Abstract

We report on femtosecond pulse combining with up to four parallel chirped-pulse fiber amplifier channels. Active phase locking is implemented using the LOCSET (Locking of Optical Coherence by Single-detector Electronic-frequency Tagging) single detector feedback technique, resulting in 96.4%, 94.0%, and 93.9% relative combining efficiency with two, three, and four channels respectively. Theoretical and experimental analysis of combining efficiency dependence on amplitude and phase noise shows convergence to a fixed value with increasing number of channels, indicating that multi-channel pulse combining with LOCSET feedback should be scalable to very large numbers of channels.

© 2012 OSA

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2012 (2)

W. H. Renninger, A. Chong, and F. W. Wise, “Pulse shaping and evolution in normal-dispersion mode-locked fiber lasers,” IEEE J. Sel. Top. Quantum Electron.18(1), 389–398 (2012).
[CrossRef]

L. Daniault, M. Hanna, L. Lombard, Y. Zaouter, E. Mottay, D. Goular, P. Bourdon, F. Druon, and P. Georges, “Impact of spectral phase mismatch on femtosecond coherent beam combining systems,” Opt. Lett.37(4), 650–652 (2012).
[CrossRef] [PubMed]

2011 (3)

2010 (6)

2009 (1)

J. Limpert, F. Roser, D. N. Schimpf, E. Seise, T. Eidam, S. Hädrich, J. Rothhardt, C. J. Misas, and A. Tünnermann, “High repetition rate gigawatt peak power fiber laser systems: challenges, design, and experiment,” IEEE J. Sel. Top. Quantum Electron.15(1), 159–169 (2009).
[CrossRef]

2008 (1)

2007 (4)

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]

W. Liang, N. Satyan, F. Aflatouni, A. Yariv, A. Kewitsch, G. Rakuljic, and H. Hashemi, “Coherent beam combining with multilevel optical phase-locked loops,” J. Opt. Soc. Am. B24(12), 2930–2939 (2007).
[CrossRef]

T. Schreiber, D. Schimpf, D. Müller, F. Röser, J. Limpert, and A. Tünnermann, “Influence of pulse shape in self-phase-modulation-limited chirped pulse fiber amplifier systems,” J. Opt. Soc. Am. B24(8), 1809–1814 (2007).
[CrossRef]

G. D. Goodno, C. P. Asman, J. Anderegg, S. Brosnan, E. C. Cheung, D. Hammons, H. Injeyan, H. Komine, W. H. Long, M. McClellan, S. J. McNaught, S. Redmond, R. Simpson, J. Sollee, M. Weber, S. B. Weiss, and M. Wickham, “Brightness-scaling potential of actively phase-locked solid-state laser arrays,” IEEE J. Sel. Top. Quantum Electron.13(3), 460–472 (2007).
[CrossRef]

2006 (2)

2005 (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]

2004 (1)

2003 (1)

J. Anderegg, S. Brosnan, M. Weber, H. Komine, and M. Wickham, “8-W coherently phased 4-element fiber array,” Proc. SPIE4974, 1–6 (2003), doi:.
[CrossRef]

1994 (1)

1993 (1)

M. Tempus, W. Luthy, and H. P. Weber, “Coherent recombination of laser beams with interferometrical phase control,” Appl. Phys., B Photophys. Laser Chem.56(2), 79–83 (1993).
[CrossRef]

1987 (1)

Aflatouni, F.

Alley, T. G.

Anderegg, J.

G. D. Goodno, C. P. Asman, J. Anderegg, S. Brosnan, E. C. Cheung, D. Hammons, H. Injeyan, H. Komine, W. H. Long, M. McClellan, S. J. McNaught, S. Redmond, R. Simpson, J. Sollee, M. Weber, S. B. Weiss, and M. Wickham, “Brightness-scaling potential of actively phase-locked solid-state laser arrays,” IEEE J. Sel. Top. Quantum Electron.13(3), 460–472 (2007).
[CrossRef]

J. Anderegg, S. Brosnan, M. Weber, H. Komine, and M. Wickham, “8-W coherently phased 4-element fiber array,” Proc. SPIE4974, 1–6 (2003), doi:.
[CrossRef]

Andersen, T. V.

Asman, C. P.

