Abstract
Based on the extended Huygens-Fresnel integral and the second-order moments of the Wigner distribution function, analytical formulae for the propagation factors (known as M 2-factors) of a non-circular (i.e., rectangular or elliptical) partially coherent flat-topped beam in turbulent atmosphere are derived. The properties of the M 2-factors of a non-circular partially coherent flat-topped beam in turbulent atmosphere and in free space are studied numerically and comparatively. It is found that the evolution properties of the M 2-factors are mainly determined by the parameters of the beam and the turbulent atmosphere. The relative M 2-factors of a non-circular partially coherent flat-topped beam can be smaller than a circular partially coherent flat-topped beam and a Gaussian Schell-model beam, particularly at long propagation ranges in turbulent atmosphere. Our results will be useful in long-distance free-space optical communications.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
N. Nishi, T. Jitsuno, K. Tsubakimoto, S. Matsuoka, N. Miyanaga, M. Nakatsuka, Opt. Rev. 7, 216 (2000)
H.T. Eyyuboğlu, A. Arpali, Y. Baykal, Opt. Express 14, 4196 (2006)
L. Wang, J. Xue, Jpn. Appl. Phys. Part 1 41, 7373 (2002)
W. Wang, P.X. Wang, Y.K. Ho, Q. Kong, Z. Chen, Y. Gu, S.J. Wang, Europhys. Lett. 73, 211 (2006)
Y. Kato, K. Mima, N. Miyanaga, S. Arinaga, Y. Kitagawa, M. Nakatsuka, C. Yamanaka, Phys. Rev. Lett. 53, 1057 (1984)
M.S. Bowers, Opt. Lett. 19, 1319 (1992)
F. Gori, Opt. Commun. 107, 335 (1994)
A.A. Tovar, J. Opt. Soc. Am. A 18, 1897 (2001)
Y. Li, Opt. Lett. 27, 1007 (2002)
Y. Li, Opt. Commun. 206, 225 (2002)
Y. Li, J. Mod. Opt. 50, 1957 (2003)
Y. Cai, Q. Lin, J. Opt. A: Pure Appl. Opt. 6, 390 (2004)
V. Bagini, R. Borghi, F. Gori, A.M. Pacileo, M. Santarsiero, J. Opt. Soc. Am. A 13, 1385 (1996)
S.A. Amarande, Opt. Commun. 129, 311 (1996)
R. Borghi, M. Santarsiero, S. Vicalvi, Opt. Commun. 154, 243 (1998)
Y. Cai, Q. Lin, J. Opt. A: Pure Appl. Opt. 5, 272 (2003)
X. Lu, Y. Cai, Opt. Commun. 269, 39 (2007)
Y. Cai, J. Opt. A: Pure Appl. Opt. 8, 537 (2006)
Y. Baykal, H.T. Eyyuboğlu, Appl. Opt. 45, 3793 (2006)
M. Alavinejad, B. Ghafary, F.D. Kashiani, Opt. Lasers Eng. 46, 1 (2008)
X. Chu, Y. Ni, G. Zhou, Opt. Commun. 274, 274 (2007)
X. Chu, Z. Liu, Y. Wu, Appl. Phys. B 92, 119 (2008)
X. Shen, L. Wang, H. Shen, Y. Han, Opt. Commun. 282, 4765 (2009)
Y. Cai, J. Opt. A: Pure Appl. Opt. 10, 075003 (2008)
L. Mandel, E. Wolf, Optical Coherence and Quantum Optics (Cambridge University Press, Cambridge, 1995)
E. Collett, E. Wolf, Opt. Lett. 2, 27 (1978)
F. Gori, Opt. Commun. 34, 301 (1978)
Q. Lin, Y. Cai, Opt. Lett. 27, 216 (2002)
Y. Cai, L. Hu, Opt. Lett. 31, 685 (2006)
P.D. Santis, F. Gori, G. Guattari, C. Palma, Opt. Commun. 29, 256 (1979)
E. Tervonen, A.T. Friberg, J. Turunen, J. Opt. Soc. Am. A 9, 796 (1992)
F. Wang, Y. Cai, J. Opt. Soc. Am. A 24, 1937 (2007)
J.C. Ricklin, F.M. Davidson, J. Opt. Soc. Am. A 19, 1794 (2002)
A. Belendez, L. Carretero, A. Fimia, Opt. Commun. 98, 236 (1993)
G.C. Dente, J.S. Osgood, Opt. Eng. 22, 720 (1983)
