Abstract

A phase controlled beam combining via nonlinear optical conversion is proposed and demonstrated. This process involves the combining of the fields at the second harmonic frequency generated by non-collinear input fields. The arrangement of the excitation configuration allows the generated second-harmonic light waves to propagate collinearly, with phases coherently correlated. The manipulation of the conversion efficiency is then possible with the phase control of the input fields. The combined second-harmonic fields are shown to be conveniently and robustly variable from zero to a maximum value that greatly exceeds the second-harmonic field generated by a single laser beam. By using a self-adaptive control algorithm, it is possible to optimize the output without prior knowledge on each beamlet property. Either the second-harmonic output beam profile or the total second-harmonic output power can be optimized with the control algorithm.

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  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]
  2. V. Daneu, A. Sanchez, T. Y. Fan, H. K. Choi, G. W. Turner, and C. C. Cook, “Spectral beam combining of a broad-stripe diode laser array in an external cavity,” Opt. Lett. 25(6), 405–407 (2000).
    [CrossRef]
  3. S. J. Augst, J. K. Ranka, T. Y. Fan, and A. Sanchez, “Beam combining of ytterbium fiber amplifiers,” J. Opt. Soc. Am. B 24(8), 1707–1715 (2007).
    [CrossRef]
  4. T. H. Loftus, A. M. Thomas, P. R. Hoffman, M. Norsen, R. Royse, A. Liu, and E. C. Honea, “Spectrally Beam-Combined Fiber Lasers for High-Average-Power Applications,” IEEE J. Sel. Top. Quantum Electron. 13(3), 487–497 (2007).
    [CrossRef]
  5. T. H. Loftus, A. M. Thomas, M. Norsen, J. Minelly, P. Jones, E. Honea, S. A. Shakir, S. Hendow, W. Culver, B. Nelson, and M. Fitelson, “Four-Channel, High Power, Passively Phase Locked Fiber Array,” in Advanced Solid-State Photonics, OSA Technical Digest Series (CD) (Optical Society of America, 2008), paper WA4, http://www.opticsinfobase.org/abstract.cfm?URI=ASSP-2008-WA4 .
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    [CrossRef] [PubMed]
  7. D. Engström, S. Hard, and P. Rudquist, “Beam steering by combining two binary phase modulated FLC SLMs,” Proc. SPIE 5181, 132–143 (2003).
    [CrossRef]
  8. 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]
  9. X. S. Xie, M. Li, J. Guo, B. Liang, Z. X. Wang, A. Sinitskii, Y. Xiang, and J. Y. Zhou, “Phase manipulated multi-beam holographic lithography for tunable optical lattices,” Opt. Express 15(11), 7032–7037 (2007), http://www.opticsinfobase.org/abstract.cfm?URI=OE-15-11-7032 .
    [CrossRef] [PubMed]
  10. J. T. Li, Y. K. Liu, X. S. Xie, P. Q. Zhang, B. Liang, L. Yan, J. Y. Zhou, G. Kurizki, D. Jacobs, K. S. Wong, and Y. C. Zhong, “Fabrication of photonic crystals with functional defects by one-step holographic lithography,” Opt. Express 16(17), 12899–12904 (2008), http://www.opticsinfobase.org/abstract.cfm?URI=oe-16-17-12899 .
    [CrossRef] [PubMed]
  11. V. Krylov, A. Rebane, A. G. Kalintsev, H. Schwoerer, and U. P. Wild, “Second-harmonic generation of amplified femtosecond Ti:sapphire laser pulses,” Opt. Lett. 20(2), 198–200 (1995).
    [CrossRef] [PubMed]
  12. K. W. DeLong, R. Trebino, J. Hunter, and W. E. White, “Frequency-resolved optical gating with the use of second-harmonic generation,” J. Opt. Soc. Am. B 11(11), 2206–2215 (1994).
    [CrossRef]
  13. N. Konforti, E. Marom, and S.-T. Wu, “Phase-only modulation with twisted nematic liquid-crystal spatial light modulators,” Opt. Lett. 13(3), 251–253 (1988).
    [CrossRef] [PubMed]
  14. D. Yelin, D. Meshulach, and Y. Silberberg, “Adaptive femtosecond pulse compression,” Opt. Lett. 22(23), 1793–1795 (1997).
    [CrossRef]
  15. W. L. Goffe, G. D. Ferrier, and J. Rogers, “Global optimization of statistical functions with simulated annealing,” J. Econom. 60(1-2), 65–99 (1994).
    [CrossRef]

