Abstract

We introduce a novel algorithm used in coherent beam combining: double stochastic approximation based on logic comparison (DSAL). Both the theoretical investigation and the numerical simulation indicated that the DSAL method can be convergent efficiently. The coherent beam combining of two W-level fiber amplifiers experiment shows that the whole system in close-loop performs well for long-time observation and nearly 72% combining efficiency was realized. In the further experiment with some improvement, the combining efficiency increased to 81%. This algorithm has widely potential application in coherent beam combining field.

©2009 Optical Society of America

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References

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  1. T. Y. Fan, “Laser Beam Combining for High-Power, High-Radiance Sources,” IEEE J. Sel.Top. Quantum Electron. 11, 567–577 (2005).
    [Crossref]
  2. J. E. Kansky, C. X. Yu, D. V. Murphy, S. E. J. Shaw, R. C. Lawrence, and C. Higgs, “Beam control of a 2D polarization maintaining fiber optic phased array with high-fiber count,” Proc. SPIE. 6306, 1–11 (2006).
  3. Y. Huo, P. K. Cheo, and G. G. King, “Fundamental mode operation of a 19-core phaselocked Yb-doped fiber amplifier,” Opt. Express. 12, 6230–6239 (2004).
    [Crossref] [PubMed]
  4. A. Shirakawa, T. Saitou, T. Sekiguchi, and K. Ueda, “Coherent addition of fiber lasers by use of a fiber coupler, #x201D; Opt. Express. 10, 1167–1172 (2002).
    [PubMed]
  5. 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, 1247–1249 (2006).
    [Crossref] [PubMed]
  6. J. Anderegg, S. Brosnan, E. Cheung, P. Epp, D. Hammons, H. Komine, M. Weber, and M. Wickham, “Coherently Coupled High Power Fiber Arrays,” Proc. SPIE 6102, 1–5 (2006).
  7. R. Xiao, J. Hou, M. Liu, and Z. F. Jiang, “Coherent combining technology of master oscillator power amplifier fiber arrays,” Opt.Express. 16, 2015–2022 (2008).
    [Crossref] [PubMed]
  8. E. C. Cheung, J. G. Ho, G. D. Goodno, R. R. Rice, J. Rothenberg, P. Thielen, M. Weber, and M. Wichham, “Diffractive-optics-based beam combination of a phase-locked fiber laser array,” Opt.Lett. 33, 354–356 (2008).
    [Crossref] [PubMed]
  9. S. J. Augst, T. Y. Fan, and A. Sanchez, “Coherent beam combining and phase noise measurements of ytterbium fiber amplifiers,” Opt. Lett. 29, 474–476(2004).
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    [Crossref] [PubMed]
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  14. 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, 1–12 (2007).
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    [Crossref]

2008 (2)

R. Xiao, J. Hou, M. Liu, and Z. F. Jiang, “Coherent combining technology of master oscillator power amplifier fiber arrays,” Opt.Express. 16, 2015–2022 (2008).
[Crossref] [PubMed]

E. C. Cheung, J. G. Ho, G. D. Goodno, R. R. Rice, J. Rothenberg, P. Thielen, M. Weber, and M. Wichham, “Diffractive-optics-based beam combination of a phase-locked fiber laser array,” Opt.Lett. 33, 354–356 (2008).
[Crossref] [PubMed]

2007 (2)

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, 480–486 (2007).
[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, 1–12 (2007).

2006 (4)

T. M. Shay, V. Benham, J. T. Baker, B. Ward, A. D. Sanchez, M. A. Culpepper, D. Pilkington, J. Spring, D. Nelson, and C. A. Lu, “First experimental demonstration of self-synchronous phase locking of an optical array,” Opt. Express. 14, 12015–12021 (2006).
[Crossref] [PubMed]

J. E. Kansky, C. X. Yu, D. V. Murphy, S. E. J. Shaw, R. C. Lawrence, and C. Higgs, “Beam control of a 2D polarization maintaining fiber optic phased array with high-fiber count,” Proc. SPIE. 6306, 1–11 (2006).

