Abstract

We generalize the recently proposed model for coherent beam combining in passive fiber laser arrays [Opt. Express 17, 19509 (2009)] to include the transient gain dynamics and the complication of counterpropagating waves, two important features characterizing actual experimental conditions. The extended model reveals that beam combining is not affected by the population relaxation process or the presence of backward propagating waves, which only serve to co-saturate the gain. The presence of nonresonant nonlinearity is found to reduce the coherent combining efficiency at high power levels. We show that the array lases at the frequencies with minimum overall losses when multiple loss mechanisms are present.

© 2010 OSA

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. H. Bruesselbach, D. C. Jones, M. S. Mangir, M. Minden, and J. L. Rogers, “Self-organized coherence in fiber laser arrays,” Opt. Lett. 30(11), 1339–1341 (2005).
    [CrossRef] [PubMed]
  2. W. Z. Chang, T. W. Wu, H. G. Winful, and A. Galvanauskas, “Array size scalability of passively coherently phased fiber laser arrays,” Opt. Express 18(9), 9634–9642 (2010).
    [CrossRef] [PubMed]
  3. D. Sabourdy, V. Kermene, A. Desfarges-Berthelemot, L. Lefort, A. Barthelemy, P. Even, and D. Pureur, “Efficient coherent combining of widely tunable fiber lasers,” Opt. Express 11(2), 87–97 (2003).
    [CrossRef] [PubMed]
  4. A. Shirakawa, K. Matsuo, and K. Ueda, “Fiber laser coherent array for power scaling, bandwidth narrowing, and coherent beam direction control,” in Conference on Fiber Lasers II, L. N. Durvasula, A. J. W. Brown, and J. Nilsson, eds. (San Jose, CA, 2005), pp. 165–174.
  5. A. Shirakawa, T. Saitou, T. Sekiguchi, and K. Ueda, “Coherent addition of fiber lasers by use of a fiber coupler,” Opt. Express 10(21), 1167–1172 (2002).
    [PubMed]
  6. J. Q. Cao, J. Hou, Q. S. Lu, and X. J. Xu, “Numerical research on self-organized coherent fiber laser arrays with circulating field theory,” J. Opt. Soc. Am. B 25(7), 1187–1192 (2008).
    [CrossRef]
  7. D. Kouznetsov, J. F. Bisson, A. Shirakawa, and K. Ueda, “Limits of coherent addition of lasers: Simple estimate,” Opt. Rev. 12(6), 445–447 (2005).
    [CrossRef]
  8. W. Ray, J. L. Rogers, and K. Wiesenfeld, “Coherence between two coupled lasers from a dynamics perspective,” Opt. Express 17(11), 9357–9368 (2009).
    [CrossRef] [PubMed]
  9. J. L. Rogers, S. Peles, and K. Wiesenfeld, “Model for high-gain fiber laser arrays,” IEEE J. Quantum Electron. 41(6), 767–773 (2005).
    [CrossRef]
  10. K. Wiesenfeld, S. Peles, and J. L. Rogers, “Effect of Gain-Dependent Phase Shift on Fiber Laser Synchronization,” IEEE J. Sel. Top. Quantum Electron. 15(2), 312–319 (2009).
    [CrossRef]
  11. T. W. Wu, W. Z. Chang, A. Galvanauskas, and H. G. Winful, “Model for passive coherent beam combining in fiber laser arrays,” Opt. Express 17(22), 19509–19518 (2009).
    [CrossRef] [PubMed]
  12. G. P. Agrawal, Nonlinear fiber optics, third edition (Academic Press, 2001), pp. 263–264.
  13. A. E. Siegman, Lasers (University Science Books (January 1986)), pp. 485–487.
  14. A. Yariv, Photonics: Optical Electronics in Modern Communications, 6th Edition (Oxford University Press, USA, 2007), pp. 563–565.
  15. V. Roy, M. Piché, F. Babin, and G. W. Schinn, “Nonlinear wave mixing in a multilongitudinal-mode erbium-doped fiber laser,” Opt. Express 13(18), 6791–6797 (2005).
    [CrossRef] [PubMed]
  16. D. Hollenbeck and C. D. Cantrell, “Parallelizable, bidirectional method for simulating optical-signal propagation,” J. Lightwave Technol. 27(12), 2140–2149 (2009).
    [CrossRef]
  17. J. Kanka, “Numerical simulation of subpicosecond soliton formation in a nonlinear coupler laser,” Opt. Lett. 19(22), 1873–1875 (1994).
    [CrossRef] [PubMed]
  18. E. Martı́-Panameño, L. C. Gomez-Pavon, A. Luis-Ramos, M. M. Méndez-Otero, and M. D. I. Castillo, “Self-mode-locking action in a dual-core ring fiber laser,” Opt. Commun. 194, 409–414 (2001).
    [CrossRef]
  19. B. N. Upadhyaya, U. Chakravarty, A. Kuruvilla, A. K. Nath, M. R. Shenoy, and K. Thyagarajan, “Effect of steady-state conditions on self-pulsing characteristics of Yb-doped cw fiber lasers,” Opt. Commun. 281(1), 146–153 (2008).
    [CrossRef]
  20. D. Sabourdy, V. Kermene, A. Desfarges-Berthelemot, M. Vampouille, and A. Barthelemy, ““Coherent combining of two Nd: YAG lasers in a Vernier-Michelson-type cavity,” Appl. Phys. B-Lasers. 75, 503–507 (2002).
    [CrossRef]
  21. E. J. Bochove, “Effect of nonlinear phase on the passive phase locking of an array of fiber lasers of random lengths,” in Integrated Photonics and Nanophotonics Research and Applications (IPNRA) (Honolulu, Hawaii, 2009).
  22. C. J. Corcoran and K. A. Pasch, “Output phase characteristics of a nonlinear regenerative fiber amplifier,” IEEE J. Quantum Electron. 43(6), 437–439 (2007).
    [CrossRef]
  23. B. S. Wang, E. Mies, M. Minden, and A. Sanchez, “All-fiber 50 W coherently combined passive laser array,” Opt. Lett. 34(7), 863–865 (2009).
    [CrossRef] [PubMed]
  24. H. Bruesselbach, M. Minden, J. L. Rogers, D. C. Jones, and M. S. Mangir, “200 W self-organized coherent fiber arrays,” in 2005 Conference on Lasers & Electro-Optics (2005), pp. 532–534.
  25. A. E. Siegman, “Resonant modes of linearly coupled multiple fiber laser structures,” unpublished at http://www.stanford.edu/~siegman/Coupled%20Fiber%20Lasers/coupled_fiber_modes.pdf (2004).

