Abstract

A novel approach of tip/tilt control by using divergence cost function in stochastic parallel gradient descent (SPGD) algorithm for coherent beam combining (CBC) is proposed and demonstrated experimentally in a seven-channel 2-W fiber amplifier array with both phase-locking and tip/tilt control, for the first time to our best knowledge. Compared with the conventional power-in-the-bucket (PIB) cost function for SPGD optimization, the tip/tilt control using divergence cost function ensures wider correction range, automatic switching control of program, and freedom of camera’s intensity-saturation. Homemade piezoelectric-ring phase-modulator (PZT PM) and adaptive fiber-optics collimator (AFOC) are developed to correct piston- and tip/tilt-type aberrations, respectively. The PIB cost function is employed for phase-locking via maximization of SPGD optimization, while the divergence cost function is used for tip/tilt control via minimization. An average of 432-μrad of divergence metrics in open loop has decreased to 89-μrad when tip/tilt control implemented. In CBC, the power in the full width at half maximum (FWHM) of the main lobe increases by 32 times, and the phase residual error is less than λ/15.

© 2013 Optical Society of America

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2013 (3)

X. Wang, X. L. Wang, P. Zhou, R. Su, C. Geng, X. Li, X. Xu, and B. Shu, “Coherent beam combination of adaptive fiber laser array with tilt-tip and phase-locking control,” Chin. Phys. B22(2), 024206 (2013).
[CrossRef]

C. Geng, B. Zhao, E. Zhang, W. Luo, Y. Tan, Y. Zhu, H. Yang, J. Mu, X. Li, K. Duan, and W. Zhao, “1.5 kW incoherent beam combining of four fiber lasers using adaptive fiber-optics collimators,” IEEE Photon. Technol. Lett.25(13), 1286–1289 (2013).
[CrossRef]

H. Chosrowjan, H. Furuse, M. Fujita, Y. Izawa, J. Kawanaka, N. Miyanaga, K. Hamamoto, and T. Yamada, “Interferometric phase shift compensation technique for high-power, tiled-aperture coherent beam combination,” Opt. Lett.38(8), 1277–1279 (2013).
[CrossRef] [PubMed]

2012 (7)

X. H. Wang, Q. Fu, F. Shen, and C. Rao, “Piston and tilt cophasing of segmented laser array using Shack-Hartmann sensor,” Opt. Express20(4), 4663–4674 (2012).
[CrossRef] [PubMed]

H. Tünnermann, Y. Feng, J. Neumann, D. Kracht, and P. Weßels, “All-fiber coherent beam combining with phase stabilization via differential pump power control,” Opt. Lett.37(7), 1202–1204 (2012).
[CrossRef] [PubMed]

G. D. Goodno and S. B. Weiss, “Automated co-alignment of coherent fiber laser arrays via active phase-locking,” Opt. Express20(14), 14945–14953 (2012).
[CrossRef] [PubMed]

W. R. Huang, J. Montoya, J. E. Kansky, S. M. Redmond, G. W. Turner, and A. Sanchez-Rubio, “High speed, high power one-dimensional beam steering from a 6-element optical phased array,” Opt. Express20(16), 17311–17318 (2012).
[CrossRef] [PubMed]

C. Geng, X. Li, X. Zhang, and C. Rao, “Experimental investigation on coherent beam combination of a three-element fiber array based on target-in-the-loop technique,” Acta Phys. Sin.61, 034204 (2012).

X. Wang, X. L. Wang, P. Zhou, R. Su, C. Geng, X. Li, X. Xu, and B. Shu, “350-W coherent beam combining of fiber amplifiers with tilt-tip and phase-locking control,” IEEE Photon. Technol. Lett.24(19), 1781–1784 (2012).
[CrossRef]

Y. Ma, P. Zhou, K. Zhang, X. Wang, H. Ma, X. Xu, L. Si, Z. Liu, and Y. Zhao, “A coherent beam combination system based on double PZT phase modulators,” Appl. Phys. B107(3), 765–769 (2012).
[CrossRef]

2011 (5)

2010 (1)

2009 (4)

M. A. Vorontsov, T. Weyrauch, L. A. Beresnev, G. W. Carhart, L. Liu, and K. Aschenbach, “Adaptive array of phase-locked fiber collimators: analysis and experimental demonstration,” IEEE J. Sel. Top. Quantum Electron.15(2), 269–280 (2009).
[CrossRef]

P. Zhou, Z. Liu, X. Wang, Y. Ma, H. Ma, and X. Xu, “Coherent beam combination of two-dimensional high power fiber amplifier array using stochastic parallel gradient descent algorithm,” Appl. Phys. Lett.94(23), 231106 (2009).
[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]

P. Bourdon, V. Jolivet, B. Bennai, L. Lombard, D. Goular, G. Canat, and O. Vasseur, “Theoretical analysis and quantitative measurements of fiber amplifier coherent combining on a remote surface through turbulence,” Proc. SPIE7195, 719527, 719527-8 (2009).
[CrossRef]

2008 (1)

2007 (2)

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. SPIE6708, 67080K, 67080K-12 (2007).
[CrossRef]

T. M. Shay, V. Benham, J. T. Baker, A. D. Sanchez, D. Pilkington, and C. A. Lu, “Self-synchronous and self-referenced coherent beam combination for large optical arrays,” IEEE J. Sel. Top. Quantum Electron.13(3), 480–486 (2007).
[CrossRef]

2006 (2)

J. E. Kansky, C. X. Yu, D. V. Murphy, S. E. Shaw, R. C. Lawrence, and C. Higgs, “Beam control of a 2D polarization maintaining fiber optic phased array with high-fiber count,” Proc. SPIE6306, 63060G, 63060G-11 (2006).
[CrossRef]

