Abstract

A novel approach to generate a spatially-distributed orbital angular momentum (OAM) beam array based on coherent combining technology is presented. The arrangement of the multiple fundamental Gaussian beams at the initial plane, as well as the intensity weights and the phase distributions of the array beams, is determined by the reversal of Huygens Fresnel diffraction and the greedy algorithm. This method ensures that a vortex beam array is formed at a specified distance, and the distance can be adjusted by phase modulation. The evolution properties of the synthesized beam array near the receiver plane are studied as well to estimate the robustness of the method. The experimental limitations of this technique are discussed, including the maximum number of beams, the relative separation of each beam and the maximum topological charges. The results illustrate that a spatially-distributed OAM beam array can be effectively generated within a finite distance interval, and the distance is adjustable. This new method enables further applications of a structured optical field, such as optical communication and spatial light structuring.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

Full Article  |  PDF Article
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2018 (2)

P. Chen, L. L. Ma, W. Duan, J. Chen, S. J. Ge, Z. H. Zhu, M. J. Tang, R. Xu, W. Gao, T. Li, W. Hu, and Y. Q. Lu, “Digitalizing self-assembled chiral superstructures for optical vortex processing,” Adv. Mater. 30(10), 1705865 (2018).
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[Crossref]

2017 (5)

2016 (4)

Z. Chen, T. Zeng, and J. Ding, “Reverse engineering approach to focus shaping,” Opt. Lett. 41(9), 1929–1932 (2016).
[Crossref] [PubMed]

V. P. Aksenov, V. V. Dudorov, and V. V. Kolosov, “Statistical characteristics of common and synthesized vortex beams in a turbulent atmosphere,” Proc. SPIE 10035, 100352P (2016).
[Crossref]

X. Chu, Q. Sun, J. Wang, P. Lü, W. Xie, and X. Xu, “Generating a Bessel-Gaussian beam for the application in optical engineering,” Sci. Rep. 5(1), 18665 (2016).
[Crossref] [PubMed]

A. Flores, I. Dajani, R. Holten, T. Ehrenreich, and B. Anderson, “Multi-kilowatt diffractive coherent combining of pseudorandom-modulated fiber amplifiers,” Opt. Eng. 55(9), 096101 (2016).
[Crossref]

2015 (2)

2013 (4)

Z. Liu, P. Zhou, X. Xu, X. Wang, and Y. Ma, “Coherent beam combining of high power fiber lasers: progress and prospect,” Sci. Chin. Technol. 56(7), 1597–1606 (2013).
[Crossref]

X. Chu, Z. Liu, and P. Zhou, “Generation of a high-power Airy beam by coherent combining technology,” Laser Phys. Lett. 10(12), 125102 (2013).
[Crossref]

Y. Yang, Y. Dong, C. Zhao, and Y. Cai, “Generation and propagation of an anomalous vortex beam,” Opt. Lett. 38(24), 5418–5421 (2013).
[Crossref] [PubMed]

S. L. Lachinova and M. A. Vorontsov, “Exotic laser beam engineering with coherent fiber-array systems,” J. Opt. 15(10), 105501 (2013).
[Crossref]

2012 (3)

2011 (2)

2010 (2)

2009 (3)

P. Zhou, Z. Liu, X. Wang, Y. Ma, H. Ma, X. Xu, and S. Guo, “Coherent beam combining of fiber amplifiers using stochastic parallel gradient descent algorithm and its application,” IEEE J. Sel. Top. Quantum Electron. 15(2), 248–256 (2009).
[Crossref]

L. Wang, L. Wang, and S. Zhu, “Formation of optical vortices using coherent laser beam arrays,” Opt. Commun. 282(6), 1088–1094 (2009).
[Crossref]

R. S. Kurti, K. Halterman, R. K. Shori, and M. J. Wardlaw, “Discrete Cylindrical Vector Beam Generation from an Array of Optical Fibers,” Opt. Express 17(16), 13982–13988 (2009).
[Crossref] [PubMed]

2006 (1)

2005 (1)

T. Y. Fan, “Laser beam combining for high-power, high-radiance sources,” IEEE J. Sel. Top. Quantum Electron. 11(3), 567–577 (2005).
[Crossref]

2004 (1)

2001 (1)

L. Paterson, M. P. MacDonald, J. Arlt, W. Sibbett, P. E. Bryant, and K. Dholakia, “Controlled rotation of optically trapped microscopic particles,” Science 292(5518), 912–914 (2001).
[Crossref] [PubMed]

1992 (1)

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45(11), 8185–8189 (1992).
[Crossref] [PubMed]

1974 (1)

J. F. Nye and M. V. Berry, “Dislocations in wave trains,” Proc. R. Soc. Lond. A Math. Phys. Sci. 336(1605), 165–190 (1974).
[Crossref]

Ahmed, N.

Aksenov, V. P.

V. P. Aksenov, V. V. Dudorov, G. A. Filimonov, V. V. Kolosov, and V. Y. Venediktov, “Vortex beams with zero orbital angular momentum and non-zero topological charge,” Opt. Laser Technol. 104, 159–163 (2018).
[Crossref]

V. P. Aksenov, V. V. Dudorov, and V. V. Kolosov, “Statistical characteristics of common and synthesized vortex beams in a turbulent atmosphere,” Proc. SPIE 10035, 100352P (2016).
[Crossref]

V. P. Aksenov, V. V. Dudorov, and V. V. Kolosov, “Characterization of vortex beams synthesized on the basis of a fiber laser array,” Proc. SPIE 9680, 96802D (2015).

Allen, L.

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45(11), 8185–8189 (1992).
[Crossref] [PubMed]

Almaiman, A.

Anderson, B.

