Skip to main content
Log in

Effects of the turbulent atmosphere and the oceanic turbulence on the propagation of a rotating elliptical Gaussian beam

  • Published:
Applied Physics B Aims and scope Submit manuscript

Abstract

Based on the extended Huygens–Fresnel integral, the average intensity, the gradient force and the effective beam width in the x- and y-directions of a rotating elliptical Gaussian (REG) beam in the turbulent atmosphere and the oceanic turbulence are explored analytically and numerically. It is shown that the intensity patterns of the REG beam in the atmospheric and the oceanic turbulences spin anticlockwise within a certain propagation range and always keep unimodal distributions during the propagation. Meanwhile, the numerical experiments of the REG beam are carried out to verify the theoretical analytical results. By comparative analysis, the effective beam widths can be adjusted by varying the turbulent characteristic parameters and the initial beam waist of the REG beam. The intensity modulation of the REG beam through the turbulent atmosphere and the oceanic turbulence can be realized.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11

Similar content being viewed by others

References

  1. J.W. Strohbehn, Laser Beam Propagation in the Atmosphere (Springer, New York, 1978)

    Book  Google Scholar 

  2. L.C. Andrews, R.L. Phillips, Laser Beam Propagation Through Random Media, 2nd edn. (SPIE, Washington, 2005)

    Book  Google Scholar 

  3. F. Wang, J. Li, G. Martinez-Piedra, O. Korotkova, Propagation dynamics of partially coherent crescent-like optical beams in free space and turbulent atmosphere. Opt. Lett. 25(21), 26055–26066 (2017)

    Google Scholar 

  4. J. Zhu, X. Li, H. Tang, K. Zhu, Propagation of multi-cosine-Laguerre–Gaussian correlated Schell-model beams in free space and atmospheric turbulence. Opt. Commun. 25(17), 20071–20086 (2017)

    Google Scholar 

  5. X. Liu, J. Yu, Y. Cai, S.A. Ponomarenko, Propagation of optical coherence lattices in the turbulent atmosphere. Opt. Lett. 41(18), 4182–4185 (2016)

    Article  ADS  Google Scholar 

  6. V.A. Banakh, L.O. Gerasimova, Strong scintillations of pulsed Laguerrian beams in a turbulent atmosphere. Opt. Express 24(17), 19264–19277 (2016)

    Article  ADS  Google Scholar 

  7. R.J. Hill, Optical propagation in turbulent water. J. Opt. Soc. Am. 68(8), 1067–1072 (1978)

    Article  ADS  Google Scholar 

  8. V.V. Nikishov, V.I. Nikishov, Spectrum of turbulent fluctuation of the sea-water refractive index. Int. J. Fluid Mech. Res. 27(1), 82–98 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  9. W. Lu, L. Liu, J. Sun, Influence of temperature and salinity fluctuations on propagation behaviour of partially coherent beams in oceanic turbulence. J. Opt. A Pure Appl. Opt. 8(12), 1052–1058 (2006)

    Article  ADS  Google Scholar 

  10. S. Arnon, D. Kedar, Non-line-of-sight underwater optical wireless communication network. J. Opt. Soc. Am. A 26(3), 530–539 (2009)

    Article  ADS  Google Scholar 

  11. W. Hou, A simple underwater imaging model. Opt. Lett. 34(17), 2688–2690 (2009)

    Article  ADS  Google Scholar 

  12. W. Hou, E. Jarosz, S. Woods, W. Goode, A. Weidemann, Impacts of underwater turbulence on acoustical and optical signals and their linkage. Opt. Express 21(4), 4367–4375 (2013)

    Article  ADS  Google Scholar 

  13. L.J. Johnson, R.J. Green, M.S. Leeson, Underwater optical wireless communications: depth-dependent beam refraction. Appl. Opt. 53(31), 7273–7277 (2014)

    Article  ADS  Google Scholar 

  14. O. Korotkova, N. Farwell, Effect of oceanic turbulence on polarization of stochastic beams. Opt. Commun. 284(7), 1740–1746 (2011)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  16. X. Huang, Z. Deng, X. Shi, Y. Bai, X. Fu, Average intensity and beam quality of optical coherence lattices in oceanic turbulence with anisotropy. Opt. Express 26(4), 4786–4797 (2018)

    Article  ADS  Google Scholar 

  17. L. Lu, P. Zhang, C. Fan, C. Qiao, Influence of oceanic turbulence on propagation of a radial Gaussian beam array. Opt. Express 23(3), 2827–2836 (2015)

    Article  ADS  Google Scholar 

  18. M. Tang, D. Zhao, Propagation of radially polarized beams in the oceanic turbulence. Appl. Phys. B 111(4), 665–670 (2013)

    Article  ADS  Google Scholar 

  19. Y. Dong, L. Guo, C. Liang, F. Wang, Y. Cai, Statistical properties of a partially coherent cylindrical vector beam in oceanic turbulence. J. Opt. Soc. Am. A 32(5), 894–901 (2015)

    Article  ADS  Google Scholar 

  20. Y. Li, L. Yu, Y. Zhang, Influence of anisotropic turbulence on the orbital angular momentum modes of Hermite–Gaussian vortex beam in the ocean. Opt. Express 25(11), 12203–12215 (2017)

    Article  ADS  Google Scholar 

  21. A. Naqwi, F. Durst, Focusing of diode laser beams: a simple mathematical model. Appl. Opt. 29(12), 1780–1785 (1990)

    Article  ADS  Google Scholar 

  22. Y. Cai, S. He, Average intensity and spreading of an elliptical Gaussian beam propagating in a turbulent atmosphere. Opt. Lett. 31(5), 568–570 (2006)