T. M. Shay, V. Benham, J. T. Baker, B. Ward, A. D. Sanchez, M. A. Culpepper, D. Pilkington, J. Spring, D. J. Nelson, and C. A. Lu, “First experimental demonstration of self-synchronous phase locking of an optical array,” Opt. Express14(25), 12015–12021 (2006).
[CrossRef] [PubMed]

2005 (3)

L. A. Beresnev and M. A. Vorontsov, “Design of adaptive fiber optics collimator for free-space communication laser transceiver,” Proc. SPIE5895, 58950R, 58950R-7 (2005).
[CrossRef]

L. Liu and M. A. Vorontsov, “Phase-locking of tiled fiber array using SPGD feedback controller,” Proc. SPIE5895, 58950P, 58950P-9 (2005).
[CrossRef]

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

1998 (1)

Aschenbach, K.

M. A. Vorontsov, T. Weyrauch, L. A. Beresnev, G. W. Carhart, L. Liu, and K. Aschenbach, “Adaptive array of phase-locked fiber collimators: analysis and experimental demonstration,” IEEE J. Sel. Top. Quantum Electron.15(2), 269–280 (2009).
[CrossRef]

Augst, S. J.

Azarian, A.

Baker, J. T.

T. M. Shay, V. Benham, J. T. Baker, A. D. Sanchez, D. Pilkington, and C. A. Lu, “Self-synchronous and self-referenced coherent beam combination for large optical arrays,” IEEE J. Sel. Top. Quantum Electron.13(3), 480–486 (2007).
[CrossRef]

T. M. Shay, V. Benham, J. T. Baker, B. Ward, A. D. Sanchez, M. A. Culpepper, D. Pilkington, J. Spring, D. J. Nelson, and C. A. Lu, “First experimental demonstration of self-synchronous phase locking of an optical array,” Opt. Express14(25), 12015–12021 (2006).
[CrossRef] [PubMed]

Benham, V.

T. M. Shay, V. Benham, J. T. Baker, A. D. Sanchez, D. Pilkington, and C. A. Lu, “Self-synchronous and self-referenced coherent beam combination for large optical arrays,” IEEE J. Sel. Top. Quantum Electron.13(3), 480–486 (2007).
[CrossRef]

T. M. Shay, V. Benham, J. T. Baker, B. Ward, A. D. Sanchez, M. A. Culpepper, D. Pilkington, J. Spring, D. J. Nelson, and C. A. Lu, “First experimental demonstration of self-synchronous phase locking of an optical array,” Opt. Express14(25), 12015–12021 (2006).
[CrossRef] [PubMed]

Bennai, B.

P. Bourdon, V. Jolivet, B. Bennai, L. Lombard, D. Goular, G. Canat, and O. Vasseur, “Theoretical analysis and quantitative measurements of fiber amplifier coherent combining on a remote surface through turbulence,” Proc. SPIE7195, 719527, 719527-8 (2009).
[CrossRef]

Beresnev, L. A.

T. Weyrauch, M. A. Vorontsov, G. W. Carhart, L. A. Beresnev, A. P. Rostov, E. E. Polnau, and J. J. Liu, “Experimental demonstration of coherent beam combining over a 7 km propagation path,” Opt. Lett.36(22), 4455–4457 (2011).
[CrossRef] [PubMed]

M. A. Vorontsov, T. Weyrauch, L. A. Beresnev, G. W. Carhart, L. Liu, and K. Aschenbach, “Adaptive array of phase-locked fiber collimators: analysis and experimental demonstration,” IEEE J. Sel. Top. Quantum Electron.15(2), 269–280 (2009).
[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. SPIE6708, 67080K, 67080K-12 (2007).
[CrossRef]

L. A. Beresnev and M. A. Vorontsov, “Design of adaptive fiber optics collimator for free-space communication laser transceiver,” Proc. SPIE5895, 58950R, 58950R-7 (2005).
[CrossRef]

Bourdon, P.

L. Lombard, A. Azarian, K. Cadoret, P. Bourdon, D. Goular, G. Canat, V. Jolivet, Y. Jaouën, and O. Vasseur, “Coherent beam combination of narrow-linewidth 1.5 μm fiber amplifiers in a long-pulse regime,” Opt. Lett.36(4), 523–525 (2011).
[CrossRef] [PubMed]

P. Bourdon, V. Jolivet, B. Bennai, L. Lombard, D. Goular, G. Canat, and O. Vasseur, “Theoretical analysis and quantitative measurements of fiber amplifier coherent combining on a remote surface through turbulence,” Proc. SPIE7195, 719527, 719527-8 (2009).
[CrossRef]

Cadoret, K.

Canat, G.

L. Lombard, A. Azarian, K. Cadoret, P. Bourdon, D. Goular, G. Canat, V. Jolivet, Y. Jaouën, and O. Vasseur, “Coherent beam combination of narrow-linewidth 1.5 μm fiber amplifiers in a long-pulse regime,” Opt. Lett.36(4), 523–525 (2011).
[CrossRef] [PubMed]

P. Bourdon, V. Jolivet, B. Bennai, L. Lombard, D. Goular, G. Canat, and O. Vasseur, “Theoretical analysis and quantitative measurements of fiber amplifier coherent combining on a remote surface through turbulence,” Proc. SPIE7195, 719527, 719527-8 (2009).
[CrossRef]

Carhart, G. W.

