Vol. 103
Latest Volume
All Volumes
PIER 176 [2023] PIER 175 [2022] PIER 174 [2022] PIER 173 [2022] PIER 172 [2021] PIER 171 [2021] PIER 170 [2021] PIER 169 [2020] PIER 168 [2020] PIER 167 [2020] PIER 166 [2019] PIER 165 [2019] PIER 164 [2019] PIER 163 [2018] PIER 162 [2018] PIER 161 [2018] PIER 160 [2017] PIER 159 [2017] PIER 158 [2017] PIER 157 [2016] PIER 156 [2016] PIER 155 [2016] PIER 154 [2015] PIER 153 [2015] PIER 152 [2015] PIER 151 [2015] PIER 150 [2015] PIER 149 [2014] PIER 148 [2014] PIER 147 [2014] PIER 146 [2014] PIER 145 [2014] PIER 144 [2014] PIER 143 [2013] PIER 142 [2013] PIER 141 [2013] PIER 140 [2013] PIER 139 [2013] PIER 138 [2013] PIER 137 [2013] PIER 136 [2013] PIER 135 [2013] PIER 134 [2013] PIER 133 [2013] PIER 132 [2012] PIER 131 [2012] PIER 130 [2012] PIER 129 [2012] PIER 128 [2012] PIER 127 [2012] PIER 126 [2012] PIER 125 [2012] PIER 124 [2012] PIER 123 [2012] PIER 122 [2012] PIER 121 [2011] PIER 120 [2011] PIER 119 [2011] PIER 118 [2011] PIER 117 [2011] PIER 116 [2011] PIER 115 [2011] PIER 114 [2011] PIER 113 [2011] PIER 112 [2011] PIER 111 [2011] PIER 110 [2010] PIER 109 [2010] PIER 108 [2010] PIER 107 [2010] PIER 106 [2010] PIER 105 [2010] PIER 104 [2010] PIER 103 [2010] PIER 102 [2010] PIER 101 [2010] PIER 100 [2010] PIER 99 [2009] PIER 98 [2009] PIER 97 [2009] PIER 96 [2009] PIER 95 [2009] PIER 94 [2009] PIER 93 [2009] PIER 92 [2009] PIER 91 [2009] PIER 90 [2009] PIER 89 [2009] PIER 88 [2008] PIER 87 [2008] PIER 86 [2008] PIER 85 [2008] PIER 84 [2008] PIER 83 [2008] PIER 82 [2008] PIER 81 [2008] PIER 80 [2008] PIER 79 [2008] PIER 78 [2008] PIER 77 [2007] PIER 76 [2007] PIER 75 [2007] PIER 74 [2007] PIER 73 [2007] PIER 72 [2007] PIER 71 [2007] PIER 70 [2007] PIER 69 [2007] PIER 68 [2007] PIER 67 [2007] PIER 66 [2006] PIER 65 [2006] PIER 64 [2006] PIER 63 [2006] PIER 62 [2006] PIER 61 [2006] PIER 60 [2006] PIER 59 [2006] PIER 58 [2006] PIER 57 [2006] PIER 56 [2006] PIER 55 [2005] PIER 54 [2005] PIER 53 [2005] PIER 52 [2005] PIER 51 [2005] PIER 50 [2005] PIER 49 [2004] PIER 48 [2004] PIER 47 [2004] PIER 46 [2004] PIER 45 [2004] PIER 44 [2004] PIER 43 [2003] PIER 42 [2003] PIER 41 [2003] PIER 40 [2003] PIER 39 [2003] PIER 38 [2002] PIER 37 [2002] PIER 36 [2002] PIER 35 [2002] PIER 34 [2001] PIER 33 [2001] PIER 32 [2001] PIER 31 [2001] PIER 30 [2001] PIER 29 [2000] PIER 28 [2000] PIER 27 [2000] PIER 26 [2000] PIER 25 [2000] PIER 24 [1999] PIER 23 [1999] PIER 22 [1999] PIER 21 [1999] PIER 20 [1998] PIER 19 [1998] PIER 18 [1998] PIER 17 [1997] PIER 16 [1997] PIER 15 [1997] PIER 14 [1996] PIER 13 [1996] PIER 12 [1996] PIER 11 [1995] PIER 10 [1995] PIER 09 [1994] PIER 08 [1994] PIER 07 [1993] PIER 06 [1992] PIER 05 [1991] PIER 04 [1991] PIER 03 [1990] PIER 02 [1990] PIER 01 [1989]
2010-04-07
Average Intensity and Spreading of Partially Coherent Standard and Elegant Laguerre-Gaussian Beams in Turbulent Atmosphere
By
Progress In Electromagnetics Research, Vol. 103, 33-56, 2010
Abstract
Analytical expressions for the average intensity, mean-squared beam width and angular spread of partially coherent standard and elegant Laguerre-Gaussian (LG) beams propagating in turbulent atmosphere are derived. The properties of the average intensity, spreading and directionality of partially coherent standard and elegant LG beams in turbulent atmosphere are studied numerically and comparatively. It is found that the beam parameters and structure constant of turbulence together determine the properties of the beams in turbulent atmosphere. Partially coherent standard and elegant LG beams with smaller coherence length, larger beam orders and longer wavelength are less affected by the turbulence. A partially coherent elegant LG beam is less affected by turbulence than a partially coherent standard LG beam under the same condition. Furthermore, it is found that there exist equivalent partially coherent standard and elegant LG beams, equivalent fully coherent standard and elegant LG beams, equivalent Gaussian Schell-model beams that may have the same directionality as a fully coherent Gaussian beam both in free space and in turbulent atmosphere. Our results will be useful in long distance free-space optical communications.
Citation
Fei Wang Yangjian Cai Halil Tanyer Eyyuboglu Yahya Kemal 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
http://www.jpier.org/PIER/pier.php?paper=10021901
References

