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Partially coherent beams with nonconventional correlation functions have been extensively studied due to their wide and important applications in free-space optical communication, particle trapping, image transmission and optical encryption. Here, we study the propagation of nonuniform cosine-Gaussian correlated Bessel-Gaussian beam (cGBCB) in detail. Analytical expressions for the cross-spectral density function of cGBCBs through paraxial ABCD system are derived based on the extended Huygens-Fresnel integral. By use of the derived formulae, the intensity distribution properties of a nonuniform cGBCB on propagation in free space are analytically investigated. Some numerical calculation results are presented and discussed graphically. It is found that when the root-mean-square correlation width δ and the parameter controlling the degree of coherence profiles β are appropriately chosen, the intensity distribution of the nonuniform cGBCB displays self-splitting properties during propagation. We point out that rather than a simple duplication, the self-splitting behaviour consists of a complex process in which the dark hollow pattern for cGBCB is gradually filled in the centre at first, then starts to split with increasing the propagation distance, and most impressively, an evolution process from a single dark hollow beam in the source plane to quadruple dark hollow profiles in certain propagation ranges can be realized. The influence of correlation function on the evolution properties of the intensity distribution is investigated, demonstrating that the values of parameters δ and β of the correlation function play a critical role in inducing the self-splitting effect for nonuniform cGBCB on propagation in free space. Therefore, it is clearly shown that modulating the correlation function of a partially coherent beam can alter the coherence length and the degree of nonuniformity, and thus provides an effective way of manipulating its propagation properties. We also find the evolution speed of the intensity distribution can be greatly affected by the topological charge n of the beam function and the parameter R controlling the hollow size of cGBCB in source plane, e. g. the intensity distribution evolves into quadruple dark hollow profiles more slowly with larger n or smaller R. As is well known, the dark-hollow intensity configurations are useful in many applications and have been extensively studied both theoretically and experimentally. Therefore, the results drawn in the paper develop an alternative way to realize dark-hollow beam array, and further pave the way for dark hollow beam applications in long-distance free-space optical communications.
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Keywords:
- partially coherent beam /
- nonconventional correlation function /
- self-splitting /
- dark-hollow beam array
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[30] Chen Y H, Ponomarenko S A, Cai Y J 2016 Appl. Phys. Lett. 109 061107
[31] Mao Y M, Mei Z R 2016 Opt. Commun. 381 222
[32] Liu X L, Yu J Y, Cai Y J, Ponomarenko S A 2016 Opt. Lett. 41 4182
[33] Song Z Z, Liu Z J, Zhou K Y, Sun Q G, Liu S T 2016 J. Opt. 18 105601
[34] Zhu K C, Zhou G Q, Li X Y, Zheng X J, Tang H Q 2008 Opt. Express 16 21315
[35] Zhu K C, Li X Y, Zheng X J, Tang H Q 2010 Appl. Phys. B 98 567
[36] Zhu K C, Li S X, Tang Y, Yu Y, Tang H Q 2012 J. Opt. Soc. Am. A 29 251