2008

E. C. Cheung, J. G. Ho, G. D. Goodno, R. R. Rice, J. Rothenberg, P. Thielen, M. Weber, and M. Wickham, “Diffractive-optics-based beam combination of a phase-locked fiber laser array,” Opt. Lett. 33(4), 354–356 (2008).
[CrossRef] [PubMed]

J. T. Li, Y. K. Liu, X. S. Xie, P. Q. Zhang, B. Liang, L. Yan, J. Y. Zhou, G. Kurizki, D. Jacobs, K. S. Wong, and Y. C. Zhong, “Fabrication of photonic crystals with functional defects by one-step holographic lithography,” Opt. Express 16(17), 12899–12904 (2008), http://www.opticsinfobase.org/abstract.cfm?URI=oe-16-17-12899 .
[CrossRef] [PubMed]

2007

X. S. Xie, M. Li, J. Guo, B. Liang, Z. X. Wang, A. Sinitskii, Y. Xiang, and J. Y. Zhou, “Phase manipulated multi-beam holographic lithography for tunable optical lattices,” Opt. Express 15(11), 7032–7037 (2007), http://www.opticsinfobase.org/abstract.cfm?URI=OE-15-11-7032 .
[CrossRef] [PubMed]

S. J. Augst, J. K. Ranka, T. Y. Fan, and A. Sanchez, “Beam combining of ytterbium fiber amplifiers,” J. Opt. Soc. Am. B 24(8), 1707–1715 (2007).
[CrossRef]

T. H. Loftus, A. M. Thomas, P. R. Hoffman, M. Norsen, R. Royse, A. Liu, and E. C. Honea, “Spectrally Beam-Combined Fiber Lasers for High-Average-Power Applications,” IEEE J. Sel. Top. Quantum Electron. 13(3), 487–497 (2007).
[CrossRef]

2005

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

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]

2003

D. Engström, S. Hard, and P. Rudquist, “Beam steering by combining two binary phase modulated FLC SLMs,” Proc. SPIE 5181, 132–143 (2003).
[CrossRef]

2000

V. Daneu, A. Sanchez, T. Y. Fan, H. K. Choi, G. W. Turner, and C. C. Cook, “Spectral beam combining of a broad-stripe diode laser array in an external cavity,” Opt. Lett. 25(6), 405–407 (2000).
[CrossRef]

1997

D. Yelin, D. Meshulach, and Y. Silberberg, “Adaptive femtosecond pulse compression,” Opt. Lett. 22(23), 1793–1795 (1997).
[CrossRef]

1995

V. Krylov, A. Rebane, A. G. Kalintsev, H. Schwoerer, and U. P. Wild, “Second-harmonic generation of amplified femtosecond Ti:sapphire laser pulses,” Opt. Lett. 20(2), 198–200 (1995).
[CrossRef] [PubMed]

1994

K. W. DeLong, R. Trebino, J. Hunter, and W. E. White, “Frequency-resolved optical gating with the use of second-harmonic generation,” J. Opt. Soc. Am. B 11(11), 2206–2215 (1994).
[CrossRef]

W. L. Goffe, G. D. Ferrier, and J. Rogers, “Global optimization of statistical functions with simulated annealing,” J. Econom. 60(1-2), 65–99 (1994).
[CrossRef]

1988

N. Konforti, E. Marom, and S.-T. Wu, “Phase-only modulation with twisted nematic liquid-crystal spatial light modulators,” Opt. Lett. 13(3), 251–253 (1988).
[CrossRef] [PubMed]

Augst, S. J.