A. Flores, I. Dajani, R. Holten, T. Ehrenreich, and B. Anderson, “Multi-kilowatt diffractive coherent combining of pseudorandom-modulated fiber amplifiers,” Opt. Eng. 55(9), 096101 (2016).
[Crossref]

Arlt, J.

L. Paterson, M. P. MacDonald, J. Arlt, W. Sibbett, P. E. Bryant, and K. Dholakia, “Controlled rotation of optically trapped microscopic particles,” Science 292(5518), 912–914 (2001).
[Crossref] [PubMed]

Ashrafi, N.

Ashrafi, S.

Augst, S. J.

Bao, C.

Barnett, S.

Beijersbergen, M. W.

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45(11), 8185–8189 (1992).
[Crossref] [PubMed]

Bernet, S.

Berry, M. V.

J. F. Nye and M. V. Berry, “Dislocations in wave trains,” Proc. R. Soc. Lond. A Math. Phys. Sci. 336(1605), 165–190 (1974).
[Crossref]

Bo, F.

Bock, R.

Bryant, P. E.

L. Paterson, M. P. MacDonald, J. Arlt, W. Sibbett, P. E. Bryant, and K. Dholakia, “Controlled rotation of optically trapped microscopic particles,” Science 292(5518), 912–914 (2001).
[Crossref] [PubMed]

Brzobohatý, O.

Cai, Y.

Cao, Y.

Chen, J.

P. Chen, L. L. Ma, W. Duan, J. Chen, S. J. Ge, Z. H. Zhu, M. J. Tang, R. Xu, W. Gao, T. Li, W. Hu, and Y. Q. Lu, “Digitalizing self-assembled chiral superstructures for optical vortex processing,” Adv. Mater. 30(10), 1705865 (2018).
[Crossref] [PubMed]

Chen, P.

P. Chen, L. L. Ma, W. Duan, J. Chen, S. J. Ge, Z. H. Zhu, M. J. Tang, R. Xu, W. Gao, T. Li, W. Hu, and Y. Q. Lu, “Digitalizing self-assembled chiral superstructures for optical vortex processing,” Adv. Mater. 30(10), 1705865 (2018).
[Crossref] [PubMed]

Chen, Z.

Chu, X.

X. Chu, Q. Sun, J. Wang, P. Lü, W. Xie, and X. Xu, “Generating a Bessel-Gaussian beam for the application in optical engineering,” Sci. Rep. 5(1), 18665 (2016).
[Crossref] [PubMed]

X. Chu, Z. Liu, and P. Zhou, “Generation of a high-power Airy beam by coherent combining technology,” Laser Phys. Lett. 10(12), 125102 (2013).
[Crossref]

Courtial, J.

Dajani, I.

A. Flores, I. Dajani, R. Holten, T. Ehrenreich, and B. Anderson, “Multi-kilowatt diffractive coherent combining of pseudorandom-modulated fiber amplifiers,” Opt. Eng. 55(9), 096101 (2016).
[Crossref]

Dholakia, K.

L. Paterson, M. P. MacDonald, J. Arlt, W. Sibbett, P. E. Bryant, and K. Dholakia, “Controlled rotation of optically trapped microscopic particles,” Science 292(5518), 912–914 (2001).
[Crossref] [PubMed]

Ding, J.

Dolinar, S.

J. Wang, J. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6(7), 488–496 (2012).
[Crossref]

Dong, Y.

Duan, W.

P. Chen, L. L. Ma, W. Duan, J. Chen, S. J. Ge, Z. H. Zhu, M. J. Tang, R. Xu, W. Gao, T. Li, W. Hu, and Y. Q. Lu, “Digitalizing self-assembled chiral superstructures for optical vortex processing,” Adv. Mater. 30(10), 1705865 (2018).
[Crossref] [PubMed]

Dudorov, V. V.

V. P. Aksenov, V. V. Dudorov, G. A. Filimonov, V. V. Kolosov, and V. Y. Venediktov, “Vortex beams with zero orbital angular momentum and non-zero topological charge,” Opt. Laser Technol. 104, 159–163 (2018).
[Crossref]

V. P. Aksenov, V. V. Dudorov, and V. V. Kolosov, “Statistical characteristics of common and synthesized vortex beams in a turbulent atmosphere,” Proc. SPIE 10035, 100352P (2016).
[Crossref]

V. P. Aksenov, V. V. Dudorov, and V. V. Kolosov, “Characterization of vortex beams synthesized on the basis of a fiber laser array,” Proc. SPIE 9680, 96802D (2015).

Ehrenreich, T.

A. Flores, I. Dajani, R. Holten, T. Ehrenreich, and B. Anderson, “Multi-kilowatt diffractive coherent combining of pseudorandom-modulated fiber amplifiers,” Opt. Eng. 55(9), 096101 (2016).
[Crossref]

Fan, T. Y.

Fazal, I. M.

J. Wang, J. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6(7), 488–496 (2012).
[Crossref]

Filimonov, G. A.

V. P. Aksenov, V. V. Dudorov, G. A. Filimonov, V. V. Kolosov, and V. Y. Venediktov, “Vortex beams with zero orbital angular momentum and non-zero topological charge,” Opt. Laser Technol. 104, 159–163 (2018).
[Crossref]

Flores, A.

A. Flores, I. Dajani, R. Holten, T. Ehrenreich, and B. Anderson, “Multi-kilowatt diffractive coherent combining of pseudorandom-modulated fiber amplifiers,” Opt. Eng. 55(9), 096101 (2016).
[Crossref]

Franke-Arnold, S.

Fu, S.

