Abstract

A coherent fiber laser array using fiber couplers is discussed. The array modes are analyzed and determined using coupled mode theory. A numerical analysis of the phase property for a 19-fiber array is performed and the results show that the array can achieve a quasi-in-phase state. The stability and the scalability of coherent combination are investigated by simulations via changing the fiber grating reflectivity, the pump parameter, and the cavity length. Considering the mutual coupling between fiber lasers and the mismatch among fiber lengths, we trace the relative phases between array elements and further provide the evidence of coherent combining for the 19-fiber array. With the increase in the fiber elements, although the system is required to operate at a lower grating reflectivity for achieving a stable laser output, the output power increases nonlinearly.

© 2010 Optical Society of America

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  3. T. M. Shay, J. T. Baker, A. D. Sanchez, C. A. Robin, C. L. Vergien, C. Zeringue, D. Gallant, C. A. Lu, B. Pulford, T. J. Bronder, and A. Lucero, “High-power phase locking of a fiber amplifier array,” in Fiber Lasers VI, D.V.Gapontsev, D.A.Kliner, J.W.Dawson, and K.Tankala, eds., Proc. SPIE 7195, 719511–719518 (2009).
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    [CrossRef] [PubMed]
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    [CrossRef]
  11. M. L. Minden, H. Bruesselbacha, J. L. Rogersa, M. S. Mangira, D. C. Jonesa, G. J. Dunninga, D. L. Hammon, A. J. Solis, and L. Vaughanb, “Self-organized coherence in fiber laser arrays,” in Fiber Lasers: Technology, Systems, and Applications, L.N.Durvasula, ed., Proc. SPIE 5335, 89–97 (2004).
  12. A. Shirakawa, T. Saitou, T. Sekiguchi, and K. Ueda, “Coherent addition of fiber lasers by use of a fiber coupler,” Opt. Express 10, 1167–1172 (2002).
    [PubMed]
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    [CrossRef] [PubMed]
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  15. A. Shirakawa, K. Matsuo, and K.-i. Ueda, “Fiber laser coherent array for power scaling of single-mode fiber laser,” in Fifth International Symposium on Laser Precision Microfabrication, I.Miyamoto, H.Helvajian, K.Itoh, K.F.Kobayashi, A.Ostendorf, and K.Sugioka, eds., Proc. SPIE 5662, 482–487 (2004).
  16. A. Shirakawa, K. Matsuo, and K.-i. Ueda, “Fiber laser coherent array for power scaling, bandwidth narrowing, and coherent beam direction control,” in Fiber Lasers II: Technology, Systems, and Applications, L.N.Durvasula, A.J. W.Brown, and J.Nilsson, eds., Proc. SPIE 5709, 165–174 (2005).
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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  22. J. K. Butler, D. E. Ackley, and M. Ettenberg, “Coupled-mode analysis of gain and wavelength oscillation characteristics of diode laser phased arrays,” IEEE J. Quantum Electron. 21, 458–464 (1985).
    [CrossRef]
  23. T. Y. Fan and A. Sanchez, “Coherent (phased array) and wavelength (spectral) beam combining compared,” in Fiber Lasers II: Technology, Systems, and Applications, L.N.Durvasula, A.J. W.Brown, and J.Nilsson, Proc. SPIE 5709, 157–164 (2005).

2008 (1)

2006 (1)

2005 (5)

H. Bruesselbach, D. C. Jones, M. S. Mangir, M. Minden, and J. L. Rogers, “Self-organized coherence in fiber laser arrays,” Opt. Lett. 30, 1339–1341 (2005).
[CrossRef] [PubMed]

C. J. Corcoran and K. A. Pasch, “Modal analysis of a self-Fourier laser cavity,” J. Opt. A, Pure Appl. Opt. 7, L1–L7 (2005).
[CrossRef]

C. J. Corcoran and F. Durville, “Experimental demonstration of a phase-locked laser array using a self-Fourier cavity,” Appl. Phys. Lett. 86, 201118 (2005).
[CrossRef]

D. Kouznetsov, J.-F. Bisson, A. Shirakawa, and K.-i. Ueda, “Limits of coherent addition of lasers: simple estimate,” Opt. Rev. 12, 445–447 (2005).
[CrossRef]