S. J. Augst, J. K. Ranka, T. Y. Fan, and A. Sanchez, “Beam combining of ytterbium fiber amplifiers,” J. Opt. Soc. Am. B 24(8), 1707–1715 (2007).
[CrossRef]

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]

Cheung, E. C.

E. C. Cheung, J. G. Ho, G. D. Goodno, R. R. Rice, J. Rothenberg, P. Thielen, M. Weber, and M. Wickham, “Diffractive-optics-based beam combination of a phase-locked fiber laser array,” Opt. Lett. 33(4), 354–356 (2008).
[CrossRef] [PubMed]

Choi, H. K.

V. Daneu, A. Sanchez, T. Y. Fan, H. K. Choi, G. W. Turner, and C. C. Cook, “Spectral beam combining of a broad-stripe diode laser array in an external cavity,” Opt. Lett. 25(6), 405–407 (2000).
[CrossRef]

Cook, C. C.

V. Daneu, A. Sanchez, T. Y. Fan, H. K. Choi, G. W. Turner, and C. C. Cook, “Spectral beam combining of a broad-stripe diode laser array in an external cavity,” Opt. Lett. 25(6), 405–407 (2000).
[CrossRef]

Daneu, V.

V. Daneu, A. Sanchez, T. Y. Fan, H. K. Choi, G. W. Turner, and C. C. Cook, “Spectral beam combining of a broad-stripe diode laser array in an external cavity,” Opt. Lett. 25(6), 405–407 (2000).
[CrossRef]

DeLong, K. W.

K. W. DeLong, R. Trebino, J. Hunter, and W. E. White, “Frequency-resolved optical gating with the use of second-harmonic generation,” J. Opt. Soc. Am. B 11(11), 2206–2215 (1994).
[CrossRef]

Engström, D.

D. Engström, S. Hard, and P. Rudquist, “Beam steering by combining two binary phase modulated FLC SLMs,” Proc. SPIE 5181, 132–143 (2003).
[CrossRef]

Fan, T. Y.

S. J. Augst, J. K. Ranka, T. Y. Fan, and A. Sanchez, “Beam combining of ytterbium fiber amplifiers,” J. Opt. Soc. Am. B 24(8), 1707–1715 (2007).
[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]

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]

V. Daneu, A. Sanchez, T. Y. Fan, H. K. Choi, G. W. Turner, and C. C. Cook, “Spectral beam combining of a broad-stripe diode laser array in an external cavity,” Opt. Lett. 25(6), 405–407 (2000).
[CrossRef]

Ferrier, G. D.

W. L. Goffe, G. D. Ferrier, and J. Rogers, “Global optimization of statistical functions with simulated annealing,” J. Econom. 60(1-2), 65–99 (1994).
[CrossRef]

Goffe, W. L.

W. L. Goffe, G. D. Ferrier, and J. Rogers, “Global optimization of statistical functions with simulated annealing,” J. Econom. 60(1-2), 65–99 (1994).
[CrossRef]

Goodno, G. D.

E. C. Cheung, J. G. Ho, G. D. Goodno, R. R. Rice, J. Rothenberg, P. Thielen, M. Weber, and M. Wickham, “Diffractive-optics-based beam combination of a phase-locked fiber laser array,” Opt. Lett. 33(4), 354–356 (2008).
[CrossRef] [PubMed]

Guo, J.

X. S. Xie, M. Li, J. Guo, B. Liang, Z. X. Wang, A. Sinitskii, Y. Xiang, and J. Y. Zhou, “Phase manipulated multi-beam holographic lithography for tunable optical lattices,” Opt. Express 15(11), 7032–7037 (2007), http://www.opticsinfobase.org/abstract.cfm?URI=OE-15-11-7032 .
[CrossRef] [PubMed]

Hard, S.

D. Engström, S. Hard, and P. Rudquist, “Beam steering by combining two binary phase modulated FLC SLMs,” Proc. SPIE 5181, 132–143 (2003).
[CrossRef]

Ho, J. G.

