Abstract

We present a dynamic model of simultaneous passive coherent beam combining and passive mode locking for coupled fiber lasers. The presence of a saturable absorber in the composite cavity results in the generation of packets of mode locked pulse trains. Within each packet the repetition rate of the pulses is determined by the length difference between the fibers.

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References

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  1. B. Wang and A. Sanchez, “All-fiber passive coherent combining of high power lasers,” Opt. Eng.50(11), 111606 (2011).
    [CrossRef]
  2. A. Shirakawa, T. Saitou, T. Sekiguchi, and K. Ueda, “Coherent addition of fiber lasers by use of a fiber coupler,” Opt. Express10(21), 1167–1172 (2002).
    [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. Express11(2), 87–97 (2003).
    [CrossRef] [PubMed]
  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]
  5. T. B. Simpson, F. Doft, P. R. Peterson, and A. Gavrielides, “Coherent combining of spectrally broadened fiber lasers,” Opt. Express15(18), 11731–11740 (2007).
    [CrossRef] [PubMed]
  6. W. Z. Chang, T. W. Wu, H. G. Winful, and A. Galvanauskas, “Array size scalability of passively coherently phased fiber laser arrays,” Opt. Express18(9), 9634–9642 (2010).
    [CrossRef] [PubMed]
  7. D. Sabourdy, A. Desfarges-Berthelemot, V. Kermene, and A. Barthelemy, “Coherent combining of Q-switched fiber lasers,” Electron. Lett.40(20), 1254–1255 (2004).
    [CrossRef]
  8. J. Lhermite, D. Sabourdy, A. Desfarges-Berthelemot, V. Kermene, A. Barthelemy, and J. L. Oudar, “Tunable high-repetition-rate fiber laser for the generation of pulse trains and packets,” Opt. Lett.32(12), 1734–1736 (2007).
    [CrossRef] [PubMed]
  9. M. E. Fermann and I. Hartl, “Ultrafast fiber laser technology,” IEEE J. Sel. Top. Quantum Electron.15(1), 191–206 (2009).
    [CrossRef]
  10. C. Zhang, W. Chang, A. Galvanauskas, and H. G. Winful, “Simultaneous passive coherent combining and mode locking in fiber laser arrays,” paper JWA28, Conference on Lasers and Electrooptics, 2011.
  11. T. W. Wu, W. Z. Chang, A. Galvanauskas, and H. G. Winful, “Model for passive coherent beam combining in fiber laser arrays,” Opt. Express17(22), 19509–19518 (2009).
    [CrossRef] [PubMed]
  12. T. W. Wu, W. Z. Chang, A. Galvanauskas, and H. G. Winful, “Dynamical, bidirectional model for coherent beam combining in passive fiber laser arrays,” Opt. Express18(25), 25873–25886 (2010).
    [CrossRef] [PubMed]
  13. C. J. Corcoran and K. A. Pasch, “Output phase characteristics of a nonlinear fiber regenerative amplifier,” IEEE J. Quantum Electron.43(6), 437–439 (2007).
    [CrossRef]

2011 (1)

B. Wang and A. Sanchez, “All-fiber passive coherent combining of high power lasers,” Opt. Eng.50(11), 111606 (2011).
[CrossRef]

2010 (2)

2009 (2)

2007 (3)

2005 (1)

2004 (1)

D. Sabourdy, A. Desfarges-Berthelemot, V. Kermene, and A. Barthelemy, “Coherent combining of Q-switched fiber lasers,” Electron. Lett.40(20), 1254–1255 (2004).
[CrossRef]

2003 (1)

2002 (1)

Barthelemy, A.

Bruesselbach, H.

Chang, W. Z.

Corcoran, C. J.

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

Desfarges-Berthelemot, A.

Doft, F.

Even, P.

Fermann, M. E.

M. E. Fermann and I. Hartl, “Ultrafast fiber laser technology,” IEEE J. Sel. Top. Quantum Electron.15(1), 191–206 (2009).
[CrossRef]

Galvanauskas, A.

Gavrielides, A.

Hartl, I.

M. E. Fermann and I. Hartl, “Ultrafast fiber laser technology,” IEEE J. Sel. Top. Quantum Electron.15(1), 191–206 (2009).
[CrossRef]

Jones, D. C.

Kermene, V.

Lefort, L.

Lhermite, J.

Mangir, M. S.

Minden, M.

Oudar, J. L.

Pasch, K. A.

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

Peterson, P. R.

Pureur, D.

Rogers, J. L.

Sabourdy, D.

Saitou, T.

Sanchez, A.

B. Wang and A. Sanchez, “All-fiber passive coherent combining of high power lasers,” Opt. Eng.50(11), 111606 (2011).
[CrossRef]

Sekiguchi, T.

Shirakawa, A.

Simpson, T. B.

Ueda, K.

Wang, B.

B. Wang and A. Sanchez, “All-fiber passive coherent combining of high power lasers,” Opt. Eng.50(11), 111606 (2011).
[CrossRef]

Winful, H. G.

Wu, T. W.