S. Fu, T. Wang, Z. Zhang, Y. Zhai, and C. Gao, “Selective acquisition of multiple states on hybrid Poincare sphere,” Appl. Phys. Lett. 110(19), 191102 (2017).
[Crossref]

Fürhapter, S.

Gao, C.

S. Fu, T. Wang, Z. Zhang, Y. Zhai, and C. Gao, “Selective acquisition of multiple states on hybrid Poincare sphere,” Appl. Phys. Lett. 110(19), 191102 (2017).
[Crossref]

Gao, W.

P. Chen, L. L. Ma, W. Duan, J. Chen, S. J. Ge, Z. H. Zhu, M. J. Tang, R. Xu, W. Gao, T. Li, W. Hu, and Y. Q. Lu, “Digitalizing self-assembled chiral superstructures for optical vortex processing,” Adv. Mater. 30(10), 1705865 (2018).
[Crossref] [PubMed]

Ge, S. J.

P. Chen, L. L. Ma, W. Duan, J. Chen, S. J. Ge, Z. H. Zhu, M. J. Tang, R. Xu, W. Gao, T. Li, W. Hu, and Y. Q. Lu, “Digitalizing self-assembled chiral superstructures for optical vortex processing,” Adv. Mater. 30(10), 1705865 (2018).
[Crossref] [PubMed]

Gibson, G.

Goldizen, K. C.

Guo, S.

P. Zhou, Z. Liu, X. Wang, Y. Ma, H. Ma, X. Xu, and S. Guo, “Coherent beam combining of fiber amplifiers using stochastic parallel gradient descent algorithm and its application,” IEEE J. Sel. Top. Quantum Electron. 15(2), 248–256 (2009).
[Crossref]

Halterman, K.

Holten, R.

A. Flores, I. Dajani, R. Holten, T. Ehrenreich, and B. Anderson, “Multi-kilowatt diffractive coherent combining of pseudorandom-modulated fiber amplifiers,” Opt. Eng. 55(9), 096101 (2016).
[Crossref]

Hu, W.

P. Chen, L. L. Ma, W. Duan, J. Chen, S. J. Ge, Z. H. Zhu, M. J. Tang, R. Xu, W. Gao, T. Li, W. Hu, and Y. Q. Lu, “Digitalizing self-assembled chiral superstructures for optical vortex processing,” Adv. Mater. 30(10), 1705865 (2018).
[Crossref] [PubMed]

Huang, H.

G. Xie, L. Li, Y. Ren, H. Huang, Y. Yan, N. Ahmed, Z. Zhao, M. P. J. Lavery, N. Ashrafi, S. Ashrafi, R. Bock, M. Tur, A. F. Molisch, and A. E. Willner, “Performance metrics and design considerations for a free-space optical orbital-angular-momentum-multiplexed communication link,” Optica 2(4), 357–364 (2015).
[Crossref]

J. Wang, J. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6(7), 488–496 (2012).
[Crossref]

Hwang, C. Y.

Jákl, P.

Jesacher, A.

Kim, K. Y.

Kolosov, V. V.

V. P. Aksenov, V. V. Dudorov, G. A. Filimonov, V. V. Kolosov, and V. Y. Venediktov, “Vortex beams with zero orbital angular momentum and non-zero topological charge,” Opt. Laser Technol. 104, 159–163 (2018).
[Crossref]

V. P. Aksenov, V. V. Dudorov, and V. V. Kolosov, “Statistical characteristics of common and synthesized vortex beams in a turbulent atmosphere,” Proc. SPIE 10035, 100352P (2016).
[Crossref]

V. P. Aksenov, V. V. Dudorov, and V. V. Kolosov, “Characterization of vortex beams synthesized on the basis of a fiber laser array,” Proc. SPIE 9680, 96802D (2015).

Kurti, R. S.

Lachinova, S. L.

S. L. Lachinova and M. A. Vorontsov, “Exotic laser beam engineering with coherent fiber-array systems,” J. Opt. 15(10), 105501 (2013).
[Crossref]

Lavery, M. P. J.

Lee, B.

Li, L.

Li, T.

P. Chen, L. L. Ma, W. Duan, J. Chen, S. J. Ge, Z. H. Zhu, M. J. Tang, R. Xu, W. Gao, T. Li, W. Hu, and Y. Q. Lu, “Digitalizing self-assembled chiral superstructures for optical vortex processing,” Adv. Mater. 30(10), 1705865 (2018).
[Crossref] [PubMed]

Li, X.

Liao, P.

Liu, C.

Liu, Z.

Z. Liu, P. Ma, R. Su, R. Tao, Y. Ma, X. Wang, and P. Zhou, “High-power coherent beam polarization combination of fiber lasers: progress and prospect,” J. Opt. Soc. Am. B 34(3), A7–A14 (2017).
[Crossref]

X. Chu, Z. Liu, and P. Zhou, “Generation of a high-power Airy beam by coherent combining technology,” Laser Phys. Lett. 10(12), 125102 (2013).
[Crossref]

Z. Liu, P. Zhou, X. Xu, X. Wang, and Y. Ma, “Coherent beam combining of high power fiber lasers: progress and prospect,” Sci. Chin. Technol. 56(7), 1597–1606 (2013).
[Crossref]

P. Ma, P. Zhou, Y. Ma, X. Wang, R. Su, and Z. Liu, “Generation of azimuthally and radially polarized beams by coherent polarization beam combination,” Opt. Lett. 37(13), 2658–2660 (2012).
[Crossref] [PubMed]

Y. Ma, P. Zhou, X. Wang, H. Ma, X. Xu, L. Si, Z. Liu, and Y. Zhao, “Coherent beam combination with single frequency dithering technique,” Opt. Lett. 35(9), 1308–1310 (2010).
[Crossref] [PubMed]

P. Zhou, Z. Liu, X. Wang, Y. Ma, H. Ma, X. Xu, and S. Guo, “Coherent beam combining of fiber amplifiers using stochastic parallel gradient descent algorithm and its application,” IEEE J. Sel. Top. Quantum Electron. 15(2), 248–256 (2009).
[Crossref]

Lu, Y. Q.

