phys. B90(1), 87–92 (2008). [CrossRef]
- X. Qian, W. Zhu, and R. Rao, “Numerical investigation on propagation effects of pseudo-partially coherent Gaussian Schell-model beams in atmospheric turbulence,” Opt. Express17(5), 3782–3791 (2009). [CrossRef] [PubMed]
- Y. Gu, O. Korotkova, and G. Gbur, “Scintillation of nonuniformly polarized beams in atmospheric turbulence,” Opt. Lett.34(15), 2261–2263 (2009). [CrossRef] [PubMed]
- P. Polynkin, A. Peleg, L. Klein, T. Rhoadarmer, and J. V. Moloney, “Optimized multiemitter beams for free-space optical communications through turbulent atmosphere,” Opt. Lett.32(8), 885–887 (2007). [CrossRef] [PubMed]
- L. Allen, M. W. Beijersbergen, R. J. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A45(11), 8185–8189 (1992). [CrossRef] [PubMed]
- G. Gibson, J. Courtial, M. J. Padgett, M. Vasnetsov, V. Pas’ko, S. Barnett, and S. Franke-Arnold, “Free-space information transfer using light beams carrying orbital angular momentum,” Opt. Express12(22), 5448–5456 (2004). [CrossRef] [PubMed]
- R. Čelechovský and Z. Bouchal, “Optical implementation of the vortex information channel,” New J. Phys.9(9), 328 (2007). [CrossRef]
- G. Gbur and R. K. Tyson, “Vortex beam propagation through atmospheric turbulence and topological charge conservation,” J. Opt. Soc. Am. A25(1), 225–230 (2008). [CrossRef] [PubMed]
- H. T. Eyyuboğlu, Y. Baykal, and X. Ji, “Scintillations of Laguerre Gaussian beams,” Appl. Phys. B98(4), 857–863 (2010). [CrossRef]
- W. Cheng, J. W. Haus, and Q. Zhan, “Propagation of vector vortex beams through a turbulent atmosphere,” Opt. Express17(20), 17829–17836 (2009). [CrossRef] [PubMed]
- J. M. Martin and S. M. Flatté, “Intensity images and statistics from numerical simulation of wave propagation in 3-D random media,” Appl. Opt.27(11), 2111–2126 (1988). [CrossRef] [PubMed]
- Y. Tian, J. Guo, R. Wang, and T. Wang, “Mathematic model analysis of Gaussian beam propagation through an arbitrary thickness random phase screen,” Opt. Express19(19), 18216–18228 (2011). [CrossRef] [PubMed]
- L. C. Andrews and R. L. Phillips, Laser beam propagation through random media (SPIE Press, Bellingham, Washington, 1998).
- V. V. Kotlyar, S. N. Khonina, A. A. Almazov, V. A. Soifer, K. Jefimovs, and J. Turunen, “Elliptic Laguerre-Gaussian beams,” J. Opt. Soc. Am. A23(1), 43–56 (2006). [CrossRef] [PubMed]
- G. P. Berman, V. N. Gorshkov, and S. V. Torous, “Scintillation reduction for laser beams propagating through turbulent atmosphere,” J. Phys. At. Mol. Opt. Phys.44(5), 055402 (2011). [CrossRef]

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