T. Weyrauch, M. A. Vorontsov, G. W. Carhart, L. A. Beresnev, A. P. Rostov, E. E. Polnau, and J. J. Liu, “Experimental demonstration of coherent beam combining over a 7 km propagation path,” Opt. Lett.36(22), 4455–4457 (2011).
[CrossRef] [PubMed]

M. A. Vorontsov, T. Weyrauch, L. A. Beresnev, G. W. Carhart, L. Liu, and K. Aschenbach, “Adaptive array of phase-locked fiber collimators: analysis and experimental demonstration,” IEEE J. Sel. Top. Quantum Electron.15(2), 269–280 (2009).
[CrossRef]

Chosrowjan, H.

Culpepper, M. A.

Duan, K.

C. Geng, B. Zhao, E. Zhang, W. Luo, Y. Tan, Y. Zhu, H. Yang, J. Mu, X. Li, K. Duan, and W. Zhao, “1.5 kW incoherent beam combining of four fiber lasers using adaptive fiber-optics collimators,” IEEE Photon. Technol. Lett.25(13), 1286–1289 (2013).
[CrossRef]

Fan, T. Y.

Feng, Y.

Fu, Q.

Fujita, M.

Furuse, H.

Geng, C.

X. Wang, X. L. Wang, P. Zhou, R. Su, C. Geng, X. Li, X. Xu, and B. Shu, “Coherent beam combination of adaptive fiber laser array with tilt-tip and phase-locking control,” Chin. Phys. B22(2), 024206 (2013).
[CrossRef]

C. Geng, B. Zhao, E. Zhang, W. Luo, Y. Tan, Y. Zhu, H. Yang, J. Mu, X. Li, K. Duan, and W. Zhao, “1.5 kW incoherent beam combining of four fiber lasers using adaptive fiber-optics collimators,” IEEE Photon. Technol. Lett.25(13), 1286–1289 (2013).
[CrossRef]

C. Geng, X. Li, X. Zhang, and C. Rao, “Experimental investigation on coherent beam combination of a three-element fiber array based on target-in-the-loop technique,” Acta Phys. Sin.61, 034204 (2012).

X. Wang, X. L. Wang, P. Zhou, R. Su, C. Geng, X. Li, X. Xu, and B. Shu, “350-W coherent beam combining of fiber amplifiers with tilt-tip and phase-locking control,” IEEE Photon. Technol. Lett.24(19), 1781–1784 (2012).
[CrossRef]

C. Geng, X. Li, X. Zhang, and C. Rao, “Coherent beam combination of an optical array using adaptive fiber optics collimators,” Opt. Commun.284(24), 5531–5536 (2011).
[CrossRef]

Goldizen, K. C.

Goodno, G. D.

Goular, D.

L. Lombard, A. Azarian, K. Cadoret, P. Bourdon, D. Goular, G. Canat, V. Jolivet, Y. Jaouën, and O. Vasseur, “Coherent beam combination of narrow-linewidth 1.5 μm fiber amplifiers in a long-pulse regime,” Opt. Lett.36(4), 523–525 (2011).
[CrossRef] [PubMed]

P. Bourdon, V. Jolivet, B. Bennai, L. Lombard, D. Goular, G. Canat, and O. Vasseur, “Theoretical analysis and quantitative measurements of fiber amplifier coherent combining on a remote surface through turbulence,” Proc. SPIE7195, 719527, 719527-8 (2009).
[CrossRef]

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]

Hamamoto, K.

Higgs, C.

J. E. Kansky, C. X. Yu, D. V. Murphy, S. E. Shaw, R. C. Lawrence, and C. Higgs, “Beam control of a 2D polarization maintaining fiber optic phased array with high-fiber count,” Proc. SPIE6306, 63060G, 63060G-11 (2006).
[CrossRef]

Huang, W. R.

Izawa, Y.

Jaouën, Y.

Jolivet, V.

L. Lombard, A. Azarian, K. Cadoret, P. Bourdon, D. Goular, G. Canat, V. Jolivet, Y. Jaouën, and O. Vasseur, “Coherent beam combination of narrow-linewidth 1.5 μm fiber amplifiers in a long-pulse regime,” Opt. Lett.36(4), 523–525 (2011).
[CrossRef] [PubMed]

P. Bourdon, V. Jolivet, B. Bennai, L. Lombard, D. Goular, G. Canat, and O. Vasseur, “Theoretical analysis and quantitative measurements of fiber amplifier coherent combining on a remote surface through turbulence,” Proc. SPIE7195, 719527, 719527-8 (2009).
[CrossRef]

Kansky, J. E.

W. R. Huang, J. Montoya, J. E. Kansky, S. M. Redmond, G. W. Turner, and A. Sanchez-Rubio, “High speed, high power one-dimensional beam steering from a 6-element optical phased array,” Opt. Express20(16), 17311–17318 (2012).
[CrossRef] [PubMed]

J. E. Kansky, C. X. Yu, D. V. Murphy, S. E. Shaw, R. C. Lawrence, and C. Higgs, “Beam control of a 2D polarization maintaining fiber optic phased array with high-fiber count,” Proc. SPIE6306, 63060G, 63060G-11 (2006).
[CrossRef]

Kawanaka, J.

Kracht, D.

Lachinova, S. L.

Lawrence, R. C.

J. E. Kansky, C. X. Yu, D. V. Murphy, S. E. Shaw, R. C. Lawrence, and C. Higgs, “Beam control of a 2D polarization maintaining fiber optic phased array with high-fiber count,” Proc. SPIE6306, 63060G, 63060G-11 (2006).
[CrossRef]

Leng, J.

Li, X.