J. L. Rogers, S. Peleš, and K. Wiesenfeld, “Model for high-gain fiber laser arrays,” IEEE J. Quantum Electron. 41, 767–773 (2005).
[CrossRef]

2004 (1)

C. J. Corcoran and K. A. Pasch, “Self-Fourier functions and coherent laser combination,” J. Phys. A 37, L461–L469 (2004).
[CrossRef]

2003 (1)

2002 (1)

2001 (1)

P. K. Cheo, A. Liu, and G. G. King, “A high-brightness laser beam from a phase-locked multicore Yb-doped fiber laser array,” IEEE Photon. Technol. Lett. 13, 439–441 (2001).
[CrossRef]

2000 (1)

1994 (1)

1985 (1)

J. K. Butler, D. E. Ackley, and M. Ettenberg, “Coupled-mode analysis of gain and wavelength oscillation characteristics of diode laser phased arrays,” IEEE J. Quantum Electron. 21, 458–464 (1985).
[CrossRef]

Ackley, D. E.

J. K. Butler, D. E. Ackley, and M. Ettenberg, “Coupled-mode analysis of gain and wavelength oscillation characteristics of diode laser phased arrays,” IEEE J. Quantum Electron. 21, 458–464 (1985).
[CrossRef]

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,” in Fiber Lasers III, A.J. W.Brown, J.Nilsson, D.J.Harter, and A.Tünnermann, eds., Proc. SPIE 6102, 202–206 (2006).

Baker, J. T.

T. M. Shay, J. T. Baker, A. D. Sanchez, C. A. Robin, C. L. Vergien, C. Zeringue, D. Gallant, C. A. Lu, B. Pulford, T. J. Bronder, and A. Lucero, “High-power phase locking of a fiber amplifier array,” in Fiber Lasers VI, D.V.Gapontsev, D.A.Kliner, J.W.Dawson, and K.Tankala, eds., Proc. SPIE 7195, 719511–719518 (2009).

Barthé0lémy, A.

Bisson, J. -F.

D. Kouznetsov, J.-F. Bisson, A. Shirakawa, and K.-i. Ueda, “Limits of coherent addition of lasers: simple estimate,” Opt. Rev. 12, 445–447 (2005).
[CrossRef]

Bronder, T. J.

T. M. Shay, J. T. Baker, A. D. Sanchez, C. A. Robin, C. L. Vergien, C. Zeringue, D. Gallant, C. A. Lu, B. Pulford, T. J. Bronder, and A. Lucero, “High-power phase locking of a fiber amplifier array,” in Fiber Lasers VI, D.V.Gapontsev, D.A.Kliner, J.W.Dawson, and K.Tankala, eds., Proc. SPIE 7195, 719511–719518 (2009).

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,” in Fiber Lasers III, A.J. W.Brown, J.Nilsson, D.J.Harter, and A.Tünnermann, eds., Proc. SPIE 6102, 202–206 (2006).

Bruesselbach, H.

Bruesselbacha, H.

M. L. Minden, H. Bruesselbacha, J. L. Rogersa, M. S. Mangira, D. C. Jonesa, G. J. Dunninga, D. L. Hammon, A. J. Solis, and L. Vaughanb, “Self-organized coherence in fiber laser arrays,” in Fiber Lasers: Technology, Systems, and Applications, L.N.Durvasula, ed., Proc. SPIE 5335, 89–97 (2004).

Butler, J. K.

J. K. Butler, D. E. Ackley, and M. Ettenberg, “Coupled-mode analysis of gain and wavelength oscillation characteristics of diode laser phased arrays,” IEEE J. Quantum Electron. 21, 458–464 (1985).
[CrossRef]

Cheo, P. K.

P. K. Cheo, A. Liu, and G. G. King, “A high-brightness laser beam from a phase-locked multicore Yb-doped fiber laser array,” IEEE Photon. Technol. Lett. 13, 439–441 (2001).
[CrossRef]

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,” in Fiber Lasers III, A.J. W.Brown, J.Nilsson, D.J.Harter, and A.Tünnermann, eds., Proc. SPIE 6102, 202–206 (2006).

Cheung, E. C.