2010 (1)

W. Z. Chang, T. W. Wu, H. G. Winful, and A. Galvanauskas, “Array size scalability of passively coherently phased fiber laser arrays,” Opt. Express 18(9), 9634–9642 (2010).
[CrossRef] [PubMed]

2009 (5)

W. Ray, J. L. Rogers, and K. Wiesenfeld, “Coherence between two coupled lasers from a dynamics perspective,” Opt. Express 17(11), 9357–9368 (2009).
[CrossRef] [PubMed]

K. Wiesenfeld, S. Peles, and J. L. Rogers, “Effect of Gain-Dependent Phase Shift on Fiber Laser Synchronization,” IEEE J. Sel. Top. Quantum Electron. 15(2), 312–319 (2009).
[CrossRef]

T. W. Wu, W. Z. Chang, A. Galvanauskas, and H. G. Winful, “Model for passive coherent beam combining in fiber laser arrays,” Opt. Express 17(22), 19509–19518 (2009).
[CrossRef] [PubMed]

D. Hollenbeck and C. D. Cantrell, “Parallelizable, bidirectional method for simulating optical-signal propagation,” J. Lightwave Technol. 27(12), 2140–2149 (2009).
[CrossRef]

B. S. Wang, E. Mies, M. Minden, and A. Sanchez, “All-fiber 50 W coherently combined passive laser array,” Opt. Lett. 34(7), 863–865 (2009).
[CrossRef] [PubMed]

2008 (2)

B. N. Upadhyaya, U. Chakravarty, A. Kuruvilla, A. K. Nath, M. R. Shenoy, and K. Thyagarajan, “Effect of steady-state conditions on self-pulsing characteristics of Yb-doped cw fiber lasers,” Opt. Commun. 281(1), 146–153 (2008).
[CrossRef]

J. Q. Cao, J. Hou, Q. S. Lu, and X. J. Xu, “Numerical research on self-organized coherent fiber laser arrays with circulating field theory,” J. Opt. Soc. Am. B 25(7), 1187–1192 (2008).
[CrossRef]

2007 (1)

C. J. Corcoran and K. A. Pasch, “Output phase characteristics of a nonlinear regenerative fiber amplifier,” IEEE J. Quantum Electron. 43(6), 437–439 (2007).
[CrossRef]

2005 (4)

H. Bruesselbach, D. C. Jones, M. S. Mangir, M. Minden, and J. L. Rogers, “Self-organized coherence in fiber laser arrays,” Opt. Lett. 30(11), 1339–1341 (2005).
[CrossRef] [PubMed]

D. Kouznetsov, J. F. Bisson, A. Shirakawa, and K. Ueda, “Limits of coherent addition of lasers: Simple estimate,” Opt. Rev. 12(6), 445–447 (2005).
[CrossRef]

V. Roy, M. Piché, F. Babin, and G. W. Schinn, “Nonlinear wave mixing in a multilongitudinal-mode erbium-doped fiber laser,” Opt. Express 13(18), 6791–6797 (2005).
[CrossRef] [PubMed]

J. L. Rogers, S. Peles, and K. Wiesenfeld, “Model for high-gain fiber laser arrays,” IEEE J. Quantum Electron. 41(6), 767–773 (2005).
[CrossRef]

2003 (1)

D. Sabourdy, V. Kermene, A. Desfarges-Berthelemot, L. Lefort, A. Barthelemy, P. Even, and D. Pureur, “Efficient coherent combining of widely tunable fiber lasers,” Opt. Express 11(2), 87–97 (2003).
[CrossRef] [PubMed]

2002 (2)

A. Shirakawa, T. Saitou, T. Sekiguchi, and K. Ueda, “Coherent addition of fiber lasers by use of a fiber coupler,” Opt. Express 10(21), 1167–1172 (2002).
[PubMed]

D. Sabourdy, V. Kermene, A. Desfarges-Berthelemot, M. Vampouille, and A. Barthelemy, ““Coherent combining of two Nd: YAG lasers in a Vernier-Michelson-type cavity,” Appl. Phys. B-Lasers. 75, 503–507 (2002).
[CrossRef]

2001 (1)

E. Martı́-Panameño, L. C. Gomez-Pavon, A. Luis-Ramos, M. M. Méndez-Otero, and M. D. I. Castillo, “Self-mode-locking action in a dual-core ring fiber laser,” Opt. Commun. 194, 409–414 (2001).
[CrossRef]

1994 (1)

J. Kanka, “Numerical simulation of subpicosecond soliton formation in a nonlinear coupler laser,” Opt. Lett. 19(22), 1873–1875 (1994).
[CrossRef] [PubMed]

Babin, F.