1. Andrews, L. C. and R. L. Phillips, Laser Beam Propagation in the Turbulent Atmosphere, 2nd Ed., SPIE press, Bellington, 2005.

2. Ricklin, J. C. and F. M. Davidson, "Atmospheric turbulence effects on a partially coherent Gaussian beam: Implications for free-space laser communication ," J. Opt. Soc. Am. A, Vol. 19, No. 9, 1794-1802, 2002.
doi:10.1364/JOSAA.19.001794

3. Young, C. Y., Y. V. Gilchrest, and B. R. Macon, "Turbulenceinduced beam spreading of higher-order mode optical waves," Opt. Eng., Vol. 41, No. 5, 1097-1103, 2002.
doi:10.1117/1.1465427

4. Eyyuboglu, H. T. and Y. Baykal, "Reciprocity of cos-Gaussian and cosh-Gaussian laser beams in turbulent atmosphere," Opt. Express, Vol. 12, No. 20, 4659-4674, 2004.
doi:10.1364/OPEX.12.004659

5. Eyyuboglu, H. T. and Y. Baykal, "Hermite-sine-Gaussian and Hermite-sinh-Gaussian laser beams in turbulent atmosphere," J. Opt. Soc. Am. A, Vol. 22, No. 12, 2709-2718, 2005.
doi:10.1364/JOSAA.22.001527

6. Eyyuboglu, H. T., "Hermite-cosine-Gaussian laser beam and its propagation characteristics in turbulent atmosphere," J. Opt. Soc. Am. A, Vol. 22, No. 8, 1527-1535, 2005.
doi:10.1364/JOSAA.22.001527

7. Cai, Y. and S. He, "Propagation of a partially coherent twisted anisotropic Gaussian Schell-model beam in a turbulent atmosphere," Appl. Phys. Lett., Vol. 89, No. 4, 041117, 2006.
doi:10.1063/1.2236463

8. Cai, Y., "Propagation of various of at-topped beams in a turbulent atmosphere," J. Opt. A, Pure Appl. Opt., Vol. 8, No. 6, 537-545, 2006.
doi:10.1088/1464-4258/8/6/008

9. Eyyuboglu, H. T., S. Altay, and Y. Baykal, "Propagation characteristics of higher-order annular Gaussian beams in atmospheric turbulence," Opt. Commun., Vol. 264, No. 1, 25-34, 2006.
doi:10.1016/j.optcom.2006.02.030

10. Chen, Z. and J. Pu, "Propagation characteristics of aberrant stochastic electromagnetic beams in a turbulent atmosphere," J. Opt. A, Pure Appl. Opt., Vol. 9, No. 12, 1123-1130, 2007.
doi:10.1088/1464-4258/9/12/002

11. Noriega-Manez, R. J. and J. C. Gutierrez-Vega, "Rytov theory for Helmholtz-Gauss beams in turbulent atmosphere," Opt. Express, Vol. 15, No. 25, 16328-16341, 2007.
doi:10.1364/OE.15.016328

12. Chu, X., "Propagation of a cosh-Gaussian beam through an optical system in turbulent atmosphere," Opt. Express, Vol. 15, No. 26, 17613-17618, 2007.
doi:10.1364/OE.15.017613

13. Cai, Y., O. Korotkova, H. T. Eyyuboglu, and Y. Baykal, "Active laser radar systems with stochastic electromagnetic beams in turbulent atmosphere," Opt. Express, Vol. 16, No. 20, 15834-15846, 2008.
doi:10.1364/OE.16.015834