E. C. Cheung, J. G. Ho, G. D. Goodno, R. R. Rice, J. Rothenberg, P. Thielen, M. Weber, and M. Wickham, “Diffractive-optics-based beam combination of a phase-locked fiber laser array,” Opt. Lett. 33(4), 354–356 (2008).
[CrossRef] [PubMed]

Hoffman, P. R.

T. H. Loftus, A. M. Thomas, P. R. Hoffman, M. Norsen, R. Royse, A. Liu, and E. C. Honea, “Spectrally Beam-Combined Fiber Lasers for High-Average-Power Applications,” IEEE J. Sel. Top. Quantum Electron. 13(3), 487–497 (2007).
[CrossRef]

Honea, E. C.

T. H. Loftus, A. M. Thomas, P. R. Hoffman, M. Norsen, R. Royse, A. Liu, and E. C. Honea, “Spectrally Beam-Combined Fiber Lasers for High-Average-Power Applications,” IEEE J. Sel. Top. Quantum Electron. 13(3), 487–497 (2007).
[CrossRef]

Hunter, J.

K. W. DeLong, R. Trebino, J. Hunter, and W. E. White, “Frequency-resolved optical gating with the use of second-harmonic generation,” J. Opt. Soc. Am. B 11(11), 2206–2215 (1994).
[CrossRef]

Jacobs, D.

J. T. Li, Y. K. Liu, X. S. Xie, P. Q. Zhang, B. Liang, L. Yan, J. Y. Zhou, G. Kurizki, D. Jacobs, K. S. Wong, and Y. C. Zhong, “Fabrication of photonic crystals with functional defects by one-step holographic lithography,” Opt. Express 16(17), 12899–12904 (2008), http://www.opticsinfobase.org/abstract.cfm?URI=oe-16-17-12899 .
[CrossRef] [PubMed]

Kalintsev, A. G.

V. Krylov, A. Rebane, A. G. Kalintsev, H. Schwoerer, and U. P. Wild, “Second-harmonic generation of amplified femtosecond Ti:sapphire laser pulses,” Opt. Lett. 20(2), 198–200 (1995).
[CrossRef] [PubMed]

Konforti, N.

N. Konforti, E. Marom, and S.-T. Wu, “Phase-only modulation with twisted nematic liquid-crystal spatial light modulators,” Opt. Lett. 13(3), 251–253 (1988).
[CrossRef] [PubMed]

Krylov, V.

V. Krylov, A. Rebane, A. G. Kalintsev, H. Schwoerer, and U. P. Wild, “Second-harmonic generation of amplified femtosecond Ti:sapphire laser pulses,” Opt. Lett. 20(2), 198–200 (1995).
[CrossRef] [PubMed]

Kurizki, G.

J. T. Li, Y. K. Liu, X. S. Xie, P. Q. Zhang, B. Liang, L. Yan, J. Y. Zhou, G. Kurizki, D. Jacobs, K. S. Wong, and Y. C. Zhong, “Fabrication of photonic crystals with functional defects by one-step holographic lithography,” Opt. Express 16(17), 12899–12904 (2008), http://www.opticsinfobase.org/abstract.cfm?URI=oe-16-17-12899 .
[CrossRef] [PubMed]

Li, J. T.

J. T. Li, Y. K. Liu, X. S. Xie, P. Q. Zhang, B. Liang, L. Yan, J. Y. Zhou, G. Kurizki, D. Jacobs, K. S. Wong, and Y. C. Zhong, “Fabrication of photonic crystals with functional defects by one-step holographic lithography,” Opt. Express 16(17), 12899–12904 (2008), http://www.opticsinfobase.org/abstract.cfm?URI=oe-16-17-12899 .
[CrossRef] [PubMed]

Li, M.