V. Roy, M. Piché, F. Babin, and G. W. Schinn, “Nonlinear wave mixing in a multilongitudinal-mode erbium-doped fiber laser,” Opt. Express 13(18), 6791–6797 (2005).
[CrossRef] [PubMed]

Barthelemy, A.

D. Sabourdy, V. Kermene, A. Desfarges-Berthelemot, L. Lefort, A. Barthelemy, P. Even, and D. Pureur, “Efficient coherent combining of widely tunable fiber lasers,” Opt. Express 11(2), 87–97 (2003).
[CrossRef] [PubMed]

D. Sabourdy, V. Kermene, A. Desfarges-Berthelemot, M. Vampouille, and A. Barthelemy, ““Coherent combining of two Nd: YAG lasers in a Vernier-Michelson-type cavity,” Appl. Phys. B-Lasers. 75, 503–507 (2002).
[CrossRef]

Bisson, J. F.

D. Kouznetsov, J. F. Bisson, A. Shirakawa, and K. Ueda, “Limits of coherent addition of lasers: Simple estimate,” Opt. Rev. 12(6), 445–447 (2005).
[CrossRef]

Bruesselbach, H.

H. Bruesselbach, D. C. Jones, M. S. Mangir, M. Minden, and J. L. Rogers, “Self-organized coherence in fiber laser arrays,” Opt. Lett. 30(11), 1339–1341 (2005).
[CrossRef] [PubMed]

Cantrell, C. D.

D. Hollenbeck and C. D. Cantrell, “Parallelizable, bidirectional method for simulating optical-signal propagation,” J. Lightwave Technol. 27(12), 2140–2149 (2009).
[CrossRef]

Cao, J. Q.

J. Q. Cao, J. Hou, Q. S. Lu, and X. J. Xu, “Numerical research on self-organized coherent fiber laser arrays with circulating field theory,” J. Opt. Soc. Am. B 25(7), 1187–1192 (2008).
[CrossRef]

Castillo, M. D. I.

E. Martı́-Panameño, L. C. Gomez-Pavon, A. Luis-Ramos, M. M. Méndez-Otero, and M. D. I. Castillo, “Self-mode-locking action in a dual-core ring fiber laser,” Opt. Commun. 194, 409–414 (2001).
[CrossRef]

Chakravarty, U.

B. N. Upadhyaya, U. Chakravarty, A. Kuruvilla, A. K. Nath, M. R. Shenoy, and K. Thyagarajan, “Effect of steady-state conditions on self-pulsing characteristics of Yb-doped cw fiber lasers,” Opt. Commun. 281(1), 146–153 (2008).
[CrossRef]

Chang, W. Z.

W. Z. Chang, T. W. Wu, H. G. Winful, and A. Galvanauskas, “Array size scalability of passively coherently phased fiber laser arrays,” Opt. Express 18(9), 9634–9642 (2010).
[CrossRef] [PubMed]

T. W. Wu, W. Z. Chang, A. Galvanauskas, and H. G. Winful, “Model for passive coherent beam combining in fiber laser arrays,” Opt. Express 17(22), 19509–19518 (2009).
[CrossRef] [PubMed]

Corcoran, C. J.

C. J. Corcoran and K. A. Pasch, “Output phase characteristics of a nonlinear regenerative fiber amplifier,” IEEE J. Quantum Electron. 43(6), 437–439 (2007).
[CrossRef]

Desfarges-Berthelemot, A.

D. Sabourdy, V. Kermene, A. Desfarges-Berthelemot, L. Lefort, A. Barthelemy, P. Even, and D. Pureur, “Efficient coherent combining of widely tunable fiber lasers,” Opt. Express 11(2), 87–97 (2003).
[CrossRef] [PubMed]

D. Sabourdy, V. Kermene, A. Desfarges-Berthelemot, M. Vampouille, and A. Barthelemy, ““Coherent combining of two Nd: YAG lasers in a Vernier-Michelson-type cavity,” Appl. Phys. B-Lasers. 75, 503–507 (2002).
[CrossRef]

Even, P.

D. Sabourdy, V. Kermene, A. Desfarges-Berthelemot, L. Lefort, A. Barthelemy, P. Even, and D. Pureur, “Efficient coherent combining of widely tunable fiber lasers,” Opt. Express 11(2), 87–97 (2003).
[CrossRef] [PubMed]

Galvanauskas, A.

W. Z. Chang, T. W. Wu, H. G. Winful, and A. Galvanauskas, “Array size scalability of passively coherently phased fiber laser arrays,” Opt. Express 18(9), 9634–9642 (2010).
[CrossRef] [PubMed]

T. W. Wu, W. Z. Chang, A. Galvanauskas, and H. G. Winful, “Model for passive coherent beam combining in fiber laser arrays,” Opt. Express 17(22), 19509–19518 (2009).
[CrossRef] [PubMed]

Gomez-Pavon, L. C.