C. Geng, B. Zhao, E. Zhang, W. Luo, Y. Tan, Y. Zhu, H. Yang, J. Mu, X. Li, K. Duan, and W. Zhao, “1.5 kW incoherent beam combining of four fiber lasers using adaptive fiber-optics collimators,” IEEE Photon. Technol. Lett.25(13), 1286–1289 (2013).
[CrossRef]

X. Wang, X. L. Wang, P. Zhou, R. Su, C. Geng, X. Li, X. Xu, and B. Shu, “Coherent beam combination of adaptive fiber laser array with tilt-tip and phase-locking control,” Chin. Phys. B22(2), 024206 (2013).
[CrossRef]

X. Wang, X. L. Wang, P. Zhou, R. Su, C. Geng, X. Li, X. Xu, and B. Shu, “350-W coherent beam combining of fiber amplifiers with tilt-tip and phase-locking control,” IEEE Photon. Technol. Lett.24(19), 1781–1784 (2012).
[CrossRef]

C. Geng, X. Li, X. Zhang, and C. Rao, “Experimental investigation on coherent beam combination of a three-element fiber array based on target-in-the-loop technique,” Acta Phys. Sin.61, 034204 (2012).

C. Geng, X. Li, X. Zhang, and C. Rao, “Coherent beam combination of an optical array using adaptive fiber optics collimators,” Opt. Commun.284(24), 5531–5536 (2011).
[CrossRef]

Liu, J. J.

Liu, L.

M. A. Vorontsov, T. Weyrauch, L. A. Beresnev, G. W. Carhart, L. Liu, and K. Aschenbach, “Adaptive array of phase-locked fiber collimators: analysis and experimental demonstration,” IEEE J. Sel. Top. Quantum Electron.15(2), 269–280 (2009).
[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. SPIE6708, 67080K, 67080K-12 (2007).
[CrossRef]

L. Liu and M. A. Vorontsov, “Phase-locking of tiled fiber array using SPGD feedback controller,” Proc. SPIE5895, 58950P, 58950P-9 (2005).
[CrossRef]

Liu, Z.

Y. Ma, P. Zhou, K. Zhang, X. Wang, H. Ma, X. Xu, L. Si, Z. Liu, and Y. Zhao, “A coherent beam combination system based on double PZT phase modulators,” Appl. Phys. B107(3), 765–769 (2012).
[CrossRef]

X. L. Wang, P. Zhou, Y. Ma, J. Leng, X. Xu, and Z. Liu, “Active phasing a nine-element 1.14 kW all-fiber two-tone MOPA array using SPGD algorithm,” Opt. Lett.36(16), 3121–3123 (2011).
[CrossRef] [PubMed]

P. Zhou, Z. Liu, X. Wang, Y. Ma, H. Ma, and X. Xu, “Coherent beam combination of two-dimensional high power fiber amplifier array using stochastic parallel gradient descent algorithm,” Appl. Phys. Lett.94(23), 231106 (2009).
[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]

Lombard, L.

L. Lombard, A. Azarian, K. Cadoret, P. Bourdon, D. Goular, G. Canat, V. Jolivet, Y. Jaouën, and O. Vasseur, “Coherent beam combination of narrow-linewidth 1.5 μm fiber amplifiers in a long-pulse regime,” Opt. Lett.36(4), 523–525 (2011).
[CrossRef] [PubMed]

P. Bourdon, V. Jolivet, B. Bennai, L. Lombard, D. Goular, G. Canat, and O. Vasseur, “Theoretical analysis and quantitative measurements of fiber amplifier coherent combining on a remote surface through turbulence,” Proc. SPIE7195, 719527, 719527-8 (2009).
[CrossRef]

Lu, C. A.

T. M. Shay, V. Benham, J. T. Baker, A. D. Sanchez, D. Pilkington, and C. A. Lu, “Self-synchronous and self-referenced coherent beam combination for large optical arrays,” IEEE J. Sel. Top. Quantum Electron.13(3), 480–486 (2007).
[CrossRef]

T. M. Shay, V. Benham, J. T. Baker, B. Ward, A. D. Sanchez, M. A. Culpepper, D. Pilkington, J. Spring, D. J. Nelson, and C. A. Lu, “First experimental demonstration of self-synchronous phase locking of an optical array,” Opt. Express14(25), 12015–12021 (2006).
[CrossRef] [PubMed]

Luo, W.

C. Geng, B. Zhao, E. Zhang, W. Luo, Y. Tan, Y. Zhu, H. Yang, J. Mu, X. Li, K. Duan, and W. Zhao, “1.5 kW incoherent beam combining of four fiber lasers using adaptive fiber-optics collimators,” IEEE Photon. Technol. Lett.25(13), 1286–1289 (2013).
[CrossRef]

Ma, H.

Y. Ma, P. Zhou, K. Zhang, X. Wang, H. Ma, X. Xu, L. Si, Z. Liu, and Y. Zhao, “A coherent beam combination system based on double PZT phase modulators,” Appl. Phys. B107(3), 765–769 (2012).
[CrossRef]

P. Zhou, Z. Liu, X. Wang, Y. Ma, H. Ma, and X. Xu, “Coherent beam combination of two-dimensional high power fiber amplifier array using stochastic parallel gradient descent algorithm,” Appl. Phys. Lett.94(23), 231106 (2009).
[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]

Ma, Y.

Y. Ma, P. Zhou, K. Zhang, X. Wang, H. Ma, X. Xu, L. Si, Z. Liu, and Y. Zhao, “A coherent beam combination system based on double PZT phase modulators,” Appl. Phys. B107(3), 765–769 (2012).
[CrossRef]

X. L. Wang, P. Zhou, Y. Ma, J. Leng, X. Xu, and Z. Liu, “Active phasing a nine-element 1.14 kW all-fiber two-tone MOPA array using SPGD algorithm,” Opt. Lett.36(16), 3121–3123 (2011).
[CrossRef] [PubMed]

P. Zhou, Z. Liu, X. Wang, Y. Ma, H. Ma, and X. Xu, “Coherent beam combination of two-dimensional high power fiber amplifier array using stochastic parallel gradient descent algorithm,” Appl. Phys. Lett.94(23), 231106 (2009).
[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]

Miyanaga, N.