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, 1247–1249 (2006).
[Crossref] [PubMed]

J. Anderegg, S. Brosnan, E. Cheung, P. Epp, D. Hammons, H. Komine, M. Weber, and M. Wickham, “Coherently Coupled High Power Fiber Arrays,” Proc. SPIE 6102, 1–5 (2006).

2005 (2)

T. Y. Fan, “Laser Beam Combining for High-Power, High-Radiance Sources,” IEEE J. Sel.Top. Quantum Electron. 11, 567–577 (2005).
[Crossref]

L. Liu and M. A. Vorontsov, “Phase-Locking of Tiled Fiber Array using SPGD Feedback Controller,” Proc. SPIE. 5895, 1–9 (2005).

2004 (2)

S. J. Augst, T. Y. Fan, and A. Sanchez, “Coherent beam combining and phase noise measurements of ytterbium fiber amplifiers,” Opt. Lett. 29, 474–476(2004).
[Crossref] [PubMed]

Y. Huo, P. K. Cheo, and G. G. King, “Fundamental mode operation of a 19-core phaselocked Yb-doped fiber amplifier,” Opt. Express. 12, 6230–6239 (2004).
[Crossref] [PubMed]

2002 (1)

A. Shirakawa, T. Saitou, T. Sekiguchi, and K. Ueda, “Coherent addition of fiber lasers by use of a fiber coupler, #x201D; Opt. Express. 10, 1167–1172 (2002).
[PubMed]

1998 (1)

1994 (1)

1977 (1)

Anderegg, J.

J. Anderegg, S. Brosnan, E. Cheung, P. Epp, D. Hammons, H. Komine, M. Weber, and M. Wickham, “Coherently Coupled High Power Fiber Arrays,” Proc. SPIE 6102, 1–5 (2006).

Augst, S. J.

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, 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. Nelson, and C. A. Lu, “First experimental demonstration of self-synchronous phase locking of an optical array,” Opt. Express. 14, 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, 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. Nelson, and C. A. Lu, “First experimental demonstration of self-synchronous phase locking of an optical array,” Opt. Express. 14, 12015–12021 (2006).
[Crossref] [PubMed]

Beresnev, L. A.

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, 1–12 (2007).

Brosnan, S.

J. Anderegg, S. Brosnan, E. Cheung, P. Epp, D. Hammons, H. Komine, M. Weber, and M. Wickham, “Coherently Coupled High Power Fiber Arrays,” Proc. SPIE 6102, 1–5 (2006).

Cheo, P. K.

Y. Huo, P. K. Cheo, and G. G. King, “Fundamental mode operation of a 19-core phaselocked Yb-doped fiber amplifier,” Opt. Express. 12, 6230–6239 (2004).
[Crossref] [PubMed]

Cheung, E.

J. Anderegg, S. Brosnan, E. Cheung, P. Epp, D. Hammons, H. Komine, M. Weber, and M. Wickham, “Coherently Coupled High Power Fiber Arrays,” Proc. SPIE 6102, 1–5 (2006).

Cheung, E. C.

E. C. Cheung, J. G. Ho, G. D. Goodno, R. R. Rice, J. Rothenberg, P. Thielen, M. Weber, and M. Wichham, “Diffractive-optics-based beam combination of a phase-locked fiber laser array,” Opt.Lett. 33, 354–356 (2008).
[Crossref] [PubMed]

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, 1247–1249 (2006).
[Crossref] [PubMed]

Culpepper, M. A.

T. M. Shay, V. Benham, J. T. Baker, B. Ward, A. D. Sanchez, M. A. Culpepper, D. Pilkington, J. Spring, D. Nelson, and C. A. Lu, “First experimental demonstration of self-synchronous phase locking of an optical array,” Opt. Express. 14, 12015–12021 (2006).
[Crossref] [PubMed]

Epp, P.