E. Martı́-Panameño, L. C. Gomez-Pavon, A. Luis-Ramos, M. M. Méndez-Otero, and M. D. I. Castillo, “Self-mode-locking action in a dual-core ring fiber laser,” Opt. Commun. 194, 409–414 (2001).
[CrossRef]

Hollenbeck, D.

D. Hollenbeck and C. D. Cantrell, “Parallelizable, bidirectional method for simulating optical-signal propagation,” J. Lightwave Technol. 27(12), 2140–2149 (2009).
[CrossRef]

Hou, J.

J. Q. Cao, J. Hou, Q. S. Lu, and X. J. Xu, “Numerical research on self-organized coherent fiber laser arrays with circulating field theory,” J. Opt. Soc. Am. B 25(7), 1187–1192 (2008).
[CrossRef]

Jones, D. C.

H. Bruesselbach, D. C. Jones, M. S. Mangir, M. Minden, and J. L. Rogers, “Self-organized coherence in fiber laser arrays,” Opt. Lett. 30(11), 1339–1341 (2005).
[CrossRef] [PubMed]

Kanka, J.

J. Kanka, “Numerical simulation of subpicosecond soliton formation in a nonlinear coupler laser,” Opt. Lett. 19(22), 1873–1875 (1994).
[CrossRef] [PubMed]

Kermene, V.

D. Sabourdy, V. Kermene, A. Desfarges-Berthelemot, L. Lefort, A. Barthelemy, P. Even, and D. Pureur, “Efficient coherent combining of widely tunable fiber lasers,” Opt. Express 11(2), 87–97 (2003).
[CrossRef] [PubMed]

D. Sabourdy, V. Kermene, A. Desfarges-Berthelemot, M. Vampouille, and A. Barthelemy, ““Coherent combining of two Nd: YAG lasers in a Vernier-Michelson-type cavity,” Appl. Phys. B-Lasers. 75, 503–507 (2002).
[CrossRef]

Kouznetsov, D.

D. Kouznetsov, J. F. Bisson, A. Shirakawa, and K. Ueda, “Limits of coherent addition of lasers: Simple estimate,” Opt. Rev. 12(6), 445–447 (2005).
[CrossRef]

Kuruvilla, A.

B. N. Upadhyaya, U. Chakravarty, A. Kuruvilla, A. K. Nath, M. R. Shenoy, and K. Thyagarajan, “Effect of steady-state conditions on self-pulsing characteristics of Yb-doped cw fiber lasers,” Opt. Commun. 281(1), 146–153 (2008).
[CrossRef]

Lefort, L.

D. Sabourdy, V. Kermene, A. Desfarges-Berthelemot, L. Lefort, A. Barthelemy, P. Even, and D. Pureur, “Efficient coherent combining of widely tunable fiber lasers,” Opt. Express 11(2), 87–97 (2003).
[CrossRef] [PubMed]

Lu, Q. S.

J. Q. Cao, J. Hou, Q. S. Lu, and X. J. Xu, “Numerical research on self-organized coherent fiber laser arrays with circulating field theory,” J. Opt. Soc. Am. B 25(7), 1187–1192 (2008).
[CrossRef]

Luis-Ramos, A.

E. Martı́-Panameño, L. C. Gomez-Pavon, A. Luis-Ramos, M. M. Méndez-Otero, and M. D. I. Castillo, “Self-mode-locking action in a dual-core ring fiber laser,” Opt. Commun. 194, 409–414 (2001).
[CrossRef]

Mangir, M. S.

H. Bruesselbach, D. C. Jones, M. S. Mangir, M. Minden, and J. L. Rogers, “Self-organized coherence in fiber laser arrays,” Opt. Lett. 30(11), 1339–1341 (2005).
[CrossRef] [PubMed]

Marti´-Panameño, E.

E. Martı́-Panameño, L. C. Gomez-Pavon, A. Luis-Ramos, M. M. Méndez-Otero, and M. D. I. Castillo, “Self-mode-locking action in a dual-core ring fiber laser,” Opt. Commun. 194, 409–414 (2001).
[CrossRef]

Méndez-Otero, M. M.

E. Martı́-Panameño, L. C. Gomez-Pavon, A. Luis-Ramos, M. M. Méndez-Otero, and M. D. I. Castillo, “Self-mode-locking action in a dual-core ring fiber laser,” Opt. Commun. 194, 409–414 (2001).
[CrossRef]

Mies, E.

B. S. Wang, E. Mies, M. Minden, and A. Sanchez, “All-fiber 50 W coherently combined passive laser array,” Opt. Lett. 34(7), 863–865 (2009).
[CrossRef] [PubMed]

Minden, M.

B. S. Wang, E. Mies, M. Minden, and A. Sanchez, “All-fiber 50 W coherently combined passive laser array,” Opt. Lett. 34(7), 863–865 (2009).
[CrossRef] [PubMed]

H. Bruesselbach, D. C. Jones, M. S. Mangir, M. Minden, and J. L. Rogers, “Self-organized coherence in fiber laser arrays,” Opt. Lett. 30(11), 1339–1341 (2005).
[CrossRef] [PubMed]

Nath, A. K.

B. N. Upadhyaya, U. Chakravarty, A. Kuruvilla, A. K. Nath, M. R. Shenoy, and K. Thyagarajan, “Effect of steady-state conditions on self-pulsing characteristics of Yb-doped cw fiber lasers,” Opt. Commun. 281(1), 146–153 (2008).
[CrossRef]

Pasch, K. A.

