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AVERAGE INTENSITY AND SPREADING OF PARTIALLY COHERENT FOUR-PETAL GAUSSIAN BEAMS IN TURBULENT ATMOSPHERE

By J. Li, Y. Chen, S. Xu, Y. Wang, M. Zhou, Q. Zhao, Y. Xin, and F. Chen

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Abstract:
The concept of partially coherent four-petal Gaussian (PCFPG) beam is introduced and described in analytical forms. Based on the Huygens-Fresnel integral formula, average intensity and beam spreading in turbulent atmosphere are derived in analytical expressions. Effects of beam parameters and atmospheric structure constant on intensity distributions and effective beam sizes are investigated in detail, respectively. Results show that PCFPG beams carrying larger coherence lengths or higher beam orders would be less affected by turbulence. It is also indicated that, when the propagation distance increases, the PCFPG beam would convert into the Gauss-like profile sooner or later, but this degradation can be reduced by modulating beam parameters. Results in this paper may provide potential applications in free-space optical communications.

Citation:
J. Li, Y. Chen, S. Xu, Y. Wang, M. Zhou, Q. Zhao, Y. Xin, and F. Chen, "Average Intensity and Spreading of Partially Coherent Four-Petal Gaussian Beams in Turbulent Atmosphere," Progress In Electromagnetics Research B, Vol. 24, 241-262, 2010.
doi:10.2528/PIERB10062306

References:
1. Andrews, L. C. and R. L. Phillips, Laser Beam Propagation Through Random Media, SPIE Press, Bellingham, Washington, 1998.

2. Gbur, G. and E. Wolf, "Spreading of partially coherent beams in random media," J. Opt. Soc. Am. A, Vol. 19, 1592-1598, 2002.
doi:10.1364/JOSAA.19.001592

3. Gbur, G. and R. K. Tyson, "Vortex beam propagation through atmospheric turbulence and topological charge conservation," J. Opt. Soc. Am. A, Vol. 25, 225-230, 2008.
doi:10.1364/JOSAA.25.000225

4. Azana, J., "Lensless imaging of an arbitrary object," Opt. Lett., Vol. 28, 501-503, 2003.
doi:10.1364/OL.28.000501

5. Ferri, F., D. Magatti, A. Gatti, M. Bache, E. Brambilla, and L. A. Lugiato, "High-resolution ghost image and ghost diffraction experiments with thermal light ," Phys. Rev. Lett., Vol. 94, 183602, 2005.
doi:10.1103/PhysRevLett.94.183602

6. Cheng, J., "Ghost imaging through turbulent atmosphere," Opt. Express, Vol. 17, 7916-7921, 2009.
doi:10.1364/OE.17.007916

7. Ricklin, J. C. and F. M. Davidson, "Atmospheric turbulence effects on a partially coherent Gaussian beam: Implications for free-space laser communications," J. Opt. Soc. Am. A, Vol. 19, 1794-1802, 2002.
doi:10.1364/JOSAA.19.001794

8. Chen, B., Z. Chen, and J. Pu, "Propagation of partially coherent Bessel-Gaussian beams in turbulent atmosphere," Opt. Laser. Technol., Vol. 40, 820-827, 2008.
doi:10.1016/j.optlastec.2007.11.011

9. Qu, J., Y. Zhong, Z. Cui, and Y. Cai, "Elegant Laguerre-Gaussian beam in a turbulent atmosphere," Opt. Commun., Vol. 283, 2772-2781, 2010.
doi:10.1016/j.optcom.2010.03.022

10. Eyyuboglu, H. T., Y. Baykal, and E. Sermutlu, "Convergence of general beams into Gaussian intensity profiles after propagation in turbulent atmosphere," Opt. Commun., Vol. 265, 399-405, 2006.
doi:10.1016/j.optcom.2006.03.071