Corcoran, C. J.

C. J. Corcoran and F. Durville, “Experimental demonstration of a phase-locked laser array using a self-Fourier cavity,” Appl. Phys. Lett. 86, 201118 (2005).
[CrossRef]

C. J. Corcoran and K. A. Pasch, “Modal analysis of a self-Fourier laser cavity,” J. Opt. A, Pure Appl. Opt. 7, L1–L7 (2005).
[CrossRef]

C. J. Corcoran and K. A. Pasch, “Self-Fourier functions and coherent laser combination,” J. Phys. A 37, L461–L469 (2004).
[CrossRef]

Desfarges-Berthelemot, A.

Dong, J.

Dunninga, G. J.

M. L. Minden, H. Bruesselbacha, J. L. Rogersa, M. S. Mangira, D. C. Jonesa, G. J. Dunninga, D. L. Hammon, A. J. Solis, and L. Vaughanb, “Self-organized coherence in fiber laser arrays,” in Fiber Lasers: Technology, Systems, and Applications, L.N.Durvasula, ed., Proc. SPIE 5335, 89–97 (2004).

Durville, F.

C. J. Corcoran and F. Durville, “Experimental demonstration of a phase-locked laser array using a self-Fourier cavity,” Appl. Phys. Lett. 86, 201118 (2005).
[CrossRef]

Epp, P.

J. Anderegg, S. Brosnan, E. Cheung, P. Epp, D. Hammons, H. Komine, M. Weber, and M. Wickham, “Coherently coupled high power fiber arrays,” in Fiber Lasers III, A.J. W.Brown, J.Nilsson, D.J.Harter, and A.Tünnermann, eds., Proc. SPIE 6102, 202–206 (2006).

Ettenberg, M.

J. K. Butler, D. E. Ackley, and M. Ettenberg, “Coupled-mode analysis of gain and wavelength oscillation characteristics of diode laser phased arrays,” IEEE J. Quantum Electron. 21, 458–464 (1985).
[CrossRef]

Fan, T. Y.

T. Y. Fan and A. Sanchez, “Coherent (phased array) and wavelength (spectral) beam combining compared,” in Fiber Lasers II: Technology, Systems, and Applications, L.N.Durvasula, A.J. W.Brown, and J.Nilsson, Proc. SPIE 5709, 157–164 (2005).

Fischer, D.

Gallant, D.

T. M. Shay, J. T. Baker, A. D. Sanchez, C. A. Robin, C. L. Vergien, C. Zeringue, D. Gallant, C. A. Lu, B. Pulford, T. J. Bronder, and A. Lucero, “High-power phase locking of a fiber amplifier array,” in Fiber Lasers VI, D.V.Gapontsev, D.A.Kliner, J.W.Dawson, and K.Tankala, eds., Proc. SPIE 7195, 719511–719518 (2009).

Glas, P.

Goodno, G. D.

Hammon, D. L.

M. L. Minden, H. Bruesselbacha, J. L. Rogersa, M. S. Mangira, D. C. Jonesa, G. J. Dunninga, D. L. Hammon, A. J. Solis, and L. Vaughanb, “Self-organized coherence in fiber laser arrays,” in Fiber Lasers: Technology, Systems, and Applications, L.N.Durvasula, ed., Proc. SPIE 5335, 89–97 (2004).

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,” in Fiber Lasers III, A.J. W.Brown, J.Nilsson, D.J.Harter, and A.Tünnermann, eds., Proc. SPIE 6102, 202–206 (2006).

He, B.

Ho, J. G.

Huang, W. -P.

Jones, D. C.

Jonesa, D. C.

M. L. Minden, H. Bruesselbacha, J. L. Rogersa, M. S. Mangira, D. C. Jonesa, G. J. Dunninga, D. L. Hammon, A. J. Solis, and L. Vaughanb, “Self-organized coherence in fiber laser arrays,” in Fiber Lasers: Technology, Systems, and Applications, L.N.Durvasula, ed., Proc. SPIE 5335, 89–97 (2004).

Kermène, V.

King, G. G.

P. K. Cheo, A. Liu, and G. G. King, “A high-brightness laser beam from a phase-locked multicore Yb-doped fiber laser array,” IEEE Photon. Technol. Lett. 13, 439–441 (2001).
[CrossRef]

Komine, H.