14. Ji, X. and G. Ji, "Spatial correlation properties of apertured partially coherent beams propagating through atmospheric turbulence ," Appl. Phys. B, Vol. 92, No. 1, 111-1118, 2008.
doi:10.1007/s00340-008-3050-2

15. Wang, T., J. Pu, and Z. Chen, "Propagation of partially coherent vortex beams in a turbulent atmosphere," Opt. Eng., Vol. 47, No. 3, 036002, 2008.
doi:10.1117/1.2896309

16. 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, No. 1, 21-28, 2008.
doi:10.1364/JOSAA.25.000021

17. Li, X., X. Chen, and X. Ji, "Influence of atmospheric turbulence on the propagation of superimposed partially coherent Hermite-Gaussian beams," Opt. Commun., Vol. 282, No. 1, 7-13, 2008.
doi:10.1016/j.optcom.2008.09.063

18. Alavinejad, M. and B. Ghafary, "Turbulence-induced degradation properties of partially coherent °at-topped beams," Opt. Lasers Eng., Vol. 46, No. 5, 357-362, 2008.
doi:10.1016/j.optlaseng.2007.12.005

19. Wu, Z., H. Wei, R. Yang, and L. Guo, "Study on scintillation considering inner and outer-scales for laser beam propagation on the slant path through the atmospheric turbulence," Progress In Electromagnetics Research, Vol. 80, 277-293, 2008.
doi:10.2528/PIER07112505

20. Zhou, G. and X. Chu, "Propagation of a partially coherent cosine-Gaussian beam through an ABCD optical system in turbulent atmosphere ," Opt. Express, Vol. 17, No. 13, 10529-10534, 2009.
doi:10.1364/OE.17.010529

21. Zhou, P., Y. Ma, X. Wang, H. Ma, X. Xu, and Z. Liu, "Average intensity of a partially coherent rectangular flat-topped laser array propagating in a turbulent atmosphere," Appl. Opt., Vol. 48, No. 28, 5251-5258, 2009.
doi:10.1364/AO.48.005251

22. Kashani, F. D., M. Alavinejad, and B. Ghafary, "Polarization characteristics of aberrated partially coherent flat-topped beam propagating through turbulent atmosphere ," Opt. Commun., Vol. 282, No. 20, 4029-4034, 2009.
doi:10.1016/j.optcom.2009.07.008

23. Chu, X., "The relay propagation of partially coherent cosh-Gaussian-Schell beams in turbulent atmosphere," Appl. Phys. B, Vol. 98, No. 2-3, 573-579, 2010.
doi:10.1007/s00340-009-3769-4

24. Alexopoulos, A., "Effect of atmospheric propagation in RCS predictions," Progress In Electromagnetics Research, Vol. 101, 277-290, 2010.
doi:10.2528/PIER09121509

25. Siegman, A. E., Lasers, University Science Books, Mill Valley, CA, 1986.

26. Takenaka, T., M. Yokota, and O. Fukumitsu, "Propagation of light beams beyond the paraxial approximation," J. Opt. Soc. Am. A, Vol. 2, No. 6, 826-829, 1985.
doi:10.1364/JOSAA.2.000826

27. Zauderer, E., "Complex argument Hermite-Gaussian and Laguerre-Gaussian beams," J. Opt. Soc. Am. A, Vol. 3, No. 4, 465-469, 1986.
doi:10.1364/JOSAA.3.000465

28. Tamm, C. and C. Weiss, "Bistability and optical switching of spatial patterns in a laser," J. Opt. Soc. Am. B, Vol. 7, No. 6, 1034-1038, 1990.
doi:10.1364/JOSAB.7.001034

29. Brambilla, M., F. Battipede, L. A. Lugiato, V. Penna, F. Prati, C. Tamm, and C. O. Weiss, "Transverse laser patterns. I. Phase singularity crystals," Phys. Rev. A, Vol. 43, No. 9, 5090-5113, 1991.
doi:10.1103/PhysRevA.43.5090

30. Saghafi, S. and C. J. R. Sheppard, "Near field and far field of elegant Hermite-Gaussian and Laguerre-Gaussian modes," J. Mod. Opt., Vol. 45, No. 10, 1999-2009, 1998.

31. Hasegawa, T. and T. Shimizu, "Frequency-doubled Hermite-Gaussian beam and the mode conversion to the Laguerre-Gaussian beam ," Opt. Commun., Vol. 160, No. 1-3, 103-108, 1999.
doi:10.1016/S0030-4018(98)00656-7

32. Chen, Y., Y. Lan, and S.Wang, "Generation of Laguerre-Gaussian modes in fiber-coupled laser diode end-pumped lasers," Appl. Phys. B, Vol. 72, No. 2, 167-170, 2001.