P. Chen, L. L. Ma, W. Duan, J. Chen, S. J. Ge, Z. H. Zhu, M. J. Tang, R. Xu, W. Gao, T. Li, W. Hu, and Y. Q. Lu, “Digitalizing self-assembled chiral superstructures for optical vortex processing,” Adv. Mater. 30(10), 1705865 (2018).
[Crossref] [PubMed]

Lü, P.

X. Chu, Q. Sun, J. Wang, P. Lü, W. Xie, and X. Xu, “Generating a Bessel-Gaussian beam for the application in optical engineering,” Sci. Rep. 5(1), 18665 (2016).
[Crossref] [PubMed]

Ma, H.

Y. Ma, P. Zhou, X. Wang, H. Ma, X. Xu, L. Si, Z. Liu, and Y. Zhao, “Coherent beam combination with single frequency dithering technique,” Opt. Lett. 35(9), 1308–1310 (2010).
[Crossref] [PubMed]

P. Zhou, Z. Liu, X. Wang, Y. Ma, H. Ma, X. Xu, and S. Guo, “Coherent beam combining of fiber amplifiers using stochastic parallel gradient descent algorithm and its application,” IEEE J. Sel. Top. Quantum Electron. 15(2), 248–256 (2009).
[Crossref]

Ma, L. L.

P. Chen, L. L. Ma, W. Duan, J. Chen, S. J. Ge, Z. H. Zhu, M. J. Tang, R. Xu, W. Gao, T. Li, W. Hu, and Y. Q. Lu, “Digitalizing self-assembled chiral superstructures for optical vortex processing,” Adv. Mater. 30(10), 1705865 (2018).
[Crossref] [PubMed]

Ma, P.

Ma, Y.

D. Zhi, R. Tao, P. Zhou, Y. Ma, W. Wu, X. Wang, and L. Si, “Propagation of ring Airy Gaussian beams with optical vortices through anisotropic non-Kolmogorov turbulence,” Opt. Commun. 387, 157–165 (2017).
[Crossref]

Z. Liu, P. Ma, R. Su, R. Tao, Y. Ma, X. Wang, and P. Zhou, “High-power coherent beam polarization combination of fiber lasers: progress and prospect,” J. Opt. Soc. Am. B 34(3), A7–A14 (2017).
[Crossref]

Z. Liu, P. Zhou, X. Xu, X. Wang, and Y. Ma, “Coherent beam combining of high power fiber lasers: progress and prospect,” Sci. Chin. Technol. 56(7), 1597–1606 (2013).
[Crossref]

P. Ma, P. Zhou, Y. Ma, X. Wang, R. Su, and Z. Liu, “Generation of azimuthally and radially polarized beams by coherent polarization beam combination,” Opt. Lett. 37(13), 2658–2660 (2012).
[Crossref] [PubMed]

Y. Ma, P. Zhou, X. Wang, H. Ma, X. Xu, L. Si, Z. Liu, and Y. Zhao, “Coherent beam combination with single frequency dithering technique,” Opt. Lett. 35(9), 1308–1310 (2010).
[Crossref] [PubMed]

P. Zhou, Z. Liu, X. Wang, Y. Ma, H. Ma, X. Xu, and S. Guo, “Coherent beam combining of fiber amplifiers using stochastic parallel gradient descent algorithm and its application,” IEEE J. Sel. Top. Quantum Electron. 15(2), 248–256 (2009).
[Crossref]

MacDonald, M. P.

L. Paterson, M. P. MacDonald, J. Arlt, W. Sibbett, P. E. Bryant, and K. Dholakia, “Controlled rotation of optically trapped microscopic particles,” Science 292(5518), 912–914 (2001).
[Crossref] [PubMed]

Maurer, C.

Molisch, A. F.

Murphy, D. V.

Nye, J. F.

J. F. Nye and M. V. Berry, “Dislocations in wave trains,” Proc. R. Soc. Lond. A Math. Phys. Sci. 336(1605), 165–190 (1974).
[Crossref]

Padgett, M.

Pas’ko, V.

Paterson, L.

L. Paterson, M. P. MacDonald, J. Arlt, W. Sibbett, P. E. Bryant, and K. Dholakia, “Controlled rotation of optically trapped microscopic particles,” Science 292(5518), 912–914 (2001).
[Crossref] [PubMed]

Redmond, S. M.

Ren, Y.

Ritsch-Marte, M.

Sanchez, A.

Shen, F.

Shori, R. K.

Si, L.

D. Zhi, R. Tao, P. Zhou, Y. Ma, W. Wu, X. Wang, and L. Si, “Propagation of ring Airy Gaussian beams with optical vortices through anisotropic non-Kolmogorov turbulence,” Opt. Commun. 387, 157–165 (2017).
[Crossref]

Y. Ma, P. Zhou, X. Wang, H. Ma, X. Xu, L. Si, Z. Liu, and Y. Zhao, “Coherent beam combination with single frequency dithering technique,” Opt. Lett. 35(9), 1308–1310 (2010).
[Crossref] [PubMed]

Sibbett, W.

L. Paterson, M. P. MacDonald, J. Arlt, W. Sibbett, P. E. Bryant, and K. Dholakia, “Controlled rotation of optically trapped microscopic particles,” Science 292(5518), 912–914 (2001).
[Crossref] [PubMed]

Šiler, M.

Spreeuw, R. J. C.

