Abstract

We present a new model for studying the beam combining mechanism, spectral and temporal dynamics, the role of nonlinearity, and the power scaling issue of discretely coupled fiber laser arrays. The model accounts for the multiple longitudinal modes of individual fiber lasers and shows directly the formation of the composite-cavity modes. Detailed output power spectra and their evolution with increasing array size and pump power are also explored for the first time. In addition, it is, to our knowledge, the only model that closely resembles the real experimental conditions in which no deliberate control of the fiber lengths (mismatch) is required while highly efficient coherent beam combining is still attained.

© 2009 Optical Society of America

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References

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  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(5), 439-441 (2001).
    [CrossRef]
  2. D. Sabourdy, V. Kermene, A. Desfarges-Berthelemot, L. Lefort, A. Barthelemy, C. Mahodaux, and D. Pureur, "Power scaling of fibre lasers with all-fibre interferometric cavity," Electron. Lett. 38(14), 692-693 (2002).
    [CrossRef]
  3. 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).
  4. T. B. Simpson, A. Gavrielides, and P. Peterson, "Extraction characteristics of a dual fiber compound cavity," Opt. Express 10(20), 1060-1073 (2002).
    [PubMed]
  5. 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]
  6. 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.
  7. A. E. Siegman, "Resonant modes of linearly coupled multiple fiber laser structures," unpublished.
  8. 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]
  9. J. E. Rothenberg, "Passive coherent phasing of fiber laser arrays," Proc. SPIE 6873, 687315.1-6873-15.9 (2008).
  10. 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]
  11. 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]
  12. 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]
  13. 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]
  14. 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]
  15. S. P. Chen, Y. G. Li, K. C. Lu, and S. H. Zhou, "Efficient coherent combining of tunable erbium-doped fibre ring lasers," J. Opt. Soc. A 9, 642-648 (2007).
  16. T. B. Simpson, F. Doft, P. R. Peterson, and A. Gavrielides, "Coherent combining of spectrally broadened fiber lasers," Opt. Express 15(18), 11731-11740 (2007).
    [CrossRef]
  17. E. Desurvire, "Anlysis of ebium-doped fiber amplifiers pumped in the I-4(15/2)-I-4(13/2) band," IEEE Photon. Technol. Lett. 1, 293-296 (1989).
    [CrossRef]
  18. E. Desurvire, C. R. Giles, and J. R. Simpson, "Gain saturation effects in high-speed, multichannel erbium=doped fiber amplifiers at ? = 1.53 ?m," J. Lightwave Technol. 7(12), 2095-2104 (1989).
    [CrossRef]
  19. C. R. Giles, E. Desurvire, and J. R. Simpson, "Transient gain and cross talk in erbium-doped fiber amplifiers," Opt. Lett. 14(16), 880-882 (1989).
    [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 75, 503-507 (2002).
    [CrossRef]
  21. M. Didomenico, "A single-frequency TEM00-mode gas laser with high output power," Appl. Phys. Lett. 8(1), 20-22 (1966).
    [CrossRef]
  22. T. Wu, W. Chang, A. Galvanauskas, and H. G. Winful, unpublished.

2009 (1)

2008 (1)

2007 (2)

S. P. Chen, Y. G. Li, K. C. Lu, and S. H. Zhou, "Efficient coherent combining of tunable erbium-doped fibre ring lasers," J. Opt. Soc. A 9, 642-648 (2007).

T. B. Simpson, F. Doft, P. R. Peterson, and A. Gavrielides, "Coherent combining of spectrally broadened fiber lasers," Opt. Express 15(18), 11731-11740 (2007).
[CrossRef]

2005 (4)

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]

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]

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]

2003 (1)

2002 (4)

D. Sabourdy, V. Kermene, A. Desfarges-Berthelemot, L. Lefort, A. Barthelemy, C. Mahodaux, and D. Pureur, "Power scaling of fibre lasers with all-fibre interferometric cavity," Electron. Lett. 38(14), 692-693 (2002).
[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).

