Abstract

Nelson et al. [Appl. Opt. 55, 1757 (2016) [CrossRef]  ] recently concluded that coherent beam combining and remote phase locking of high-power lasers are fundamentally limited by the laser source linewidth. These conclusions are incorrect and not relevant to practical high-power coherently combined laser architectures.

© 2016 Optical Society of America

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References

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  1. W. Nelson, P. Sprangle, and C. C. Davis, “Atmospheric propagation and combining of high power lasers,” Appl. Opt. 55, 1757–1764 (2016).
    [Crossref]
  2. P. Sprangle, B. Hafizi, A. Ting, and R. Fischer, “High-power lasers for directed-energy applications,” Appl. Opt. 54, F201–F209 (2015).
    [Crossref]
  3. A. Brignon, ed., Coherent Laser Beam Combining (Wiley, 2013), Chap. 1–9.
  4. V. Khitrov, K. Farley, R. Leveille, J. Galipeau, I. Majid, S. Christensen, B. Samson, and K. Tankala, “kW level narrow linewidth Yb fiber amplifiers for beam combining,” Proc. SPIE 7686, 76860A (2010).
    [Crossref]
  5. G. D. Goodno, S. J. McNaught, J. E. Rothenberg, T. McComb, P. A. Thielen, M. G. Wickham, and M. E. Weber, “Active phase and polarization locking of a 1.4-kW fiber amplifier,” Opt. Lett. 35, 1542–1544 (2010).
    [Crossref]
  6. I. Dajani, A. Flores, R. Holten, B. Anderson, B. Pulford, and T. Ehrenreich, “Multi-kilowatt power scaling and coherent beam combining of narrow linewidth fiber lasers,” Proc. SPIE 9728, 972801 (2016).
    [Crossref]
  7. R. Yagodkin, N. Platonov, A. Yusim, and V. P. Gapontsev, “>1.5 kW narrow linewidth CW diffraction-limited fiber amplifier with 40 nm bandwidth,” Proc. SPIE 9728, 972807 (2016).
    [Crossref]
  8. The effect of amplitude fluctuations on CBC is not treated correctly in [1]. The behavior of an active phase-locking system is erroneously simulated by equating the complex fields Ui(ω) of all beams i, j at frequencies within the phase-locking control bandwidth Ω, i.e., Ui(ω)=Uj(ω) for |ω−ω0|<Ω, where ω0 is the center optical frequency. But in reality, phase locking does not affect the channel powers, so that in general |Ui(ω)|≠|Uj(ω)|. For the laser oscillator model used in [1], each channel’s RMS power fluctuation is nearly equal to its average power. Even with perfect, infinite-bandwidth phase locking, the coherent combining efficiency of an ensemble of such lasers would be significantly degraded due to power imbalance [9,10]. Hence, regardless of the bandwidth of the PLLs, the architecture of Fig. 1(a) is not viable without some corresponding high bandwidth control to equalize the channel amplitudes (powers). The analysis in [1] makes no mention of amplitude locking, nor is it clear how one might implement amplitude locking without imposing loss.
  9. T. Y. Fan, “The effect of amplitude (power) variations on beam combining efficiency for phased arrays,” IEEE J. Sel. Top. Quantum Electron. 15, 291–293 (2009).
    [Crossref]
  10. G. D. Goodno, C. C. Shih, and J. E. Rothenberg, “Perturbative analysis of coherent combining efficiency with mismatched lasers,” Opt. Express 18, 25403–25414 (2010).
    [Crossref]
  11. S. J. Augst, J. K. Ranka, T. Y. Fan, and A. Sanchez, “Beam combining of ytterbium fiber amplifiers,” J. Opt. Soc. Am. B 24, 1707–1715 (2007).
    [Crossref]
  12. S. J. McNaught, P. A. Thielen, L. N. Adams, J. G. Ho, A. M. Johnson, J. P. Machan, J. E. Rothenberg, C. C. Shih, M. P. Wacks, M. E. Weber, and G. D. Goodno, “Scalable coherent combining of kilowatt fiber amplifiers into a 2.4-kW beam,” IEEE J. Sel. Top. Quantum Electron. 20, 174–181 (2014).
    [Crossref]
  13. 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, 2686–2688 (2011).
    [Crossref]
  14. S. M. Redmond, T. Y. Fan, D. J. Ripin, C. X. Yu, S. J. Augst, P. A. Thielen, J. E. Rothenberg, and G. D. Goodno, “Diffractive coherent combining of a 2.5 kW fiber laser array into a 1.9 kW Gaussian beam,” Opt. Lett. 37, 2832–2834 (2012).
    [Crossref]
  15. A. Flores, T. Ehrenreich, R. Holten, B. Anderson, and I. Dajani, “Multi-kW coherent combining of fiber lasers seeded with pseudo random phase modulated light,” Proc. SPIE 9728, 97281Y (2016).
    [Crossref]
  16. A. Klenke, E. Seise, J. Limpert, and A. Tünnermann, “Basic considerations on coherent combining of ultrashort laser pulses,” Opt. Express 19, 25379–25387 (2011).
    [Crossref]
  17. A. Klenke, S. Breitkopf, M. Kienel, T. Gottschall, T. Eidam, S. Hädrich, J. Rothhardt, J. Limpert, and A. Tünnermann, “530  W, 1.3  mJ, four-channel coherently combined femtosecond fiber chirped-pulse amplification system,” Opt. Lett. 38, 2283–2285 (2013).
    [Crossref]
  18. S. B. Weiss, M. E. Weber, and G. D. Goodno, “Group delay locking of coherently combined broadband lasers,” Opt. Lett. 37, 455–457 (2012).
    [Crossref]
  19. M. A. Vorontsov and T. Weyrauch, “High-power lasers for directed-energy applications: comment,” Appl. Opt. (submitted).
  20. G. Mourou, B. Brocklesby, T. Tajima, and J. Limpert, “The future is fiber accelerators,” Nat. Photonics 7, 258–261 (2013).
    [Crossref]
  21. G. D. Goodno, “Coherently combined fiber lasers for directed energy,” SPIE Newsroom, doi: 10.1117/2.1201409.005621 (12September, 2014).
    [Crossref]