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45(11), 8185–8189 (1992).
[Crossref] [PubMed]

Su, R.

Sun, Q.

X. Chu, Q. Sun, J. Wang, P. Lü, W. Xie, and X. Xu, “Generating a Bessel-Gaussian beam for the application in optical engineering,” Sci. Rep. 5(1), 18665 (2016).
[Crossref] [PubMed]

Tang, M. J.

P. Chen, L. L. Ma, W. Duan, J. Chen, S. J. Ge, Z. H. Zhu, M. J. Tang, R. Xu, W. Gao, T. Li, W. Hu, and Y. Q. Lu, “Digitalizing self-assembled chiral superstructures for optical vortex processing,” Adv. Mater. 30(10), 1705865 (2018).
[Crossref] [PubMed]

Tao, R.

D. Zhi, R. Tao, P. Zhou, Y. Ma, W. Wu, X. Wang, and L. Si, “Propagation of ring Airy Gaussian beams with optical vortices through anisotropic non-Kolmogorov turbulence,” Opt. Commun. 387, 157–165 (2017).
[Crossref]

Z. Liu, P. Ma, R. Su, R. Tao, Y. Ma, X. Wang, and P. Zhou, “High-power coherent beam polarization combination of fiber lasers: progress and prospect,” J. Opt. Soc. Am. B 34(3), A7–A14 (2017).
[Crossref]

Tur, M.

Vasnetsov, M.

Venediktov, V. Y.

V. P. Aksenov, V. V. Dudorov, G. A. Filimonov, V. V. Kolosov, and V. Y. Venediktov, “Vortex beams with zero orbital angular momentum and non-zero topological charge,” Opt. Laser Technol. 104, 159–163 (2018).
[Crossref]

Vorontsov, M. A.

S. L. Lachinova and M. A. Vorontsov, “Exotic laser beam engineering with coherent fiber-array systems,” J. Opt. 15(10), 105501 (2013).
[Crossref]

Wang, J.

X. Chu, Q. Sun, J. Wang, P. Lü, W. Xie, and X. Xu, “Generating a Bessel-Gaussian beam for the application in optical engineering,” Sci. Rep. 5(1), 18665 (2016).
[Crossref] [PubMed]

J. Wang, J. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6(7), 488–496 (2012).
[Crossref]

Wang, L.

L. Wang, L. Wang, and S. Zhu, “Formation of optical vortices using coherent laser beam arrays,” Opt. Commun. 282(6), 1088–1094 (2009).
[Crossref]

L. Wang, L. Wang, and S. Zhu, “Formation of optical vortices using coherent laser beam arrays,” Opt. Commun. 282(6), 1088–1094 (2009).
[Crossref]

Wang, S.

Wang, T.

S. Fu, T. Wang, Z. Zhang, Y. Zhai, and C. Gao, “Selective acquisition of multiple states on hybrid Poincare sphere,” Appl. Phys. Lett. 110(19), 191102 (2017).
[Crossref]

Wang, X.

D. Zhi, R. Tao, P. Zhou, Y. Ma, W. Wu, X. Wang, and L. Si, “Propagation of ring Airy Gaussian beams with optical vortices through anisotropic non-Kolmogorov turbulence,” Opt. Commun. 387, 157–165 (2017).
[Crossref]

X. Wang, B. Zhu, Y. Dong, S. Wang, Z. Zhu, F. Bo, and X. Li, “Generation of equilateral-polygon-like flat-top focus by tightly focusing radially polarized beams superposed with off-axis vortex arrays,” Opt. Express 25(22), 26844–26852 (2017).
[Crossref] [PubMed]

Z. Liu, P. Ma, R. Su, R. Tao, Y. Ma, X. Wang, and P. Zhou, “High-power coherent beam polarization combination of fiber lasers: progress and prospect,” J. Opt. Soc. Am. B 34(3), A7–A14 (2017).
[Crossref]

Z. Liu, P. Zhou, X. Xu, X. Wang, and Y. Ma, “Coherent beam combining of high power fiber lasers: progress and prospect,” Sci. Chin. Technol. 56(7), 1597–1606 (2013).
[Crossref]

P. Ma, P. Zhou, Y. Ma, X. Wang, R. Su, and Z. Liu, “Generation of azimuthally and radially polarized beams by coherent polarization beam combination,” Opt. Lett. 37(13), 2658–2660 (2012).
[Crossref] [PubMed]

Y. Ma, P. Zhou, X. Wang, H. Ma, X. Xu, L. Si, Z. Liu, and Y. Zhao, “Coherent beam combination with single frequency dithering technique,” Opt. Lett. 35(9), 1308–1310 (2010).
[Crossref] [PubMed]

Y. Zheng, X. Wang, F. Shen, and X. Li, “Generation of dark hollow beam via coherent combination based on adaptive optics,” Opt. Express 18(26), 26946–26958 (2010).
[Crossref] [PubMed]

P. Zhou, Z. Liu, X. Wang, Y. Ma, H. Ma, X. Xu, and S. Guo, “Coherent beam combining of fiber amplifiers using stochastic parallel gradient descent algorithm and its application,” IEEE J. Sel. Top. Quantum Electron. 15(2), 248–256 (2009).
[Crossref]

Wang, Z.

Wardlaw, M. J.

Willner, A. E.

Willner, A. J.

Woerdman, J. P.

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45(11), 8185–8189 (1992).
[Crossref] [PubMed]

Wu, W.

D. Zhi, R. Tao, P. Zhou, Y. Ma, W. Wu, X. Wang, and L. Si, “Propagation of ring Airy Gaussian beams with optical vortices through anisotropic non-Kolmogorov turbulence,” Opt. Commun. 387, 157–165 (2017).
[Crossref]

Xie, G.

