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The analytical formula for the beam propagation factor ( M 2-factor) of cosh-Gaussian (ChG) array beams propagating through atmospheric turbulence is derived, and the influence of turbulence on the M 2-factor is studied by using the relative M 2-factor. It is shown that the M 2-factor is not a propagation invariant in turbulence, and the turbulence results in an increase of the M 2-factor. For the incoherent combination, the M 2-factor of ChG array beams increases with increasing propagation distance, beam parameter, relative beam separation distance and beam number. For the coherent combination, the M 2-factor of ChG array beams increases with oscillatory behavior as the beam parameter or the relative beam separation distance increases. For the coherent combination the M 2-factor is always smaller than that for the incoherent combination. However, for the incoherent combination the M 2-factor is always less sensitive to turbulence than that for the coherent combination. In particular, the influence of turbulence on the M 2-factor can be reduced by a suitable choice of the relative beam separation distance. With increasing beam number, the M 2-factor becomes more sensitive to turbulence for the coherent combination, while for the incoherent combination the M 2-factor becomes less sensitive to turbulence.
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Keywords:
- beam propagation factor (M2-factor) /
- beam quality /
- cosh-Gaussian (ChG) array beam /
- atmospheric turbulence
[1] Siegman A E 1990 Proc. SPIE 2 1224
[2] Lü B D, Zhang B, Luo S R 1999 Appl. Opt. 20 4581
[3] SPIE Press)
[4] Zhou G 2009 Appl. Phys. B 96 149
[5] Mahdieh M H 2007 Opt. Commun. 281 3395
[6] Dan Y, Zhang B 2008 Opt. Expr. 16 15563
[7] Lü B D, Ma H 2000 J. Opt. Soc. Am. A 17 2005
[8] Tang Q J, Chen D M, Yu Y A, Hu Q Q 2006 Chin. Phys. 15 2609
[9] Xiao R, Hou J, Jiang Z F 2008 Acta Phys. Sin. 57 853 (in Chinese) [肖 瑞、 侯 静、 姜宗福 2008 57 853]
[10] Ji X L, Zhang T R, Jia X H 2009 J. Opt. A: Pure Appl. Opt. 11 105705
[11] Zhu Y, Zhao D, Du X 2008 Opt. Expr. 16 18437
[12] Cai Y, Chen Y, Eyyuboglu H T, Baykal Y 2007 Appl. Phys. B 88 467
[13] Ji X L, Zhang E T, Lü B D 2008 J. Opt. Soc. Am. B 25 825
[14] Li X Q, Ji X L, Eyyubo lu H T, Baykal Y 2010 Appl. Phys. B 98 557
[15] Zhang E T, Ji X L, Lü B D 2009 Chin. Phys. B 18 571
[16] Casperson L W, Hall D G, Tovar A A 1998 J. Opt. Soc. Am. A 15 954
[17] Zhou G 2010 Opt. & Laser Technology 42 489
[18] Yu S, Guo H, Fu X, Hu W 2002 Opt. Commun. 204 59
[19] Deng D 2004 Phys. Lett. A 333 485
[20] Mandel L, Wolf E 1995 Optical Coherence and Quantum Optics (Cambridge: Cambridge Uinversity Press)
[21] Dan Y, Zhang B 2009 Opt. Lett. 34 563
[22] Serna J, Martinez-Herreor R, Mejias P M 1991 J. Opt. Soc. Am. A 8 1094
[23] Andrews L C, Phillips R L 2005 Laser Beam Propagation through Random Media 2nd ed. (Bellingham, Washington:
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[1] Siegman A E 1990 Proc. SPIE 2 1224
[2] Lü B D, Zhang B, Luo S R 1999 Appl. Opt. 20 4581
[3] SPIE Press)
[4] Zhou G 2009 Appl. Phys. B 96 149
[5] Mahdieh M H 2007 Opt. Commun. 281 3395
[6] Dan Y, Zhang B 2008 Opt. Expr. 16 15563
[7] Lü B D, Ma H 2000 J. Opt. Soc. Am. A 17 2005
[8] Tang Q J, Chen D M, Yu Y A, Hu Q Q 2006 Chin. Phys. 15 2609
[9] Xiao R, Hou J, Jiang Z F 2008 Acta Phys. Sin. 57 853 (in Chinese) [肖 瑞、 侯 静、 姜宗福 2008 57 853]
[10] Ji X L, Zhang T R, Jia X H 2009 J. Opt. A: Pure Appl. Opt. 11 105705
[11] Zhu Y, Zhao D, Du X 2008 Opt. Expr. 16 18437
[12] Cai Y, Chen Y, Eyyuboglu H T, Baykal Y 2007 Appl. Phys. B 88 467
[13] Ji X L, Zhang E T, Lü B D 2008 J. Opt. Soc. Am. B 25 825
[14] Li X Q, Ji X L, Eyyubo lu H T, Baykal Y 2010 Appl. Phys. B 98 557
[15] Zhang E T, Ji X L, Lü B D 2009 Chin. Phys. B 18 571
[16] Casperson L W, Hall D G, Tovar A A 1998 J. Opt. Soc. Am. A 15 954
[17] Zhou G 2010 Opt. & Laser Technology 42 489
[18] Yu S, Guo H, Fu X, Hu W 2002 Opt. Commun. 204 59
[19] Deng D 2004 Phys. Lett. A 333 485
[20] Mandel L, Wolf E 1995 Optical Coherence and Quantum Optics (Cambridge: Cambridge Uinversity Press)
[21] Dan Y, Zhang B 2009 Opt. Lett. 34 563
[22] Serna J, Martinez-Herreor R, Mejias P M 1991 J. Opt. Soc. Am. A 8 1094
[23] Andrews L C, Phillips R L 2005 Laser Beam Propagation through Random Media 2nd ed. (Bellingham, Washington:
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