X. S. Xie, M. Li, J. Guo, B. Liang, Z. X. Wang, A. Sinitskii, Y. Xiang, and J. Y. Zhou, “Phase manipulated multi-beam holographic lithography for tunable optical lattices,” Opt. Express 15(11), 7032–7037 (2007), http://www.opticsinfobase.org/abstract.cfm?URI=OE-15-11-7032 .
[CrossRef] [PubMed]

Liang, B.

J. T. Li, Y. K. Liu, X. S. Xie, P. Q. Zhang, B. Liang, L. Yan, J. Y. Zhou, G. Kurizki, D. Jacobs, K. S. Wong, and Y. C. Zhong, “Fabrication of photonic crystals with functional defects by one-step holographic lithography,” Opt. Express 16(17), 12899–12904 (2008), http://www.opticsinfobase.org/abstract.cfm?URI=oe-16-17-12899 .
[CrossRef] [PubMed]

X. S. Xie, M. Li, J. Guo, B. Liang, Z. X. Wang, A. Sinitskii, Y. Xiang, and J. Y. Zhou, “Phase manipulated multi-beam holographic lithography for tunable optical lattices,” Opt. Express 15(11), 7032–7037 (2007), http://www.opticsinfobase.org/abstract.cfm?URI=OE-15-11-7032 .
[CrossRef] [PubMed]

Liu, A.

T. H. Loftus, A. M. Thomas, P. R. Hoffman, M. Norsen, R. Royse, A. Liu, and E. C. Honea, “Spectrally Beam-Combined Fiber Lasers for High-Average-Power Applications,” IEEE J. Sel. Top. Quantum Electron. 13(3), 487–497 (2007).
[CrossRef]

Liu, Y. K.

J. T. Li, Y. K. Liu, X. S. Xie, P. Q. Zhang, B. Liang, L. Yan, J. Y. Zhou, G. Kurizki, D. Jacobs, K. S. Wong, and Y. C. Zhong, “Fabrication of photonic crystals with functional defects by one-step holographic lithography,” Opt. Express 16(17), 12899–12904 (2008), http://www.opticsinfobase.org/abstract.cfm?URI=oe-16-17-12899 .
[CrossRef] [PubMed]

Loftus, T. H.

T. H. Loftus, A. M. Thomas, P. R. Hoffman, M. Norsen, R. Royse, A. Liu, and E. C. Honea, “Spectrally Beam-Combined Fiber Lasers for High-Average-Power Applications,” IEEE J. Sel. Top. Quantum Electron. 13(3), 487–497 (2007).
[CrossRef]

Marom, E.

N. Konforti, E. Marom, and S.-T. Wu, “Phase-only modulation with twisted nematic liquid-crystal spatial light modulators,” Opt. Lett. 13(3), 251–253 (1988).
[CrossRef] [PubMed]

Meshulach, D.

D. Yelin, D. Meshulach, and Y. Silberberg, “Adaptive femtosecond pulse compression,” Opt. Lett. 22(23), 1793–1795 (1997).
[CrossRef]

Norsen, M.

T. H. Loftus, A. M. Thomas, P. R. Hoffman, M. Norsen, R. Royse, A. Liu, and E. C. Honea, “Spectrally Beam-Combined Fiber Lasers for High-Average-Power Applications,” IEEE J. Sel. Top. Quantum Electron. 13(3), 487–497 (2007).
[CrossRef]

Ranka, J. K.

S. J. Augst, J. K. Ranka, T. Y. Fan, and A. Sanchez, “Beam combining of ytterbium fiber amplifiers,” J. Opt. Soc. Am. B 24(8), 1707–1715 (2007).
[CrossRef]

Rebane, A.

V. Krylov, A. Rebane, A. G. Kalintsev, H. Schwoerer, and U. P. Wild, “Second-harmonic generation of amplified femtosecond Ti:sapphire laser pulses,” Opt. Lett. 20(2), 198–200 (1995).
[CrossRef] [PubMed]

Rice, R. R.

E. C. Cheung, J. G. Ho, G. D. Goodno, R. R. Rice, J. Rothenberg, P. Thielen, M. Weber, and M. Wickham, “Diffractive-optics-based beam combination of a phase-locked fiber laser array,” Opt. Lett. 33(4), 354–356 (2008).
[CrossRef] [PubMed]

Rogers, J.