Montoya, J.

Mu, J.

C. Geng, B. Zhao, E. Zhang, W. Luo, Y. Tan, Y. Zhu, H. Yang, J. Mu, X. Li, K. Duan, and W. Zhao, “1.5 kW incoherent beam combining of four fiber lasers using adaptive fiber-optics collimators,” IEEE Photon. Technol. Lett.25(13), 1286–1289 (2013).
[CrossRef]

Murphy, D. V.

C. X. Yu, S. J. Augst, S. M. Redmond, K. C. Goldizen, D. V. Murphy, A. Sanchez, and T. Y. Fan, “Coherent combining of a 4 kW, eight-element fiber amplifier array,” Opt. Lett.36(14), 2686–2688 (2011).
[CrossRef] [PubMed]

J. E. Kansky, C. X. Yu, D. V. Murphy, S. E. Shaw, R. C. Lawrence, and C. Higgs, “Beam control of a 2D polarization maintaining fiber optic phased array with high-fiber count,” Proc. SPIE6306, 63060G, 63060G-11 (2006).
[CrossRef]

Nelson, D. J.

Neumann, J.

Pilkington, D.

T. M. Shay, V. Benham, J. T. Baker, A. D. Sanchez, D. Pilkington, and C. A. Lu, “Self-synchronous and self-referenced coherent beam combination for large optical arrays,” IEEE J. Sel. Top. Quantum Electron.13(3), 480–486 (2007).
[CrossRef]

T. M. Shay, V. Benham, J. T. Baker, B. Ward, A. D. Sanchez, M. A. Culpepper, D. Pilkington, J. Spring, D. J. Nelson, and C. A. Lu, “First experimental demonstration of self-synchronous phase locking of an optical array,” Opt. Express14(25), 12015–12021 (2006).
[CrossRef] [PubMed]

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. SPIE6708, 67080K, 67080K-12 (2007).
[CrossRef]

Polnau, E. E.

Rao, C.

X. H. Wang, Q. Fu, F. Shen, and C. Rao, “Piston and tilt cophasing of segmented laser array using Shack-Hartmann sensor,” Opt. Express20(4), 4663–4674 (2012).
[CrossRef] [PubMed]

C. Geng, X. Li, X. Zhang, and C. Rao, “Experimental investigation on coherent beam combination of a three-element fiber array based on target-in-the-loop technique,” Acta Phys. Sin.61, 034204 (2012).

C. Geng, X. Li, X. Zhang, and C. Rao, “Coherent beam combination of an optical array using adaptive fiber optics collimators,” Opt. Commun.284(24), 5531–5536 (2011).
[CrossRef]

Redmond, S. M.

Rostov, A. P.

Rothenberg, J. E.

Sanchez, A.

Sanchez, A. D.

T. M. Shay, V. Benham, J. T. Baker, A. D. Sanchez, D. Pilkington, and C. A. Lu, “Self-synchronous and self-referenced coherent beam combination for large optical arrays,” IEEE J. Sel. Top. Quantum Electron.13(3), 480–486 (2007).
[CrossRef]

T. M. Shay, V. Benham, J. T. Baker, B. Ward, A. D. Sanchez, M. A. Culpepper, D. Pilkington, J. Spring, D. J. Nelson, and C. A. Lu, “First experimental demonstration of self-synchronous phase locking of an optical array,” Opt. Express14(25), 12015–12021 (2006).
[CrossRef] [PubMed]

Sanchez-Rubio, A.

Shaw, S. E.

J. E. Kansky, C. X. Yu, D. V. Murphy, S. E. Shaw, R. C. Lawrence, and C. Higgs, “Beam control of a 2D polarization maintaining fiber optic phased array with high-fiber count,” Proc. SPIE6306, 63060G, 63060G-11 (2006).
[CrossRef]

Shay, T. M.

T. M. Shay, V. Benham, J. T. Baker, A. D. Sanchez, D. Pilkington, and C. A. Lu, “Self-synchronous and self-referenced coherent beam combination for large optical arrays,” IEEE J. Sel. Top. Quantum Electron.13(3), 480–486 (2007).
[CrossRef]

T. M. Shay, V. Benham, J. T. Baker, B. Ward, A. D. Sanchez, M. A. Culpepper, D. Pilkington, J. Spring, D. J. Nelson, and C. A. Lu, “First experimental demonstration of self-synchronous phase locking of an optical array,” Opt. Express14(25), 12015–12021 (2006).
[CrossRef] [PubMed]

Shen, F.

Shih, C. C.

Shu, B.

X. Wang, X. L. Wang, P. Zhou, R. Su, C. Geng, X. Li, X. Xu, and B. Shu, “Coherent beam combination of adaptive fiber laser array with tilt-tip and phase-locking control,” Chin. Phys. B22(2), 024206 (2013).
[CrossRef]

X. Wang, X. L. Wang, P. Zhou, R. Su, C. Geng, X. Li, X. Xu, and B. Shu, “350-W coherent beam combining of fiber amplifiers with tilt-tip and phase-locking control,” IEEE Photon. Technol. Lett.24(19), 1781–1784 (2012).
[CrossRef]

Si, L.

Y. Ma, P. Zhou, K. Zhang, X. Wang, H. Ma, X. Xu, L. Si, Z. Liu, and Y. Zhao, “A coherent beam combination system based on double PZT phase modulators,” Appl. Phys. B107(3), 765–769 (2012).
[CrossRef]

Sivokon, V. P.

