Abstract

A novel method for generating a dark hollow beam (DHB) is proposed and studied both theoretically and experimentally. A coherent combination technique for laser arrays is implemented based on adaptive optics (AO). A beam arraying structure and an active segmented mirror are designed and described. Piston errors are extracted by a zero-order interference detection system with the help of a custom-made photo-detectors array. An algorithm called the extremum approach is adopted to calculate feedback control signals. A dynamic piston error is imported by LiNbO3 to test the capability of the AO servo. In a closed loop the stable and clear DHB is obtained. The experimental results confirm the feasibility of the concept.

© 2010 OSA

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. G. D. Goodno, H. Komine, S. J. McNaught, S. B. Weiss, S. Redmond, W. Long, R. Simpson, E. C. Cheung, D. Howland, P. Epp, M. Weber, M. McClellan, J. Sollee, and H. Injeyan, “Coherent combination of high-power, zigzag slab lasers,” Opt. Lett. 31(9), 1247–1249 (2006).
    [CrossRef] [PubMed]
  2. S. J. Augst, T. Y. Fan, and A. Sanchez, “Coherent beam combining and phase noise measurements of ytterbium fiber amplifiers,” Opt. Lett. 29(5), 474–476 (2004).
    [CrossRef] [PubMed]
  3. L. A. Beresnev, T. Weyrauch, M. A. Vorontsov, L. Liu, and G. W. Carhart, “Development of adaptive fiber collimators for conformal fiber-based beam projection systems,” Proc. SPIE 7090, 709008 (2008).
    [CrossRef]
  4. H. Bruesselbach, S. Q. Wang, M. Minden, D. C. Jones, and M. Mangir, “Power-scalable phase-compensating fiber-array transceiver for laser communications through the atmosphere,” J. Opt. Soc. Am. B 22(2), 347–353 (2005).
    [CrossRef]
  5. R. Xiao, J. Hou, M. Liu, and Z. F. Jiang, “Coherent combining technology of master oscillator power amplifier fiber arrays,” Opt. Express 16(3), 2015–2022 (2008).
    [CrossRef] [PubMed]
  6. W. M. Neubert, K. H. Kudielka, W. R. Leeb, and A. L. Scholtz, “Experimental demonstration of an optical phased array antenna for laser space communications,” Appl. Opt. 33(18), 3820–3830 (1994).
    [CrossRef] [PubMed]
  7. B. Lü and H. Ma, “Beam propagation properties of radial laser array,” J. Opt. Soc. Am. A 17(11), 2005–2009 (2000).
    [CrossRef]
  8. K. Gao, L. Xu, R. Zheng, G. Chen, H. Zheng, and H. Ming, “Flat-top laser beam generated by coherent beam combining of Gaussian laser,” Chin. Opt. Lett. 8(1), 45–47 (2010).
    [CrossRef]
  9. L. G. Wang, L. Q. Wang, and S. Y. Zhu, “Formation of optical vortices using coherent laser beam arrays,” Opt. Commun. 282(6), 1088–1094 (2009).
    [CrossRef]
  10. J. Li, H. Zhang, and B. Lü, “Composite coherence vortices in a radial beam array propagating through atmospheric turbulence along a slant path,” J. Opt. A, Pure Appl. Opt. 12(6), 065401 (2010).
  11. K. T. Gahagan and G. A. Swartzlander, “Trapping of low-index microparticles in an optical vortex,” J. Opt. Soc. Am. B 15(2), 524–534 (1998).
    [CrossRef]
  12. M. Miyazaki and Y. Hayasaki, “Motion control of low-index microspheres in liquid based on optical repulsive force of a focused beam array,” Opt. Lett. 34(6), 821–823 (2009).
    [CrossRef] [PubMed]
  13. J. P. Yin, Y. F. Zhu, W. J. He, and Z. Z. Wang, “Atom guiding and cooling in dark hollow laser beam,” Phys. Rev. A 58(1), 509–513 (1998).
    [CrossRef]
  14. Z. Y. Wang, Y. M. Dong, and Q. Lin, “Atomic trapping and guiding by quasi-dark hollow beam,” J. Opt. A, Pure Appl. Opt. 7(3), 147–153 (2005).
    [CrossRef]
  15. G. Gbur and R. K. Tyson, “Vortex beam propagation through atmospheric turbulence and topological charge conservation,” J. Opt. Soc. Am. A 25(1), 225–230 (2008).
    [CrossRef]
  16. J. Arlt, K. Dholakia, L. Allen, and M. J. Padgett, “The production of multiringed Laguerre–Gaussian modes by computer-generated holograms,” J. Mod. Opt. 45(6), 1231–1237 (1998).
    [CrossRef]
  17. Z. J. Liu, J. Dai, X. Sun, and S. Liu, “Generation of hollow Gaussian beam by phase-only filtering,” Opt. Express 16(24), 19926–19933 (2008).
    [CrossRef] [PubMed]
  18. G. Schweiger, R. Nett, B. Ozel, and T. Weigel, “Generation of hollow beams by spiral rays in multimode light guides,” Opt. Express 18(5), 4510–4517 (2010).
    [CrossRef] [PubMed]
  19. H. Fujiwara, K. E. Brown, and D. D. Dlott, “High-energy flat-top beams for laser launching using a Gaussian mirror,” Appl. Opt. 49(19), 3723–3731 (2010).
    [CrossRef] [PubMed]
  20. D. M. Dagenais, J. A. Woodroffe, and I. Itzkan, “Optical beam shaping of a high power laser for uniform target illumination,” Appl. Opt. 24(5), 671–675 (1985).
    [CrossRef] [PubMed]
  21. S. A. Collins., “Lens-system diffraction integral written in terms of matrix optics,” J. Opt. Soc. Am. 60(9), 1168–1177 (1970).
    [CrossRef]
  22. R. Yang, P. Yang, L. Dong, M. Ao, and B. Xu, “A strip extracting algorithm for phase noise measurement and coherent beam combining of fiber amplifiers,” Appl. Phys. B 99(1-2), 19–22 (2010).
    [CrossRef]
  23. X. L. Wang, Y. X. Ma, P. Zhou, H. T. Ma, X. Li, X. X. Xu, and Z. J. Liu, “Coherent beam combining of two W-level fiber amplifiers in turbulence atmospheric environment based on stochastic parallel gradient descent algorithm,” Laser Phys. 19(5), 984–988 (2009).
    [CrossRef]
  24. M. M. Colavita, M. Shao, and D. H. Staelin, “Atmospheric phase measurements with the Mark III stellar interferometer,” Appl. Opt. 26(19), 4106–4112 (1987).
    [CrossRef] [PubMed]
  25. L. Liu, M. A. Vorontsov, E. Polnau, T. Weyrauch, and L. A. Beresnev, “Adaptive phase-locked fiber array with wavefront phase tip-tilt compensation using piezoelectric fiber positioners,” Proc. SPIE 6708, 67080K (2007).
    [CrossRef]

