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Usually, high-power laser beams are amplitude modulated and have phase fluctuations (PFs). The analytic formula of the effective radius R of curvature of truncated laser beams with amplitude modulations (AMs) and PFs propagating through atmospheric turbulence is derived by using the statistical optics method. It is shown that the R in free space increases with the increases of the phase fluctuation parameter, the intensity modulation parameter and the truncated parameter. And the influence of turbulence on the R also increases with the increases of the three parameters. Furthermore, the R of Gaussian beams is largest in free space, but it is most affected by turbulence. Therefore, in turbulence the R of truncated laser beams with AMs and PFs is even larger than that of Gaussian beams when the propagation distance is large enough. In particular, the relative effective radius Rr of curvature varies non-monotonically with propagation distance, and there exists a minimum at a propagation distance where the influence of turbulence on the R is largest. In addition, the position where the Rr reaches its minimum increases with the increasees of intensity modulation and phase fluctuation.
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Keywords:
- truncated laser beams with amplitude modulations and phase fluctuations /
- effective radius of curvature /
- atmospheric turbulence
[1] Manes K R, Simmons W W 1985 J. Opt. Soc. Am. A 2 528
[2] Simmons W W, Hunt J T, Warren W E 1981 IEEE J. Quantum Electron. QE-17 1727
[3] Lü B D, Ji X L 2004 J. Opt. A: Pure Appl. Opt. 6 161
[4] Jiang H L, Zhao D M 2006 Opt. Commun. 264 18
[5] Gbur G, Wolf E 2002 J. Opt. Soc. Am. A 19 1592
[6] Dogariu A, Amarande S 2003 Opt. Lett. 28 10
[7] Dan Y Q, Zhang B 2009 Opt. Lett. 34 563
[8] Pu J X, Korotkova O 2009 Opt. Commun. 282 1691
[9] Korotkova O, Wolf E 2007 Opt. Lett. 32 2137
[10] Zhou G Q 2011 Opt. Express 19 3945
[11] Mao H D, Zhao D M 2010 Opt. Express 18 1741
[12] Chu X X 2011 Opt. Lett. 36 2701
[13] Wu G H, Guo H, Yu S, Luo B 2010 Opt. Lett. 35 715
[14] Ji X L, Pu Z C 2010 Chin. Phys. B 19 029201
[15] Chen X W, Ji X L 2010 Chin. Phys. B 19 024203
[16] Tao R M, Si L, Ma Y X, Zou Y C, Zhou P 2011 Chin. Phys. B 20 094208
[17] Chu X X 2011 Chin. Phys. B 20 014207
[18] Ji X L, Li X Q 2011 Appl. Phys. B 104 207
[19] Wen J J, Breazeal M A 1988 J. Acoust. Soc. Am. 83 1752
[20] Li X Q, Ji X L 2011 J. Modern Opt. 58 1060
[21] Miguel A P, Javier A, Eusebio B 1992 Appl. Opt. 31 6389
[22] Ricklin J C, Davidson F M 2002 J. Opt. Soc. Am. A 19 1794
[23] Weber H 1992 Opt. Quantum Electron. 24 1027
[24] Ji X L, Eyyuboğlu H T, Baykal Y 2010 Opt. Express 18 6922
[25] Ji X L 2010 Acta Phys. Sin. 59 3953 (in Chinese) [季小玲 2010 59 3953]
[26] Andrews L C, Phillips R L 2005 Laser Beam Propagation through Random Media (2nd Ed.) ( Bellingham, Washington: SPIE Press)
[27] Serna J, Martinez-Herreor R, Mejias P M 1991 Opt. Soc. Am. A 8 1094
[28] Ji X L, Dou L Y 2012 Opt. Laser Technol. 44 21
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[1] Manes K R, Simmons W W 1985 J. Opt. Soc. Am. A 2 528
[2] Simmons W W, Hunt J T, Warren W E 1981 IEEE J. Quantum Electron. QE-17 1727
[3] Lü B D, Ji X L 2004 J. Opt. A: Pure Appl. Opt. 6 161
[4] Jiang H L, Zhao D M 2006 Opt. Commun. 264 18
[5] Gbur G, Wolf E 2002 J. Opt. Soc. Am. A 19 1592
[6] Dogariu A, Amarande S 2003 Opt. Lett. 28 10
[7] Dan Y Q, Zhang B 2009 Opt. Lett. 34 563
[8] Pu J X, Korotkova O 2009 Opt. Commun. 282 1691
[9] Korotkova O, Wolf E 2007 Opt. Lett. 32 2137
[10] Zhou G Q 2011 Opt. Express 19 3945
[11] Mao H D, Zhao D M 2010 Opt. Express 18 1741
[12] Chu X X 2011 Opt. Lett. 36 2701
[13] Wu G H, Guo H, Yu S, Luo B 2010 Opt. Lett. 35 715
[14] Ji X L, Pu Z C 2010 Chin. Phys. B 19 029201
[15] Chen X W, Ji X L 2010 Chin. Phys. B 19 024203
[16] Tao R M, Si L, Ma Y X, Zou Y C, Zhou P 2011 Chin. Phys. B 20 094208
[17] Chu X X 2011 Chin. Phys. B 20 014207
[18] Ji X L, Li X Q 2011 Appl. Phys. B 104 207
[19] Wen J J, Breazeal M A 1988 J. Acoust. Soc. Am. 83 1752
[20] Li X Q, Ji X L 2011 J. Modern Opt. 58 1060
[21] Miguel A P, Javier A, Eusebio B 1992 Appl. Opt. 31 6389
[22] Ricklin J C, Davidson F M 2002 J. Opt. Soc. Am. A 19 1794
[23] Weber H 1992 Opt. Quantum Electron. 24 1027
[24] Ji X L, Eyyuboğlu H T, Baykal Y 2010 Opt. Express 18 6922
[25] Ji X L 2010 Acta Phys. Sin. 59 3953 (in Chinese) [季小玲 2010 59 3953]
[26] Andrews L C, Phillips R L 2005 Laser Beam Propagation through Random Media (2nd Ed.) ( Bellingham, Washington: SPIE Press)
[27] Serna J, Martinez-Herreor R, Mejias P M 1991 Opt. Soc. Am. A 8 1094
[28] Ji X L, Dou L Y 2012 Opt. Laser Technol. 44 21
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