T. B. Simpson, A. Gavrielides, and P. Peterson, "Extraction characteristics of a dual fiber compound cavity," Opt. Express 10(20), 1060-1073 (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 75, 503-507 (2002).
[CrossRef]

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(5), 439-441 (2001).
[CrossRef]

1989 (3)

E. Desurvire, "Anlysis of ebium-doped fiber amplifiers pumped in the I-4(15/2)-I-4(13/2) band," IEEE Photon. Technol. Lett. 1, 293-296 (1989).
[CrossRef]

E. Desurvire, C. R. Giles, and J. R. Simpson, "Gain saturation effects in high-speed, multichannel erbium=doped fiber amplifiers at ? = 1.53 ?m," J. Lightwave Technol. 7(12), 2095-2104 (1989).
[CrossRef]

C. R. Giles, E. Desurvire, and J. R. Simpson, "Transient gain and cross talk in erbium-doped fiber amplifiers," Opt. Lett. 14(16), 880-882 (1989).
[CrossRef]

1966 (1)

M. Didomenico, "A single-frequency TEM00-mode gas laser with high output power," Appl. Phys. Lett. 8(1), 20-22 (1966).
[CrossRef]

Babin, F.

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]

D. Sabourdy, V. Kermene, A. Desfarges-Berthelemot, L. Lefort, A. Barthelemy, C. Mahodaux, and D. Pureur, "Power scaling of fibre lasers with all-fibre interferometric cavity," Electron. Lett. 38(14), 692-693 (2002).
[CrossRef]

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 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.

Cao, J. Q.

Chen, S. P.

S. P. Chen, Y. G. Li, K. C. Lu, and S. H. Zhou, "Efficient coherent combining of tunable erbium-doped fibre ring lasers," J. Opt. Soc. A 9, 642-648 (2007).

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(5), 439-441 (2001).
[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]

D. Sabourdy, V. Kermene, A. Desfarges-Berthelemot, L. Lefort, A. Barthelemy, C. Mahodaux, and D. Pureur, "Power scaling of fibre lasers with all-fibre interferometric cavity," Electron. Lett. 38(14), 692-693 (2002).
[CrossRef]

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 75, 503-507 (2002).
[CrossRef]

Desurvire, E.

E. Desurvire, "Anlysis of ebium-doped fiber amplifiers pumped in the I-4(15/2)-I-4(13/2) band," IEEE Photon. Technol. Lett. 1, 293-296 (1989).
[CrossRef]

E. Desurvire, C. R. Giles, and J. R. Simpson, "Gain saturation effects in high-speed, multichannel erbium=doped fiber amplifiers at ? = 1.53 ?m," J. Lightwave Technol. 7(12), 2095-2104 (1989).
[CrossRef]

C. R. Giles, E. Desurvire, and J. R. Simpson, "Transient gain and cross talk in erbium-doped fiber amplifiers," Opt. Lett. 14(16), 880-882 (1989).
[CrossRef]

Didomenico, M.

M. Didomenico, "A single-frequency TEM00-mode gas laser with high output power," Appl. Phys. Lett. 8(1), 20-22 (1966).
[CrossRef]

Doft, F.

Even, P.

Gavrielides, A.

Giles, C. R.

C. R. Giles, E. Desurvire, and J. R. Simpson, "Transient gain and cross talk in erbium-doped fiber amplifiers," Opt. Lett. 14(16), 880-882 (1989).
[CrossRef]

E. Desurvire, C. R. Giles, and J. R. Simpson, "Gain saturation effects in high-speed, multichannel erbium=doped fiber amplifiers at ? = 1.53 ?m," J. Lightwave Technol. 7(12), 2095-2104 (1989).
[CrossRef]

Hou, J.

Jones, D. C.