2016 (4)

W. Nelson, P. Sprangle, and C. C. Davis, “Atmospheric propagation and combining of high power lasers,” Appl. Opt. 55, 1757–1764 (2016).
[Crossref]

I. Dajani, A. Flores, R. Holten, B. Anderson, B. Pulford, and T. Ehrenreich, “Multi-kilowatt power scaling and coherent beam combining of narrow linewidth fiber lasers,” Proc. SPIE 9728, 972801 (2016).
[Crossref]

R. Yagodkin, N. Platonov, A. Yusim, and V. P. Gapontsev, “>1.5 kW narrow linewidth CW diffraction-limited fiber amplifier with 40 nm bandwidth,” Proc. SPIE 9728, 972807 (2016).
[Crossref]

A. Flores, T. Ehrenreich, R. Holten, B. Anderson, and I. Dajani, “Multi-kW coherent combining of fiber lasers seeded with pseudo random phase modulated light,” Proc. SPIE 9728, 97281Y (2016).
[Crossref]

2015 (1)

2014 (1)

S. J. McNaught, P. A. Thielen, L. N. Adams, J. G. Ho, A. M. Johnson, J. P. Machan, J. E. Rothenberg, C. C. Shih, M. P. Wacks, M. E. Weber, and G. D. Goodno, “Scalable coherent combining of kilowatt fiber amplifiers into a 2.4-kW beam,” IEEE J. Sel. Top. Quantum Electron. 20, 174–181 (2014).
[Crossref]

2013 (2)

2012 (2)

2011 (2)

2010 (3)

2009 (1)

T. Y. Fan, “The effect of amplitude (power) variations on beam combining efficiency for phased arrays,” IEEE J. Sel. Top. Quantum Electron. 15, 291–293 (2009).
[Crossref]

2007 (1)

Adams, L. N.

S. J. McNaught, P. A. Thielen, L. N. Adams, J. G. Ho, A. M. Johnson, J. P. Machan, J. E. Rothenberg, C. C. Shih, M. P. Wacks, M. E. Weber, and G. D. Goodno, “Scalable coherent combining of kilowatt fiber amplifiers into a 2.4-kW beam,” IEEE J. Sel. Top. Quantum Electron. 20, 174–181 (2014).
[Crossref]

Anderson, B.

