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The expressions for the Rayleigh range zR, the turbulence distance zT and the far-field angle θ of Gaussian array beams propagating through non-Kolmogorov turbulence are derived. Influence of generalized exponent factor α of the atmospheric power spectrum and the type of beam combinations on the spreading of Gaussian array beams is studied. It is shown that for both coherent and incoherent combinations, the dependence of zR, zT and θ on α is not monotonic. When α=3.108, zR and zT reach their minima, and θ reaches its maximum. This means that the spreading is largest, and the spreading is enormously affected by turbulence when α=3.108. For the incoherent combination the spreading is larger than that for the coherent combination, but for the incoherent combination the spreading is less affected by turbulence than that for the coherent combination. It may be that, for the small free-space diffraction we have zT zR, i.e., the spreading is affected by turbulence within the Rayleigh range; for the large free-space diffraction we have zT > zR, i.e., the spreading is less affected by the turbulence within the Rayleigh range.
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Keywords:
- non-Kolmogorov turbulence /
- coherent and incoherent combinations /
- Rayleigh range and turbulence distance /
- far-field angle
[1] Strohschei J D, Herb J J, Clarence E C 1988 Appl. Opt. 37 1045
[2] Brunel M, Floch A L, Bretenaker F, Marty J, Molva E 1988 Appl. Opt. 37 2402
[3] Fante R L 1985 Progress in Optics XXⅡ: Wave propagation in random media: a systems approach, Chap. VI edited by Wolf E (Elsevier, Amsterdam)
[4] Anddrews L C, Phillips R L 2005 Laser Beam Propagation through Random Media (Bellingham, Washington: SPIE Press)
[5] Ji X L, Eyyuboglu H T, Baykal Y 2010 Opt. Express 18 6922
[6] Zhang E T, Ji X L, L B D 2009 Chin. Phys. B 18 571
[7] Gbur G, Wolf E 2002 J. Opt. Soc. Am. A 19 1592
[8] Wang T, Pu J X 2007 Acta Phys. Sin. 56 6754 (in Chinese) [王涛, 蒲继雄 2007 56 6754]
[9] Dan Y Q, Zhang B 2009 Opt. Lett. 34 563
[10] Mao H D, Zhao D M 2010 Opt. Express 18 1741
[11] Zhou G Q 2011 Opt. Express 19 3945
[12] Li Y Q Wu Z S 2012 Chin. Phys. B 21 054203
[13] Li X Q, Ji X L, Zhu J H 2013 Acta Phys. Sin. 62 044217 (in Chinese) [李晓庆, 季小玲, 朱建华 2013 62 044217]
[14] Ma Y, Ji X L Acta Phys. Sin. 62 094214 (in Chinese) [马媛, 季小玲 2013 62 094214]
[15] Kolmogorov A N 1941 C. R. Acad. Sci. URSS 30 301
[16] Rao C H, Jiang W H, Ling N 2000 J. Mod. Opt. 47 1111
[17] Zilberman A, Golbraikh E, Kopeika N S 2005 Proc. SPIE 5987 598702
[18] Toselli I, Andrews L C, Phillips R L, Ferrero V 2007 Proc. SPIE 6551 65510E-1
[19] Toselli I, Andrews L C, Phillips R L, Ferrero V 2008 Opt. Eng. 47 026003
[20] Wu G H, Guo H, S. Yu S, Luo B 2010 Opt. Lett. 35 715