W. L. Goffe, G. D. Ferrier, and J. Rogers, “Global optimization of statistical functions with simulated annealing,” J. Econom. 60(1-2), 65–99 (1994).
[CrossRef]

Rothenberg, J.

E. C. Cheung, J. G. Ho, G. D. Goodno, R. R. Rice, J. Rothenberg, P. Thielen, M. Weber, and M. Wickham, “Diffractive-optics-based beam combination of a phase-locked fiber laser array,” Opt. Lett. 33(4), 354–356 (2008).
[CrossRef] [PubMed]

Royse, R.

T. H. Loftus, A. M. Thomas, P. R. Hoffman, M. Norsen, R. Royse, A. Liu, and E. C. Honea, “Spectrally Beam-Combined Fiber Lasers for High-Average-Power Applications,” IEEE J. Sel. Top. Quantum Electron. 13(3), 487–497 (2007).
[CrossRef]

Rudquist, P.

D. Engström, S. Hard, and P. Rudquist, “Beam steering by combining two binary phase modulated FLC SLMs,” Proc. SPIE 5181, 132–143 (2003).
[CrossRef]

Sanchez, A.

S. J. Augst, J. K. Ranka, T. Y. Fan, and A. Sanchez, “Beam combining of ytterbium fiber amplifiers,” J. Opt. Soc. Am. B 24(8), 1707–1715 (2007).
[CrossRef]

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]

V. Daneu, A. Sanchez, T. Y. Fan, H. K. Choi, G. W. Turner, and C. C. Cook, “Spectral beam combining of a broad-stripe diode laser array in an external cavity,” Opt. Lett. 25(6), 405–407 (2000).
[CrossRef]

Schwoerer, H.

V. Krylov, A. Rebane, A. G. Kalintsev, H. Schwoerer, and U. P. Wild, “Second-harmonic generation of amplified femtosecond Ti:sapphire laser pulses,” Opt. Lett. 20(2), 198–200 (1995).
[CrossRef] [PubMed]

Silberberg, Y.

D. Yelin, D. Meshulach, and Y. Silberberg, “Adaptive femtosecond pulse compression,” Opt. Lett. 22(23), 1793–1795 (1997).
[CrossRef]

Sinitskii, A.

X. S. Xie, M. Li, J. Guo, B. Liang, Z. X. Wang, A. Sinitskii, Y. Xiang, and J. Y. Zhou, “Phase manipulated multi-beam holographic lithography for tunable optical lattices,” Opt. Express 15(11), 7032–7037 (2007), http://www.opticsinfobase.org/abstract.cfm?URI=OE-15-11-7032 .
[CrossRef] [PubMed]

Thielen, P.

E. C. Cheung, J. G. Ho, G. D. Goodno, R. R. Rice, J. Rothenberg, P. Thielen, M. Weber, and M. Wickham, “Diffractive-optics-based beam combination of a phase-locked fiber laser array,” Opt. Lett. 33(4), 354–356 (2008).
[CrossRef] [PubMed]

Thomas, A. M.

T. H. Loftus, A. M. Thomas, P. R. Hoffman, M. Norsen, R. Royse, A. Liu, and E. C. Honea, “Spectrally Beam-Combined Fiber Lasers for High-Average-Power Applications,” IEEE J. Sel. Top. Quantum Electron. 13(3), 487–497 (2007).
[CrossRef]

Trebino, R.

K. W. DeLong, R. Trebino, J. Hunter, and W. E. White, “Frequency-resolved optical gating with the use of second-harmonic generation,” J. Opt. Soc. Am. B 11(11), 2206–2215 (1994).
[CrossRef]

Turner, G. W.

V. Daneu, A. Sanchez, T. Y. Fan, H. K. Choi, G. W. Turner, and C. C. Cook, “Spectral beam combining of a broad-stripe diode laser array in an external cavity,” Opt. Lett. 25(6), 405–407 (2000).
[CrossRef]

Wang, Z. X.