G. D. Goodno, C. P. Asman, J. Anderegg, S. Brosnan, E. C. Cheung, D. Hammons, H. Injeyan, H. Komine, W. H. Long, M. McClellan, S. J. McNaught, S. Redmond, R. Simpson, J. Sollee, M. Weber, S. B. Weiss, and M. Wickham, “Brightness-scaling potential of actively phase-locked solid-state laser arrays,” IEEE J. Sel. Top. Quantum Electron.13(3), 460–472 (2007).
[CrossRef]

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(3), 480–486 (2007).
[CrossRef]

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]

Bourdon, P.

Bratcher, A.

Brosnan, S.

G. D. Goodno, C. P. Asman, J. Anderegg, S. Brosnan, E. C. Cheung, D. Hammons, H. Injeyan, H. Komine, W. H. Long, M. McClellan, S. J. McNaught, S. Redmond, R. Simpson, J. Sollee, M. Weber, S. B. Weiss, and M. Wickham, “Brightness-scaling potential of actively phase-locked solid-state laser arrays,” IEEE J. Sel. Top. Quantum Electron.13(3), 460–472 (2007).
[CrossRef]

J. Anderegg, S. Brosnan, M. Weber, H. Komine, and M. Wickham, “8-W coherently phased 4-element fiber array,” Proc. SPIE4974, 1–6 (2003), doi:.
[CrossRef]

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]

G. D. Goodno, C. P. Asman, J. Anderegg, S. Brosnan, E. C. Cheung, D. Hammons, H. Injeyan, H. Komine, W. H. Long, M. McClellan, S. J. McNaught, S. Redmond, R. Simpson, J. Sollee, M. Weber, S. B. Weiss, and M. Wickham, “Brightness-scaling potential of actively phase-locked solid-state laser arrays,” IEEE J. Sel. Top. Quantum Electron.13(3), 460–472 (2007).
[CrossRef]

G. D. Goodno, H. Komine, S. J. McNaught, S. B. Weiss, S. Redmond, W. Long, R. Simpson, E. C. Cheung, D. Howland, P. Epp, M. Weber, M. McClellan, J. Sollee, and H. Injeyan, “Coherent combination of high-power, zigzag slab lasers,” Opt. Lett.31(9), 1247–1249 (2006).
[CrossRef] [PubMed]

Chong, A.

W. H. Renninger, A. Chong, and F. W. Wise, “Pulse shaping and evolution in normal-dispersion mode-locked fiber lasers,” IEEE J. Sel. Top. Quantum Electron.18(1), 389–398 (2012).
[CrossRef]

Clarkson, W. A.

Daniault, L.

Druon, F.

Eidam, T.

T. Eidam, S. Hanf, E. Seise, T. V. Andersen, T. Gabler, C. Wirth, T. Schreiber, J. Limpert, and A. Tünnermann, “Femtosecond fiber CPA system emitting 830 W average output power,” Opt. Lett.35(2), 94–96 (2010).
[CrossRef] [PubMed]

J. Limpert, F. Roser, D. N. Schimpf, E. Seise, T. Eidam, S. Hädrich, J. Rothhardt, C. J. Misas, and A. Tünnermann, “High repetition rate gigawatt peak power fiber laser systems: challenges, design, and experiment,” IEEE J. Sel. Top. Quantum Electron.15(1), 159–169 (2009).
[CrossRef]

Epp, P.

Fan, T. Y.

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]

Flores, A. S.

Gabler, T.

Georges, P.

Goodno, G. D.

Goular, D.

Hädrich, S.

J. Limpert, F. Roser, D. N. Schimpf, E. Seise, T. Eidam, S. Hädrich, J. Rothhardt, C. J. Misas, and A. Tünnermann, “High repetition rate gigawatt peak power fiber laser systems: challenges, design, and experiment,” IEEE J. Sel. Top. Quantum Electron.15(1), 159–169 (2009).
[CrossRef]

Hammons, D.

G. D. Goodno, C. P. Asman, J. Anderegg, S. Brosnan, E. C. Cheung, D. Hammons, H. Injeyan, H. Komine, W. H. Long, M. McClellan, S. J. McNaught, S. Redmond, R. Simpson, J. Sollee, M. Weber, S. B. Weiss, and M. Wickham, “Brightness-scaling potential of actively phase-locked solid-state laser arrays,” IEEE J. Sel. Top. Quantum Electron.13(3), 460–472 (2007).
[CrossRef]

Hanf, S.

Hanna, M.

Hashemi, H.

Ho, J. G.

Holz, M.

Howland, D.

Injeyan, H.