Xie, W.

X. Chu, Q. Sun, J. Wang, P. Lü, W. Xie, and X. Xu, “Generating a Bessel-Gaussian beam for the application in optical engineering,” Sci. Rep. 5(1), 18665 (2016).
[Crossref] [PubMed]

Xu, R.

P. Chen, L. L. Ma, W. Duan, J. Chen, S. J. Ge, Z. H. Zhu, M. J. Tang, R. Xu, W. Gao, T. Li, W. Hu, and Y. Q. Lu, “Digitalizing self-assembled chiral superstructures for optical vortex processing,” Adv. Mater. 30(10), 1705865 (2018).
[Crossref] [PubMed]

Xu, X.

X. Chu, Q. Sun, J. Wang, P. Lü, W. Xie, and X. Xu, “Generating a Bessel-Gaussian beam for the application in optical engineering,” Sci. Rep. 5(1), 18665 (2016).
[Crossref] [PubMed]

Z. Liu, P. Zhou, X. Xu, X. Wang, and Y. Ma, “Coherent beam combining of high power fiber lasers: progress and prospect,” Sci. Chin. Technol. 56(7), 1597–1606 (2013).
[Crossref]

Y. Ma, P. Zhou, X. Wang, H. Ma, X. Xu, L. Si, Z. Liu, and Y. Zhao, “Coherent beam combination with single frequency dithering technique,” Opt. Lett. 35(9), 1308–1310 (2010).
[Crossref] [PubMed]

P. Zhou, Z. Liu, X. Wang, Y. Ma, H. Ma, X. Xu, and S. Guo, “Coherent beam combining of fiber amplifiers using stochastic parallel gradient descent algorithm and its application,” IEEE J. Sel. Top. Quantum Electron. 15(2), 248–256 (2009).
[Crossref]

Yan, Y.

Yang, J.

J. Wang, J. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6(7), 488–496 (2012).
[Crossref]

Yang, Y.

Yu, C. X.

Yue, Y.

J. Wang, J. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6(7), 488–496 (2012).
[Crossref]

Zemánek, P.

Zeng, T.

Zhai, Y.

S. Fu, T. Wang, Z. Zhang, Y. Zhai, and C. Gao, “Selective acquisition of multiple states on hybrid Poincare sphere,” Appl. Phys. Lett. 110(19), 191102 (2017).
[Crossref]

Zhang, Z.

S. Fu, T. Wang, Z. Zhang, Y. Zhai, and C. Gao, “Selective acquisition of multiple states on hybrid Poincare sphere,” Appl. Phys. Lett. 110(19), 191102 (2017).
[Crossref]

Zhao, C.

Zhao, Y.

Zhao, Z.

Zheng, Y.

Zhi, D.

D. Zhi, R. Tao, P. Zhou, Y. Ma, W. Wu, X. Wang, and L. Si, “Propagation of ring Airy Gaussian beams with optical vortices through anisotropic non-Kolmogorov turbulence,” Opt. Commun. 387, 157–165 (2017).
[Crossref]

Zhou, P.

D. Zhi, R. Tao, P. Zhou, Y. Ma, W. Wu, X. Wang, and L. Si, “Propagation of ring Airy Gaussian beams with optical vortices through anisotropic non-Kolmogorov turbulence,” Opt. Commun. 387, 157–165 (2017).
[Crossref]

Z. Liu, P. Ma, R. Su, R. Tao, Y. Ma, X. Wang, and P. Zhou, “High-power coherent beam polarization combination of fiber lasers: progress and prospect,” J. Opt. Soc. Am. B 34(3), A7–A14 (2017).
[Crossref]

Z. Liu, P. Zhou, X. Xu, X. Wang, and Y. Ma, “Coherent beam combining of high power fiber lasers: progress and prospect,” Sci. Chin. Technol. 56(7), 1597–1606 (2013).
[Crossref]

X. Chu, Z. Liu, and P. Zhou, “Generation of a high-power Airy beam by coherent combining technology,” Laser Phys. Lett. 10(12), 125102 (2013).
[Crossref]

P. Ma, P. Zhou, Y. Ma, X. Wang, R. Su, and Z. Liu, “Generation of azimuthally and radially polarized beams by coherent polarization beam combination,” Opt. Lett. 37(13), 2658–2660 (2012).
[Crossref] [PubMed]

Y. Ma, P. Zhou, X. Wang, H. Ma, X. Xu, L. Si, Z. Liu, and Y. Zhao, “Coherent beam combination with single frequency dithering technique,” Opt. Lett. 35(9), 1308–1310 (2010).
[Crossref] [PubMed]

P. Zhou, Z. Liu, X. Wang, Y. Ma, H. Ma, X. Xu, and S. Guo, “Coherent beam combining of fiber amplifiers using stochastic parallel gradient descent algorithm and its application,” IEEE J. Sel. Top. Quantum Electron. 15(2), 248–256 (2009).
[Crossref]

Zhu, B.

Zhu, S.

L. Wang, L. Wang, and S. Zhu, “Formation of optical vortices using coherent laser beam arrays,” Opt. Commun. 282(6), 1088–1094 (2009).
[Crossref]

Zhu, Z.

Zhu, Z. H.

P. Chen, L. L. Ma, W. Duan, J. Chen, S. J. Ge, Z. H. Zhu, M. J. Tang, R. Xu, W. Gao, T. Li, W. Hu, and Y. Q. Lu, “Digitalizing self-assembled chiral superstructures for optical vortex processing,” Adv. Mater. 30(10), 1705865 (2018).
[Crossref] [PubMed]

Ziyadi, M.