A. Flores, T. Ehrenreich, R. Holten, B. Anderson, and I. Dajani, “Multi-kW coherent combining of fiber lasers seeded with pseudo random phase modulated light,” Proc. SPIE 9728, 97281Y (2016).
[Crossref]

I. Dajani, A. Flores, R. Holten, B. Anderson, B. Pulford, and T. Ehrenreich, “Multi-kilowatt power scaling and coherent beam combining of narrow linewidth fiber lasers,” Proc. SPIE 9728, 972801 (2016).
[Crossref]

Augst, S. J.

Breitkopf, S.

Brocklesby, B.

G. Mourou, B. Brocklesby, T. Tajima, and J. Limpert, “The future is fiber accelerators,” Nat. Photonics 7, 258–261 (2013).
[Crossref]

Christensen, S.

V. Khitrov, K. Farley, R. Leveille, J. Galipeau, I. Majid, S. Christensen, B. Samson, and K. Tankala, “kW level narrow linewidth Yb fiber amplifiers for beam combining,” Proc. SPIE 7686, 76860A (2010).
[Crossref]

Dajani, I.

I. Dajani, A. Flores, R. Holten, B. Anderson, B. Pulford, and T. Ehrenreich, “Multi-kilowatt power scaling and coherent beam combining of narrow linewidth fiber lasers,” Proc. SPIE 9728, 972801 (2016).
[Crossref]

A. Flores, T. Ehrenreich, R. Holten, B. Anderson, and I. Dajani, “Multi-kW coherent combining of fiber lasers seeded with pseudo random phase modulated light,” Proc. SPIE 9728, 97281Y (2016).
[Crossref]

Davis, C. C.

Ehrenreich, T.

I. Dajani, A. Flores, R. Holten, B. Anderson, B. Pulford, and T. Ehrenreich, “Multi-kilowatt power scaling and coherent beam combining of narrow linewidth fiber lasers,” Proc. SPIE 9728, 972801 (2016).
[Crossref]

A. Flores, T. Ehrenreich, R. Holten, B. Anderson, and I. Dajani, “Multi-kW coherent combining of fiber lasers seeded with pseudo random phase modulated light,” Proc. SPIE 9728, 97281Y (2016).
[Crossref]

Eidam, T.

Fan, T. Y.

Farley, K.

V. Khitrov, K. Farley, R. Leveille, J. Galipeau, I. Majid, S. Christensen, B. Samson, and K. Tankala, “kW level narrow linewidth Yb fiber amplifiers for beam combining,” Proc. SPIE 7686, 76860A (2010).
[Crossref]

Fischer, R.

Flores, A.

I. Dajani, A. Flores, R. Holten, B. Anderson, B. Pulford, and T. Ehrenreich, “Multi-kilowatt power scaling and coherent beam combining of narrow linewidth fiber lasers,” Proc. SPIE 9728, 972801 (2016).
[Crossref]

A. Flores, T. Ehrenreich, R. Holten, B. Anderson, and I. Dajani, “Multi-kW coherent combining of fiber lasers seeded with pseudo random phase modulated light,” Proc. SPIE 9728, 97281Y (2016).
[Crossref]

Galipeau, J.

V. Khitrov, K. Farley, R. Leveille, J. Galipeau, I. Majid, S. Christensen, B. Samson, and K. Tankala, “kW level narrow linewidth Yb fiber amplifiers for beam combining,” Proc. SPIE 7686, 76860A (2010).
[Crossref]

Gapontsev, V. P.

R. Yagodkin, N. Platonov, A. Yusim, and V. P. Gapontsev, “>1.5 kW narrow linewidth CW diffraction-limited fiber amplifier with 40 nm bandwidth,” Proc. SPIE 9728, 972807 (2016).
[Crossref]

Goldizen, K. C.

Goodno, G. D.

Gottschall, T.

Hädrich, S.

Hafizi, B.

Ho, J. G.