G. D. Goodno, C. P. Asman, J. Anderegg, S. Brosnan, E. C. Cheung, D. Hammons, H. Injeyan, H. Komine, W. H. Long, M. McClellan, S. J. McNaught, S. Redmond, R. Simpson, J. Sollee, M. Weber, S. B. Weiss, and M. Wickham, “Brightness-scaling potential of actively phase-locked solid-state laser arrays,” IEEE J. Sel. Top. Quantum Electron.13(3), 460–472 (2007).
[CrossRef]

G. D. Goodno, H. Komine, S. J. McNaught, S. B. Weiss, S. Redmond, W. Long, R. Simpson, E. C. Cheung, D. Howland, P. Epp, M. Weber, M. McClellan, J. Sollee, and H. Injeyan, “Coherent combination of high-power, zigzag slab lasers,” Opt. Lett.31(9), 1247–1249 (2006).
[CrossRef] [PubMed]

Kewitsch, A.

Klenke, A.

Komine, H.

G. D. Goodno, C. P. Asman, J. Anderegg, S. Brosnan, E. C. Cheung, D. Hammons, H. Injeyan, H. Komine, W. H. Long, M. McClellan, S. J. McNaught, S. Redmond, R. Simpson, J. Sollee, M. Weber, S. B. Weiss, and M. Wickham, “Brightness-scaling potential of actively phase-locked solid-state laser arrays,” IEEE J. Sel. Top. Quantum Electron.13(3), 460–472 (2007).
[CrossRef]

G. D. Goodno, H. Komine, S. J. McNaught, S. B. Weiss, S. Redmond, W. Long, R. Simpson, E. C. Cheung, D. Howland, P. Epp, M. Weber, M. McClellan, J. Sollee, and H. Injeyan, “Coherent combination of high-power, zigzag slab lasers,” Opt. Lett.31(9), 1247–1249 (2006).
[CrossRef] [PubMed]

J. Anderegg, S. Brosnan, M. Weber, H. Komine, and M. Wickham, “8-W coherently phased 4-element fiber array,” Proc. SPIE4974, 1–6 (2003), doi:.
[CrossRef]

Kracht, D.

Leger, J. R.

Liang, W.

Limpert, J.

Lombard, L.

Long, W.

Long, W. H.

G. D. Goodno, C. P. Asman, J. Anderegg, S. Brosnan, E. C. Cheung, D. Hammons, H. Injeyan, H. Komine, W. H. Long, M. McClellan, S. J. McNaught, S. Redmond, R. Simpson, J. Sollee, M. Weber, S. B. Weiss, and M. Wickham, “Brightness-scaling potential of actively phase-locked solid-state laser arrays,” IEEE J. Sel. Top. Quantum Electron.13(3), 460–472 (2007).
[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]

Luthy, W.

M. Tempus, W. Luthy, and H. P. Weber, “Coherent recombination of laser beams with interferometrical phase control,” Appl. Phys., B Photophys. Laser Chem.56(2), 79–83 (1993).
[CrossRef]

McClellan, M.

G. D. Goodno, C. P. Asman, J. Anderegg, S. Brosnan, E. C. Cheung, D. Hammons, H. Injeyan, H. Komine, W. H. Long, M. McClellan, S. J. McNaught, S. Redmond, R. Simpson, J. Sollee, M. Weber, S. B. Weiss, and M. Wickham, “Brightness-scaling potential of actively phase-locked solid-state laser arrays,” IEEE J. Sel. Top. Quantum Electron.13(3), 460–472 (2007).
[CrossRef]

G. D. Goodno, H. Komine, S. J. McNaught, S. B. Weiss, S. Redmond, W. Long, R. Simpson, E. C. Cheung, D. Howland, P. Epp, M. Weber, M. McClellan, J. Sollee, and H. Injeyan, “Coherent combination of high-power, zigzag slab lasers,” Opt. Lett.31(9), 1247–1249 (2006).
[CrossRef] [PubMed]

McNaught, S. J.

G. D. Goodno, C. P. Asman, J. Anderegg, S. Brosnan, E. C. Cheung, D. Hammons, H. Injeyan, H. Komine, W. H. Long, M. McClellan, S. J. McNaught, S. Redmond, R. Simpson, J. Sollee, M. Weber, S. B. Weiss, and M. Wickham, “Brightness-scaling potential of actively phase-locked solid-state laser arrays,” IEEE J. Sel. Top. Quantum Electron.13(3), 460–472 (2007).
[CrossRef]

G. D. Goodno, H. Komine, S. J. McNaught, S. B. Weiss, S. Redmond, W. Long, R. Simpson, E. C. Cheung, D. Howland, P. Epp, M. Weber, M. McClellan, J. Sollee, and H. Injeyan, “Coherent combination of high-power, zigzag slab lasers,” Opt. Lett.31(9), 1247–1249 (2006).
[CrossRef] [PubMed]

Misas, C. J.