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]

D. Sabourdy, V. Kermene, A. Desfarges-Berthelemot, L. Lefort, A. Barthelemy, C. Mahodaux, and D. Pureur, "Power scaling of fibre lasers with all-fibre interferometric cavity," Electron. Lett. 38(14), 692-693 (2002).
[CrossRef]

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 75, 503-507 (2002).
[CrossRef]

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(5), 439-441 (2001).
[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]

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]

D. Sabourdy, V. Kermene, A. Desfarges-Berthelemot, L. Lefort, A. Barthelemy, C. Mahodaux, and D. Pureur, "Power scaling of fibre lasers with all-fibre interferometric cavity," Electron. Lett. 38(14), 692-693 (2002).
[CrossRef]

Li, Y. G.

S. P. Chen, Y. G. Li, K. C. Lu, and S. H. Zhou, "Efficient coherent combining of tunable erbium-doped fibre ring lasers," J. Opt. Soc. A 9, 642-648 (2007).

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(5), 439-441 (2001).
[CrossRef]

Lu, K. C.

S. P. Chen, Y. G. Li, K. C. Lu, and S. H. Zhou, "Efficient coherent combining of tunable erbium-doped fibre ring lasers," J. Opt. Soc. A 9, 642-648 (2007).

Lu, Q. S.

Mahodaux, C.

D. Sabourdy, V. Kermene, A. Desfarges-Berthelemot, L. Lefort, A. Barthelemy, C. Mahodaux, and D. Pureur, "Power scaling of fibre lasers with all-fibre interferometric cavity," Electron. Lett. 38(14), 692-693 (2002).
[CrossRef]

Mangir, M. S.

Minden, M.

Peles, S.

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]

Peterson, P.

Peterson, P. R.

Piché, M.

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]

D. Sabourdy, V. Kermene, A. Desfarges-Berthelemot, L. Lefort, A. Barthelemy, C. Mahodaux, and D. Pureur, "Power scaling of fibre lasers with all-fibre interferometric cavity," Electron. Lett. 38(14), 692-693 (2002).
[CrossRef]

Ray, W.

Rogers, J. L.

Roy, V.

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]

D. Sabourdy, V. Kermene, A. Desfarges-Berthelemot, L. Lefort, A. Barthelemy, C. Mahodaux, and D. Pureur, "Power scaling of fibre lasers with all-fibre interferometric cavity," Electron. Lett. 38(14), 692-693 (2002).
[CrossRef]

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 75, 503-507 (2002).
[CrossRef]

Saitou, T.

Schinn, G. W.

Sekiguchi, T.

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).

Simpson, J. R.

C. R. Giles, E. Desurvire, and J. R. Simpson, "Transient gain and cross talk in erbium-doped fiber amplifiers," Opt. Lett. 14(16), 880-882 (1989).
[CrossRef]

E. Desurvire, C. R. Giles, and J. R. Simpson, "Gain saturation effects in high-speed, multichannel erbium=doped fiber amplifiers at ? = 1.53 ?m," J. Lightwave Technol. 7(12), 2095-2104 (1989).
[CrossRef]

Simpson, T. B.

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).

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 75, 503-507 (2002).
[CrossRef]

Wiesenfeld, K.

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]

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]

Xu, X. J.

Zhou, S. H.

S. P. Chen, Y. G. Li, K. C. Lu, and S. H. Zhou, "Efficient coherent combining of tunable erbium-doped fibre ring lasers," J. Opt. Soc. A 9, 642-648 (2007).

Appl. Phys. B (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 75, 503-507 (2002).
[CrossRef]

Appl. Phys. Lett. (1)

M. Didomenico, "A single-frequency TEM00-mode gas laser with high output power," Appl. Phys. Lett. 8(1), 20-22 (1966).
[CrossRef]

Electron. Lett. (1)

D. Sabourdy, V. Kermene, A. Desfarges-Berthelemot, L. Lefort, A. Barthelemy, C. Mahodaux, and D. Pureur, "Power scaling of fibre lasers with all-fibre interferometric cavity," Electron. Lett. 38(14), 692-693 (2002).
[CrossRef]