Spring, J.

Su, R.

X. Wang, X. L. Wang, P. Zhou, R. Su, C. Geng, X. Li, X. Xu, and B. Shu, “Coherent beam combination of adaptive fiber laser array with tilt-tip and phase-locking control,” Chin. Phys. B22(2), 024206 (2013).
[CrossRef]

X. Wang, X. L. Wang, P. Zhou, R. Su, C. Geng, X. Li, X. Xu, and B. Shu, “350-W coherent beam combining of fiber amplifiers with tilt-tip and phase-locking control,” IEEE Photon. Technol. Lett.24(19), 1781–1784 (2012).
[CrossRef]

Tan, Y.

C. Geng, B. Zhao, E. Zhang, W. Luo, Y. Tan, Y. Zhu, H. Yang, J. Mu, X. Li, K. Duan, and W. Zhao, “1.5 kW incoherent beam combining of four fiber lasers using adaptive fiber-optics collimators,” IEEE Photon. Technol. Lett.25(13), 1286–1289 (2013).
[CrossRef]

Tünnermann, H.

Turner, G. W.

Vasseur, O.

L. Lombard, A. Azarian, K. Cadoret, P. Bourdon, D. Goular, G. Canat, V. Jolivet, Y. Jaouën, and O. Vasseur, “Coherent beam combination of narrow-linewidth 1.5 μm fiber amplifiers in a long-pulse regime,” Opt. Lett.36(4), 523–525 (2011).
[CrossRef] [PubMed]

P. Bourdon, V. Jolivet, B. Bennai, L. Lombard, D. Goular, G. Canat, and O. Vasseur, “Theoretical analysis and quantitative measurements of fiber amplifier coherent combining on a remote surface through turbulence,” Proc. SPIE7195, 719527, 719527-8 (2009).
[CrossRef]

Vorontsov, M. A.

T. Weyrauch, M. A. Vorontsov, G. W. Carhart, L. A. Beresnev, A. P. Rostov, E. E. Polnau, and J. J. Liu, “Experimental demonstration of coherent beam combining over a 7 km propagation path,” Opt. Lett.36(22), 4455–4457 (2011).
[CrossRef] [PubMed]

M. A. Vorontsov, T. Weyrauch, L. A. Beresnev, G. W. Carhart, L. Liu, and K. Aschenbach, “Adaptive array of phase-locked fiber collimators: analysis and experimental demonstration,” IEEE J. Sel. Top. Quantum Electron.15(2), 269–280 (2009).
[CrossRef]

S. L. Lachinova and M. A. Vorontsov, “Laser beam projection with adaptive array of fiber collimators. II. Analysis of atmospheric compensation efficiency,” J. Opt. Soc. Am. A25(8), 1960–1973 (2008).
[CrossRef] [PubMed]

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. SPIE6708, 67080K, 67080K-12 (2007).
[CrossRef]

L. Liu and M. A. Vorontsov, “Phase-locking of tiled fiber array using SPGD feedback controller,” Proc. SPIE5895, 58950P, 58950P-9 (2005).
[CrossRef]

L. A. Beresnev and M. A. Vorontsov, “Design of adaptive fiber optics collimator for free-space communication laser transceiver,” Proc. SPIE5895, 58950R, 58950R-7 (2005).
[CrossRef]

M. A. Vorontsov and V. P. Sivokon, “Stochastic parallel-gradient-descent technique for high-resolution wave-front phase-distortion correction,” J. Opt. Soc. Am. A15(10), 2745–2758 (1998).
[CrossRef]

Wang, X.

X. Wang, X. L. Wang, P. Zhou, R. Su, C. Geng, X. Li, X. Xu, and B. Shu, “Coherent beam combination of adaptive fiber laser array with tilt-tip and phase-locking control,” Chin. Phys. B22(2), 024206 (2013).
[CrossRef]

X. Wang, X. L. Wang, P. Zhou, R. Su, C. Geng, X. Li, X. Xu, and B. Shu, “350-W coherent beam combining of fiber amplifiers with tilt-tip and phase-locking control,” IEEE Photon. Technol. Lett.24(19), 1781–1784 (2012).
[CrossRef]

Y. Ma, P. Zhou, K. Zhang, X. Wang, H. Ma, X. Xu, L. Si, Z. Liu, and Y. Zhao, “A coherent beam combination system based on double PZT phase modulators,” Appl. Phys. B107(3), 765–769 (2012).
[CrossRef]

P. Zhou, Z. Liu, X. Wang, Y. Ma, H. Ma, and X. Xu, “Coherent beam combination of two-dimensional high power fiber amplifier array using stochastic parallel gradient descent algorithm,” Appl. Phys. Lett.94(23), 231106 (2009).
[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]

Wang, X. H.

Wang, X. L.

X. Wang, X. L. Wang, P. Zhou, R. Su, C. Geng, X. Li, X. Xu, and B. Shu, “Coherent beam combination of adaptive fiber laser array with tilt-tip and phase-locking control,” Chin. Phys. B22(2), 024206 (2013).
[CrossRef]

X. Wang, X. L. Wang, P. Zhou, R. Su, C. Geng, X. Li, X. Xu, and B. Shu, “350-W coherent beam combining of fiber amplifiers with tilt-tip and phase-locking control,” IEEE Photon. Technol. Lett.24(19), 1781–1784 (2012).
[CrossRef]

X. L. Wang, P. Zhou, Y. Ma, J. Leng, X. Xu, and Z. Liu, “Active phasing a nine-element 1.14 kW all-fiber two-tone MOPA array using SPGD algorithm,” Opt. Lett.36(16), 3121–3123 (2011).
[CrossRef] [PubMed]

Ward, B.