2010 (5)

K. Gao, L. Xu, R. Zheng, G. Chen, H. Zheng, and H. Ming, “Flat-top laser beam generated by coherent beam combining of Gaussian laser,” Chin. Opt. Lett. 8(1), 45–47 (2010).
[CrossRef]

J. Li, H. Zhang, and B. Lü, “Composite coherence vortices in a radial beam array propagating through atmospheric turbulence along a slant path,” J. Opt. A, Pure Appl. Opt. 12(6), 065401 (2010).

G. Schweiger, R. Nett, B. Ozel, and T. Weigel, “Generation of hollow beams by spiral rays in multimode light guides,” Opt. Express 18(5), 4510–4517 (2010).
[CrossRef] [PubMed]

H. Fujiwara, K. E. Brown, and D. D. Dlott, “High-energy flat-top beams for laser launching using a Gaussian mirror,” Appl. Opt. 49(19), 3723–3731 (2010).
[CrossRef] [PubMed]

R. Yang, P. Yang, L. Dong, M. Ao, and B. Xu, “A strip extracting algorithm for phase noise measurement and coherent beam combining of fiber amplifiers,” Appl. Phys. B 99(1-2), 19–22 (2010).
[CrossRef]

2009 (3)

X. L. Wang, Y. X. Ma, P. Zhou, H. T. Ma, X. Li, X. X. Xu, and Z. J. Liu, “Coherent beam combining of two W-level fiber amplifiers in turbulence atmospheric environment based on stochastic parallel gradient descent algorithm,” Laser Phys. 19(5), 984–988 (2009).
[CrossRef]