J. Limpert, F. Roser, D. N. Schimpf, E. Seise, T. Eidam, S. Hädrich, J. Rothhardt, C. J. Misas, and A. Tünnermann, “High repetition rate gigawatt peak power fiber laser systems: challenges, design, and experiment,” IEEE J. Sel. Top. Quantum Electron.15(1), 159–169 (2009).
[CrossRef]

Mottay, E.

Müller, D.

Nabors, C. D.

Neumann, J.

Nilsson, 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]

Pöld, J. H.

Pulford, B.

Rakuljic, G.

Redmond, S.

G. D. Goodno, C. P. Asman, J. Anderegg, S. Brosnan, E. C. Cheung, D. Hammons, H. Injeyan, H. Komine, W. H. Long, M. McClellan, S. J. McNaught, S. Redmond, R. Simpson, J. Sollee, M. Weber, S. B. Weiss, and M. Wickham, “Brightness-scaling potential of actively phase-locked solid-state laser arrays,” IEEE J. Sel. Top. Quantum Electron.13(3), 460–472 (2007).
[CrossRef]

G. D. Goodno, H. Komine, S. J. McNaught, S. B. Weiss, S. Redmond, W. Long, R. Simpson, E. C. Cheung, D. Howland, P. Epp, M. Weber, M. McClellan, J. Sollee, and H. Injeyan, “Coherent combination of high-power, zigzag slab lasers,” Opt. Lett.31(9), 1247–1249 (2006).
[CrossRef] [PubMed]

Renninger, W. H.

W. H. Renninger, A. Chong, and F. W. Wise, “Pulse shaping and evolution in normal-dispersion mode-locked fiber lasers,” IEEE J. Sel. Top. Quantum Electron.18(1), 389–398 (2012).
[CrossRef]

Rice, R. R.

Richardson, D. J.

Roser, F.

J. Limpert, F. Roser, D. N. Schimpf, E. Seise, T. Eidam, S. Hädrich, J. Rothhardt, C. J. Misas, and A. Tünnermann, “High repetition rate gigawatt peak power fiber laser systems: challenges, design, and experiment,” IEEE J. Sel. Top. Quantum Electron.15(1), 159–169 (2009).
[CrossRef]

Röser, F.

Rothenberg, J.

Rothenberg, J. E.

Rothhardt, J.

J. Limpert, F. Roser, D. N. Schimpf, E. Seise, T. Eidam, S. Hädrich, J. Rothhardt, C. J. Misas, and A. Tünnermann, “High repetition rate gigawatt peak power fiber laser systems: challenges, design, and experiment,” IEEE J. Sel. Top. Quantum Electron.15(1), 159–169 (2009).
[CrossRef]

Sanchez, A.

Sanchez, A. D.

R. Uberna, A. Bratcher, T. G. Alley, A. D. Sanchez, A. S. Flores, and B. Pulford, “Coherent combination of high power fiber amplifiers in a two-dimensional re-imaging waveguide,” Opt. Express18(13), 13547–13553 (2010).
[CrossRef] [PubMed]

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]

Satyan, N.

Schimpf, D.

Schimpf, D. N.

J. Limpert, F. Roser, D. N. Schimpf, E. Seise, T. Eidam, S. Hädrich, J. Rothhardt, C. J. Misas, and A. Tünnermann, “High repetition rate gigawatt peak power fiber laser systems: challenges, design, and experiment,” IEEE J. Sel. Top. Quantum Electron.15(1), 159–169 (2009).
[CrossRef]

Schreiber, T.

Seise, E.

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, “Theory of electronically phased coherent beam combination without a reference beam,” Opt. Express14(25), 12188–12195 (2006).
[CrossRef] [PubMed]

Shih, C. C.

Simpson, R.