J. Anderegg, S. Brosnan, E. Cheung, P. Epp, D. Hammons, H. Komine, M. Weber, and M. Wickham, “Coherently coupled high power fiber arrays,” in Fiber Lasers III, A.J. W.Brown, J.Nilsson, D.J.Harter, and A.Tünnermann, eds., Proc. SPIE 6102, 202–206 (2006).

Kouznetsov, D.

D. Kouznetsov, J.-F. Bisson, A. Shirakawa, and K.-i. Ueda, “Limits of coherent addition of lasers: simple estimate,” Opt. Rev. 12, 445–447 (2005).
[CrossRef]

Lefort, L.

Leitner, M.

Li, L.

Liu, A.

P. K. Cheo, A. Liu, and G. G. King, “A high-brightness laser beam from a phase-locked multicore Yb-doped fiber laser array,” IEEE Photon. Technol. Lett. 13, 439–441 (2001).
[CrossRef]

Lou, Q.

Love, J. D.

A. W. Snyder and J. D. Love, Optical Waveguide Theory (Chapman and Hall, 1983).

Lu, C. A.

T. M. Shay, J. T. Baker, A. D. Sanchez, C. A. Robin, C. L. Vergien, C. Zeringue, D. Gallant, C. A. Lu, B. Pulford, T. J. Bronder, and A. Lucero, “High-power phase locking of a fiber amplifier array,” in Fiber Lasers VI, D.V.Gapontsev, D.A.Kliner, J.W.Dawson, and K.Tankala, eds., Proc. SPIE 7195, 719511–719518 (2009).

Lucero, A.

T. M. Shay, J. T. Baker, A. D. Sanchez, C. A. Robin, C. L. Vergien, C. Zeringue, D. Gallant, C. A. Lu, B. Pulford, T. J. Bronder, and A. Lucero, “High-power phase locking of a fiber amplifier array,” in Fiber Lasers VI, D.V.Gapontsev, D.A.Kliner, J.W.Dawson, and K.Tankala, eds., Proc. SPIE 7195, 719511–719518 (2009).

Mangir, M. S.

Mangira, M. S.

M. L. Minden, H. Bruesselbacha, J. L. Rogersa, M. S. Mangira, D. C. Jonesa, G. J. Dunninga, D. L. Hammon, A. J. Solis, and L. Vaughanb, “Self-organized coherence in fiber laser arrays,” in Fiber Lasers: Technology, Systems, and Applications, L.N.Durvasula, ed., Proc. SPIE 5335, 89–97 (2004).

Matsuo, K.

A. Shirakawa, K. Matsuo, and K.-i. Ueda, “Fiber laser coherent array for power scaling of single-mode fiber laser,” in Fifth International Symposium on Laser Precision Microfabrication, I.Miyamoto, H.Helvajian, K.Itoh, K.F.Kobayashi, A.Ostendorf, and K.Sugioka, eds., Proc. SPIE 5662, 482–487 (2004).

A. Shirakawa, K. Matsuo, and K.-i. Ueda, “Fiber laser coherent array for power scaling, bandwidth narrowing, and coherent beam direction control,” in Fiber Lasers II: Technology, Systems, and Applications, L.N.Durvasula, A.J. W.Brown, and J.Nilsson, eds., Proc. SPIE 5709, 165–174 (2005).

Minden, M.

Minden, M. L.

M. L. Minden, H. Bruesselbacha, J. L. Rogersa, M. S. Mangira, D. C. Jonesa, G. J. Dunninga, D. L. Hammon, A. J. Solis, and L. Vaughanb, “Self-organized coherence in fiber laser arrays,” in Fiber Lasers: Technology, Systems, and Applications, L.N.Durvasula, ed., Proc. SPIE 5335, 89–97 (2004).

Napartovich, A. P.

Pasch, K. A.

C. J. Corcoran and K. A. Pasch, “Modal analysis of a self-Fourier laser cavity,” J. Opt. A, Pure Appl. Opt. 7, L1–L7 (2005).
[CrossRef]

C. J. Corcoran and K. A. Pasch, “Self-Fourier functions and coherent laser combination,” J. Phys. A 37, L461–L469 (2004).
[CrossRef]

Peleš, S.

