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Bessel beam is an important member of the family of non-diffracting beams and has some unique properties which can be used in many areas, such as micro particle manipulating, material processing and optical communication. However, the source of Bessel beam generated by the existing methods can be used only in a short distance due to its low power. In this paper, according to the coherent combining technology, we propose a method to generate a second-order Bessel-Gaussian (BG) beam by loading discrete vortex phase on specific spatially distributed Gaussian beam array. The coherent combining technology can enhance the output power by increasing the number of beams and use the phase-locking technique to maintain the beam quality. The experimental scheme is described as follows. The expanded Gaussian beam is first split by an amplitude-based spatial light modulator, then the Gaussian beam array is incident on a phase-only spatial light modulator to load the discrete vortex phase, and finally the Gaussian beam array loaded with phase can synthesize BG beam in free space. Due to the diffraction effect of the sub-beams, the optical field distribution between the adjacent sub-beams which are loaded with phase differences, are superimposed. As a result, the optical field distribution of the approximate beam can be obtained by coherent synthesis in free space. After that, the degree of similarity between simulated results and theoretical data is analyzed by correlation coefficient, including the comparison of light intensity between experiment and simulation, and the power-in-the-bucket is used to evaluate beam quality. In addition, the topological charge of the synthesized BG beams is verified by the interference method. By studying the number of beams, the waist radius and the radius of the ring, we find some interesting results which are summarized as follows. Firstly, the closed arrangement of Gaussian beam arrays can improve the quality of the synthesized BG beam. Secondly, the smaller the phase difference between the sub-beams, the more easily the discontinuous piston phase approaches to the vortex phase. Therefore, increasing the number of sub-beams can significantly improve the beam quality of the synthesized BG beam and obtain a higher order synthetic BG beam. Finally, we define the parameter k to represent the tightness of a circular array of Gaussian beams. The present study shows that when the parameter k is close to 1, the best experimental results can be obtained. Therefore, the proposed method has important guidance in generating various vortex beams or enhancing the vortex beam power.
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Keywords:
- vortex beam /
- coherent combing technology /
- power-in-the-bucket /
- topological charges
[1] Yin J P, Liu N C, Xia Y, Yun M 2004 Prog. Phys. 24 336 (in Chinese) [印建平, 刘南春, 夏勇, 恽旻 2004 物理学进展 24 336]
[2] Shu W X, Ke Y G, Liu Y C, Ling X H, Luo H L, Yin X B 2016 Phys. Rev. A 93 013839
[3] Liu Y C, Ke Y G, Zhou J X, Liu Y Y, Luo H L, Wen S C, Fan D Y 2017 Sci. Rep. 7 44096
[4] Liu Z X, Liu Y Y, Ke Y G, Liu Y C, Shu W X, Luo H L, Wen S C 2017 Photon. Res. 5 15
[5] Allegre O J, Jin Y, Perrie W, Ouyang J, Fearon E, Edwardson S P, Dearden G 2013 Opt. Express 21 21198
[6] Yan Y, Xie G D, Lavery M P J, Huang H, Ahmed N, Bao C J, Ren Y X, Cao Y W, Li L, Zhao Z, Molish F, Tur M, Padgett M J, Willner A E 2014 Nat. Commun. 5 4876