C. J. Corcoran and K. A. Pasch, “Output phase characteristics of a nonlinear regenerative fiber amplifier,” IEEE J. Quantum Electron. 43(6), 437–439 (2007).
[CrossRef]

Peles, S.

K. Wiesenfeld, S. Peles, and J. L. Rogers, “Effect of Gain-Dependent Phase Shift on Fiber Laser Synchronization,” IEEE J. Sel. Top. Quantum Electron. 15(2), 312–319 (2009).
[CrossRef]

J. L. Rogers, S. Peles, and K. Wiesenfeld, “Model for high-gain fiber laser arrays,” IEEE J. Quantum Electron. 41(6), 767–773 (2005).
[CrossRef]

Piché, M.

V. Roy, M. Piché, F. Babin, and G. W. Schinn, “Nonlinear wave mixing in a multilongitudinal-mode erbium-doped fiber laser,” Opt. Express 13(18), 6791–6797 (2005).
[CrossRef] [PubMed]

Pureur, D.

D. Sabourdy, V. Kermene, A. Desfarges-Berthelemot, L. Lefort, A. Barthelemy, P. Even, and D. Pureur, “Efficient coherent combining of widely tunable fiber lasers,” Opt. Express 11(2), 87–97 (2003).
[CrossRef] [PubMed]

Ray, W.

W. Ray, J. L. Rogers, and K. Wiesenfeld, “Coherence between two coupled lasers from a dynamics perspective,” Opt. Express 17(11), 9357–9368 (2009).
[CrossRef] [PubMed]

Rogers, J. L.

W. Ray, J. L. Rogers, and K. Wiesenfeld, “Coherence between two coupled lasers from a dynamics perspective,” Opt. Express 17(11), 9357–9368 (2009).
[CrossRef] [PubMed]

K. Wiesenfeld, S. Peles, and J. L. Rogers, “Effect of Gain-Dependent Phase Shift on Fiber Laser Synchronization,” IEEE J. Sel. Top. Quantum Electron. 15(2), 312–319 (2009).
[CrossRef]

J. L. Rogers, S. Peles, and K. Wiesenfeld, “Model for high-gain fiber laser arrays,” IEEE J. Quantum Electron. 41(6), 767–773 (2005).
[CrossRef]

H. Bruesselbach, D. C. Jones, M. S. Mangir, M. Minden, and J. L. Rogers, “Self-organized coherence in fiber laser arrays,” Opt. Lett. 30(11), 1339–1341 (2005).
[CrossRef] [PubMed]

Roy, V.

V. Roy, M. Piché, F. Babin, and G. W. Schinn, “Nonlinear wave mixing in a multilongitudinal-mode erbium-doped fiber laser,” Opt. Express 13(18), 6791–6797 (2005).
[CrossRef] [PubMed]

Sabourdy, D.

D. Sabourdy, V. Kermene, A. Desfarges-Berthelemot, L. Lefort, A. Barthelemy, P. Even, and D. Pureur, “Efficient coherent combining of widely tunable fiber lasers,” Opt. Express 11(2), 87–97 (2003).
[CrossRef] [PubMed]

D. Sabourdy, V. Kermene, A. Desfarges-Berthelemot, M. Vampouille, and A. Barthelemy, ““Coherent combining of two Nd: YAG lasers in a Vernier-Michelson-type cavity,” Appl. Phys. B-Lasers. 75, 503–507 (2002).
[CrossRef]

Saitou, T.

A. Shirakawa, T. Saitou, T. Sekiguchi, and K. Ueda, “Coherent addition of fiber lasers by use of a fiber coupler,” Opt. Express 10(21), 1167–1172 (2002).
[PubMed]

Sanchez, A.

B. S. Wang, E. Mies, M. Minden, and A. Sanchez, “All-fiber 50 W coherently combined passive laser array,” Opt. Lett. 34(7), 863–865 (2009).
[CrossRef] [PubMed]

Schinn, G. W.

V. Roy, M. Piché, F. Babin, and G. W. Schinn, “Nonlinear wave mixing in a multilongitudinal-mode erbium-doped fiber laser,” Opt. Express 13(18), 6791–6797 (2005).
[CrossRef] [PubMed]

Sekiguchi, T.

A. Shirakawa, T. Saitou, T. Sekiguchi, and K. Ueda, “Coherent addition of fiber lasers by use of a fiber coupler,” Opt. Express 10(21), 1167–1172 (2002).
[PubMed]

Shenoy, M. R.

B. N. Upadhyaya, U. Chakravarty, A. Kuruvilla, A. K. Nath, M. R. Shenoy, and K. Thyagarajan, “Effect of steady-state conditions on self-pulsing characteristics of Yb-doped cw fiber lasers,” Opt. Commun. 281(1), 146–153 (2008).
[CrossRef]

Shirakawa, A.

D. Kouznetsov, J. F. Bisson, A. Shirakawa, and K. Ueda, “Limits of coherent addition of lasers: Simple estimate,” Opt. Rev. 12(6), 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(21), 1167–1172 (2002).
[PubMed]

Thyagarajan, K.

B. N. Upadhyaya, U. Chakravarty, A. Kuruvilla, A. K. Nath, M. R. Shenoy, and K. Thyagarajan, “Effect of steady-state conditions on self-pulsing characteristics of Yb-doped cw fiber lasers,” Opt. Commun. 281(1), 146–153 (2008).
[CrossRef]

Ueda, K.