M. Miyazaki and Y. Hayasaki, “Motion control of low-index microspheres in liquid based on optical repulsive force of a focused beam array,” Opt. Lett. 34(6), 821–823 (2009).
[CrossRef] [PubMed]

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

2008 (4)

2007 (1)

L. Liu, M. A. Vorontsov, E. Polnau, T. Weyrauch, and L. A. Beresnev, “Adaptive phase-locked fiber array with wavefront phase tip-tilt compensation using piezoelectric fiber positioners,” Proc. SPIE 6708, 67080K (2007).
[CrossRef]

2006 (1)

2005 (2)

2004 (1)

2000 (1)

1998 (3)

J. Arlt, K. Dholakia, L. Allen, and M. J. Padgett, “The production of multiringed Laguerre–Gaussian modes by computer-generated holograms,” J. Mod. Opt. 45(6), 1231–1237 (1998).
[CrossRef]

J. P. Yin, Y. F. Zhu, W. J. He, and Z. Z. Wang, “Atom guiding and cooling in dark hollow laser beam,” Phys. Rev. A 58(1), 509–513 (1998).
[CrossRef]

K. T. Gahagan and G. A. Swartzlander, “Trapping of low-index microparticles in an optical vortex,” J. Opt. Soc. Am. B 15(2), 524–534 (1998).
[CrossRef]

1994 (1)

1987 (1)

1985 (1)

1970 (1)

Allen, L.

J. Arlt, K. Dholakia, L. Allen, and M. J. Padgett, “The production of multiringed Laguerre–Gaussian modes by computer-generated holograms,” J. Mod. Opt. 45(6), 1231–1237 (1998).
[CrossRef]

Ao, M.

R. Yang, P. Yang, L. Dong, M. Ao, and B. Xu, “A strip extracting algorithm for phase noise measurement and coherent beam combining of fiber amplifiers,” Appl. Phys. B 99(1-2), 19–22 (2010).
[CrossRef]

Arlt, J.

J. Arlt, K. Dholakia, L. Allen, and M. J. Padgett, “The production of multiringed Laguerre–Gaussian modes by computer-generated holograms,” J. Mod. Opt. 45(6), 1231–1237 (1998).
[CrossRef]

Augst, S. J.

Beresnev, L. A.

L. A. Beresnev, T. Weyrauch, M. A. Vorontsov, L. Liu, and G. W. Carhart, “Development of adaptive fiber collimators for conformal fiber-based beam projection systems,” Proc. SPIE 7090, 709008 (2008).
[CrossRef]

L. Liu, M. A. Vorontsov, E. Polnau, T. Weyrauch, and L. A. Beresnev, “Adaptive phase-locked fiber array with wavefront phase tip-tilt compensation using piezoelectric fiber positioners,” Proc. SPIE 6708, 67080K (2007).
[CrossRef]

Brown, K. E.

Bruesselbach, H.

Carhart, G. W.

L. A. Beresnev, T. Weyrauch, M. A. Vorontsov, L. Liu, and G. W. Carhart, “Development of adaptive fiber collimators for conformal fiber-based beam projection systems,” Proc. SPIE 7090, 709008 (2008).
[CrossRef]

Chen, G.

Cheung, E. C.

Colavita, M. M.

Collins, S. A.

Dagenais, D. M.

Dai, J.

Dholakia, K.

J. Arlt, K. Dholakia, L. Allen, and M. J. Padgett, “The production of multiringed Laguerre–Gaussian modes by computer-generated holograms,” J. Mod. Opt. 45(6), 1231–1237 (1998).
[CrossRef]

Dlott, D. D.

Dong, L.

R. Yang, P. Yang, L. Dong, M. Ao, and B. Xu, “A strip extracting algorithm for phase noise measurement and coherent beam combining of fiber amplifiers,” Appl. Phys. B 99(1-2), 19–22 (2010).
[CrossRef]

Dong, Y. M.

Z. Y. Wang, Y. M. Dong, and Q. Lin, “Atomic trapping and guiding by quasi-dark hollow beam,” J. Opt. A, Pure Appl. Opt. 7(3), 147–153 (2005).
[CrossRef]

Epp, P.

Fan, T. Y.

Fujiwara, H.

Gahagan, K. T.