Fan, T. Y.

T. Y. Fan, “Laser Beam Combining for High-Power, High-Radiance Sources,” IEEE J. Sel.Top. Quantum Electron. 11, 567–577 (2005).
[Crossref]

S. J. Augst, T. Y. Fan, and A. Sanchez, “Coherent beam combining and phase noise measurements of ytterbium fiber amplifiers,” Opt. Lett. 29, 474–476(2004).
[Crossref] [PubMed]

Goodno, G. D.

E. C. Cheung, J. G. Ho, G. D. Goodno, R. R. Rice, J. Rothenberg, P. Thielen, M. Weber, and M. Wichham, “Diffractive-optics-based beam combination of a phase-locked fiber laser array,” Opt.Lett. 33, 354–356 (2008).
[Crossref] [PubMed]

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, 1247–1249 (2006).
[Crossref] [PubMed]

Hammons, D.

J. Anderegg, S. Brosnan, E. Cheung, P. Epp, D. Hammons, H. Komine, M. Weber, and M. Wickham, “Coherently Coupled High Power Fiber Arrays,” Proc. SPIE 6102, 1–5 (2006).

Higgs, C.

J. E. Kansky, C. X. Yu, D. V. Murphy, S. E. J. Shaw, R. C. Lawrence, and C. Higgs, “Beam control of a 2D polarization maintaining fiber optic phased array with high-fiber count,” Proc. SPIE. 6306, 1–11 (2006).

Ho, J. G.

E. C. Cheung, J. G. Ho, G. D. Goodno, R. R. Rice, J. Rothenberg, P. Thielen, M. Weber, and M. Wichham, “Diffractive-optics-based beam combination of a phase-locked fiber laser array,” Opt.Lett. 33, 354–356 (2008).
[Crossref] [PubMed]

Hou, J.

R. Xiao, J. Hou, M. Liu, and Z. F. Jiang, “Coherent combining technology of master oscillator power amplifier fiber arrays,” Opt.Express. 16, 2015–2022 (2008).
[Crossref] [PubMed]

Howland, D.

Huo, Y.

Y. Huo, P. K. Cheo, and G. G. King, “Fundamental mode operation of a 19-core phaselocked Yb-doped fiber amplifier,” Opt. Express. 12, 6230–6239 (2004).
[Crossref] [PubMed]

Injeyan, H.

Jiang, Z. F.

R. Xiao, J. Hou, M. Liu, and Z. F. Jiang, “Coherent combining technology of master oscillator power amplifier fiber arrays,” Opt.Express. 16, 2015–2022 (2008).
[Crossref] [PubMed]

Kansky, J. E.

J. E. Kansky, C. X. Yu, D. V. Murphy, S. E. J. Shaw, R. C. Lawrence, and C. Higgs, “Beam control of a 2D polarization maintaining fiber optic phased array with high-fiber count,” Proc. SPIE. 6306, 1–11 (2006).

King, G. G.

Y. Huo, P. K. Cheo, and G. G. King, “Fundamental mode operation of a 19-core phaselocked Yb-doped fiber amplifier,” Opt. Express. 12, 6230–6239 (2004).
[Crossref] [PubMed]

Komine, H.

Lawrence, R. C.

J. E. Kansky, C. X. Yu, D. V. Murphy, S. E. J. Shaw, R. C. Lawrence, and C. Higgs, “Beam control of a 2D polarization maintaining fiber optic phased array with high-fiber count,” Proc. SPIE. 6306, 1–11 (2006).

Liu, L.

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, 1–12 (2007).

L. Liu and M. A. Vorontsov, “Phase-Locking of Tiled Fiber Array using SPGD Feedback Controller,” Proc. SPIE. 5895, 1–9 (2005).

Liu, M.