Weiss, S. B.

Weßels, P.

Weyrauch, T.

T. Weyrauch, M. A. Vorontsov, G. W. Carhart, L. A. Beresnev, A. P. Rostov, E. E. Polnau, and J. J. Liu, “Experimental demonstration of coherent beam combining over a 7 km propagation path,” Opt. Lett.36(22), 4455–4457 (2011).
[CrossRef] [PubMed]

M. A. Vorontsov, T. Weyrauch, L. A. Beresnev, G. W. Carhart, L. Liu, and K. Aschenbach, “Adaptive array of phase-locked fiber collimators: analysis and experimental demonstration,” IEEE J. Sel. Top. Quantum Electron.15(2), 269–280 (2009).
[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. SPIE6708, 67080K, 67080K-12 (2007).
[CrossRef]

Xu, X.

X. Wang, X. L. Wang, P. Zhou, R. Su, C. Geng, X. Li, X. Xu, and B. Shu, “Coherent beam combination of adaptive fiber laser array with tilt-tip and phase-locking control,” Chin. Phys. B22(2), 024206 (2013).
[CrossRef]

X. Wang, X. L. Wang, P. Zhou, R. Su, C. Geng, X. Li, X. Xu, and B. Shu, “350-W coherent beam combining of fiber amplifiers with tilt-tip and phase-locking control,” IEEE Photon. Technol. Lett.24(19), 1781–1784 (2012).
[CrossRef]

Y. Ma, P. Zhou, K. Zhang, X. Wang, H. Ma, X. Xu, L. Si, Z. Liu, and Y. Zhao, “A coherent beam combination system based on double PZT phase modulators,” Appl. Phys. B107(3), 765–769 (2012).
[CrossRef]

X. L. Wang, P. Zhou, Y. Ma, J. Leng, X. Xu, and Z. Liu, “Active phasing a nine-element 1.14 kW all-fiber two-tone MOPA array using SPGD algorithm,” Opt. Lett.36(16), 3121–3123 (2011).
[CrossRef] [PubMed]

P. Zhou, Z. Liu, X. Wang, Y. Ma, H. Ma, and X. Xu, “Coherent beam combination of two-dimensional high power fiber amplifier array using stochastic parallel gradient descent algorithm,” Appl. Phys. Lett.94(23), 231106 (2009).
[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]

Yamada, T.

Yang, H.

C. Geng, B. Zhao, E. Zhang, W. Luo, Y. Tan, Y. Zhu, H. Yang, J. Mu, X. Li, K. Duan, and W. Zhao, “1.5 kW incoherent beam combining of four fiber lasers using adaptive fiber-optics collimators,” IEEE Photon. Technol. Lett.25(13), 1286–1289 (2013).
[CrossRef]

Yu, C. X.

C. X. Yu, S. J. Augst, S. M. Redmond, K. C. Goldizen, D. V. Murphy, A. Sanchez, and T. Y. Fan, “Coherent combining of a 4 kW, eight-element fiber amplifier array,” Opt. Lett.36(14), 2686–2688 (2011).
[CrossRef] [PubMed]

J. E. Kansky, C. X. Yu, D. V. Murphy, S. E. Shaw, R. C. Lawrence, and C. Higgs, “Beam control of a 2D polarization maintaining fiber optic phased array with high-fiber count,” Proc. SPIE6306, 63060G, 63060G-11 (2006).
[CrossRef]

Zhang, E.

C. Geng, B. Zhao, E. Zhang, W. Luo, Y. Tan, Y. Zhu, H. Yang, J. Mu, X. Li, K. Duan, and W. Zhao, “1.5 kW incoherent beam combining of four fiber lasers using adaptive fiber-optics collimators,” IEEE Photon. Technol. Lett.25(13), 1286–1289 (2013).
[CrossRef]

Zhang, K.

Y. Ma, P. Zhou, K. Zhang, X. Wang, H. Ma, X. Xu, L. Si, Z. Liu, and Y. Zhao, “A coherent beam combination system based on double PZT phase modulators,” Appl. Phys. B107(3), 765–769 (2012).
[CrossRef]

Zhang, X.

C. Geng, X. Li, X. Zhang, and C. Rao, “Experimental investigation on coherent beam combination of a three-element fiber array based on target-in-the-loop technique,” Acta Phys. Sin.61, 034204 (2012).

C. Geng, X. Li, X. Zhang, and C. Rao, “Coherent beam combination of an optical array using adaptive fiber optics collimators,” Opt. Commun.284(24), 5531–5536 (2011).
[CrossRef]

Zhao, B.

C. Geng, B. Zhao, E. Zhang, W. Luo, Y. Tan, Y. Zhu, H. Yang, J. Mu, X. Li, K. Duan, and W. Zhao, “1.5 kW incoherent beam combining of four fiber lasers using adaptive fiber-optics collimators,” IEEE Photon. Technol. Lett.25(13), 1286–1289 (2013).
[CrossRef]

Zhao, W.

C. Geng, B. Zhao, E. Zhang, W. Luo, Y. Tan, Y. Zhu, H. Yang, J. Mu, X. Li, K. Duan, and W. Zhao, “1.5 kW incoherent beam combining of four fiber lasers using adaptive fiber-optics collimators,” IEEE Photon. Technol. Lett.25(13), 1286–1289 (2013).
[CrossRef]

Zhao, Y.

Y. Ma, P. Zhou, K. Zhang, X. Wang, H. Ma, X. Xu, L. Si, Z. Liu, and Y. Zhao, “A coherent beam combination system based on double PZT phase modulators,” Appl. Phys. B107(3), 765–769 (2012).
[CrossRef]

Zhou, P.