33. Jarutis, V., R. Paskauskas, and A. Stabinis, "Focusing of Laguerre-Gaussian beams by axicon," Opt. Commun., Vol. 184, No. 1-4, 105-112, 2000.
doi:10.1016/S0030-4018(00)00961-5

34. Simon, R. and G. S. Agarwal, "Wigner representation of Laguerre-Gaussian beams," Opt. Lett., Vol. 25, No. 18, 1313-1315, 2000.
doi:10.1364/OL.25.001313

35. Arlt, J., R. Kuhn, and K. Dholakia, "Spatial transformation of Laguerre-Gaussian laser modes," J. Mod. Opt., Vol. 48, No. 5, 783-787, 2001.

36. Borghi, R., "Elegant Laguerre-Gauss beams as a new tool for describing axisymmetric flattened Gaussian beams ," J. Opt. Soc. Am. A, Vol. 18, No. 7, 1627-1633, 2001.
doi:10.1364/JOSAA.18.001627

37. Orlov, S. and A. Stabinis, "Free-space propagation of light field created by Bessel-Gauss and Laguerre-Gauss singular beams," Opt. Commun., Vol. 226, No. 1-6, 97-105, 2003.
doi:10.1016/j.optcom.2003.09.005

38. Bandres, M. A. and J. C. Gutierrez-Vega, "Higher-order complex source for elegant Laguerre-Gaussian waves," Opt. Lett., Vol. 29, No. 19, 2213-2215, 2004.
doi:10.1364/OL.29.002213

39. Mei, Z. and D. Zhao, "Propagation of Laguerre-Gaussian and elegant Laguerre-Gaussian beams in apertured fractional Hankel transform systems ," J. Opt. Soc. Am. A, Vol. 21, No. 12, 2375-2381, 2004.
doi:10.1364/JOSAA.21.002375

40. Cai, Y. and S. He, "Propagation of a Laguerre-Gaussian beam through a slightly misaligned paraxial optical system," Appl. Phys. B, Vol. 84, No. 3, 493-500, 2006.
doi:10.1007/s00340-006-2321-z

41. April, A. and Nonparaxial elegant Laguerre-Gaussian beams, "Opt. Lett.,", Vol. 33, No. 12, 1392-1394, 2008.

42. Mei, Z. and J. Gu, "Comparative studies of paraxial and nonparaxial vectorial elegant Laguerre-Gaussian beams," Opt. Express, Vol. 17, No. 17, 14865-14871, 2009.
doi:10.1364/OE.17.014865

43. Wang, F., Y. Cai, and O. Korotkova, "Partially coherent standard and elegant Laguerre-Gaussian beams of all orders," Opt. Express, Vol. 17, No. 25, 22366-22379, 2009.
doi:10.1364/OE.17.022366

44. Gori, F., "Collet-wolf sources and multimode lasers," Opt. Commun., Vol. 34, No. 3, 301-305, 1980.
doi:10.1016/0030-4018(80)90382-X

45. Friberg, A. T. and R. J. Sudol, "Propagation parameters of Gaussian Schell-model beams," Opt. Commun., Vol. 41, No. 6, 383-387, 1982.
doi:10.1016/0030-4018(82)90161-4

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

47. Wang, F. and Y. Cai, "Experimental observation of fractional Fourier transform for a partially coherent optical beam with Gaussian statistics ," J. Opt. Soc. Am. A, Vol. 24, No. 7, 1937-1944, 2007.
doi:10.1364/JOSAA.24.001937

48. Sidoro, K. and R. E. Luis, "Relations between Hermite and Laguerre Gaussian modes," IEEE J. Quantum. Electron., Vol. 29, No. 9, 2563-2567, 1993.

49. Erdelyi, A., W. Magnus, and F. Oberhettinger, Tables of Integral Transforms, McGraw-Hill, 1954.

50. Abramowitz, M. and I. Stegun, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, U.S. Department of Commerce, 1970.
doi:10.1364/JOSA.60.000667

50. Ho, T. L., "Coherence degration of Gaussian beams in a turbulent atmosphere ," J. Opt. Soc. Am, Vol. 60, No. 5, 667-673, 1970.
doi:10.1364/JOSA.60.000667

52. Siegman, A. E., New developments in laser resonators, Proc. SPIE, No. 1224, 2-14, 1990.

53. 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

54. Shirai, T., A. Dogariu, and E. Wolf, "Directionality of Gaussian Schell-model beams propagating in atmospheric turbulence," Opt. Lett., Vol. 28, No. 8, 610-612, 2003.
doi:10.1364/OL.28.000610