J. L. Rogers, S. Peleš, and K. Wiesenfeld, “Model for high-gain fiber laser arrays,” IEEE J. Quantum Electron. 41, 767–773 (2005).
[CrossRef]

Pulford, B.

T. M. Shay, J. T. Baker, A. D. Sanchez, C. A. Robin, C. L. Vergien, C. Zeringue, D. Gallant, C. A. Lu, B. Pulford, T. J. Bronder, and A. Lucero, “High-power phase locking of a fiber amplifier array,” in Fiber Lasers VI, D.V.Gapontsev, D.A.Kliner, J.W.Dawson, and K.Tankala, eds., Proc. SPIE 7195, 719511–719518 (2009).

Qi, Y.

Rice, R. R.

Robin, C. A.

T. M. Shay, J. T. Baker, A. D. Sanchez, C. A. Robin, C. L. Vergien, C. Zeringue, D. Gallant, C. A. Lu, B. Pulford, T. J. Bronder, and A. Lucero, “High-power phase locking of a fiber amplifier array,” in Fiber Lasers VI, D.V.Gapontsev, D.A.Kliner, J.W.Dawson, and K.Tankala, eds., Proc. SPIE 7195, 719511–719518 (2009).

Rogers, J. L.

H. Bruesselbach, D. C. Jones, M. S. Mangir, M. Minden, and J. L. Rogers, “Self-organized coherence in fiber laser arrays,” Opt. Lett. 30, 1339–1341 (2005).
[CrossRef] [PubMed]

J. L. Rogers, S. Peleš, and K. Wiesenfeld, “Model for high-gain fiber laser arrays,” IEEE J. Quantum Electron. 41, 767–773 (2005).
[CrossRef]

Rogersa, J. L.

M. L. Minden, H. Bruesselbacha, J. L. Rogersa, M. S. Mangira, D. C. Jonesa, G. J. Dunninga, D. L. Hammon, A. J. Solis, and L. Vaughanb, “Self-organized coherence in fiber laser arrays,” in Fiber Lasers: Technology, Systems, and Applications, L.N.Durvasula, ed., Proc. SPIE 5335, 89–97 (2004).

Rothenberg, J.

Sabourdy, D.

Saitou, T.

Sanchez, A.

T. Y. Fan and A. Sanchez, “Coherent (phased array) and wavelength (spectral) beam combining compared,” in Fiber Lasers II: Technology, Systems, and Applications, L.N.Durvasula, A.J. W.Brown, and J.Nilsson, Proc. SPIE 5709, 157–164 (2005).

Sanchez, A. D.

T. M. Shay, J. T. Baker, A. D. Sanchez, C. A. Robin, C. L. Vergien, C. Zeringue, D. Gallant, C. A. Lu, B. Pulford, T. J. Bronder, and A. Lucero, “High-power phase locking of a fiber amplifier array,” in Fiber Lasers VI, D.V.Gapontsev, D.A.Kliner, J.W.Dawson, and K.Tankala, eds., Proc. SPIE 7195, 719511–719518 (2009).

Sekiguchi, T.

Shay, T. M.

T. M. Shay, J. T. Baker, A. D. Sanchez, C. A. Robin, C. L. Vergien, C. Zeringue, D. Gallant, C. A. Lu, B. Pulford, T. J. Bronder, and A. Lucero, “High-power phase locking of a fiber amplifier array,” in Fiber Lasers VI, D.V.Gapontsev, D.A.Kliner, J.W.Dawson, and K.Tankala, eds., Proc. SPIE 7195, 719511–719518 (2009).

Shirakawa, A.

D. Kouznetsov, J.-F. Bisson, A. Shirakawa, and K.-i. Ueda, “Limits of coherent addition of lasers: simple estimate,” Opt. Rev. 12, 445–447 (2005).
[CrossRef]

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

A. Shirakawa, K. Matsuo, and K.-i. Ueda, “Fiber laser coherent array for power scaling, bandwidth narrowing, and coherent beam direction control,” in Fiber Lasers II: Technology, Systems, and Applications, L.N.Durvasula, A.J. W.Brown, and J.Nilsson, eds., Proc. SPIE 5709, 165–174 (2005).