G. D. Goodno, C. P. Asman, J. Anderegg, S. Brosnan, E. C. Cheung, D. Hammons, H. Injeyan, H. Komine, W. H. Long, M. McClellan, S. J. McNaught, S. Redmond, R. Simpson, J. Sollee, M. Weber, S. B. Weiss, and M. Wickham, “Brightness-scaling potential of actively phase-locked solid-state laser arrays,” IEEE J. Sel. Top. Quantum Electron.13(3), 460–472 (2007).
[CrossRef]

G. D. Goodno, H. Komine, S. J. McNaught, S. B. Weiss, S. Redmond, W. Long, R. Simpson, E. C. Cheung, D. Howland, P. Epp, M. Weber, M. McClellan, J. Sollee, and H. Injeyan, “Coherent combination of high-power, zigzag slab lasers,” Opt. Lett.31(9), 1247–1249 (2006).
[CrossRef] [PubMed]

Sollee, J.

G. D. Goodno, C. P. Asman, J. Anderegg, S. Brosnan, E. C. Cheung, D. Hammons, H. Injeyan, H. Komine, W. H. Long, M. McClellan, S. J. McNaught, S. Redmond, R. Simpson, J. Sollee, M. Weber, S. B. Weiss, and M. Wickham, “Brightness-scaling potential of actively phase-locked solid-state laser arrays,” IEEE J. Sel. Top. Quantum Electron.13(3), 460–472 (2007).
[CrossRef]

G. D. Goodno, H. Komine, S. J. McNaught, S. B. Weiss, S. Redmond, W. Long, R. Simpson, E. C. Cheung, D. Howland, P. Epp, M. Weber, M. McClellan, J. Sollee, and H. Injeyan, “Coherent combination of high-power, zigzag slab lasers,” Opt. Lett.31(9), 1247–1249 (2006).
[CrossRef] [PubMed]

Swanson, G. J.

Tempus, M.

M. Tempus, W. Luthy, and H. P. Weber, “Coherent recombination of laser beams with interferometrical phase control,” Appl. Phys., B Photophys. Laser Chem.56(2), 79–83 (1993).
[CrossRef]

Thielen, P.

Tiemann, B. G.

R. Uberna, A. Bratcher, and B. G. Tiemann, “Coherent polarization beam combination,” IEEE J. Quantum Electron.46(8), 1191–1196 (2010).
[CrossRef]

Tünnermann, A.

Tünnermann, H.

Uberna, R.

Weber, H. P.

M. Tempus, W. Luthy, and H. P. Weber, “Coherent recombination of laser beams with interferometrical phase control,” Appl. Phys., B Photophys. Laser Chem.56(2), 79–83 (1993).
[CrossRef]

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]

G. D. Goodno, C. P. Asman, J. Anderegg, S. Brosnan, E. C. Cheung, D. Hammons, H. Injeyan, H. Komine, W. H. Long, M. McClellan, S. J. McNaught, S. Redmond, R. Simpson, J. Sollee, M. Weber, S. B. Weiss, and M. Wickham, “Brightness-scaling potential of actively phase-locked solid-state laser arrays,” IEEE J. Sel. Top. Quantum Electron.13(3), 460–472 (2007).
[CrossRef]

G. D. Goodno, H. Komine, S. J. McNaught, S. B. Weiss, S. Redmond, W. Long, R. Simpson, E. C. Cheung, D. Howland, P. Epp, M. Weber, M. McClellan, J. Sollee, and H. Injeyan, “Coherent combination of high-power, zigzag slab lasers,” Opt. Lett.31(9), 1247–1249 (2006).
[CrossRef] [PubMed]

J. Anderegg, S. Brosnan, M. Weber, H. Komine, and M. Wickham, “8-W coherently phased 4-element fiber array,” Proc. SPIE4974, 1–6 (2003), doi:.
[CrossRef]

Weiss, S. B.

G. D. Goodno, C. P. Asman, J. Anderegg, S. Brosnan, E. C. Cheung, D. Hammons, H. Injeyan, H. Komine, W. H. Long, M. McClellan, S. J. McNaught, S. Redmond, R. Simpson, J. Sollee, M. Weber, S. B. Weiss, and M. Wickham, “Brightness-scaling potential of actively phase-locked solid-state laser arrays,” IEEE J. Sel. Top. Quantum Electron.13(3), 460–472 (2007).
[CrossRef]

G. D. Goodno, H. Komine, S. J. McNaught, S. B. Weiss, S. Redmond, W. Long, R. Simpson, E. C. Cheung, D. Howland, P. Epp, M. Weber, M. McClellan, J. Sollee, and H. Injeyan, “Coherent combination of high-power, zigzag slab lasers,” Opt. Lett.31(9), 1247–1249 (2006).
[CrossRef] [PubMed]

Weßels, P.