11. Ji, X., E. Zhang, and B. Lü, "Superimposed partially coherent beams propagating through atmospheric turbulence," J. Opt. Soc. Am. B, Vol. 25, 825-833, 2008.
doi:10.1364/JOSAB.25.000825

12. Manez, R. J. and J. C. Gutiérrez, "Rytov theory for Helmholtz-Gauss beams in turbulent atmosphere," Opt. Express, Vol. 15, 16328-16341, 2007.
doi:10.1364/OE.15.016328

13. Razzaghi, D., F. Hajiesmaeilbaigi, and M. Alavinejad, "Turbulence induced changes in spectrum and time shape of fully coherent Gaussian pulses propagating in atmosphere," Opt. Commun., Vol. 283, 2318-2323, 2010.
doi:10.1016/j.optcom.2010.01.048

14. Eyyuboglu, H. T., Y. Baykal, and X. Ji, "Radius of curvature variations for annular, dark hollow and flat topped beams in turbulence," Appl. Phys. B, Vol. 99, No. 4, 801-807, 2010.
doi:10.1007/s00340-010-3955-4

15. Shchepakina, E. and O. Korotkova, "Second-order statistics of stochastic electromagnetic beams propagating through non-Kolmogorov turbulence," Opt. Express, Vol. 18, 10650-10658, 2010.
doi:10.1364/OE.18.010650

16. Chen, W., J. W. Haus, and Q. Zhan, "Propagation of scalar and vector vortex beams through turbulent atmosphere," Proc. of SPIE, Vol. 7200, 720004, 2009.
doi:10.1117/12.809138

17. Wang, F., Y. Cai, and O. Korotkova, "Partially coherent standard and elegant Laguerre-Gaussian beams of all orders," Opt. Express, Vol. 17, 22366-22379, 2009.
doi:10.1364/OE.17.022366

18. Shirai, T., A. Dogariu, and E. Wolf, "Directionality of Gaussian Schell-model beams propagating in atmospheric turbulence," Opt. Lett., Vol. 28, 610-612, 2003.
doi:10.1364/OL.28.000610

19. Korotkova, O., M. Salem, and E. Wolf, "The far-zone behavior of the degree of polarization of electromagnetic beams propagating through atmospheric turbulence," Opt. Commun., Vol. 233, 225-230, 2004.
doi:10.1016/j.optcom.2004.01.005

20. Korotkova, O., "Control of the intensity fluctuations of random electromagnetic beam on propagation in weak turbulent atmosphere," Proc. of SPIE, Vol. 6105, 61050, 2006.
doi:10.1117/12.644254

21. Cai, Y. and S. He, "Propagation of a partially coherent twisted anisotropic Gaussian Schell-model beam in turbulent atmosphere," Appl. Phys. Lett., Vol. 89, 041117, 2006.
doi:10.1063/1.2236463

22. Arpali, C., C. Yazicioglu, H. T. Eyyuboglu, S. A. Arpali, and Y. Baykal, "Simulator for general-type beam propagation in turbulent atmosphere," Opt. Express, Vol. 14, 8918-8928, 2006.
doi:10.1364/OE.14.008918

23. Eyyuboglu, H. T., "Hermite-cosine-Gaussian laser beam and its propagation characteristics in turbulent atmosphere," J. Opt. Soc. Am. A, Vol. 22, 1527-1535, 2005.
doi:10.1364/JOSAA.22.001527

24. Ji, X., X. Chen, and B. Lu, "Spreading and directionality of partially coherent Hermite-Gaussian beams propagating through atmospheric turbulence," J. Opt. Soc. Am. A, Vol. 25, 21-28, 2008.
doi:10.1364/JOSAA.25.000021

25. Yuan, Y., Y. Cai, J. Qu, H. T. Eyyuboglu, and Y. Baykal, "Average intensity and spreading of an elegant Hermite-Gaussian beam in turbulent atmosphere," Opt. Express, Vol. 17, 11130-11139, 2009.
doi:10.1364/OE.17.011130