R. Xiao, J. Hou, M. Liu, and Z. F. Jiang, “Coherent combining technology of master oscillator power amplifier fiber arrays,” Opt.Express. 16, 2015–2022 (2008).
[Crossref] [PubMed]

Long, W.

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, 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. Nelson, and C. A. Lu, “First experimental demonstration of self-synchronous phase locking of an optical array,” Opt. Express. 14, 12015–12021 (2006).
[Crossref] [PubMed]

McClellan, M.

McNaught, S. J.

Murphy, D. V.

J. E. Kansky, C. X. Yu, D. V. Murphy, S. E. J. Shaw, R. C. Lawrence, and C. Higgs, “Beam control of a 2D polarization maintaining fiber optic phased array with high-fiber count,” Proc. SPIE. 6306, 1–11 (2006).

Nabors, C. D.

Nelson, D.

T. M. Shay, V. Benham, J. T. Baker, B. Ward, A. D. Sanchez, M. A. Culpepper, D. Pilkington, J. Spring, D. Nelson, and C. A. Lu, “First experimental demonstration of self-synchronous phase locking of an optical array,” Opt. Express. 14, 12015–12021 (2006).
[Crossref] [PubMed]

O’Meara, T. R.

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, 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. Nelson, and C. A. Lu, “First experimental demonstration of self-synchronous phase locking of an optical array,” Opt. Express. 14, 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. SPIE. 6708, 1–12 (2007).

Redmond, S.

Rice, R. R.

E. C. Cheung, J. G. Ho, G. D. Goodno, R. R. Rice, J. Rothenberg, P. Thielen, M. Weber, and M. Wichham, “Diffractive-optics-based beam combination of a phase-locked fiber laser array,” Opt.Lett. 33, 354–356 (2008).
[Crossref] [PubMed]

Rothenberg, J.

E. C. Cheung, J. G. Ho, G. D. Goodno, R. R. Rice, J. Rothenberg, P. Thielen, M. Weber, and M. Wichham, “Diffractive-optics-based beam combination of a phase-locked fiber laser array,” Opt.Lett. 33, 354–356 (2008).
[Crossref] [PubMed]

Saitou, T.

A. Shirakawa, T. Saitou, T. Sekiguchi, and K. Ueda, “Coherent addition of fiber lasers by use of a fiber coupler, #x201D; Opt. Express. 10, 1167–1172 (2002).
[PubMed]

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, 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. Nelson, and C. A. Lu, “First experimental demonstration of self-synchronous phase locking of an optical array,” Opt. Express. 14, 12015–12021 (2006).
[Crossref] [PubMed]

Sekiguchi, T.

A. Shirakawa, T. Saitou, T. Sekiguchi, and K. Ueda, “Coherent addition of fiber lasers by use of a fiber coupler, #x201D; Opt. Express. 10, 1167–1172 (2002).
[PubMed]

Shaw, S. E. J.

J. E. Kansky, C. X. Yu, D. V. Murphy, S. E. J. Shaw, R. C. Lawrence, and C. Higgs, “Beam control of a 2D polarization maintaining fiber optic phased array with high-fiber count,” Proc. SPIE. 6306, 1–11 (2006).

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, 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. Nelson, and C. A. Lu, “First experimental demonstration of self-synchronous phase locking of an optical array,” Opt. Express. 14, 12015–12021 (2006).
[Crossref] [PubMed]

Shirakawa, A.

A. Shirakawa, T. Saitou, T. Sekiguchi, and K. Ueda, “Coherent addition of fiber lasers by use of a fiber coupler, #x201D; Opt. Express. 10, 1167–1172 (2002).
[PubMed]

Simpson, R.

Sivokon, V. P.

Sollee, J.

Spall, J. C.

J. C. Spall, Introduction to stochastic search and optimization (John Wiley & Sons, Inc.2003).
[Crossref]

Spring, J.