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]

G. D. Goodno, C. P. Asman, J. Anderegg, S. Brosnan, E. C. Cheung, D. Hammons, H. Injeyan, H. Komine, W. H. Long, M. McClellan, S. J. McNaught, S. Redmond, R. Simpson, J. Sollee, M. Weber, S. B. Weiss, and M. Wickham, “Brightness-scaling potential of actively phase-locked solid-state laser arrays,” IEEE J. Sel. Top. Quantum Electron.13(3), 460–472 (2007).
[CrossRef]

J. Anderegg, S. Brosnan, M. Weber, H. Komine, and M. Wickham, “8-W coherently phased 4-element fiber array,” Proc. SPIE4974, 1–6 (2003), doi:.
[CrossRef]

Willke, B.

Wirth, C.

Wise, F. W.

W. H. Renninger, A. Chong, and F. W. Wise, “Pulse shaping and evolution in normal-dispersion mode-locked fiber lasers,” IEEE J. Sel. Top. Quantum Electron.18(1), 389–398 (2012).
[CrossRef]

Yariv, A.

Zaouter, Y.

Appl. Opt. (1)

Appl. Phys., B Photophys. Laser Chem. (1)

M. Tempus, W. Luthy, and H. P. Weber, “Coherent recombination of laser beams with interferometrical phase control,” Appl. Phys., B Photophys. Laser Chem.56(2), 79–83 (1993).
[CrossRef]

IEEE J. Quantum Electron. (1)

R. Uberna, A. Bratcher, and B. G. Tiemann, “Coherent polarization beam combination,” IEEE J. Quantum Electron.46(8), 1191–1196 (2010).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (5)

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]

J. Limpert, F. Roser, D. N. Schimpf, E. Seise, T. Eidam, S. Hädrich, J. Rothhardt, C. J. Misas, and A. Tünnermann, “High repetition rate gigawatt peak power fiber laser systems: challenges, design, and experiment,” IEEE J. Sel. Top. Quantum Electron.15(1), 159–169 (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]

G. D. Goodno, C. P. Asman, J. Anderegg, S. Brosnan, E. C. Cheung, D. Hammons, H. Injeyan, H. Komine, W. H. Long, M. McClellan, S. J. McNaught, S. Redmond, R. Simpson, J. Sollee, M. Weber, S. B. Weiss, and M. Wickham, “Brightness-scaling potential of actively phase-locked solid-state laser arrays,” IEEE J. Sel. Top. Quantum Electron.13(3), 460–472 (2007).
[CrossRef]

W. H. Renninger, A. Chong, and F. W. Wise, “Pulse shaping and evolution in normal-dispersion mode-locked fiber lasers,” IEEE J. Sel. Top. Quantum Electron.18(1), 389–398 (2012).
[CrossRef]

J. Opt. Soc. Am. B (3)

Opt. Express (6)

Opt. Lett. (7)

L. Daniault, M. Hanna, L. Lombard, Y. Zaouter, E. Mottay, D. Goular, P. Bourdon, F. Druon, and P. Georges, “Impact of spectral phase mismatch on femtosecond coherent beam combining systems,” Opt. Lett.37(4), 650–652 (2012).
[CrossRef] [PubMed]

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]

L. Daniault, M. Hanna, L. Lombard, Y. Zaouter, E. Mottay, D. Goular, P. Bourdon, F. Druon, and P. Georges, “Coherent beam combining of two femtosecond fiber chirped-pulse amplifiers,” Opt. Lett.36(5), 621–623 (2011).
[CrossRef] [PubMed]

G. J. Swanson, J. R. Leger, and M. Holz, “Aperture filling of phase-locked laser arrays,” Opt. Lett.12(4), 245–247 (1987).
[CrossRef] [PubMed]

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]

G. D. Goodno, H. Komine, S. J. McNaught, S. B. Weiss, S. Redmond, W. Long, R. Simpson, E. C. Cheung, D. Howland, P. Epp, M. Weber, M. McClellan, J. Sollee, and H. Injeyan, “Coherent combination of high-power, zigzag slab lasers,” Opt. Lett.31(9), 1247–1249 (2006).
[CrossRef] [PubMed]