26. Li, J., Y. Chen, Q. Zhao, and M. Zhou, "Effect of astigmatism on states of polarization of aberrant stochastic electromagnetic beams in turbulent atmosphere," J. Opt. Soc. Am. A, Vol. 26, 2121-2127, 2009.
doi:10.1364/JOSAA.26.002121

27. Chu, X., Z. Liu, and Y. Wu, "Propagation of a general multi-Gaussian beam in turbulent atmosphere in a slant path," J. Opt. Soc. Am. A, Vol. 25, 74-79, 2008.
doi:10.1364/JOSAA.25.000074

28. Zhou, P., Z. Liu, X. Xu, and X. Chu, "Propagation of phase-locked partially coherent flattened beam array in turbulent atmosphere," Opt. & Laser. Eng., Vol. 47, 1254-1258, 2009.
doi:10.1016/j.optlaseng.2009.05.008

29. Dan, Y. and B. Zhang, "Second moments of partially coherent beams in atmospheric turbulence," Opt. Lett., Vol. 34, 563-565, 2009.
doi:10.1364/OL.34.000563

30. Zhou, G. and X. Chu, "Average intensity and spreading of a Lorentz-Gauss beam in turbulent atmosphere," Opt. Express, Vol. 18, 726-731, 2010.
doi:10.1364/OE.18.000726

31. Cai, Y., Y. Chen, H. T. Eyyuboglu, and Y. Baykal, "Scintillation index of elliptical Gaussian beam in turbulent atmosphere," Opt. Lett., Vol. 32, 2405-2407, 2007.
doi:10.1364/OL.32.002405

32. Voelz, D. G. and X. Xiao, "Metric for optimizing spatially partially coherent beams for propagation through turbulence," Opt. Eng., Vol. 48, 036001, 2009.
doi:10.1117/1.3090435

33. Gu, Y. and G. Gbur, "Measurement of atmospheric turbulences strength by vortex beam," Opt. Commun., Vol. 283, 1209-1212, 2010.
doi:10.1016/j.optcom.2009.11.049

34. Grynberg, G., A. Maitre, and A. Petrossian, "Flowerlike patterns generated by a laser beam transmitted through a rubidium cell with single feedback mirror," Phys. Rev. Lett., Vol. 72, 2379-2382, 1994.
doi:10.1103/PhysRevLett.72.2379

35. Zhang, B. and D. Zhao, "Focusing properties of Fresnel zone plates with spiral phase ," Opt. Express, Vol. 18, 12818-12823, 2010.
doi:10.1364/OE.18.012818

36. Golub, I. and T. Mirtchev, "Absorption-free beam generated by a phase-engineered optical element," Opt. Lett., Vol. 34, 1528-1530, 2009.
doi:10.1364/OL.34.001528

37. Pu, J., S. Nemoto, and X. Liu, "Beam shaping of focused partially coherent beams by use of the spatial coherence effect," Appl. Opt., Vol. 43, 5281-5286, 2004.
doi:10.1364/AO.43.005281

38. Lindfors, K., T. Setälä, and M. Kaivola, "Degree of polarization in tightly focused optical fields," J. Opt. Soc. Am. A, Vol. 22, 561-568, 2005.
doi:10.1364/JOSAA.22.000561

39. Zhan, Q. and J. R. Leger, "Focus shaping using cylindrical vector beams," Opt. Express, Vol. 10, 324-331, 2002.

40. Sabatke, D., A. Locke, E. L. Dereniak, M. Descour, J. Garcia, T. Hamilton, and R. W. McMillan, "Snapshot imaging spectropolarimeter," Opt. Eng., Vol. 41, 1048-1054, 2002.
doi:10.1117/1.1467934

41. Ganic, D., X. Gan, and M. Gu, "Focusing of doughnut laser beams by a high numerical-aperture objective in free space," Opt. Express, Vol. 11, 2747-2752, 2003.
doi:10.1364/OE.11.002747