IEEE J. Quantum Electron. (1)

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 Photon. Technol. Lett. (2)

E. Desurvire, "Anlysis of ebium-doped fiber amplifiers pumped in the I-4(15/2)-I-4(13/2) band," IEEE Photon. Technol. Lett. 1, 293-296 (1989).
[CrossRef]

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(5), 439-441 (2001).
[CrossRef]

J. Lightwave Technol. (1)

E. Desurvire, C. R. Giles, and J. R. Simpson, "Gain saturation effects in high-speed, multichannel erbium=doped fiber amplifiers at ? = 1.53 ?m," J. Lightwave Technol. 7(12), 2095-2104 (1989).
[CrossRef]

J. Opt. Soc. A (1)

S. P. Chen, Y. G. Li, K. C. Lu, and S. H. Zhou, "Efficient coherent combining of tunable erbium-doped fibre ring lasers," J. Opt. Soc. A 9, 642-648 (2007).

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

Opt. Express (6)

Opt. Lett. (2)

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 (4)

J. E. Rothenberg, "Passive coherent phasing of fiber laser arrays," Proc. SPIE 6873, 687315.1-6873-15.9 (2008).

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.

A. E. Siegman, "Resonant modes of linearly coupled multiple fiber laser structures," unpublished.

T. Wu, W. Chang, A. Galvanauskas, and H. G. Winful, unpublished.

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Figures (8)

Fig. 1.
Fig. 1.

A two-channel fiber laser array structure.

Fig. 2.
Fig. 2.

A two-channel fiber laser array in the unidirectional configuration.

Fig. 3.
Fig. 3.

Output powers of single Er-doped fiber laser in the time (left) and spectral (right) domains for (a) γ=0.003 m-1W-1 and (b) γ=0 m-1W-1. The power reflectivity is 4% as indicated in the figure.

Fig. 4.
Fig. 4.

A unidirectional Er-doped fiber laser array with L1 =24.3 and L2 =24.0 m in Fig. 2. The output powers from (a) upper port with partial reflectivity and (b) lower, angle-cleaved, port. The separation between spikes is measured to be 0.667 GHz.

Fig. 5.
Fig. 5.

, Power spectrum of a two-channel fiber laser array with L1 =24.08 m and L2 =24.0 m. P1 in (a) refers to the output power from the port of 4% reflectivity, and P2 (b) is from the angle-cleaved one. The spikes are separated by 2.5 GHz. The spectrum of the green-circled spike of (a) is further zoomed in for (c) linear and (d) nonlinear arrays.

Fig. 6.
Fig. 6.

Er-doped fiber laser arrays configured in Fig. 2 with L1 =24.001 and L2 =24.0 m. The computation window in frequency domain covers more than 1 THz. The left plots refer to the output powers from the port with partial reflectivity, while the right ones show the other, anglecleaved, one. No frequency-dependent losses are applied for (a) and b equals 0.13 ps2m-1 in (b).

Fig. 7.
Fig. 7.

Beat spectra of amplified spontaneous emission for the higher reflectivity port (red curves) and the zero-reflectivity port (blue curves) an Er-doped fiber laser array with round-trip path length difference of 0.682 m. (a) Simulation result obtained by averaging the spectrum over 500 consecutive roundtrips (b) Experimental beat spectrum measurement from Ref [3], used with permission. (c) Simulation of spectrum above threshold.

Fig. 8.
Fig. 8.

Four-channel fiber laser array (a) spectrum of amplified spontaneous emissions with pattern periods measured to be 6.67 GHz. (b) Major output powers in the temporal (left) and spectral (right) domains.

Tables (1)

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Table 1., parameters and values

Equations (4)

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Ejz=12(gjα)Ejβ1Ejt+12(biβ2)2Ejt2+iγEj2Ej
ΔNjt=Rp(t)ΔNjτσEi2hνAeffΔNj
(A1A2)=12 (1jj1) (E1E2)
gj=g0j(1+0TEj2dtTPsat)

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