    Article  ADS  Google Scholar 

  23. T. Alieva, E. Abramochkin, A. Asenjo-Garcia, E. Razueva, Rotating beams in isotropic optical system. Opt. Express 18(4), 3568–3573 (2010)

    Article  ADS  Google Scholar 

  24. A.M. Goncharenko, Y.A. Logvin, A.M. Samson, P.S. Shapovalov, Rotating elliptical gaussian beams in nonlinear media. Opt. Commun. 81(3–4), 225–230 (1991)

    Article  ADS  Google Scholar 

  25. D. Deng, Propagation of rotating parabolic cylindrical beams in nonlocal nonlinear medium. Opt. Commun. 285(19), 3976–3981 (2012)

    Article  ADS  Google Scholar 

  26. X. Peng, C. Chen, B. Chen, D. Deng, Propagation of rotating elliptical Gaussian beams from right-handed material to left-handed material. Chin. Phys. B 24(12), 124201 (2015)

    Article  ADS  Google Scholar 

  27. H. Yu, W. She, Rotation dynamics of particles trapped in a rotating beam. J. Opt. Soc. Am. A 32(1), 90–100 (2015)

    Article  ADS  Google Scholar 

  28. L. Paterson, M.P. MacDonald, J. Arlt, W. Sibbett, P.E. Bryant, K. Dholakia, Controlled rotation of optically trapped microscopic particles. Science 292, 912–914 (2001)

    Article  ADS  Google Scholar 

  29. A.I. Bishop, T.A. Nieminen, N.R. Heckenberg, H. Rubinsztein-Dunlop, Optical microrheology using rotating laser-trapped particles. Phys. Rev. Lett. 92(19), 198104 (2004)

    Article  ADS  Google Scholar 

  30. Y. Dan, B. Zhang, P. Pan, Propagation of partially coherent flat-topped beams through a turbulent atmosphere. J. Opt. Soc. Am. A 25(9), 2223–2231 (2008)

    Article  ADS  Google Scholar 

  31. J. Yu, Y. Chen, L. Liu, X. Liu, Y. Cai, Splitting and combining properties of an elegant Hermite–Gaussian correlated Schell-model beam in Kolmogorov and non-Kolmogorov turbulence. Opt. Express 23(10), 13467–13481 (2015)

    Article  ADS  Google Scholar 

  32. Y. Cai, S. He, Propagation of various dark hollow beams in a turbulent atmosphere. Opt. Express 14(4), 1353–1367 (2006)

    Article  ADS  Google Scholar 

  33. X. Ji, X. Chen, S. Chen, X. Li, B. Lü, Influence of atmospheric turbulence on the spatial correlation properties of partially coherent flat-topped beams. J. Opt. Soc. Am. A 24(11), 3554–3563 (2007)

    Article  ADS  Google Scholar 

  34. C.Y. Young, Y.V. Gilchrest, B.R. Macon, Turbulence induced beam spreading of higher order mode optical waves. Opt. Eng. 41(5), 1097–1103 (2002)

    Article  ADS  Google Scholar 

  35. S.A. Thorpe, The Turbulent Ocean (Cambridge University Press, New York, 2007)

    Google Scholar 

  36. I.S. Gradshteyn, I.M. Ryzhik, Table of Integrals, Series, and Products (Academic Press, New York, 1980)

    MATH  Google Scholar 

  37. Y. Yuan, Y. Cai, J. Qu, H.T. Eyyuboǧlu, Y. Baykal, Average intensity and spreading of an elegant Hermite–Gaussian beam in turbulent atmosphere. Opt. Express 17(13), 11130–11139 (2009)

    Article  ADS  Google Scholar 

  38. P. Zhou, Y. Ma, X. Wang, H. Zhao, Z. Liu, Average spreading of a Gaussian beam array in non-Kolmogorov turbulence. Opt. Lett. 35(7), 1043–1045 (2010)

    Article  ADS  Google Scholar 

  39. A. Bekshaev, M. Soskin, Rotational transformations and transverse energy flow in paraxial light beams: linear azimuthons. Opt. Lett. 31(14), 2199–2201 (2006)

    Article  ADS  Google Scholar 

  40. D. Deng, Q. Guo, Spinning parabolic cylindrical beams in free space. Europhys. Lett. 95, 54001 (2011)

    Article  ADS  Google Scholar 

  41. D. Deng, Q. Guo, W. Hu, Complex-variable-function Gaussian beam in strongly nonlocal nonlinear media. Phys. Rev. A 79, 023803 (2009)

    Article  ADS  Google Scholar 

  42. Y. Harada, T. Asakura, Radiation forces on a dielectric sphere in the Rayleigh scattering regime. Opt. Commun. 124(5–6), 529–541 (1996)

    Article  ADS  Google Scholar 

Download references

Acknowledgements

This work was supported by the National Natural Science Foundation of China (11775083, 11374108, 11674107) and the National Training Program of Innovation and Entrepreneurship for Undergraduates.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Dongmei Deng.

Additional information

Jianbin Zhang, Jintao Xie contributed to the work equally.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Zhang, J., Xie, J., Ye, F. et al. Effects of the turbulent atmosphere and the oceanic turbulence on the propagation of a rotating elliptical Gaussian beam. Appl. Phys. B 124, 168 (2018). https://doi.org/10.1007/s00340-018-7038-2

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s00340-018-7038-2

Navigation