42. Wada, A., Y. Miyamoto, T. Ohtani, N. Nishihara, and M. Takeda, "Effects of astigmatic aberration in holographic generation of Laguerre-Gaussian beam," Proc. of SPIE, Vol. 5137, 177-180, 2003.
doi:10.1117/12.517961

43. Berre, M. L., A. S. Patrascu, E. Ressayre, and A. Tallet, "Daisy patterns in the passive ring cavity with diffusion effects," Opt. Commun., Vol. 123, 810-824, 1996.
doi:10.1016/0030-4018(95)00472-6

44. Firth, W. J., A. J. Scroggie, and G. S. Mcdonald, "Hexagonal patterns in optical bistability," Phys. Rev. A, Vol. 46, 3609-3612, 1992.
doi:10.1103/PhysRevA.46.R3609

45. Cai, Y. and Q. Lin, "Four-beamlets laser array and its propagation," Opt. Laser. Technol., Vol. 37, 483-489, 2005.
doi:10.1016/j.optlastec.2004.07.003

46. Duan, K. and B. Lu, "Four-petal Gaussian beams and their propagation," Opt. Commun., Vol. 261, 327-331, 2006.
doi:10.1016/j.optcom.2005.12.037

47. Gao, Z. and B. Lu, "Vectorial nonparaxial four-petal Gaussian beams and their propagation in free space," Chin. Phys. Lett., Vol. 23, 2070-2073, 2006.

48. Chu, X., Z. Liu, and Y. Wu, "Propagation of four-petal Gaussian beams in turbulent atmosphere," Chin. Phys. Lett., Vol. 25, 485-488, 2008.

49. Zhou, G. and Y. Fan, ".M2 factor of four-petal Gaussian beam," Chin. Phys. B, Vol. 17, 3708-3712, 2008.

50. Tang, B., Y. Jin, M. Jiang, and X. Jiang, "Diffraction properties of four-petal Gaussian beams in uniaxially anisotropic crystal," Chin. Opt. Lett., Vol. 6, 779-781, 2008.
doi:10.3788/COL20080610.0779

51. Tang, B., "Propagation properties of four-petal Gaussian beams in apertured factional Fourier transforming systems," J. Mod. Opt., Vol. 56, 1860-1867, 2009.
doi:10.1080/09500340903377725

52. Li, J., Y. Chen, Y. Xin, M. Zhou, and S. Xu, "Vectorial structural characteristics of four-petal Gaussian beams in the far field," Eur. Phys. J. Appl. Phys., Vol. 50, 30702, 2010.
doi:10.1051/epjap/2010051

53. Mandel, L. and E. Wolf, Optical Coherence and Quantum Optics, Cambridge U. Press, 1995.

54. Wang, F., Y. Cai, H. T. Eyyuboglu, and Y. Baykal, "Average intensity and spreading of partially coherent standard and elegant Laguerre-Gaussian beams in turbulent atmosphere," Progress In Electromagnetics Research, Vol. 103, 33-56, 2010.
doi:10.2528/PIER10021901

55. Li, J., Y. Chen, Y. Xin, M. Zhou, and S. Xu, "Diffraction properties of partially coherent vectorial four-petal Gaussian beams," Opt. Commun., Vol. 283, 3105-3114, 2010.
doi:10.1016/j.optcom.2010.04.009

56. Carter, W. H., "Spot size and divergence for Hermite-Gaussian beams of any order," Appl. Opt., Vol. 19, 1027-1029, 1980.
doi:10.1364/AO.19.001027

57. Gbur, G. and E. Wolf, "The Rayleigh range of partially coherent beams," Opt. Commun., Vol. 199, 295-304, 2001.
doi:10.1016/S0030-4018(01)01467-5

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

59. Abramowitz, M. and I. Stegun, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Table, U. S. Department of Commerce, 1970.

60. Bracewell, R. N., The Fourier Transform and Its Applications, 2nd Ed., McGraw-Hill, 1986.


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