Abstract

We present a phenomenological model that describes the self-starting properties of a passively Q-switched fiber laser with a nonlinear mirror. The model predicts a self-pulsing behavior above a critical value of the pumping parameter and is in good agreement with experimental data reported for an Yb-doped fiber laser with a liquefying gallium mirror.

© 2001 Optical Society of America

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References

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  1. P. Petropoulos, H. L. Hofferhaus, D. J. Richardson, S. Dhanjal, and N. I. Zheludev, “Passive Q-switching of fiber lasers using a broadband liquefying gallium mirror,” Appl. Phys. Lett. 74, 3619–3621 (1999).
    [CrossRef]
  2. P. Petropoulos, S. Dhanjal, D. J. Richardson, and N. I. Zheludev, “Passive Q-switching of an Er3+:Yb3+ fiber laser with a fibrised liquefying gallium mirror,” Opt. Commun. 166, 239–243 (1999).
    [CrossRef]
  3. S. V. Chernikov, Y. Zhu, J. R. Taylor, and V. P. Gapontsev, “Supercontiuum self-Q-switched ytterbium fiber laser,” Opt. Lett. 22, 298–300 (1997).
    [CrossRef] [PubMed]
  4. F. Sanchez and G. Stephan, “General analysis of instabili-ties in erbium-doped fiber lasers,” Phys. Rev. E 53, 2110–2122 (1996).
    [CrossRef]
  5. Z. J. Chen, A. B. Grudinin, J. Porta, and J. D. Minelly, “En-hanced Q-switching in double-clad fiber lasers,” Opt. Lett. 23, 454–456 (1998).
    [CrossRef]
  6. S. D. Jackson and T. A. King, “Dynamics of the output of heavily Tm-doped double-clad silica fiber lasers,” J. Opt. Soc. Am. B 16, 2178–2188 (1999).
    [CrossRef]
  7. P. Glas, M. Naumann, A. Schirrmacher, L. Däweritz, and R. Hey, “Self-pulsing versus self-locking in cw pumped neodymium doped double-clad fiber laser,” Opt. Commun. 161, 345–358 (1999).
    [CrossRef]
  8. W. W. Rigrod, “Gain saturation and output power of optical masers,” J. Appl. Phys. 34, 2602–2609 (1963).
    [CrossRef]
  9. T. Chartier, F. Sanchez, and G. Stephan, “General model for a multimode Nd-doped fiber laser. II. Steady-state analysis of length-dependent polarization effects,” Appl. Phys. B 70, 33–43 (2000).
    [CrossRef]
  10. T. Chartier, B. Meziane, F. Sanchez, G. Stephan, and P. L. François, “Optical feedback effects in Nd-doped fiber lasers with broadband spectra,” Appl. Opt. 35, 2016–2022 (1996).
    [CrossRef] [PubMed]
  11. J. D. Crawford, “Introduction to bifurcation theory,” Rev. Mod. Phys. 63, 991–1037 (1991).
    [CrossRef]

2000 (1)

T. Chartier, F. Sanchez, and G. Stephan, “General model for a multimode Nd-doped fiber laser. II. Steady-state analysis of length-dependent polarization effects,” Appl. Phys. B 70, 33–43 (2000).
[CrossRef]

1999 (4)

S. D. Jackson and T. A. King, “Dynamics of the output of heavily Tm-doped double-clad silica fiber lasers,” J. Opt. Soc. Am. B 16, 2178–2188 (1999).
[CrossRef]

P. Petropoulos, H. L. Hofferhaus, D. J. Richardson, S. Dhanjal, and N. I. Zheludev, “Passive Q-switching of fiber lasers using a broadband liquefying gallium mirror,” Appl. Phys. Lett. 74, 3619–3621 (1999).
[CrossRef]

P. Petropoulos, S. Dhanjal, D. J. Richardson, and N. I. Zheludev, “Passive Q-switching of an Er3+:Yb3+ fiber laser with a fibrised liquefying gallium mirror,” Opt. Commun. 166, 239–243 (1999).
[CrossRef]

P. Glas, M. Naumann, A. Schirrmacher, L. Däweritz, and R. Hey, “Self-pulsing versus self-locking in cw pumped neodymium doped double-clad fiber laser,” Opt. Commun. 161, 345–358 (1999).
[CrossRef]

1998 (1)

1997 (1)

1996 (2)

1991 (1)

J. D. Crawford, “Introduction to bifurcation theory,” Rev. Mod. Phys. 63, 991–1037 (1991).
[CrossRef]

1963 (1)

W. W. Rigrod, “Gain saturation and output power of optical masers,” J. Appl. Phys. 34, 2602–2609 (1963).
[CrossRef]

Chartier, T.