S. J. McNaught, P. A. Thielen, L. N. Adams, J. G. Ho, A. M. Johnson, J. P. Machan, J. E. Rothenberg, C. C. Shih, M. P. Wacks, M. E. Weber, and G. D. Goodno, “Scalable coherent combining of kilowatt fiber amplifiers into a 2.4-kW beam,” IEEE J. Sel. Top. Quantum Electron. 20, 174–181 (2014).
[Crossref]

Holten, R.

I. Dajani, A. Flores, R. Holten, B. Anderson, B. Pulford, and T. Ehrenreich, “Multi-kilowatt power scaling and coherent beam combining of narrow linewidth fiber lasers,” Proc. SPIE 9728, 972801 (2016).
[Crossref]

A. Flores, T. Ehrenreich, R. Holten, B. Anderson, and I. Dajani, “Multi-kW coherent combining of fiber lasers seeded with pseudo random phase modulated light,” Proc. SPIE 9728, 97281Y (2016).
[Crossref]

Johnson, A. M.

S. J. McNaught, P. A. Thielen, L. N. Adams, J. G. Ho, A. M. Johnson, J. P. Machan, J. E. Rothenberg, C. C. Shih, M. P. Wacks, M. E. Weber, and G. D. Goodno, “Scalable coherent combining of kilowatt fiber amplifiers into a 2.4-kW beam,” IEEE J. Sel. Top. Quantum Electron. 20, 174–181 (2014).
[Crossref]

Khitrov, V.

V. Khitrov, K. Farley, R. Leveille, J. Galipeau, I. Majid, S. Christensen, B. Samson, and K. Tankala, “kW level narrow linewidth Yb fiber amplifiers for beam combining,” Proc. SPIE 7686, 76860A (2010).
[Crossref]

Kienel, M.

Klenke, A.

Leveille, R.

V. Khitrov, K. Farley, R. Leveille, J. Galipeau, I. Majid, S. Christensen, B. Samson, and K. Tankala, “kW level narrow linewidth Yb fiber amplifiers for beam combining,” Proc. SPIE 7686, 76860A (2010).
[Crossref]

Limpert, J.

Machan, J. P.

S. J. McNaught, P. A. Thielen, L. N. Adams, J. G. Ho, A. M. Johnson, J. P. Machan, J. E. Rothenberg, C. C. Shih, M. P. Wacks, M. E. Weber, and G. D. Goodno, “Scalable coherent combining of kilowatt fiber amplifiers into a 2.4-kW beam,” IEEE J. Sel. Top. Quantum Electron. 20, 174–181 (2014).
[Crossref]

Majid, I.

V. Khitrov, K. Farley, R. Leveille, J. Galipeau, I. Majid, S. Christensen, B. Samson, and K. Tankala, “kW level narrow linewidth Yb fiber amplifiers for beam combining,” Proc. SPIE 7686, 76860A (2010).
[Crossref]

McComb, T.

McNaught, S. J.

S. J. McNaught, P. A. Thielen, L. N. Adams, J. G. Ho, A. M. Johnson, J. P. Machan, J. E. Rothenberg, C. C. Shih, M. P. Wacks, M. E. Weber, and G. D. Goodno, “Scalable coherent combining of kilowatt fiber amplifiers into a 2.4-kW beam,” IEEE J. Sel. Top. Quantum Electron. 20, 174–181 (2014).
[Crossref]

G. D. Goodno, S. J. McNaught, J. E. Rothenberg, T. McComb, P. A. Thielen, M. G. Wickham, and M. E. Weber, “Active phase and polarization locking of a 1.4-kW fiber amplifier,” Opt. Lett. 35, 1542–1544 (2010).
[Crossref]

Mourou, G.

G. Mourou, B. Brocklesby, T. Tajima, and J. Limpert, “The future is fiber accelerators,” Nat. Photonics 7, 258–261 (2013).
[Crossref]

Murphy, D. V.

Nelson, W.

Platonov, N.

R. Yagodkin, N. Platonov, A. Yusim, and V. P. Gapontsev, “>1.5 kW narrow linewidth CW diffraction-limited fiber amplifier with 40 nm bandwidth,” Proc. SPIE 9728, 972807 (2016).
[Crossref]

Pulford, B.