D. Kouznetsov, J. F. Bisson, A. Shirakawa, and K. Ueda, “Limits of coherent addition of lasers: Simple estimate,” Opt. Rev. 12(6), 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(21), 1167–1172 (2002).
[PubMed]

Upadhyaya, B. N.

B. N. Upadhyaya, U. Chakravarty, A. Kuruvilla, A. K. Nath, M. R. Shenoy, and K. Thyagarajan, “Effect of steady-state conditions on self-pulsing characteristics of Yb-doped cw fiber lasers,” Opt. Commun. 281(1), 146–153 (2008).
[CrossRef]

Vampouille, M.

D. Sabourdy, V. Kermene, A. Desfarges-Berthelemot, M. Vampouille, and A. Barthelemy, ““Coherent combining of two Nd: YAG lasers in a Vernier-Michelson-type cavity,” Appl. Phys. B-Lasers. 75, 503–507 (2002).
[CrossRef]

Wang, B. S.

B. S. Wang, E. Mies, M. Minden, and A. Sanchez, “All-fiber 50 W coherently combined passive laser array,” Opt. Lett. 34(7), 863–865 (2009).
[CrossRef] [PubMed]

Wiesenfeld, K.

K. Wiesenfeld, S. Peles, and J. L. Rogers, “Effect of Gain-Dependent Phase Shift on Fiber Laser Synchronization,” IEEE J. Sel. Top. Quantum Electron. 15(2), 312–319 (2009).
[CrossRef]

W. Ray, J. L. Rogers, and K. Wiesenfeld, “Coherence between two coupled lasers from a dynamics perspective,” Opt. Express 17(11), 9357–9368 (2009).
[CrossRef] [PubMed]

J. L. Rogers, S. Peles, and K. Wiesenfeld, “Model for high-gain fiber laser arrays,” IEEE J. Quantum Electron. 41(6), 767–773 (2005).
[CrossRef]

Winful, H. G.

W. Z. Chang, T. W. Wu, H. G. Winful, and A. Galvanauskas, “Array size scalability of passively coherently phased fiber laser arrays,” Opt. Express 18(9), 9634–9642 (2010).
[CrossRef] [PubMed]

T. W. Wu, W. Z. Chang, A. Galvanauskas, and H. G. Winful, “Model for passive coherent beam combining in fiber laser arrays,” Opt. Express 17(22), 19509–19518 (2009).
[CrossRef] [PubMed]

Wu, T. W.

W. Z. Chang, T. W. Wu, H. G. Winful, and A. Galvanauskas, “Array size scalability of passively coherently phased fiber laser arrays,” Opt. Express 18(9), 9634–9642 (2010).
[CrossRef] [PubMed]

T. W. Wu, W. Z. Chang, A. Galvanauskas, and H. G. Winful, “Model for passive coherent beam combining in fiber laser arrays,” Opt. Express 17(22), 19509–19518 (2009).
[CrossRef] [PubMed]

Xu, X. J.

J. Q. Cao, J. Hou, Q. S. Lu, and X. J. Xu, “Numerical research on self-organized coherent fiber laser arrays with circulating field theory,” J. Opt. Soc. Am. B 25(7), 1187–1192 (2008).
[CrossRef]

Appl. Phys. B-Lasers. (1)

D. Sabourdy, V. Kermene, A. Desfarges-Berthelemot, M. Vampouille, and A. Barthelemy, ““Coherent combining of two Nd: YAG lasers in a Vernier-Michelson-type cavity,” Appl. Phys. B-Lasers. 75, 503–507 (2002).
[CrossRef]

IEEE J. Quantum Electron. (2)

C. J. Corcoran and K. A. Pasch, “Output phase characteristics of a nonlinear regenerative fiber amplifier,” IEEE J. Quantum Electron. 43(6), 437–439 (2007).
[CrossRef]

J. L. Rogers, S. Peles, and K. Wiesenfeld, “Model for high-gain fiber laser arrays,” IEEE J. Quantum Electron. 41(6), 767–773 (2005).
[CrossRef]

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

K. Wiesenfeld, S. Peles, and J. L. Rogers, “Effect of Gain-Dependent Phase Shift on Fiber Laser Synchronization,” IEEE J. Sel. Top. Quantum Electron. 15(2), 312–319 (2009).
[CrossRef]

J. Lightwave Technol. (1)

D. Hollenbeck and C. D. Cantrell, “Parallelizable, bidirectional method for simulating optical-signal propagation,” J. Lightwave Technol. 27(12), 2140–2149 (2009).
[CrossRef]

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

J. Q. Cao, J. Hou, Q. S. Lu, and X. J. Xu, “Numerical research on self-organized coherent fiber laser arrays with circulating field theory,” J. Opt. Soc. Am. B 25(7), 1187–1192 (2008).
[CrossRef]

Opt. Commun. (2)

E. Martı́-Panameño, L. C. Gomez-Pavon, A. Luis-Ramos, M. M. Méndez-Otero, and M. D. I. Castillo, “Self-mode-locking action in a dual-core ring fiber laser,” Opt. Commun. 194, 409–414 (2001).
[CrossRef]

B. N. Upadhyaya, U. Chakravarty, A. Kuruvilla, A. K. Nath, M. R. Shenoy, and K. Thyagarajan, “Effect of steady-state conditions on self-pulsing characteristics of Yb-doped cw fiber lasers,” Opt. Commun. 281(1), 146–153 (2008).
[CrossRef]