Gao, K.

Gbur, G.

Goodno, G. D.

Hayasaki, Y.

He, W. J.

J. P. Yin, Y. F. Zhu, W. J. He, and Z. Z. Wang, “Atom guiding and cooling in dark hollow laser beam,” Phys. Rev. A 58(1), 509–513 (1998).
[CrossRef]

Hou, J.

Howland, D.

Injeyan, H.

Itzkan, I.

Jiang, Z. F.

Jones, D. C.

Komine, H.

Kudielka, K. H.

Leeb, W. R.

Li, J.

J. Li, H. Zhang, and B. Lü, “Composite coherence vortices in a radial beam array propagating through atmospheric turbulence along a slant path,” J. Opt. A, Pure Appl. Opt. 12(6), 065401 (2010).

Li, X.

X. L. Wang, Y. X. Ma, P. Zhou, H. T. Ma, X. Li, X. X. Xu, and Z. J. Liu, “Coherent beam combining of two W-level fiber amplifiers in turbulence atmospheric environment based on stochastic parallel gradient descent algorithm,” Laser Phys. 19(5), 984–988 (2009).
[CrossRef]

Lin, Q.

Z. Y. Wang, Y. M. Dong, and Q. Lin, “Atomic trapping and guiding by quasi-dark hollow beam,” J. Opt. A, Pure Appl. Opt. 7(3), 147–153 (2005).
[CrossRef]

Liu, L.

L. A. Beresnev, T. Weyrauch, M. A. Vorontsov, L. Liu, and G. W. Carhart, “Development of adaptive fiber collimators for conformal fiber-based beam projection systems,” Proc. SPIE 7090, 709008 (2008).
[CrossRef]

L. Liu, M. A. Vorontsov, E. Polnau, T. Weyrauch, and L. A. Beresnev, “Adaptive phase-locked fiber array with wavefront phase tip-tilt compensation using piezoelectric fiber positioners,” Proc. SPIE 6708, 67080K (2007).
[CrossRef]

Liu, M.

Liu, S.

Liu, Z. J.

X. L. Wang, Y. X. Ma, P. Zhou, H. T. Ma, X. Li, X. X. Xu, and Z. J. Liu, “Coherent beam combining of two W-level fiber amplifiers in turbulence atmospheric environment based on stochastic parallel gradient descent algorithm,” Laser Phys. 19(5), 984–988 (2009).
[CrossRef]

Z. J. Liu, J. Dai, X. Sun, and S. Liu, “Generation of hollow Gaussian beam by phase-only filtering,” Opt. Express 16(24), 19926–19933 (2008).
[CrossRef] [PubMed]

Long, W.

Lü, B.

J. Li, H. Zhang, and B. Lü, “Composite coherence vortices in a radial beam array propagating through atmospheric turbulence along a slant path,” J. Opt. A, Pure Appl. Opt. 12(6), 065401 (2010).

B. Lü and H. Ma, “Beam propagation properties of radial laser array,” J. Opt. Soc. Am. A 17(11), 2005–2009 (2000).
[CrossRef]

Ma, H.

Ma, H. T.

X. L. Wang, Y. X. Ma, P. Zhou, H. T. Ma, X. Li, X. X. Xu, and Z. J. Liu, “Coherent beam combining of two W-level fiber amplifiers in turbulence atmospheric environment based on stochastic parallel gradient descent algorithm,” Laser Phys. 19(5), 984–988 (2009).
[CrossRef]

Ma, Y. X.

X. L. Wang, Y. X. Ma, P. Zhou, H. T. Ma, X. Li, X. X. Xu, and Z. J. Liu, “Coherent beam combining of two W-level fiber amplifiers in turbulence atmospheric environment based on stochastic parallel gradient descent algorithm,” Laser Phys. 19(5), 984–988 (2009).
[CrossRef]

Mangir, M.

McClellan, M.

McNaught, S. J.

Minden, M.

Ming, H.

Miyazaki, M.

Nett, R.

Neubert, W. M.

Ozel, B.

Padgett, M. J.

J. Arlt, K. Dholakia, L. Allen, and M. J. Padgett, “The production of multiringed Laguerre–Gaussian modes by computer-generated holograms,” J. Mod. Opt. 45(6), 1231–1237 (1998).
[CrossRef]

Polnau, E.