X. Wang, X. L. Wang, P. Zhou, R. Su, C. Geng, X. Li, X. Xu, and B. Shu, “Coherent beam combination of adaptive fiber laser array with tilt-tip and phase-locking control,” Chin. Phys. B22(2), 024206 (2013).
[CrossRef]

X. Wang, X. L. Wang, P. Zhou, R. Su, C. Geng, X. Li, X. Xu, and B. Shu, “350-W coherent beam combining of fiber amplifiers with tilt-tip and phase-locking control,” IEEE Photon. Technol. Lett.24(19), 1781–1784 (2012).
[CrossRef]

Y. Ma, P. Zhou, K. Zhang, X. Wang, H. Ma, X. Xu, L. Si, Z. Liu, and Y. Zhao, “A coherent beam combination system based on double PZT phase modulators,” Appl. Phys. B107(3), 765–769 (2012).
[CrossRef]

X. L. Wang, P. Zhou, Y. Ma, J. Leng, X. Xu, and Z. Liu, “Active phasing a nine-element 1.14 kW all-fiber two-tone MOPA array using SPGD algorithm,” Opt. Lett.36(16), 3121–3123 (2011).
[CrossRef] [PubMed]

P. Zhou, Z. Liu, X. Wang, Y. Ma, H. Ma, and X. Xu, “Coherent beam combination of two-dimensional high power fiber amplifier array using stochastic parallel gradient descent algorithm,” Appl. Phys. Lett.94(23), 231106 (2009).
[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]

Zhu, Y.

C. Geng, B. Zhao, E. Zhang, W. Luo, Y. Tan, Y. Zhu, H. Yang, J. Mu, X. Li, K. Duan, and W. Zhao, “1.5 kW incoherent beam combining of four fiber lasers using adaptive fiber-optics collimators,” IEEE Photon. Technol. Lett.25(13), 1286–1289 (2013).
[CrossRef]

Acta Phys. Sin. (1)

C. Geng, X. Li, X. Zhang, and C. Rao, “Experimental investigation on coherent beam combination of a three-element fiber array based on target-in-the-loop technique,” Acta Phys. Sin.61, 034204 (2012).

Appl. Phys. B (1)

Y. Ma, P. Zhou, K. Zhang, X. Wang, H. Ma, X. Xu, L. Si, Z. Liu, and Y. Zhao, “A coherent beam combination system based on double PZT phase modulators,” Appl. Phys. B107(3), 765–769 (2012).
[CrossRef]

Appl. Phys. Lett. (1)

P. Zhou, Z. Liu, X. Wang, Y. Ma, H. Ma, and X. Xu, “Coherent beam combination of two-dimensional high power fiber amplifier array using stochastic parallel gradient descent algorithm,” Appl. Phys. Lett.94(23), 231106 (2009).
[CrossRef]

Chin. Phys. B (1)

X. Wang, X. L. Wang, P. Zhou, R. Su, C. Geng, X. Li, X. Xu, and B. Shu, “Coherent beam combination of adaptive fiber laser array with tilt-tip and phase-locking control,” Chin. Phys. B22(2), 024206 (2013).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (4)

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]

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

M. A. Vorontsov, T. Weyrauch, L. A. Beresnev, G. W. Carhart, L. Liu, and K. Aschenbach, “Adaptive array of phase-locked fiber collimators: analysis and experimental demonstration,” IEEE J. Sel. Top. Quantum Electron.15(2), 269–280 (2009).
[CrossRef]

T. M. Shay, V. Benham, J. T. Baker, A. D. Sanchez, D. Pilkington, and C. A. Lu, “Self-synchronous and self-referenced coherent beam combination for large optical arrays,” IEEE J. Sel. Top. Quantum Electron.13(3), 480–486 (2007).
[CrossRef]

IEEE Photon. Technol. Lett. (2)

X. Wang, X. L. Wang, P. Zhou, R. Su, C. Geng, X. Li, X. Xu, and B. Shu, “350-W coherent beam combining of fiber amplifiers with tilt-tip and phase-locking control,” IEEE Photon. Technol. Lett.24(19), 1781–1784 (2012).
[CrossRef]

C. Geng, B. Zhao, E. Zhang, W. Luo, Y. Tan, Y. Zhu, H. Yang, J. Mu, X. Li, K. Duan, and W. Zhao, “1.5 kW incoherent beam combining of four fiber lasers using adaptive fiber-optics collimators,” IEEE Photon. Technol. Lett.25(13), 1286–1289 (2013).
[CrossRef]

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

Opt. Commun. (1)

C. Geng, X. Li, X. Zhang, and C. Rao, “Coherent beam combination of an optical array using adaptive fiber optics collimators,” Opt. Commun.284(24), 5531–5536 (2011).
[CrossRef]

Opt. Express (5)

Opt. Lett. (6)

Proc. SPIE (5)

L. A. Beresnev and M. A. Vorontsov, “Design of adaptive fiber optics collimator for free-space communication laser transceiver,” Proc. SPIE5895, 58950R, 58950R-7 (2005).
[CrossRef]

L. Liu and M. A. Vorontsov, “Phase-locking of tiled fiber array using SPGD feedback controller,” Proc. SPIE5895, 58950P, 58950P-9 (2005).
[CrossRef]

J. E. Kansky, C. X. Yu, D. V. Murphy, S. E. Shaw, R. C. Lawrence, and C. Higgs, “Beam control of a 2D polarization maintaining fiber optic phased array with high-fiber count,” Proc. SPIE6306, 63060G, 63060G-11 (2006).
[CrossRef]

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