[21] Shchepakina E and Korotkova O 2010 Opt. Express 18 10650
[22] He X M, L B D 2011 Chin. Phys. B 20 094210
[23] Huang Y P, Zhao G P, Xiao X, Wang F H 2012 Acta Phys. Sin. 61 144202 [黄永平, 赵光普, 肖希, 王藩侯 2012 61 144202]
[24] He X M, L B D 2012 Acta Phys. Sin. 61 054201 (in Chinese) [何雪梅, 吕百达 2012 61 054201]
[25] Deng J P, Ji X L, Lu L 2013 Acta Phys. Sin. 62 144211 (in Chinese) [邓金平, 季小玲, 陆璐 2013 62 144211]
[26] Tao R M, Si L, Ma Y X, Zhou P, Liu Z J 2012 Appl. Opt. 51 5609
[27] Tang H, Ou B L, Luo B, Guo H, Dang A H 2011 J. Opt. Soc. Am. A 28 1016
[28] Siegman A E 1986 Lasers (Mill Valley, CA: University Science Books)
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[1] Strohschei J D, Herb J J, Clarence E C 1988 Appl. Opt. 37 1045
[2] Brunel M, Floch A L, Bretenaker F, Marty J, Molva E 1988 Appl. Opt. 37 2402
[3] Fante R L 1985 Progress in Optics XXⅡ: Wave propagation in random media: a systems approach, Chap. VI edited by Wolf E (Elsevier, Amsterdam)
[4] Anddrews L C, Phillips R L 2005 Laser Beam Propagation through Random Media (Bellingham, Washington: SPIE Press)
[5] Ji X L, Eyyuboglu H T, Baykal Y 2010 Opt. Express 18 6922
[6] Zhang E T, Ji X L, L B D 2009 Chin. Phys. B 18 571
[7] Gbur G, Wolf E 2002 J. Opt. Soc. Am. A 19 1592
[8] Wang T, Pu J X 2007 Acta Phys. Sin. 56 6754 (in Chinese) [王涛, 蒲继雄 2007 56 6754]
[9] Dan Y Q, Zhang B 2009 Opt. Lett. 34 563
[10] Mao H D, Zhao D M 2010 Opt. Express 18 1741
[11] Zhou G Q 2011 Opt. Express 19 3945
[12] Li Y Q Wu Z S 2012 Chin. Phys. B 21 054203
[13] Li X Q, Ji X L, Zhu J H 2013 Acta Phys. Sin. 62 044217 (in Chinese) [李晓庆, 季小玲, 朱建华 2013 62 044217]
[14] Ma Y, Ji X L Acta Phys. Sin. 62 094214 (in Chinese) [马媛, 季小玲 2013 62 094214]
[15] Kolmogorov A N 1941 C. R. Acad. Sci. URSS 30 301
[16] Rao C H, Jiang W H, Ling N 2000 J. Mod. Opt. 47 1111
[17] Zilberman A, Golbraikh E, Kopeika N S 2005 Proc. SPIE 5987 598702
[18] Toselli I, Andrews L C, Phillips R L, Ferrero V 2007 Proc. SPIE 6551 65510E-1
[19] Toselli I, Andrews L C, Phillips R L, Ferrero V 2008 Opt. Eng. 47 026003
[20] Wu G H, Guo H, S. Yu S, Luo B 2010 Opt. Lett. 35 715
[21] Shchepakina E and Korotkova O 2010 Opt. Express 18 10650
[22] He X M, L B D 2011 Chin. Phys. B 20 094210
[23] Huang Y P, Zhao G P, Xiao X, Wang F H 2012 Acta Phys. Sin. 61 144202 [黄永平, 赵光普, 肖希, 王藩侯 2012 61 144202]
[24] He X M, L B D 2012 Acta Phys. Sin. 61 054201 (in Chinese) [何雪梅, 吕百达 2012 61 054201]
[25] Deng J P, Ji X L, Lu L 2013 Acta Phys. Sin. 62 144211 (in Chinese) [邓金平, 季小玲, 陆璐 2013 62 144211]
[26] Tao R M, Si L, Ma Y X, Zhou P, Liu Z J 2012 Appl. Opt. 51 5609
[27] Tang H, Ou B L, Luo B, Guo H, Dang A H 2011 J. Opt. Soc. Am. A 28 1016
[28] Siegman A E 1986 Lasers (Mill Valley, CA: University Science Books)
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