Adv. Mater. (1)

P. Chen, L. L. Ma, W. Duan, J. Chen, S. J. Ge, Z. H. Zhu, M. J. Tang, R. Xu, W. Gao, T. Li, W. Hu, and Y. Q. Lu, “Digitalizing self-assembled chiral superstructures for optical vortex processing,” Adv. Mater. 30(10), 1705865 (2018).
[Crossref] [PubMed]

Appl. Phys. Lett. (1)

S. Fu, T. Wang, Z. Zhang, Y. Zhai, and C. Gao, “Selective acquisition of multiple states on hybrid Poincare sphere,” Appl. Phys. Lett. 110(19), 191102 (2017).
[Crossref]

IEEE J. Sel. Top. Quantum Electron. (2)

T. Y. Fan, “Laser beam combining for high-power, high-radiance sources,” IEEE J. Sel. Top. Quantum Electron. 11(3), 567–577 (2005).
[Crossref]

P. Zhou, Z. Liu, X. Wang, Y. Ma, H. Ma, X. Xu, and S. Guo, “Coherent beam combining of fiber amplifiers using stochastic parallel gradient descent algorithm and its application,” IEEE J. Sel. Top. Quantum Electron. 15(2), 248–256 (2009).
[Crossref]

J. Opt. (1)

S. L. Lachinova and M. A. Vorontsov, “Exotic laser beam engineering with coherent fiber-array systems,” J. Opt. 15(10), 105501 (2013).
[Crossref]

J. Opt. Soc. Am. B (1)

Laser Phys. Lett. (1)

X. Chu, Z. Liu, and P. Zhou, “Generation of a high-power Airy beam by coherent combining technology,” Laser Phys. Lett. 10(12), 125102 (2013).
[Crossref]

Nat. Photonics (1)

J. Wang, J. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6(7), 488–496 (2012).
[Crossref]

Opt. Commun. (2)

L. Wang, L. Wang, and S. Zhu, “Formation of optical vortices using coherent laser beam arrays,” Opt. Commun. 282(6), 1088–1094 (2009).
[Crossref]

D. Zhi, R. Tao, P. Zhou, Y. Ma, W. Wu, X. Wang, and L. Si, “Propagation of ring Airy Gaussian beams with optical vortices through anisotropic non-Kolmogorov turbulence,” Opt. Commun. 387, 157–165 (2017).
[Crossref]

Opt. Eng. (1)

A. Flores, I. Dajani, R. Holten, T. Ehrenreich, and B. Anderson, “Multi-kilowatt diffractive coherent combining of pseudorandom-modulated fiber amplifiers,” Opt. Eng. 55(9), 096101 (2016).
[Crossref]

Opt. Express (7)

R. S. Kurti, K. Halterman, R. K. Shori, and M. J. Wardlaw, “Discrete Cylindrical Vector Beam Generation from an Array of Optical Fibers,” Opt. Express 17(16), 13982–13988 (2009).
[Crossref] [PubMed]

Y. Zheng, X. Wang, F. Shen, and X. Li, “Generation of dark hollow beam via coherent combination based on adaptive optics,” Opt. Express 18(26), 26946–26958 (2010).
[Crossref] [PubMed]

G. Gibson, J. Courtial, M. Padgett, M. Vasnetsov, V. Pas’ko, S. Barnett, and S. Franke-Arnold, “Free-space information transfer using light beams carrying orbital angular momentum,” Opt. Express 12(22), 5448–5456 (2004).
[Crossref] [PubMed]

S. Bernet, A. Jesacher, S. Fürhapter, C. Maurer, and M. Ritsch-Marte, “Quantitative imaging of complex samples by spiral phase contrast microscopy,” Opt. Express 14(9), 3792–3805 (2006).
[Crossref] [PubMed]

M. Šiler, P. Jákl, O. Brzobohatý, and P. Zemánek, “Optical forces induced behavior of a particle in a non-diffracting vortex beam,” Opt. Express 20(22), 24304–24319 (2012).
[Crossref] [PubMed]

C. Y. Hwang, K. Y. Kim, and B. Lee, “Bessel-like beam generation by superposing multiple Airy beams,” Opt. Express 19(8), 7356–7364 (2011).
[Crossref] [PubMed]

X. Wang, B. Zhu, Y. Dong, S. Wang, Z. Zhu, F. Bo, and X. Li, “Generation of equilateral-polygon-like flat-top focus by tightly focusing radially polarized beams superposed with off-axis vortex arrays,” Opt. Express 25(22), 26844–26852 (2017).
[Crossref] [PubMed]

Opt. Laser Technol. (1)

V. P. Aksenov, V. V. Dudorov, G. A. Filimonov, V. V. Kolosov, and V. Y. Venediktov, “Vortex beams with zero orbital angular momentum and non-zero topological charge,” Opt. Laser Technol. 104, 159–163 (2018).
[Crossref]

Opt. Lett. (6)

Optica (1)

Phys. Rev. A (1)

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45(11), 8185–8189 (1992).
[Crossref] [PubMed]

Proc. R. Soc. Lond. A Math. Phys. Sci. (1)

J. F. Nye and M. V. Berry, “Dislocations in wave trains,” Proc. R. Soc. Lond. A Math. Phys. Sci. 336(1605), 165–190 (1974).
[Crossref]

Proc. SPIE (2)

V. P. Aksenov, V. V. Dudorov, and V. V. Kolosov, “Characterization of vortex beams synthesized on the basis of a fiber laser array,” Proc. SPIE 9680, 96802D (2015).