T. M. Shay, V. Benham, J. T. Baker, B. Ward, A. D. Sanchez, M. A. Culpepper, D. Pilkington, J. Spring, D. Nelson, and C. A. Lu, “First experimental demonstration of self-synchronous phase locking of an optical array,” Opt. Express. 14, 12015–12021 (2006).
[Crossref] [PubMed]

Thielen, P.

E. C. Cheung, J. G. Ho, G. D. Goodno, R. R. Rice, J. Rothenberg, P. Thielen, M. Weber, and M. Wichham, “Diffractive-optics-based beam combination of a phase-locked fiber laser array,” Opt.Lett. 33, 354–356 (2008).
[Crossref] [PubMed]

Ueda, K.

A. Shirakawa, T. Saitou, T. Sekiguchi, and K. Ueda, “Coherent addition of fiber lasers by use of a fiber coupler, #x201D; Opt. Express. 10, 1167–1172 (2002).
[PubMed]

Vorontsov, M. A.

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, 1–12 (2007).

L. Liu and M. A. Vorontsov, “Phase-Locking of Tiled Fiber Array using SPGD Feedback Controller,” Proc. SPIE. 5895, 1–9 (2005).

M. A. Vorontsov and V. P. Sivokon, “Stochastic parallel-gradient-descent technique for high-resolution wave-front phase-distortion correction” J. Opt. Soc. Am. A 15, 2745–2758 (1998).
[Crossref]

Ward, B.

T. M. Shay, V. Benham, J. T. Baker, B. Ward, A. D. Sanchez, M. A. Culpepper, D. Pilkington, J. Spring, D. Nelson, and C. A. Lu, “First experimental demonstration of self-synchronous phase locking of an optical array,” Opt. Express. 14, 12015–12021 (2006).
[Crossref] [PubMed]

Weber, M.

E. C. Cheung, J. G. Ho, G. D. Goodno, R. R. Rice, J. Rothenberg, P. Thielen, M. Weber, and M. Wichham, “Diffractive-optics-based beam combination of a phase-locked fiber laser array,” Opt.Lett. 33, 354–356 (2008).
[Crossref] [PubMed]

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, 1247–1249 (2006).
[Crossref] [PubMed]

J. Anderegg, S. Brosnan, E. Cheung, P. Epp, D. Hammons, H. Komine, M. Weber, and M. Wickham, “Coherently Coupled High Power Fiber Arrays,” Proc. SPIE 6102, 1–5 (2006).

Weiss, S. B.

Weyrauch, T.

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, 1–12 (2007).

Wichham, M.

E. C. Cheung, J. G. Ho, G. D. Goodno, R. R. Rice, J. Rothenberg, P. Thielen, M. Weber, and M. Wichham, “Diffractive-optics-based beam combination of a phase-locked fiber laser array,” Opt.Lett. 33, 354–356 (2008).
[Crossref] [PubMed]

Wickham, M.

J. Anderegg, S. Brosnan, E. Cheung, P. Epp, D. Hammons, H. Komine, M. Weber, and M. Wickham, “Coherently Coupled High Power Fiber Arrays,” Proc. SPIE 6102, 1–5 (2006).

Xiao, R.

R. Xiao, J. Hou, M. Liu, and Z. F. Jiang, “Coherent combining technology of master oscillator power amplifier fiber arrays,” Opt.Express. 16, 2015–2022 (2008).
[Crossref] [PubMed]

Yu, C. X.

J. E. Kansky, C. X. Yu, D. V. Murphy, S. E. J. Shaw, R. C. Lawrence, and C. Higgs, “Beam control of a 2D polarization maintaining fiber optic phased array with high-fiber count,” Proc. SPIE. 6306, 1–11 (2006).