I. Dajani, A. Flores, R. Holten, B. Anderson, B. Pulford, and T. Ehrenreich, “Multi-kilowatt power scaling and coherent beam combining of narrow linewidth fiber lasers,” Proc. SPIE 9728, 972801 (2016).
[Crossref]

Ranka, J. K.

Redmond, S. M.

Ripin, D. J.

Rothenberg, J. E.

Rothhardt, J.

Samson, B.

V. Khitrov, K. Farley, R. Leveille, J. Galipeau, I. Majid, S. Christensen, B. Samson, and K. Tankala, “kW level narrow linewidth Yb fiber amplifiers for beam combining,” Proc. SPIE 7686, 76860A (2010).
[Crossref]

Sanchez, A.

Seise, E.

Shih, C. C.

S. J. McNaught, P. A. Thielen, L. N. Adams, J. G. Ho, A. M. Johnson, J. P. Machan, J. E. Rothenberg, C. C. Shih, M. P. Wacks, M. E. Weber, and G. D. Goodno, “Scalable coherent combining of kilowatt fiber amplifiers into a 2.4-kW beam,” IEEE J. Sel. Top. Quantum Electron. 20, 174–181 (2014).
[Crossref]

G. D. Goodno, C. C. Shih, and J. E. Rothenberg, “Perturbative analysis of coherent combining efficiency with mismatched lasers,” Opt. Express 18, 25403–25414 (2010).
[Crossref]

Sprangle, P.

Tajima, T.

G. Mourou, B. Brocklesby, T. Tajima, and J. Limpert, “The future is fiber accelerators,” Nat. Photonics 7, 258–261 (2013).
[Crossref]

Tankala, K.

V. Khitrov, K. Farley, R. Leveille, J. Galipeau, I. Majid, S. Christensen, B. Samson, and K. Tankala, “kW level narrow linewidth Yb fiber amplifiers for beam combining,” Proc. SPIE 7686, 76860A (2010).
[Crossref]

Thielen, P. A.

Ting, A.

Tünnermann, A.

Vorontsov, M. A.

M. A. Vorontsov and T. Weyrauch, “High-power lasers for directed-energy applications: comment,” Appl. Opt. (submitted).

Wacks, M. P.

S. J. McNaught, P. A. Thielen, L. N. Adams, J. G. Ho, A. M. Johnson, J. P. Machan, J. E. Rothenberg, C. C. Shih, M. P. Wacks, M. E. Weber, and G. D. Goodno, “Scalable coherent combining of kilowatt fiber amplifiers into a 2.4-kW beam,” IEEE J. Sel. Top. Quantum Electron. 20, 174–181 (2014).
[Crossref]

Weber, M. E.

S. J. McNaught, P. A. Thielen, L. N. Adams, J. G. Ho, A. M. Johnson, J. P. Machan, J. E. Rothenberg, C. C. Shih, M. P. Wacks, M. E. Weber, and G. D. Goodno, “Scalable coherent combining of kilowatt fiber amplifiers into a 2.4-kW beam,” IEEE J. Sel. Top. Quantum Electron. 20, 174–181 (2014).
[Crossref]

S. B. Weiss, M. E. Weber, and G. D. Goodno, “Group delay locking of coherently combined broadband lasers,” Opt. Lett. 37, 455–457 (2012).
[Crossref]

G. D. Goodno, S. J. McNaught, J. E. Rothenberg, T. McComb, P. A. Thielen, M. G. Wickham, and M. E. Weber, “Active phase and polarization locking of a 1.4-kW fiber amplifier,” Opt. Lett. 35, 1542–1544 (2010).
[Crossref]

Weiss, S. B.

Weyrauch, T.

M. A. Vorontsov and T. Weyrauch, “High-power lasers for directed-energy applications: comment,” Appl. Opt. (submitted).

Wickham, M. G.

Yagodkin, R.

R. Yagodkin, N. Platonov, A. Yusim, and V. P. Gapontsev, “>1.5 kW narrow linewidth CW diffraction-limited fiber amplifier with 40 nm bandwidth,” Proc. SPIE 9728, 972807 (2016).
[Crossref]

Yu, C. X.