T. Eidam, S. Hanf, E. Seise, T. V. Andersen, T. Gabler, C. Wirth, T. Schreiber, J. Limpert, and A. Tünnermann, “Femtosecond fiber CPA system emitting 830 W average output power,” Opt. Lett.35(2), 94–96 (2010).
[CrossRef] [PubMed]

Proc. SPIE (1)

J. Anderegg, S. Brosnan, M. Weber, H. Komine, and M. Wickham, “8-W coherently phased 4-element fiber array,” Proc. SPIE4974, 1–6 (2003), doi:.
[CrossRef]

Other (1)

E. C. Cheung, M. Weber, and R. R. Rice, “Phase locking of a pulsed fiber amplifier,” in Advanced Solid-State Photonics, OSA Technical Digest Series (CD) (Optical Society of America, 2008), paper WA2.

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Figures (12)

Fig. 1
Fig. 1

Experimental setup for four channel monolithic fiber pulse combining.

Fig. 2
Fig. 2

Schematic and 3D rendering of the micro-optic delay line.

Fig. 3
Fig. 3

Power noise in the unlocked state for one, two, three, and four channels: (a) time domain, (b) frequency domain. The DET data indicates our detector noise floor.

Fig. 4
Fig. 4

Pulse quality results: (a) normalized spectrum of individual channels and all four channels combined, (b) normalized autocorrelation traces of individual channels and all four channels combined – the dashed line shows the calculated (from the spectral measurement) bandwidth limited autocorrelation of the combined pulse.

Fig. 5
Fig. 5

Combining efficiency and power noise: (a) combining efficiency for two, three, and four channel locking over a five minute time period, (b) four channel locked and unlocked noise.

Fig. 6
Fig. 6

Four channel combining efficiency with feedback blocks. The momentary drop-outs in the combined signal are due to intentional interruptions to demonstrate system robustness and its reaction to abrupt external interruptions in system operation.

Fig. 7
Fig. 7

Effect of phase modulation on the combining efficiency: (a) experimental and theoretical combining efficiency as a function of phase modulation amplitude, (b) theoretical combining efficiency as a function of number of channels for different values of phase modulation amplitude.

Fig. 8
Fig. 8

Scalability of a multi-channel combining system with LOCSET locking at β = 0.25 and different magnitudes of errors: (a) only power variation errors, (b) only temporal phase errors.

Fig. 9
Fig. 9

Combining efficiency for very large arrays as a function of power and phase noise magnitude: (a) combining efficiency as a function of amplitude noise only, and (b) of phase noise only.

Fig. 10
Fig. 10

Beam splitter: (a) when only beam P1 is present, (b) when only beam P2 is present.

Fig. 11
Fig. 11

Beam combiner.

Fig. 12
Fig. 12

Schematic of a general N→1 binary-tree beam combiner.

Equations (37)