A. Shirakawa, K. Matsuo, and K.-i. Ueda, “Fiber laser coherent array for power scaling of single-mode fiber laser,” in Fifth International Symposium on Laser Precision Microfabrication, I.Miyamoto, H.Helvajian, K.Itoh, K.F.Kobayashi, A.Ostendorf, and K.Sugioka, eds., Proc. SPIE 5662, 482–487 (2004).

Snyder, A. W.

A. W. Snyder and J. D. Love, Optical Waveguide Theory (Chapman and Hall, 1983).

Solis, A. J.

M. L. Minden, H. Bruesselbacha, J. L. Rogersa, M. S. Mangira, D. C. Jonesa, G. J. Dunninga, D. L. Hammon, A. J. Solis, and L. Vaughanb, “Self-organized coherence in fiber laser arrays,” in Fiber Lasers: Technology, Systems, and Applications, L.N.Durvasula, ed., Proc. SPIE 5335, 89–97 (2004).

Su, Z.

Thielen, P.

Ueda, K.

Ueda, K. -i.

D. Kouznetsov, J.-F. Bisson, A. Shirakawa, and K.-i. Ueda, “Limits of coherent addition of lasers: simple estimate,” Opt. Rev. 12, 445–447 (2005).
[CrossRef]

A. Shirakawa, K. Matsuo, and K.-i. Ueda, “Fiber laser coherent array for power scaling of single-mode fiber laser,” in Fifth International Symposium on Laser Precision Microfabrication, I.Miyamoto, H.Helvajian, K.Itoh, K.F.Kobayashi, A.Ostendorf, and K.Sugioka, eds., Proc. SPIE 5662, 482–487 (2004).

A. Shirakawa, K. Matsuo, and K.-i. Ueda, “Fiber laser coherent array for power scaling, bandwidth narrowing, and coherent beam direction control,” in Fiber Lasers II: Technology, Systems, and Applications, L.N.Durvasula, A.J. W.Brown, and J.Nilsson, eds., Proc. SPIE 5709, 165–174 (2005).

Vaughanb, L.

M. L. Minden, H. Bruesselbacha, J. L. Rogersa, M. S. Mangira, D. C. Jonesa, G. J. Dunninga, D. L. Hammon, A. J. Solis, and L. Vaughanb, “Self-organized coherence in fiber laser arrays,” in Fiber Lasers: Technology, Systems, and Applications, L.N.Durvasula, ed., Proc. SPIE 5335, 89–97 (2004).

Vergien, C. L.

T. M. Shay, J. T. Baker, A. D. Sanchez, C. A. Robin, C. L. Vergien, C. Zeringue, D. Gallant, C. A. Lu, B. Pulford, T. J. Bronder, and A. Lucero, “High-power phase locking of a fiber amplifier array,” in Fiber Lasers VI, D.V.Gapontsev, D.A.Kliner, J.W.Dawson, and K.Tankala, eds., Proc. SPIE 7195, 719511–719518 (2009).

Vysotsky, D. V.

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, 354–356 (2008).
[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,” in Fiber Lasers III, A.J. W.Brown, J.Nilsson, D.J.Harter, and A.Tünnermann, eds., Proc. SPIE 6102, 202–206 (2006).

Wei, Y.

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, 354–356 (2008).
[CrossRef] [PubMed]

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[CrossRef]

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[CrossRef]

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T. M. Shay, J. T. Baker, A. D. Sanchez, C. A. Robin, C. L. Vergien, C. Zeringue, D. Gallant, C. A. Lu, B. Pulford, T. J. Bronder, and A. Lucero, “High-power phase locking of a fiber amplifier array,” in Fiber Lasers VI, D.V.Gapontsev, D.A.Kliner, J.W.Dawson, and K.Tankala, eds., Proc. SPIE 7195, 719511–719518 (2009).

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Figures (10)

Fig. 1
Fig. 1

Physical model for fiber laser array using fiber couplers.

Fig. 2
Fig. 2

Electric fields of the array modes for the five-fiber array.