Opt. Express (6)

W. Ray, J. L. Rogers, and K. Wiesenfeld, “Coherence between two coupled lasers from a dynamics perspective,” Opt. Express 17(11), 9357–9368 (2009).
[CrossRef] [PubMed]

V. Roy, M. Piché, F. Babin, and G. W. Schinn, “Nonlinear wave mixing in a multilongitudinal-mode erbium-doped fiber laser,” Opt. Express 13(18), 6791–6797 (2005).
[CrossRef] [PubMed]

T. W. Wu, W. Z. Chang, A. Galvanauskas, and H. G. Winful, “Model for passive coherent beam combining in fiber laser arrays,” Opt. Express 17(22), 19509–19518 (2009).
[CrossRef] [PubMed]

W. Z. Chang, T. W. Wu, H. G. Winful, and A. Galvanauskas, “Array size scalability of passively coherently phased fiber laser arrays,” Opt. Express 18(9), 9634–9642 (2010).
[CrossRef] [PubMed]

D. Sabourdy, V. Kermene, A. Desfarges-Berthelemot, L. Lefort, A. Barthelemy, P. Even, and D. Pureur, “Efficient coherent combining of widely tunable fiber lasers,” Opt. Express 11(2), 87–97 (2003).
[CrossRef] [PubMed]

A. Shirakawa, T. Saitou, T. Sekiguchi, and K. Ueda, “Coherent addition of fiber lasers by use of a fiber coupler,” Opt. Express 10(21), 1167–1172 (2002).
[PubMed]

Opt. Lett. (3)

H. Bruesselbach, D. C. Jones, M. S. Mangir, M. Minden, and J. L. Rogers, “Self-organized coherence in fiber laser arrays,” Opt. Lett. 30(11), 1339–1341 (2005).
[CrossRef] [PubMed]

J. Kanka, “Numerical simulation of subpicosecond soliton formation in a nonlinear coupler laser,” Opt. Lett. 19(22), 1873–1875 (1994).
[CrossRef] [PubMed]

B. S. Wang, E. Mies, M. Minden, and A. Sanchez, “All-fiber 50 W coherently combined passive laser array,” Opt. Lett. 34(7), 863–865 (2009).
[CrossRef] [PubMed]

Opt. Rev. (1)

D. Kouznetsov, J. F. Bisson, A. Shirakawa, and K. Ueda, “Limits of coherent addition of lasers: Simple estimate,” Opt. Rev. 12(6), 445–447 (2005).
[CrossRef]

Other (7)

A. Shirakawa, K. Matsuo, and K. Ueda, “Fiber laser coherent array for power scaling, bandwidth narrowing, and coherent beam direction control,” in Conference on Fiber Lasers II, L. N. Durvasula, A. J. W. Brown, and J. Nilsson, eds. (San Jose, CA, 2005), pp. 165–174.

G. P. Agrawal, Nonlinear fiber optics, third edition (Academic Press, 2001), pp. 263–264.

A. E. Siegman, Lasers (University Science Books (January 1986)), pp. 485–487.

A. Yariv, Photonics: Optical Electronics in Modern Communications, 6th Edition (Oxford University Press, USA, 2007), pp. 563–565.

H. Bruesselbach, M. Minden, J. L. Rogers, D. C. Jones, and M. S. Mangir, “200 W self-organized coherent fiber arrays,” in 2005 Conference on Lasers & Electro-Optics (2005), pp. 532–534.

A. E. Siegman, “Resonant modes of linearly coupled multiple fiber laser structures,” unpublished at http://www.stanford.edu/~siegman/Coupled%20Fiber%20Lasers/coupled_fiber_modes.pdf (2004).

E. J. Bochove, “Effect of nonlinear phase on the passive phase locking of an array of fiber lasers of random lengths,” in Integrated Photonics and Nanophotonics Research and Applications (IPNRA) (Honolulu, Hawaii, 2009).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (11)

Fig. 1
Fig. 1

A two-channel fiber laser array.

Fig. 2
Fig. 2

The spatial distributions of one of the fiber laser (L1 = 24.3 m) are plotted as an example for (a) both propagating waves and (b) the gain field along the z axis. The three curves consisting of red circles present the self-consistent steady-state solutions obtained from our model, while that of solid black lines are calculated from Matlab with its built-in BVP solver. As for array dynamics, the time evolution of the output power and the averaged gain variable (over z) of each fiber are displayed in (c) and (d). The output power refers to the combined power coming out of the partially-reflected, R1, port as seen in Fig. 1.

Fig. 4
Fig. 4

Evolution diagram of the output power spectrum for (a) the array modes, (b) the zoom-in longitudinal modes and (c) the relative phase difference Δ ϕ (π) between two incident (backward) waves at z = 0. All of them start from random and noisy spontaneous emissions. The free spectral range in (b) is 4.1MHz.

Fig. 3
Fig. 3

An Er-doped fiber laser array in Fig. 1 with L1 24.3 and L2 24.0 m. The output powers from (a) upper port with partial reflectivity and (b) lower, angle-cleaved, port are plotted for time (left) and frequency (right) domains respectively. The separation between spikes in the frequency domain is 0.333 GHz.