Electron. Lett. (1)

D. Sabourdy, A. Desfarges-Berthelemot, V. Kermene, and A. Barthelemy, “Coherent combining of Q-switched fiber lasers,” Electron. Lett.40(20), 1254–1255 (2004).
[CrossRef]

IEEE J. Quantum Electron. (1)

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

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

M. E. Fermann and I. Hartl, “Ultrafast fiber laser technology,” IEEE J. Sel. Top. Quantum Electron.15(1), 191–206 (2009).
[CrossRef]

Opt. Eng. (1)

B. Wang and A. Sanchez, “All-fiber passive coherent combining of high power lasers,” Opt. Eng.50(11), 111606 (2011).
[CrossRef]

Opt. Express (6)

Opt. Lett. (2)

Other (1)

C. Zhang, W. Chang, A. Galvanauskas, and H. G. Winful, “Simultaneous passive coherent combining and mode locking in fiber laser arrays,” paper JWA28, Conference on Lasers and Electrooptics, 2011.

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Figures (13)

Fig. 1
Fig. 1

The Michelson interferometer structure for mode locking of two coupled fiber lasers. There is an angle cleave at Port 1 while a saturable absorber (SA) mirror is connected to the output port 2 to provide feedback and a mode locking mechanism.

Fig. 2
Fig. 2

(a): The spectral profile (blue, solid lines) at Port 2 of two-channel beam combining with lengths 8.053 m and 8.071 m in the absence of a saturable absorber; the phase difference Δϕ between two adjacent longitudinal modes around the array modes (green crosses). (b): The related temporal profile at Port 2 for one roundtrip time. Note the fast oscillation with a frequency of about 5.5 GHz.

Fig. 3
Fig. 3

The spectral profile (a) of two-channel beam combining and mode locking with fiber lengths 8.053 m and 8.071 m at Port 2 without nonlinearity. A saturable absorber partial mirror is used at Port 2. In the zoomed figure (b), the phase difference between two adjacent longitudinal modes is also plotted (green crosses). The phase difference Δϕ remains at around 1.31π for the frequencies around the array mode.

Fig. 4
Fig. 4

The temporal profile at Port 2 of two fiber beam combining and mode locking with lengths 8.053 m and 8.071 m without nonlinearity. The figures are zoomed in from (a) one roundtrip time to (c) one single pulse.

Fig. 5
Fig. 5

The Mach-Zehnder interferometer structure for two-channel beam combining. An angle cleave and a partial mirror are connected to the left hand side 50:50 directional coupler, and another angle cleave and a saturable absorber mirror are connected to the other 50:50 directional coupler.

Fig. 6
Fig. 6

The pulse packet output for the Mach-Zehnder ring cavity structure shown in Fig. 5, in the absence of nonlinearity. The length differences between two channels are (a) 5.1 mm, (b) 3.5 mm and (c) 2.1 mm respectively.

Fig. 7
Fig. 7

Comparison between simulation results (left) and the experimental results of Lhermite et. al. [8] (right) for (a) ΔL = 5.1 mm, (b) ΔL = 3.5 mm, and (c) ΔL = 2.1 mm. The corrected pulse separations are included in parentheses on the experimental plots. Experimental figure used by permission.

Fig. 8
Fig. 8

The time series (left) as well as intensity autocorrelation traces (right) for increased nonlinearity γ=0.004 m 1 W 1 , with (a) ΔL = 5.1 mm, (b) ΔL = 3.5 mm, and (c) ΔL = 2.1 mm.

Fig. 9
Fig. 9

Frequency spectra (blue, solid curves) and spectral phase (green crosses) in two-fiber-laser beam combining and mode locking for γ=0.004 m 1 W 1 , with (a) ΔL = 5.1 mm, (b) ΔL = 3.5 mm, and (c) ΔL = 2.1 mm.

Fig. 10
Fig. 10

The structure of four-element fiber laser array with tree structure.

Fig. 11
Fig. 11

The spectrum in log scale (a) and temporal profile for one roundtrip time (b) for four-channel combining without saturable absorber. The four fiber lengths are independently randomly selected: 8.000 m, 8.011 m, 8.024 m and 8.041 m. Here the Kerr nonlinearity is 0.003 m−1W−1.

Fig. 12
Fig. 12

The spectral (a) and temporal profiles (b) for four-channel coupling with saturable absorber and with 0.003 m−1W−1 Kerr nonlinearity. The fiber lengths are 8.000 m, 8.011 m, 8.024 m and 8.041 m. (b) denotes one roundtrip time and it is further zoomed to (c) and (d).

Fig. 13
Fig. 13

The spectral (a, b) and temporal (c, d, e) profiles for four-channel combining with saturable absorber and with 0.003 m−1W−1 Kerr nonlinearity. Here the four fiber lengths 8.050 m, 8.260 m, 8.200 m and 8.530 m are carefully designed for a 30 mm GCD for their differences.

Tables (1)

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Table 1 Parameter values used in simulations.

Equations (3)

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E j z = 1 2 ( g j α) E j β 1 E j t + 1 2 (bi β 2 ) 2 E j t 2 +iγ | E j | 2 E j ,
g= g 0 1+ 0 T | E | 2 dt T P sat ,
α SA = α 0 1+ | E | 2 P SA ,

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