Fig. 3
Fig. 3

The impact of fiber grating reflectivity on output power. (a) Three-fiber array with the fiber length of l = 7.5   m and pump parameter G p = 3 . (b) Seven-fiber array with fiber length of l = 9   m and pump parameter G p = 3 .

Fig. 4
Fig. 4

The impact of pump parameter on output power. (a) Three-fiber array with the grating reflectivity of r = 0.25 and fiber length of l = 7.5   m . (b) Seven-fiber array with the grating reflectivity of r = 0.05 and fiber length of l = 9   m .

Fig. 5
Fig. 5

The impact of fiber length on output power. (a) Three-fiber array with the pump parameter G p = 3 and grating reflectivity r = 0.25 . (b) Seven-fiber array with the pump parameter G p = 3 and grating reflectivity r = 0.05 .

Fig. 6
Fig. 6

The scalability of fiber laser array. Three-fiber array with r = 0.25 , l = 7.5   m , and G p = 5 . Five-fiber array with r = 0.1 , l = 9   m , and G p = 4 . Seven-fiber array with r = 0.05 , l = 9   m , and G p = 6 . Eight-fiber array with r = 0.05 , l = 9   m , and G p = 4 . 13-fiber array with r = 0.03 , l = 9   m , and G p = 5 . 18-fiber array with r = 0.025 , l = 9   m , and G p = 3 . 19-fiber array with r = 0.025 , l = 7.5   m , and G p = 5 .

Fig. 7
Fig. 7

Time series for output power of 19-fiber array. The pump parameter is 0.2, the fiber length is 9 m, and the grating reflectivity is 0.02.

Fig. 8
Fig. 8

Phase property for the 19-fiber array. The pump parameter is 0.2, the fiber length is 9 m, and the grating reflectivity is 0.02. (a) One to ten iterations corresponding to section A of Fig. 7. (b) 6991–7000 iterations corresponding to section B of Fig. 7.

Fig. 9
Fig. 9

Time series for maximum phase error. The pump parameter is 0.2, the fiber length is 9 m, and the grating reflectivity is 0.02. (a) Section C of the unstable state in Fig. 7. (b) Section D of stable state in Fig. 7.

Fig. 10
Fig. 10

Electric fields of the array mode for 19-fiber array.

Tables (1)

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Table 1 Parameters

Equations (17)

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E n ( t + T ) = m = 1 N A n m ( t ) E m ( t ) ,
G n ( t + T ) = G n ( t ) + ε [ G n p ( t ) G n ( t ) ] 2 ε I sat ( 1 e G n ( t ) ) I n ( t ) ,
A n m = r l S n l e G l + j Φ l S l m ,
d E n d z j ( β n + C n n ) E n = j m = 1 , m n N C n m E m ,
d E n d z = j M E ,
M = ( β 1 C 12 . . . C 1 N C 21 β 2 . . . C 2 N . . . . . . . . . . . . . . . . . . C N 1 C N 2 . . . β N ) ,     E = ( E 1 E 2 . . E N ) .
E n ( L + ) = exp ( j L L + M d z ) E n ( L ) = exp ( j M L ) E n ( L ) .
S = e j M L .
C i j = k 4 ε 0 μ 0 Z ( n cl 2 n co 2 ) φ i φ j d Z .
F 0 ( r ) = exp { 1 2 ( r r 0 ) 2 } ,
F 0 ( R ) V 2 K 0 ( W R ) 0 R { 1 f ( R ) } I 0 ( W R ) exp ( R 2 2 R 0 2 ) d R ,
E n ( t + T ) = e j σ n z E n ( t ) ,
E ̂ ( t + T ) = r A B A E ̂ ( t ) .
A = S = e j L M = ( e j L β e j L C . . . e j L C e j L C e j L β . . . e j L C . . . . . . . . . . . . . . . . . . e j L C e j L C . . . e j L β ) ,
B = ( e G 1 + j Φ 1 e G 2 + j Φ 2 . . . e G n + j Φ n ) .
P = ( P 1 P 2 . . . P 2 P 2 P 1 . . . P 2 . . . . . . . . . . . . . . . . . . P 2 P 2 . . . P 1 ) .
P E ̂ = exp ( j σ z ) E ̂ .

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