L. Liu, M. A. Vorontsov, E. Polnau, T. Weyrauch, and L. A. Beresnev, “Adaptive phase-locked fiber array with wavefront phase tip-tilt compensation using piezoelectric fiber positioners,” Proc. SPIE 6708, 67080K (2007).
[CrossRef]

Redmond, S.

Sanchez, A.

Scholtz, A. L.

Schweiger, G.

Shao, M.

Simpson, R.

Sollee, J.

Staelin, D. H.

Sun, X.

Swartzlander, G. A.

Tyson, R. K.

Vorontsov, M. A.

L. A. Beresnev, T. Weyrauch, M. A. Vorontsov, L. Liu, and G. W. Carhart, “Development of adaptive fiber collimators for conformal fiber-based beam projection systems,” Proc. SPIE 7090, 709008 (2008).
[CrossRef]

L. Liu, M. A. Vorontsov, E. Polnau, T. Weyrauch, and L. A. Beresnev, “Adaptive phase-locked fiber array with wavefront phase tip-tilt compensation using piezoelectric fiber positioners,” Proc. SPIE 6708, 67080K (2007).
[CrossRef]

Wang, L. G.

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

Wang, L. Q.

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

Wang, S. Q.

Wang, X. L.

X. L. Wang, Y. X. Ma, P. Zhou, H. T. Ma, X. Li, X. X. Xu, and Z. J. Liu, “Coherent beam combining of two W-level fiber amplifiers in turbulence atmospheric environment based on stochastic parallel gradient descent algorithm,” Laser Phys. 19(5), 984–988 (2009).
[CrossRef]

Wang, Z. Y.

Z. Y. Wang, Y. M. Dong, and Q. Lin, “Atomic trapping and guiding by quasi-dark hollow beam,” J. Opt. A, Pure Appl. Opt. 7(3), 147–153 (2005).
[CrossRef]

Wang, Z. Z.

J. P. Yin, Y. F. Zhu, W. J. He, and Z. Z. Wang, “Atom guiding and cooling in dark hollow laser beam,” Phys. Rev. A 58(1), 509–513 (1998).
[CrossRef]

Weber, M.

Weigel, T.

Weiss, S. B.

Weyrauch, T.

L. A. Beresnev, T. Weyrauch, M. A. Vorontsov, L. Liu, and G. W. Carhart, “Development of adaptive fiber collimators for conformal fiber-based beam projection systems,” Proc. SPIE 7090, 709008 (2008).
[CrossRef]

L. Liu, M. A. Vorontsov, E. Polnau, T. Weyrauch, and L. A. Beresnev, “Adaptive phase-locked fiber array with wavefront phase tip-tilt compensation using piezoelectric fiber positioners,” Proc. SPIE 6708, 67080K (2007).
[CrossRef]

Woodroffe, J. A.

Xiao, R.

Xu, B.

R. Yang, P. Yang, L. Dong, M. Ao, and B. Xu, “A strip extracting algorithm for phase noise measurement and coherent beam combining of fiber amplifiers,” Appl. Phys. B 99(1-2), 19–22 (2010).
[CrossRef]

Xu, L.

Xu, X. X.

X. L. Wang, Y. X. Ma, P. Zhou, H. T. Ma, X. Li, X. X. Xu, and Z. J. Liu, “Coherent beam combining of two W-level fiber amplifiers in turbulence atmospheric environment based on stochastic parallel gradient descent algorithm,” Laser Phys. 19(5), 984–988 (2009).
[CrossRef]

Yang, P.

R. Yang, P. Yang, L. Dong, M. Ao, and B. Xu, “A strip extracting algorithm for phase noise measurement and coherent beam combining of fiber amplifiers,” Appl. Phys. B 99(1-2), 19–22 (2010).
[CrossRef]

Yang, R.

R. Yang, P. Yang, L. Dong, M. Ao, and B. Xu, “A strip extracting algorithm for phase noise measurement and coherent beam combining of fiber amplifiers,” Appl. Phys. B 99(1-2), 19–22 (2010).
[CrossRef]

Yin, J. P.

J. P. Yin, Y. F. Zhu, W. J. He, and Z. Z. Wang, “Atom guiding and cooling in dark hollow laser beam,” Phys. Rev. A 58(1), 509–513 (1998).
[CrossRef]

Zhang, H.