[37] Deng D, Li Y, Han Y H, Su X Y, Ye J F, Gao J M, Sun Q Q, Qu S L 2016 Opt. Express 24 19695
[38] Liu H L, Lu Y F, Xia J, Chen D, He W, Pu X Y 2016 Opt. Express 24 28270
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[40] Zhu K C, Tang H Q, Zheng X J, Tang Y 2014 Acta Phys. Sin. 63 104210(in Chinese)[朱开成, 唐慧琴, 郑小娟, 唐英2014物理学报63 104210]
[41] Tang H Q, Zhu K C 2013 Opt. Lasers Technol. 54 68
[42] Gradshtevn I S, Ryzhik I M 1980 Table of Integral, Series, and Products (New York:Academic Press) p307
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[1] Mandel L, Wolf E 1995 Optical Coherence and Quantum Optics (Cambridge:Cambridge University Press) pp33-39
[2] Wolf E, Collett E 1978 Opt. Commun. 25 293
[3] Gori F, Guattari G, Padovani C 1987 Opt. Commun. 64 311
[4] Ponomarenko S A 2001 J. Opt. Soc. Am. A 18 150
[5] Li J, Gao X M, Chen Y R 2012 Opt. Commun. 285 3403
[6] Cang J, Xiu P, Liu X 2013 Opt. Laser Technol. 54 35
[7] Gori F, Santarsiero M 2007 Opt. Lett. 32 3531
[8] Chen Y H, Gu J X, Wang F, Cai Y J 2015 Phys. Rev. A 91 013823
[9] Yu J Y, Chen Y H, Liu L, Liu X L, Cai Y J 2015 Opt. Express 23 13467
[10] Chen Y H, Yu J Y, Yuan Y S, Wang F, Cai Y J 2016 Appl. Phys. B 122 31
[11] Yu J Y, Chen Y H, Cai Y J 2016 Acta Phys. Sin. 65 214202 (in Chinese)[余佳益, 陈亚红, 蔡阳健2016物理学报65 214202]
[12] Liang C H, Wang F, Liu X L, Cai Y J, Korotkova O 2014 Opt. Lett. 39 769
[13] Mei Z R 2014 Opt. Express 22 13029
[14] Mei Z R, Korotkova O 2013 Opt. Lett. 38 91
[15] Wang F, Liu X, Yuan Y, Cai Y J 2013 Opt. Lett. 38 1814
[16] Chen Y H, Cai Y J 2014 Opt. Lett. 39 2549
[17] Chen Y H, Wang F, Zhao C L, Cai Y J 2014 Opt. Express 22 5826
[18] Chen Y H, Liu L, Wang F, Zhao C L, Cai Y J 2014 Opt. Express 22 13975
[19] Guo L N, Chen Y H, Liu L, Cai Y J 2015 Opt. Commun. 352 127
[20] Xu H F, Zhang Z, Qu J, Huang W 2016 J. Mod. Opt. 63 1429
[21] Qiu Y L, Chen Z X, He Y J 2017 Opt. Commun. 389 303
[22] Mei Z R, Korotkova O 2013 Opt. Lett. 38 2578
[23] Mei Z R, Schchepakina E, Korotkova O 2013 Opt. Express 21 17512
[24] Pan L, Ding C, Wang H 2014 Opt. Express 22 11670
[25] Xu H F, Zhang Z, Qu J, Huang W 2014 Opt. Express 22 22479
[26] Ding C L, Liao L M, Wang H X, Zhang Y T, Pan L Z 2015 J. Opt. 17 035615
[27] Zhu S J, Chen Y H, Wang J, Wang H Y, Li Z H, Cai Y J 2015 Opt. Express 23 33099
[28] Song Z Z, Liu Z J, Zhou K Y, Sun Q G, Liu S T 2017 Chin. Phys. B 26 024201
[29] Ma L Y, Ponomarenko S M 2015 Opt. Express 23 1848
[30] Chen Y H, Ponomarenko S A, Cai Y J 2016 Appl. Phys. Lett. 109 061107
[31] Mao Y M, Mei Z R 2016 Opt. Commun. 381 222
[32] Liu X L, Yu J Y, Cai Y J, Ponomarenko S A 2016 Opt. Lett. 41 4182
[33] Song Z Z, Liu Z J, Zhou K Y, Sun Q G, Liu S T 2016 J. Opt. 18 105601
[34] Zhu K C, Zhou G Q, Li X Y, Zheng X J, Tang H Q 2008 Opt. Express 16 21315
[35] Zhu K C, Li X Y, Zheng X J, Tang H Q 2010 Appl. Phys. B 98 567
[36] Zhu K C, Li S X, Tang Y, Yu Y, Tang H Q 2012 J. Opt. Soc. Am. A 29 251
[37] Deng D, Li Y, Han Y H, Su X Y, Ye J F, Gao J M, Sun Q Q, Qu S L 2016 Opt. Express 24 19695
[38] Liu H L, Lu Y F, Xia J, Chen D, He W, Pu X Y 2016 Opt. Express 24 28270
[39] Zhou Q, Lu J F, Yin J P 2015 Acta Phys. Sin. 64 053701 (in Chinese)[周琦, 陆俊发, 印建平2015物理学报64 053701]
[40] Zhu K C, Tang H Q, Zheng X J, Tang Y 2014 Acta Phys. Sin. 63 104210(in Chinese)[朱开成, 唐慧琴, 郑小娟, 唐英2014物理学报63 104210]
[41] Tang H Q, Zhu K C 2013 Opt. Lasers Technol. 54 68
[42] Gradshtevn I S, Ryzhik I M 1980 Table of Integral, Series, and Products (New York:Academic Press) p307
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