X. S. Xie, M. Li, J. Guo, B. Liang, Z. X. Wang, A. Sinitskii, Y. Xiang, and J. Y. Zhou, “Phase manipulated multi-beam holographic lithography for tunable optical lattices,” Opt. Express 15(11), 7032–7037 (2007), http://www.opticsinfobase.org/abstract.cfm?URI=OE-15-11-7032 .
[CrossRef] [PubMed]

Weber, M.

E. C. Cheung, J. G. Ho, G. D. Goodno, R. R. Rice, J. Rothenberg, P. Thielen, M. Weber, and M. Wickham, “Diffractive-optics-based beam combination of a phase-locked fiber laser array,” Opt. Lett. 33(4), 354–356 (2008).
[CrossRef] [PubMed]

White, W. E.

K. W. DeLong, R. Trebino, J. Hunter, and W. E. White, “Frequency-resolved optical gating with the use of second-harmonic generation,” J. Opt. Soc. Am. B 11(11), 2206–2215 (1994).
[CrossRef]

Wickham, M.

E. C. Cheung, J. G. Ho, G. D. Goodno, R. R. Rice, J. Rothenberg, P. Thielen, M. Weber, and M. Wickham, “Diffractive-optics-based beam combination of a phase-locked fiber laser array,” Opt. Lett. 33(4), 354–356 (2008).
[CrossRef] [PubMed]

Wild, U. P.

V. Krylov, A. Rebane, A. G. Kalintsev, H. Schwoerer, and U. P. Wild, “Second-harmonic generation of amplified femtosecond Ti:sapphire laser pulses,” Opt. Lett. 20(2), 198–200 (1995).
[CrossRef] [PubMed]

Wong, K. S.

J. T. Li, Y. K. Liu, X. S. Xie, P. Q. Zhang, B. Liang, L. Yan, J. Y. Zhou, G. Kurizki, D. Jacobs, K. S. Wong, and Y. C. Zhong, “Fabrication of photonic crystals with functional defects by one-step holographic lithography,” Opt. Express 16(17), 12899–12904 (2008), http://www.opticsinfobase.org/abstract.cfm?URI=oe-16-17-12899 .
[CrossRef] [PubMed]

Wu, S.-T.

N. Konforti, E. Marom, and S.-T. Wu, “Phase-only modulation with twisted nematic liquid-crystal spatial light modulators,” Opt. Lett. 13(3), 251–253 (1988).
[CrossRef] [PubMed]

Xiang, Y.

X. S. Xie, M. Li, J. Guo, B. Liang, Z. X. Wang, A. Sinitskii, Y. Xiang, and J. Y. Zhou, “Phase manipulated multi-beam holographic lithography for tunable optical lattices,” Opt. Express 15(11), 7032–7037 (2007), http://www.opticsinfobase.org/abstract.cfm?URI=OE-15-11-7032 .
[CrossRef] [PubMed]

Xie, X. S.

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Figures (5)

Fig. 1
Fig. 1

(a) Experimental setup for phase controlled beam combining with nonlinear frequency conversion, (b) configuration of four beams for generating and combining two-SHG signals.

Fig. 2
Fig. 2

Intensity output of the combined SHG beam with the phase delay of one beam. (a) Experimentally observed result and (b) numerical simulation result.

Fig. 3
Fig. 3

Intensity pattern of the combined SHG output with four, (b) six and (c) twelve input beamlets. The corresponding masks are also shown at lower right corner in each figure.

Fig. 4
Fig. 4

Beam profile of (a) the clean SHG output, and (b) the maximum SHG-energy output for the optimized phases of 12 input beamlets.

Fig. 5
Fig. 5

The optimized beam profile of the combined beam for the second harmonic of the Ti:sapphire laser output.

Equations (1)

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E s h g χ ( 2 ω ) [ E ( t ) E ( t ) + E ( t ) E ( t τ ) ] I = E s h g × E s h g *

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