[7] Liu Y D, Gao C Q, Gao M W, Li F 2007 Acta Phys. Sin. 56 854 (in Chinese) [刘义东, 高春清, 高明伟, 李丰 2007 56 854]
[8] Padgett M, Bowman R 2011 Nature Photon. 5 343
[9] He Y L, Liu Z X, Liu Y C, Zhou J X, Ke Y G, Luo H L, Wen S C 2015 Opt. Lett. 40 5506
[10] Ngcobo S, Aameur K, Passilly N, Hasnaoui A, Forbes A 2013 Appl. Opt. 52 2093
[11] Lin D, Daniel J M O, Clarkson W A 2014 Opt. Lett. 39 3903
[12] Kim D J, Kim J W, Clarkson W A 2014 Appl. Phys. B 117 459
[13] Li Y, Li W, Zhang Z, Miller K, Shori R 2016 Opt. Express 24 1658
[14] Liu Z J, Zhou P, Hou J, Xu X J 2009 Chin. J. Lasers 36 518 (in Chinese) [刘泽金, 周朴, 侯静, 许晓军 2009 中国激光 36 518]
[15] Chu X X, Liu Z J, Zhou P 2013 Laser Phys. Lett. 10 5102
[16] Zhu K C, Tang H Q, Sun X M, Wang X W, Liu T N 2002 Opt. Commun. 207 29
[17] Zhu K C, Tang H Q, Wang X W, Liu T N 2002 Optik 113 222
[18] Zhu K C, Zhou G Q, Li X G, Zheng X J, Tang H Q 2008 Opt. Express 16 21315
[19] Chu X X, Sun Q, Wang J, Lu P, Xie W K, Xu X J 2015 Sci. Rep. 5 18665
[20] Feng G Y, Zhou S H 2009 Chin. J. Lasers 36 1643 (in Chinese) [冯国英, 周寿桓 2009 中国激光 36 1643]
[21] Wang Q M 2008 M. S. Dissertation (Hangzhou: Zhejiang University) (in Chinese) [王启明 2008 硕士学位论文 (杭州: 浙江大学)]
[22] Li Y Y, Chen Z Y, Liu H, Pu J X 2010 Acta Phys. Sin. 59 1740 (in Chinese) [李阳月, 陈子阳, 刘辉, 蒲继雄 2010 59 1740]
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[1] Yin J P, Liu N C, Xia Y, Yun M 2004 Prog. Phys. 24 336 (in Chinese) [印建平, 刘南春, 夏勇, 恽旻 2004 物理学进展 24 336]
[2] Shu W X, Ke Y G, Liu Y C, Ling X H, Luo H L, Yin X B 2016 Phys. Rev. A 93 013839
[3] Liu Y C, Ke Y G, Zhou J X, Liu Y Y, Luo H L, Wen S C, Fan D Y 2017 Sci. Rep. 7 44096
[4] Liu Z X, Liu Y Y, Ke Y G, Liu Y C, Shu W X, Luo H L, Wen S C 2017 Photon. Res. 5 15
[5] Allegre O J, Jin Y, Perrie W, Ouyang J, Fearon E, Edwardson S P, Dearden G 2013 Opt. Express 21 21198
[6] Yan Y, Xie G D, Lavery M P J, Huang H, Ahmed N, Bao C J, Ren Y X, Cao Y W, Li L, Zhao Z, Molish F, Tur M, Padgett M J, Willner A E 2014 Nat. Commun. 5 4876
[7] Liu Y D, Gao C Q, Gao M W, Li F 2007 Acta Phys. Sin. 56 854 (in Chinese) [刘义东, 高春清, 高明伟, 李丰 2007 56 854]
[8] Padgett M, Bowman R 2011 Nature Photon. 5 343
[9] He Y L, Liu Z X, Liu Y C, Zhou J X, Ke Y G, Luo H L, Wen S C 2015 Opt. Lett. 40 5506
[10] Ngcobo S, Aameur K, Passilly N, Hasnaoui A, Forbes A 2013 Appl. Opt. 52 2093
[11] Lin D, Daniel J M O, Clarkson W A 2014 Opt. Lett. 39 3903
[12] Kim D J, Kim J W, Clarkson W A 2014 Appl. Phys. B 117 459
[13] Li Y, Li W, Zhang Z, Miller K, Shori R 2016 Opt. Express 24 1658
[14] Liu Z J, Zhou P, Hou J, Xu X J 2009 Chin. J. Lasers 36 518 (in Chinese) [刘泽金, 周朴, 侯静, 许晓军 2009 中国激光 36 518]
[15] Chu X X, Liu Z J, Zhou P 2013 Laser Phys. Lett. 10 5102
[16] Zhu K C, Tang H Q, Sun X M, Wang X W, Liu T N 2002 Opt. Commun. 207 29
[17] Zhu K C, Tang H Q, Wang X W, Liu T N 2002 Optik 113 222
[18] Zhu K C, Zhou G Q, Li X G, Zheng X J, Tang H Q 2008 Opt. Express 16 21315
[19] Chu X X, Sun Q, Wang J, Lu P, Xie W K, Xu X J 2015 Sci. Rep. 5 18665
[20] Feng G Y, Zhou S H 2009 Chin. J. Lasers 36 1643 (in Chinese) [冯国英, 周寿桓 2009 中国激光 36 1643]
[21] Wang Q M 2008 M. S. Dissertation (Hangzhou: Zhejiang University) (in Chinese) [王启明 2008 硕士学位论文 (杭州: 浙江大学)]
[22] Li Y Y, Chen Z Y, Liu H, Pu J X 2010 Acta Phys. Sin. 59 1740 (in Chinese) [李阳月, 陈子阳, 刘辉, 蒲继雄 2010 59 1740]
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