Appl. Opt. (1)

IEEE J. Sel. Top. Quantum Electron. (1)

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, 480–486 (2007).
[Crossref]

IEEE J. Sel.Top. Quantum Electron. (1)

T. Y. Fan, “Laser Beam Combining for High-Power, High-Radiance Sources,” IEEE J. Sel.Top. Quantum Electron. 11, 567–577 (2005).
[Crossref]

J. Opt. Soc. Am. (1)

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

Opt. Express. (3)

T. M. Shay, V. Benham, J. T. Baker, B. Ward, A. D. Sanchez, M. A. Culpepper, D. Pilkington, J. Spring, D. Nelson, and C. A. Lu, “First experimental demonstration of self-synchronous phase locking of an optical array,” Opt. Express. 14, 12015–12021 (2006).
[Crossref] [PubMed]

Y. Huo, P. K. Cheo, and G. G. King, “Fundamental mode operation of a 19-core phaselocked Yb-doped fiber amplifier,” Opt. Express. 12, 6230–6239 (2004).
[Crossref] [PubMed]

A. Shirakawa, T. Saitou, T. Sekiguchi, and K. Ueda, “Coherent addition of fiber lasers by use of a fiber coupler, #x201D; Opt. Express. 10, 1167–1172 (2002).
[PubMed]

Opt. Lett. (2)

Opt.Express. (1)

R. Xiao, J. Hou, M. Liu, and Z. F. Jiang, “Coherent combining technology of master oscillator power amplifier fiber arrays,” Opt.Express. 16, 2015–2022 (2008).
[Crossref] [PubMed]

Opt.Lett. (1)

E. C. Cheung, J. G. Ho, G. D. Goodno, R. R. Rice, J. Rothenberg, P. Thielen, M. Weber, and M. Wichham, “Diffractive-optics-based beam combination of a phase-locked fiber laser array,” Opt.Lett. 33, 354–356 (2008).
[Crossref] [PubMed]

Proc. SPIE (1)

J. Anderegg, S. Brosnan, E. Cheung, P. Epp, D. Hammons, H. Komine, M. Weber, and M. Wickham, “Coherently Coupled High Power Fiber Arrays,” Proc. SPIE 6102, 1–5 (2006).

Proc. SPIE. (3)

J. E. Kansky, C. X. Yu, D. V. Murphy, S. E. J. Shaw, R. C. Lawrence, and C. Higgs, “Beam control of a 2D polarization maintaining fiber optic phased array with high-fiber count,” Proc. SPIE. 6306, 1–11 (2006).

L. Liu and M. A. Vorontsov, “Phase-Locking of Tiled Fiber Array using SPGD Feedback Controller,” Proc. SPIE. 5895, 1–9 (2005).

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, 1–12 (2007).

Other (1)

J. C. Spall, Introduction to stochastic search and optimization (John Wiley & Sons, Inc.2003).
[Crossref]

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Figures (8)

Fig. 1.
Fig. 1. Schematic diagram of a CBC system
Fig. 2.
Fig. 2. The effect of the DSAL algorithm (left-to-right: the intensity distribution of near-field, far-field before and after 300 loops up-to-down: the simulation of 1×2, 2×2, 3×3, 4×4, 5×5, 6×6 laser array).
Fig. 3.
Fig. 3. The converging curve of different array
Fig. 4.
Fig. 4. The far-field intensity comparison.
Fig. 5.
Fig. 5. The probability distribution of energy in the pinhole.
Fig. 6.
Fig. 6. Schematic diagram of the experiment system.
Fig. 7.
Fig. 7. Experimental results.
Fig. 8.
Fig. 8. The long-exposure intensity distribution

Equations (7)

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S=exp (σΦ2)+1NxNy[1exp(σΦ2)]
JJ0exp(σΦ2)J0(1σΦ2)
ϕk(m+1)=ϕk(m)+[u(J+J)u(JJ)]·δk
u(J±J)u[(σΦ±δ2σΦ2)]u[k=1N(δk±2ϕk(m))δk]u(σδ22ρσΦσδ)
ϕk(m+1)=ϕk(m)
ϕk(m+1)=ϕk(m)
σm+12σm2=σδ22ρσΦσδ <0

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