Yusim, A.

R. Yagodkin, N. Platonov, A. Yusim, and V. P. Gapontsev, “>1.5 kW narrow linewidth CW diffraction-limited fiber amplifier with 40 nm bandwidth,” Proc. SPIE 9728, 972807 (2016).
[Crossref]

Appl. Opt. (2)

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

T. Y. Fan, “The effect of amplitude (power) variations on beam combining efficiency for phased arrays,” IEEE J. Sel. Top. Quantum Electron. 15, 291–293 (2009).
[Crossref]

S. J. McNaught, P. A. Thielen, L. N. Adams, J. G. Ho, A. M. Johnson, J. P. Machan, J. E. Rothenberg, C. C. Shih, M. P. Wacks, M. E. Weber, and G. D. Goodno, “Scalable coherent combining of kilowatt fiber amplifiers into a 2.4-kW beam,” IEEE J. Sel. Top. Quantum Electron. 20, 174–181 (2014).
[Crossref]

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

Nat. Photonics (1)

G. Mourou, B. Brocklesby, T. Tajima, and J. Limpert, “The future is fiber accelerators,” Nat. Photonics 7, 258–261 (2013).
[Crossref]

Opt. Express (2)

Opt. Lett. (5)

Proc. SPIE (4)

A. Flores, T. Ehrenreich, R. Holten, B. Anderson, and I. Dajani, “Multi-kW coherent combining of fiber lasers seeded with pseudo random phase modulated light,” Proc. SPIE 9728, 97281Y (2016).
[Crossref]

V. Khitrov, K. Farley, R. Leveille, J. Galipeau, I. Majid, S. Christensen, B. Samson, and K. Tankala, “kW level narrow linewidth Yb fiber amplifiers for beam combining,” Proc. SPIE 7686, 76860A (2010).
[Crossref]

I. Dajani, A. Flores, R. Holten, B. Anderson, B. Pulford, and T. Ehrenreich, “Multi-kilowatt power scaling and coherent beam combining of narrow linewidth fiber lasers,” Proc. SPIE 9728, 972801 (2016).
[Crossref]

R. Yagodkin, N. Platonov, A. Yusim, and V. P. Gapontsev, “>1.5 kW narrow linewidth CW diffraction-limited fiber amplifier with 40 nm bandwidth,” Proc. SPIE 9728, 972807 (2016).
[Crossref]

Other (4)

The effect of amplitude fluctuations on CBC is not treated correctly in [1]. The behavior of an active phase-locking system is erroneously simulated by equating the complex fields Ui(ω) of all beams i, j at frequencies within the phase-locking control bandwidth Ω, i.e., Ui(ω)=Uj(ω) for |ω−ω0|<Ω, where ω0 is the center optical frequency. But in reality, phase locking does not affect the channel powers, so that in general |Ui(ω)|≠|Uj(ω)|. For the laser oscillator model used in [1], each channel’s RMS power fluctuation is nearly equal to its average power. Even with perfect, infinite-bandwidth phase locking, the coherent combining efficiency of an ensemble of such lasers would be significantly degraded due to power imbalance [9,10]. Hence, regardless of the bandwidth of the PLLs, the architecture of Fig. 1(a) is not viable without some corresponding high bandwidth control to equalize the channel amplitudes (powers). The analysis in [1] makes no mention of amplitude locking, nor is it clear how one might implement amplitude locking without imposing loss.

M. A. Vorontsov and T. Weyrauch, “High-power lasers for directed-energy applications: comment,” Appl. Opt. (submitted).

G. D. Goodno, “Coherently combined fiber lasers for directed energy,” SPIE Newsroom, doi: 10.1117/2.1201409.005621 (12September, 2014).
[Crossref]

A. Brignon, ed., Coherent Laser Beam Combining (Wiley, 2013), Chap. 1–9.

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Figures (1)

Fig. 1.
Fig. 1. (a) CBC architecture of N optically independent lasers with (optional) laser amplifiers. (b) Typical actively phase-locked CBC MOPA architecture with a single MO split to seed N laser amplifier channels.

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