J. Li, H. Zhang, and B. Lü, “Composite coherence vortices in a radial beam array propagating through atmospheric turbulence along a slant path,” J. Opt. A, Pure Appl. Opt. 12(6), 065401 (2010).

Zheng, H.

Zheng, R.

Zhou, P.

X. L. Wang, Y. X. Ma, P. Zhou, H. T. Ma, X. Li, X. X. Xu, and Z. J. Liu, “Coherent beam combining of two W-level fiber amplifiers in turbulence atmospheric environment based on stochastic parallel gradient descent algorithm,” Laser Phys. 19(5), 984–988 (2009).
[CrossRef]

Zhu, S. Y.

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

Zhu, Y. F.

J. P. Yin, Y. F. Zhu, W. J. He, and Z. Z. Wang, “Atom guiding and cooling in dark hollow laser beam,” Phys. Rev. A 58(1), 509–513 (1998).
[CrossRef]

Appl. Opt. (4)

Appl. Phys. B (1)

R. Yang, P. Yang, L. Dong, M. Ao, and B. Xu, “A strip extracting algorithm for phase noise measurement and coherent beam combining of fiber amplifiers,” Appl. Phys. B 99(1-2), 19–22 (2010).
[CrossRef]

Chin. Opt. Lett. (1)

J. Mod. Opt. (1)

J. Arlt, K. Dholakia, L. Allen, and M. J. Padgett, “The production of multiringed Laguerre–Gaussian modes by computer-generated holograms,” J. Mod. Opt. 45(6), 1231–1237 (1998).
[CrossRef]

J. Opt. A, Pure Appl. Opt. (2)

Z. Y. Wang, Y. M. Dong, and Q. Lin, “Atomic trapping and guiding by quasi-dark hollow beam,” J. Opt. A, Pure Appl. Opt. 7(3), 147–153 (2005).
[CrossRef]

J. Li, H. Zhang, and B. Lü, “Composite coherence vortices in a radial beam array propagating through atmospheric turbulence along a slant path,” J. Opt. A, Pure Appl. Opt. 12(6), 065401 (2010).

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (2)

J. Opt. Soc. Am. B (2)

Laser Phys. (1)

X. L. Wang, Y. X. Ma, P. Zhou, H. T. Ma, X. Li, X. X. Xu, and Z. J. Liu, “Coherent beam combining of two W-level fiber amplifiers in turbulence atmospheric environment based on stochastic parallel gradient descent algorithm,” Laser Phys. 19(5), 984–988 (2009).
[CrossRef]

Opt. Commun. (1)

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

Opt. Express (3)

Opt. Lett. (3)

Phys. Rev. A (1)

J. P. Yin, Y. F. Zhu, W. J. He, and Z. Z. Wang, “Atom guiding and cooling in dark hollow laser beam,” Phys. Rev. A 58(1), 509–513 (1998).
[CrossRef]

Proc. SPIE (2)

L. A. Beresnev, T. Weyrauch, M. A. Vorontsov, L. Liu, and G. W. Carhart, “Development of adaptive fiber collimators for conformal fiber-based beam projection systems,” Proc. SPIE 7090, 709008 (2008).
[CrossRef]

L. Liu, M. A. Vorontsov, E. Polnau, T. Weyrauch, and L. A. Beresnev, “Adaptive phase-locked fiber array with wavefront phase tip-tilt compensation using piezoelectric fiber positioners,” Proc. SPIE 6708, 67080K (2007).
[CrossRef]

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (11)

Fig. 1
Fig. 1

Schematic diagram of the laser array on input plane. The red part indicates the actual laser array in our experiment. The dashed lines represent the annular area where the beams are located symmetrically.

Fig. 2
Fig. 2

Beam path of the laser array passing through a thin lens.

Fig. 3
Fig. 3

Numerical simulation of DHB generation. (a) The phase distribution of the near field. The center and surroundings obey ( ϕ 1 ϕ 0 ) = π . (b) The amplitude distribution of the near field. The center and surroundings obey a 1 = 1 / 6 a 0 . (c) The far field of the DHB.

Fig. 4
Fig. 4

Far fields deriving from different near fields. (a) Different amplitude distributions. The phases keep ( ϕ 1 ϕ 0 ) = π . (b) Different phase distributions. The amplitudes keep a 1 = 0.17 a 0 .