Fig. 5
Fig. 5

A two-channel fiber laser array is simulated with γ = 0.9 W−1m−1. The array outputs are plotted in (a) and (b) respectively for both temporal (left) and spectral (right) domains. The relative phase difference of the circled spectral packets (in (a)) is plotted in (c) for nonlinear and in (d) for linear fiber laser arrays.

Fig. 6
Fig. 6

The logarithmic plot of the output power ratio in terms of relative phase Δ ϕ .

Fig. 7
Fig. 7

A unidirectional two-channel fiber laser array.

Fig. 8
Fig. 8

Power spectra of a two channel fiber laser array with fiber lengths 24.0005m and 24.0m for (a) b = 0 ps2m−1 and (b) b = 0.13 ps2m−1.

Fig. 9
Fig. 9

The frequency dependent losses (m−1), plotted in the log scale with blue lines, are overlapped with the lasing spectrum of the output fields (red spikes) for (a) zero and (b) nonzero b coefficients respectively.

Fig. A1
Fig. A1

A four-channel fiber laser array. The figure is taken and modified from Ref [25].

Fig. A2
Fig. A2

Coherent combining of a four-channel fiber laser array with lengths 24.0, 24.3, 23.733 and 24.633 m. The period of the power spectrum pattern indicated by the red arrow is measured to be 66.7 GHz.

Equations (19)

Equations on this page are rendered with MathJax. Learn more.

E j f z = 1 2 ( g j α ) E j f β 1 E j f t + 1 2 ( b i β 2 ) 2 E j f t 2 + i γ ( | E j f | 2 + 2 | E j b | 2 ) E j f
E j b z = 1 2 ( g j α ) E j b + β 1 E j b t 1 2 ( b i β 2 ) 2 E j b t 2 i γ ( 2 | E j f | 2 + | E j b | 2 ) E j b
τ d g j ( z , t ) d t = g 0 j g j ( z , t ) | E j f | 2 + | E j b | 2 P s a t g j ( z , t )
( A 1 A 2 ) = 1 2 ( 1 j j 1 ) ( E 1 b E 2 b )
τ d g j ( z , t ) d t = g 0 j g j ( z , t ) 1 P s a t ( d | E j f | 2 d z d | E j b | 2 d z )
τ d g ˜ j ( t ) d t = g ˜ 0 j g ˜ j ( t ) 1 P s a t ( | E j f ( z 0 + ) | 2 | E j f ( z 0 ) | 2 | E j b ( z 0 + ) | 2 + | E j b ( z 0 ) | 2 )
τ d g ˜ j ( t ) d t = g ˜ 0 j g ˜ j ( t ) 1 P s a t [ | E j f ( z 0 ) | 2 ( e g ˜ j ( z 0 ) 1 ) + | E j b ( z 0 + ) | 2 ( e g ˜ j ( z 0 + ) 1 ) ]
g ˜ j ' = g ˜ j + d g ˜ j d t Δ t
N channel combined power efficiency = P o u t / 1 N P i
P 1 P 2 = 1 sin ( Δ ϕ ) 1 + sin ( Δ ϕ )
P ( 1 + sin ( Δ ϕ ) ) × R × 1 2 exp [ ( g α b ω 2 ) L ] = P
g = α + b ω 2 log ( R ( 1 + sin ( Δ ϕ ) ) / 2 ) L
2 π n 1 f c 0 2 ( L 2 L 1 ) = 3 π 2 + m 1 2 π 2 π n 1 f c 0 2 ( L 3 L 4 ) = 3 π 2 + m 2 2 π 2 π n 1 f c 0 2 ( L 3 L 2 ) = 3 π 2 + m 3 2 π
1 2 [ 1 j j 1 ] [ e j 2 k L 1 e j 2 k L 2 ] = 1 2 [ e j 2 k L 1 j e j 2 k L 2 j e j 2 k L 1 + e j 2 k L 2 ]
2 π n 1 f ¯ c 0 2 ( L 2 L 1 ) = 3 π 2 + m 1 2 π + Δ ϕ 1 2 π n 1 f ¯ c 0 2 ( L 3 L 4 ) = 3 π 2 + m 2 2 π + Δ ϕ 2 2 π n 1 f ¯ c 0 2 ( L 3 L 2 ) = 3 π 2 + m 3 2 π + Δ ϕ 3
2 π n 1 ( f ¯ + Δ v ) c 0 2 ( L 2 L 1 ) = 3 π 2 + ( m 1 + p 1 ) 2 π + Δ ϕ 1 2 π n 1 ( f ¯ + Δ v ) c 0 2 ( L 3 L 4 ) = 3 π 2 + ( m 2 + p 2 ) 2 π + Δ ϕ 2 2 π n 1 ( f ¯ + Δ v ) c 0 2 ( L 2 L 3 ) = 3 π 2 + ( m 3 + p 3 ) 2 π + Δ ϕ 3
2 π n 1 Δ v c 0 2 ( L 2 L 1 ) = p 1 2 π 2 π n 1 Δ v c 0 2 ( L 3 L 4 ) = p 2 2 π 2 π n 1 Δ v c 0 2 ( L 2 L 3 ) = p 3 2 π
Δ ν = c 0 2 n 1 Δ L c = LCM[ c 0 2 n 1 ( L 1 L 2 ) , c 0 2 n 1 ( L 2 L 3 ) , c 0 2 n 1 ( L 3 L 4 ) ]
Δ v = c 0 2 n 1 Δ L gcd

Metrics