Y. Cai, S. He, Appl. Phys. Lett. 89, 041117 (2006)
Y. Cai, U. Peschel, Opt. Express 15, 15480 (2007)
Y. Cai, S. Zhu, Opt. Lett. 29, 2716 (2004)
Y. Cai, S. Zhu, Phys. Rev. E 71, 056607 (2005)
Y. Cai, Q. Lin, O. Korotkova, Opt. Express 17, 2450 (2009)
C. Zhao, Y. Cai, O. Korotkova, Opt. Express 17, 21472 (2009)
R. Borghi, M. Santarsiero, Opt. Lett. 23, 313 (1998)
D.W. Coutts, IEEE J. Quantum Electron. 38, 1217 (2002)
J. Turunen, P. Paallonen, M. Kuittinen, P. Laakkonen, J. Simonen, T. Kajava, M. Kaivola, J. Mod. Opt. 47, 2467 (2000)
F. Wang, Y. Cai, Opt. Lett. 33, 1795 (2008)
D. Ge, Y. Cai, Q. Lin, Appl. Opt. 43, 4732 (2004)
Y. Cai, S. He, J. Opt. Soc. Am. A 23, 2623 (2006)
F.D. Kashani, M. Alavinejad, B. Ghafary, Laser Technol. 41, 659 (2009)
Y. Cai, Q. Lin, Opt. Commun. 239, 33 (2004)
Y. Cai, X. Lu, H.T. Eyyuboğlu, Y. Baykal, Opt. Commun. 281, 3221 (2008)
C. Zhao, Y. Cai, X. Lu, H.T. Eyyuboğlu, Opt. Express 17, 1753 (2009)
D. Liu, Z. Zhou, J. Opt. Soc. Am. A 26, 924 (2009)
Y. Zhang, B. Zhang, Q. Wen, Opt. Commun. 266, 407 (2006)
B. Zhang, Q. Wen, X. Guo, Optik 117, 123 (2006)
M. Alavinejad, B. Ghafary, Opt. Lasers Eng. 46, 357 (2008)
F.D. Kashani, M. Alavinejad, B. Ghafary, Opt. Commun. 282, 4029 (2009)
Y. Baykal, H.T. Eyyuboğlu, Appl. Opt. 46, 5044 (2007)
Y. Dan, B. Zhang, P. Pan, J. Opt. Soc. Am. A 25, 2223 (2008)
X. Ji, J. Mod. Opt. 55, 2105 (2008)
X. Ji, X. Chen, S. Chen, X. Li, B. Lu, J. Opt. Soc. Am. A 24, 3554 (2007)
X. Chu, Z. Li, Y. Wu, Opt. Commun. 282, 4486 (2009)
Y. Dan, B. Zhang, Opt. Express 16, 15563 (2008)
Y. Baykal, H.T. Eyyuboğlu, Y. Cai, Atmos. Ocean. Opt. 20, 1105 (2007)
M. Alavinejad, M. Khatiri, B. Chafary, Opt. Commun. 282, 3541 (2009)
A.E. Siegman, Proc. SPIE 1224, 2C14 (1990). New developments in laser resonators, in Optical Resonators, ed. by D.A. Holmes
S.N. Vlasov, V.A. Petrishchev, V.I. Talanov, Vyss. Uchebn. Zaved. Ser. Radiofiz. 14, 1353 (1971)
A.K. Potemkin, E.A. Khazanov, Quantum Electron. 35, 1042 (2005)
R. Martinez-Herrero, P.M. Mejias, Opt. Lett. 18, 1669 (1993)
M. Santarsiero, F. Gori, J. Opt. Soc. Am. A 16, 106 (1999)
B. Zhang, X. Chu, Q. Li, J. Opt. Soc. Am. A 19, 1370 (2002)
X. Ji, T. Zhang, X. Jia, J. Opt. A: Pure Appl. Opt. 11, 105705 (2009)
G. Zhou, J. Opt. A: Pure Appl. Opt. 12, 015701 (2010)
R. Martinez-Herrero, P.M. Mejias, H. Weber, Opt. Quantum Electron. 25, 423 (1993)
Y. Yuan, Y. Cai, J. Qu, H.T. Eyyuboğlu, Y. Baykal, O. Korotkova, Opt. Express 17, 17344 (2009)
L.C. Andrews, R.L. Phillips, Laser Beam Propagation in the Turbulent Atmosphere, 2nd edn. (SPIE, Bellington, 2005)
M. Abramowitz, I.A. Stegun (eds.), Handbook of Mathematical Functions (Academic Press, San Diego, 2000)
A. Erdelyi, W. Magnus, F. Oberhettinger, Tables of Integral Transforms (McGraw-Hill, New York, 1954)
H.T. Eyyuboğlu, Appl. Phys. B 94, 489 (2009)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Ding, J., Cheng, F. & Cai, Y. M 2-factors of a non-circular partially coherent flat-topped beam. Appl. Phys. B 102, 673–687 (2011). https://doi.org/10.1007/s00340-010-4116-5
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00340-010-4116-5