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η relative = P comb ( k=1,N P k out ) 2 .
η relative (β)= k=1 N P k out + k=2 N 2 P 1 out P k out J 0 (β) + k=2 N m=2, mk N P m out P k out J 0 2 (β) ( k=1 N P k out ) 2 ,
η relative = k=1 N P k out + k=2 N 2 P 1 out P k out cos( ϕ k ϕ 1 ) J 0 (β) + k=2 N m=2, mk N P m out P k out cos( ϕ k ϕ m ) J 0 2 (β) ( k=1 N P k out ) 2 .
< η relative >= N+ [ 1 1 8 ( σ P P avg out ) 2 3 16 ( σ P P avg out ) 4 ] 2 e σ ϕ 2 J 0 (β)[ 2(N1)+(N1)(N2) J 0 (β) ] N 2 .
P comb =c ε 0 nA ( E 1 out cos( ωt+ ϕ 1 )+ E 2 out cos( ωt+ ϕ 2 ) ) 2 = P 1 out + P 2 out +2 P 1 out P 2 out cosΔϕ.
P comb_inphase = P 1 out + P 2 out +2 P 1 out P 2 out = ( P 1 out + P 2 out ) 2 .
P 1 / = X 1 P tot / .
P 1 in P 2 in = X 1 η 2 X 2 η 1 = X 1 η 2 ( 1 X 1 ) η 1 .
P comb_MAX = ( P 1 out + P 2 out ) 2 = ( X 1 P tot / +( 1 X 1 ) P tot / ) 2 = P tot / = η 1 P 1 in + η 2 P 2 in .
η abs = P comb P 1 in + P 2 in ; η relative = P comb P comb_MAX ; η combiner = P comb_MAX P 1 in + P 2 in = η 1 P 1 in + η 2 P 2 in P 1 in + P 2 in .
η abs = η combiner η relative .
K= 2 m1 + 2 m2 +...+ 2 0 = 2 m 1=N1.
k m / k m / , k m1 / ,..., k i / ,..., k 2 / , k 1 / .
P k m out = η k m m X k m m ... η k i i X k i i ... η k 1 1 X k 1 1 P k m in ,
E ˜ comb =( η 1 1 X 1 1 E 1 1 e i ϕ 1 1 + η 2 1 X 2 1 E 2 1 e i ϕ 2 1 ).
E 1 1 =( η 1 2 X 1 2 E 1 2 e i ϕ 1 2 + η 2 2 X 2 2 E 2 2 e i ϕ 2 2 ), E 2 1 =( η 3 2 X 3 2 E 3 2 e i φ 3 2 + η 4 2 X 4 2 E 4 2 e i φ 4 2 ).
E ˜ comb = k m =1,N η k m m X k m m ... η k 1 1 X k 1 1 E k m in e i( ωt+ ϕ km m +...+ ϕ k1 1 ) .
E ˜ comb = k m =1,N η k m m X k m m ... η k 1 1 X k 1 1 E k m in e i( ωt+ ϕ km out ) .
P comb =c ε 0 nA ( 1 2 k m =1,N η k m m X k m m ... η k 1 1 X k 1 1 E k m in e i( ωt+ ϕ km out ) + 1 2 c.c. ) 2 = c ε 0 nA 2 k n =1,N k m =1,N η k n n X k n n ... η k 1 1 X k 1 1 η k m m X k m m ... η k 1 1 X k 1 1 × E k n in E k m in cos( ϕ km out ϕ kn out ) = i=1,N P i out + j=1,N ji i=1,N P j out P i out cosΔ ϕ ji .
P comb_MAX = ( i=1,N P i out ) 2 .
Lets denote P k m / = η k m m ... η k i i ... η k 1 1 P k m in and P tot / = k m =1,N P k m /
P k m out = η k m m X k m m ... η k i i X k i i ... η k 1 1 X k 1 1 P k m in = X k m m ... X k i i ... X k 1 1 P k m / .
P k m / = X k m m ... X k i i ... X k 1 1 P tot / .
P comb_MAX = P tot / ( k m =1,N ( X k m m ... X k i i ... X k 1 1 ) ) 2 .
k m =1,N ( X k m m ... X k i i ... X k 1 1 ) =1.
P comb_MAX = P tot / = k m =1,N P k m / = k m =1,N ( η k m m ... η k i i ... η k 1 1 P k m in ) .
η abs = P comb k m =1,N P k m in ,
η relative = P comb P comb_MAX = P comb ( k m =1,N P k m out ) 2 = P comb k m =1,N ( η k m m ... η k i i ... η k 1 1 P k m in ) ,
η combiner = P comb_MAX k m =1,N P k m in = ( k m =1,N P k m out ) 2 k m =1,N P k m in = k m =1,N ( η k m m ... η k i i ... η k 1 1 P k m in ) k m =1,N P k m in .
η abs = η combiner η relative .
E comb (t)= E 1 out cos( ω L t+ ϕ 1 )+ k=2 N E k out cos( ω L t+ ϕ k + β k sin( ω k t ) ) ,
P comb (t,β)= c ε 0 nA T t 1 2 T t+ 1 2 T | E comb (τ) | 2 dτ =c ε 0 nA [ 1 2 k=1 N E k out E k out + k=2 N E 1 out E k out cos(βsin( ω k t)) + 1 2 k=2 N m=2, mk N E m out E k out [ cos(βsin( ω k t)) cos(βsin( ω m t)) +sin(βsin( ω k t)) sin(βsin( ω m t)) ] ].
P comb (β)= 1 T 2 0 T 2 P comb (t,β)dt ,
P max comb = c ε 0 nA 2 ( k=1 N E k out ) 2 .
η relative (β)= P comb (β) / P max comb .
cos(βsin( ω k t))= J 0 (β)+2 m=1 J 2m ( β)cos(2m ω k t), sin(βsin( ω k t))=2 n=1 J 2n1 ( β)sin((2n1) ω k t),
η relative (β)= k=1 N E k out 2 + k=2 N 2 E 1 out E k out J 0 (β) + k=2 N m=2, mk N E m out E k out J 0 2 (β) ( k=1 N E k out ) 2 .

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