V. P. Aksenov, V. V. Dudorov, and V. V. Kolosov, “Statistical characteristics of common and synthesized vortex beams in a turbulent atmosphere,” Proc. SPIE 10035, 100352P (2016).
[Crossref]

Sci. Chin. Technol. (1)

Z. Liu, P. Zhou, X. Xu, X. Wang, and Y. Ma, “Coherent beam combining of high power fiber lasers: progress and prospect,” Sci. Chin. Technol. 56(7), 1597–1606 (2013).
[Crossref]

Sci. Rep. (1)

X. Chu, Q. Sun, J. Wang, P. Lü, W. Xie, and X. Xu, “Generating a Bessel-Gaussian beam for the application in optical engineering,” Sci. Rep. 5(1), 18665 (2016).
[Crossref] [PubMed]

Science (1)

L. Paterson, M. P. MacDonald, J. Arlt, W. Sibbett, P. E. Bryant, and K. Dholakia, “Controlled rotation of optically trapped microscopic particles,” Science 292(5518), 912–914 (2001).
[Crossref] [PubMed]

Other (4)

T. H. Cormen, C. E. Leiserson, R. L. Rivest, and C. Stein, Introduction to algorithms (Massachusetts Institute of Technology, 2009), Chap. 16.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1968), Chap. 4.

Communications Office MIT Lincoln Laboratory, “MIT Lincoln Laboratory demonstrates novel laser at technology expo,” http://www.ll.mit.edu/news/wait-what.html (2015).

M. R. Andrew and R. W. Berdine, Introduction to High Power Fiber Lasers (NM: Directed Energy Professional Society, 2009), Chap. 9.

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Figures (11)

Fig. 1
Fig. 1 The sketch for the generation of a vortex beam array based on coherent combining technology. (a) The optical field generated by the reversal of Huygens Fresnel diffraction. (b) The arrangement of the Gaussian beam array at the source plane. (c) The process of generating the vortex beam array.
Fig. 2
Fig. 2 Intensity (upper) and phase (below) distributions in the x-y plane of (a) the forward propagation and (b) the reverse propagation at the same distance symmetrically. (c) illustrates the differences of the intensity and phase distributions between (a) and (b).
Fig. 3
Fig. 3 (a) Division of the intensity pattern obtained by the reversal of Huygens Fresnel diffraction. (b) Configuration of the Gaussian beam array designed by the greedy algorithm. (c) Differences of the intensity distributions between (a) and (b).
Fig. 4
Fig. 4 (a) Intensity distribution of the Gaussian beam array to generate the vortex beam arrays with TC = ± 1. (b) Intensity distribution of the Gaussian beam array to generate the vortex beam arrays with TC = ± 2. (c), (d), (e) and (f) refer to the phase distributions of the Gaussian beam arrays to generate the vortex beam arrays with TC = 1, TC = 2, TC = −1 and TC = −2, respectively.
Fig. 5
Fig. 5 Intensity (upper) and phase (below) distributions of the synthesized vortex beam arrays with (a) TC = 1, (b) TC = −1, (c) TC = 2 and (d) TC = −2 at the receiver plane.
Fig. 6
Fig. 6 Phase distributions at the source plane to generate multiple vortex beams at (a) L = 1km, (b) L = 2km, (c) L = 4km, (d) L = 6km. Intensity distributions at the receiver plane at (e) L = 1km, (f) L = 2km, (g) L = 4km, (h) L = 6km. Phase distributions at the receiver plane at (i) L = 1km, (j) L = 2km, (k) L = 4km, (l) L = 6km.
Fig. 7
Fig. 7 Evolution of the intensity (upper) and phase (below) distributions at different positions near the receiver plane: (a) ΔL = −0.075L, (b) ΔL = −0.05L, (c) ΔL = −0.025L, (d) ΔL = 0.025L, (e) ΔL = 0.05L and (f) ΔL = 0.075L.
Fig. 8
Fig. 8 (a) The number of Gaussian beams required to generate four vortex beams with different separations. σ accounts for the waist width of each vortex beam. (b) The number of Gaussian beams required to generate vortex beam arrays with different TCs.
Fig. 9
Fig. 9 The minimum number of Gaussian beams required to generate NV vortex beams with TC = 1.
Fig. 10
Fig. 10 The sketch for the potential application in free-space optical communication. NPBS: non-polarizing beam splitter.
Fig. 11
Fig. 11 (a) Intensity distribution of the Gaussian beam array for spatial light structuring. (b) Phase distribution of the Gaussian beam array for spatial light structuring. (c) Intensity distribution of the high localized power beam array generated from the Gaussian beam array.

Equations (5)

Equations on this page are rendered with MathJax. Learn more.

U( x,y,z=L )= e ikL iλL U( ξ,η,z=0 ) e i k 2L [ ( xξ ) 2 + ( yη ) 2 ] dξdη
U( ξ,η,z=0 )=iλL e ik(L) U( x,y,z=L ) e i k 2(L) [ ( xξ ) 2 + ( yη ) 2 ] dxdy
{ min A,a,b,d, w 0 ,N | I ideal I array | s.t. I array = j=1 N I j , I j = A j 2 exp[ 2 ( ξ a j ) 2 + ( η b j ) 2 w 0j 2 ]circ[ ( ξ a j ) 2 + ( η b j ) 2 d j ], p,q{ 1,2,...,N },| a p a q , b p b q | d p + d q .
U array ( ξ,η,z=0 )= j=1 N A j exp[ ( ξ a j ) 2 + ( η b j ) 2 w 0j 2 ] ×exp{ iarg[ U ideal ( ξ,η,z=0 ) ] } ×circ[ ( ξ a j ) 2 + ( η b j ) 2 d j ]
U array ( x,y,z=L )= e ikL iλL U array ( ξ,η,z=0 ) e i k 2L [ ( xξ ) 2 + ( yη ) 2 ] dξdη

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