Fig. 5
Fig. 5

Experimental configuration of seven-laser CBC system based on AO. The thin line represents the fiber link and the thick represents the cable link.

Fig. 6
Fig. 6

Key devices of AO servo. (a) The ASM and the HVA. (b) The BAS. (c) Schematic diagram of the hexagonal pyramid.

Fig. 7
Fig. 7

Key devices of piston extracting system. (a) The beam expander. (b) The PDs array.

Fig. 8
Fig. 8

Voltage signals recorded by oscilloscope. (a) The sine wave provided by function generator. (b) The PD output signal of center channel in open loop and (c) in closed loop. The Y-axis (voltage) scales are respectively 200 mV, 2 V,2 V and the x-axis (time) scales are both 2 ms.

Fig. 9
Fig. 9

Evolution curves of piston errors between reference channel and unit channels. The upper is the center channel, and the lower is the representative one of six surrounding channels.

Fig. 10
Fig. 10

AO capability analysis. (a) The phase spectral density in two stages. (b) The error rejection transfer function.

Fig. 11
Fig. 11

10 s long-exposure patterns of far-field. (a) Open loop. (b) Closed loop. (c)Theoretical simulation. The intensity-scale bar is distinguished.

Equations (19)

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

E ( x , y ; Z = 0 ) = j = 0 N 1 E j ( x , y ; Z = 0 ) = j = 0 N 1 a j exp ( i ϕ j ) exp [ ( x x j ) 2 + ( y y j ) 2 ω j 2 ] ,
E j ( u , v ; Z = z ) = i k 2 π B exp ( i k L ) + + E j ( x , y ; Z = 0 ) × exp { i k 2 B [ A ( x 2 + y 2 ) + D ( u 2 + v 2 ) 2 ( x u + y v ) ] } d x d y .
E j ( u , v ; Z = z ) = a j ( i z R α ) exp ( i k L + i ϕ j ) exp [ i k A ( x j 2 + y j 2 ) 2 α ] × exp [ i k ( x j u + y j v ) α ] exp [ i k β ( u 2 + v 2 ) 2 ] ,
E ( u , v ; Z = z ) = j = 0 N 1 E j ( u , v ; Z = z ) = ( i z R α ) exp ( i k L ) exp [ i k β ( u 2 + v 2 ) 2 ] × j = 0 N 1 a j exp [ i k A ( x j 2 + y j 2 ) 2 i k ( x j u + y j v ) 2 α + i ϕ j ] ,
I ( u , v ; Z = z ) = E ( u , v ; Z = z ) E * ( u , v ; Z = z ) .
( A B C D ) = ( 1 z 0 1 ) ( 1 0 1 / f 1 ) ( 1 l 0 1 ) = ( 1 z f z + ( 1 z f ) l 1 f 1 l f ) .
( A B C D ) = ( 0 f 1 f 1 ) .
I ( 0 , 0 ; Z = z ) = 0.
( j = 0 N 1 a j exp ( i ϕ j ) ) ( j = 0 N 1 a j exp ( i ϕ j ) ) * = 0.
a 0 2 + 36 a 1 2 + 12 a 0 a 1 cos ( ϕ 1 ϕ 0 ) = 0.
a 1 = 1 / 6 a 0 ( 0.17 a 0 ) , ( ϕ 1 ϕ 0 ) = π .
Z j = u j + u r e f = a j exp ( i ϕ j ) + a r e f exp ( i ϕ r e f ) .
I = Z j Z j * = a j 2 + a r e f 2 + 2 a j a r e f cos ( ϕ r e f ϕ j ) .
θ t i l t << arcsin λ π 2 ω 0 .
V j ( k + 1 ) = V j ( k ) + γ j ( V j s t d V j ( k ) ) .
I j max = a j 2 + a r e f 2 + 2 a j a r e f , I j min = a j 2 + a r e f 2 2 a j a r e f .
I = ( I j max + I j min ) / 2 + cos ( ϕ r e f ϕ j ) ( I j max I j min ) / 2.
ϕ r e f ϕ j = arccos [ 2 V ( V j max + V j min ) V j max V j min ] .
E R T F = log 10 ( P S D c l o s e P S D o p e n ) .

Metrics