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The analytical expression for the effective radius of curvature R of a partially coherent flat-topped beam propagating through atmospheric turbulence is derived. It is shown that R decreases due to turbulence. However, position zmin where R reaches its minimum will change due to the turbulence when the strength of turbulence is strong enough. The effective radius of curvature R increases with the increase of beam coherence parameter β when the strength of turbulence is weak, while R decreases with β increasing when the strength of turbulence is strong. The R decreases slowly with the increase of beam order M(N). The R of partially coherent flat-topped beam with larger β and smaller M(N) is more sensitive to turbulence. In addition, in free space the wavefront of partially coherent flat-topped beam can be regarded as a spherical surface in the far-field, which is independent of the beam parameters. However, in turbulence the effective radius of curvature depends on the beam parameters in the near field and also in the far field.
[1] ［1］Gbur G, Wolf E 2002 J. Opt. Soc. Am. A 19 1592
[2] ［2］ Dogariu A, Amarande S 2003 Opt. Lett. 28 10
[3] ［3］ Shirai T, Dogariu A, Wolf E 2003 J. Opt. Soc. Am. A 20 1094
[4] ［4］ Cai Y J, He S 2006 Appl. Phys. Lett. 89 041117
[5] ［5］ Zhang E T, Ji X L, Lü B D 2009 Chin. Phys. B 18 571
[6] ［6］ Roychowdhury H, Wolf E 2004 Opt. Commun. 241 11
[7] ［7］ Ji X L, Zhang E T, Lü B D 2006 Opt. Commun. 259 1
[8] ［8］ Lu W, Liu L, Sun J, Yang Q, Zhu Y 2007 Opt. Commun. 271 1
[9] ［9］ Ji X L, Chen X W, Chen S H, Li X Q, Lü B D 2007 J. Opt. Soc. Am. A 24 3554
[10] ］ Korotkova O, Salem M, Wolf E 2004 Opt. Commun. 233 225
[11] ］ Salem M, Korotkova O, Dogariu A, Wolf E 2004 Waves Rand. Med. 14 513
[12] ］ Eyyuboglu H T, Baykal Y, Cai Y 2007 Appl. Phys. B 89 91
[13] ］ Ji X L, Huang T X, Lü B D 2006 Acta Phys. Sin. 55 978 (in Chinese) ［季小玲、黄太星、吕百达2006物理学报55 978］
[14] ］ Wang T, Pu J X 2007 Acta Phys. Sin. 56 6754 (in Chinese) ［王涛、蒲继雄 2007物理学报 56 6754］
[15] ］ Zhang E T, Ji X L, Lü B D 2009 Chin. Phys. B 18 571
[16] ］ Chen X W, Ji X L 2010 Chin. Phys. B 19 024203
[17] ］ Ji X L, Pu Z C 2010 Chin. Phys. B 19 029201
[18] ］ Ricklin J C, Davidson F M 2002 J. Opt. Soc. Am. A 19 1794
[19] ］ Seshadri S R 2000 J. Opt. Soc. Am. A 17 780
[20] ］ Zahid M, Zubairy M S 1989 Opt. Commun. 70 361
[21] ］ Li Y 2002 Opt. Commun. 206 225
[22] ］ Mandel L, Wolf E 1995 Optical Coherence and Quantum Optics (Cambridge: Cambridge University Press)
[23] ］ Siegman A E 1990 Proc. SPIE 1224 2
[24] ］ Friberg A T, Turunen J 1988 J. Opt. Soc. Am. A 5 713
[25] ］ Dan Y, Zhang B 2009 Opt. Lett. 34 563
[26] ］ Weber H 1992 Opt. Quantum Electron. 24 1027
[27] ］ Andrews L C, Phillips R L 1998 Laser Beam Propagation Through Random Media (Bellingham, Washington: SPIE Press)
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[1] ［1］Gbur G, Wolf E 2002 J. Opt. Soc. Am. A 19 1592
[2] ［2］ Dogariu A, Amarande S 2003 Opt. Lett. 28 10
[3] ［3］ Shirai T, Dogariu A, Wolf E 2003 J. Opt. Soc. Am. A 20 1094
[4] ［4］ Cai Y J, He S 2006 Appl. Phys. Lett. 89 041117
[5] ［5］ Zhang E T, Ji X L, Lü B D 2009 Chin. Phys. B 18 571
[6] ［6］ Roychowdhury H, Wolf E 2004 Opt. Commun. 241 11
[7] ［7］ Ji X L, Zhang E T, Lü B D 2006 Opt. Commun. 259 1
[8] ［8］ Lu W, Liu L, Sun J, Yang Q, Zhu Y 2007 Opt. Commun. 271 1
[9] ［9］ Ji X L, Chen X W, Chen S H, Li X Q, Lü B D 2007 J. Opt. Soc. Am. A 24 3554
[10] ］ Korotkova O, Salem M, Wolf E 2004 Opt. Commun. 233 225
[11] ］ Salem M, Korotkova O, Dogariu A, Wolf E 2004 Waves Rand. Med. 14 513
[12] ］ Eyyuboglu H T, Baykal Y, Cai Y 2007 Appl. Phys. B 89 91
[13] ］ Ji X L, Huang T X, Lü B D 2006 Acta Phys. Sin. 55 978 (in Chinese) ［季小玲、黄太星、吕百达2006物理学报55 978］
[14] ］ Wang T, Pu J X 2007 Acta Phys. Sin. 56 6754 (in Chinese) ［王涛、蒲继雄 2007物理学报 56 6754］
[15] ］ Zhang E T, Ji X L, Lü B D 2009 Chin. Phys. B 18 571
[16] ］ Chen X W, Ji X L 2010 Chin. Phys. B 19 024203
[17] ］ Ji X L, Pu Z C 2010 Chin. Phys. B 19 029201
[18] ］ Ricklin J C, Davidson F M 2002 J. Opt. Soc. Am. A 19 1794
[19] ］ Seshadri S R 2000 J. Opt. Soc. Am. A 17 780
[20] ］ Zahid M, Zubairy M S 1989 Opt. Commun. 70 361
[21] ］ Li Y 2002 Opt. Commun. 206 225
[22] ］ Mandel L, Wolf E 1995 Optical Coherence and Quantum Optics (Cambridge: Cambridge University Press)
[23] ］ Siegman A E 1990 Proc. SPIE 1224 2
[24] ］ Friberg A T, Turunen J 1988 J. Opt. Soc. Am. A 5 713
[25] ］ Dan Y, Zhang B 2009 Opt. Lett. 34 563
[26] ］ Weber H 1992 Opt. Quantum Electron. 24 1027
[27] ］ Andrews L C, Phillips R L 1998 Laser Beam Propagation Through Random Media (Bellingham, Washington: SPIE Press)
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