T. Chartier, F. Sanchez, and G. Stephan, “General model for a multimode Nd-doped fiber laser. II. Steady-state analysis of length-dependent polarization effects,” Appl. Phys. B 70, 33–43 (2000).
[CrossRef]

T. Chartier, B. Meziane, F. Sanchez, G. Stephan, and P. L. François, “Optical feedback effects in Nd-doped fiber lasers with broadband spectra,” Appl. Opt. 35, 2016–2022 (1996).
[CrossRef] [PubMed]

Chen, Z. J.

Chernikov, S. V.

Crawford, J. D.

J. D. Crawford, “Introduction to bifurcation theory,” Rev. Mod. Phys. 63, 991–1037 (1991).
[CrossRef]

Däweritz, L.

P. Glas, M. Naumann, A. Schirrmacher, L. Däweritz, and R. Hey, “Self-pulsing versus self-locking in cw pumped neodymium doped double-clad fiber laser,” Opt. Commun. 161, 345–358 (1999).
[CrossRef]

Dhanjal, S.

P. Petropoulos, H. L. Hofferhaus, D. J. Richardson, S. Dhanjal, and N. I. Zheludev, “Passive Q-switching of fiber lasers using a broadband liquefying gallium mirror,” Appl. Phys. Lett. 74, 3619–3621 (1999).
[CrossRef]

P. Petropoulos, S. Dhanjal, D. J. Richardson, and N. I. Zheludev, “Passive Q-switching of an Er3+:Yb3+ fiber laser with a fibrised liquefying gallium mirror,” Opt. Commun. 166, 239–243 (1999).
[CrossRef]

François, P. L.

Gapontsev, V. P.

Glas, P.

P. Glas, M. Naumann, A. Schirrmacher, L. Däweritz, and R. Hey, “Self-pulsing versus self-locking in cw pumped neodymium doped double-clad fiber laser,” Opt. Commun. 161, 345–358 (1999).
[CrossRef]

Grudinin, A. B.

Hey, R.

P. Glas, M. Naumann, A. Schirrmacher, L. Däweritz, and R. Hey, “Self-pulsing versus self-locking in cw pumped neodymium doped double-clad fiber laser,” Opt. Commun. 161, 345–358 (1999).
[CrossRef]

Hofferhaus, H. L.

P. Petropoulos, H. L. Hofferhaus, D. J. Richardson, S. Dhanjal, and N. I. Zheludev, “Passive Q-switching of fiber lasers using a broadband liquefying gallium mirror,” Appl. Phys. Lett. 74, 3619–3621 (1999).
[CrossRef]

Jackson, S. D.

King, T. A.

Meziane, B.

Minelly, J. D.

Naumann, M.

P. Glas, M. Naumann, A. Schirrmacher, L. Däweritz, and R. Hey, “Self-pulsing versus self-locking in cw pumped neodymium doped double-clad fiber laser,” Opt. Commun. 161, 345–358 (1999).
[CrossRef]

Petropoulos, P.

P. Petropoulos, H. L. Hofferhaus, D. J. Richardson, S. Dhanjal, and N. I. Zheludev, “Passive Q-switching of fiber lasers using a broadband liquefying gallium mirror,” Appl. Phys. Lett. 74, 3619–3621 (1999).
[CrossRef]

P. Petropoulos, S. Dhanjal, D. J. Richardson, and N. I. Zheludev, “Passive Q-switching of an Er3+:Yb3+ fiber laser with a fibrised liquefying gallium mirror,” Opt. Commun. 166, 239–243 (1999).
[CrossRef]

Porta, J.

Richardson, D. J.

P. Petropoulos, H. L. Hofferhaus, D. J. Richardson, S. Dhanjal, and N. I. Zheludev, “Passive Q-switching of fiber lasers using a broadband liquefying gallium mirror,” Appl. Phys. Lett. 74, 3619–3621 (1999).
[CrossRef]

P. Petropoulos, S. Dhanjal, D. J. Richardson, and N. I. Zheludev, “Passive Q-switching of an Er3+:Yb3+ fiber laser with a fibrised liquefying gallium mirror,” Opt. Commun. 166, 239–243 (1999).
[CrossRef]

Rigrod, W. W.

W. W. Rigrod, “Gain saturation and output power of optical masers,” J. Appl. Phys. 34, 2602–2609 (1963).
[CrossRef]

Sanchez, F.

T. Chartier, F. Sanchez, and G. Stephan, “General model for a multimode Nd-doped fiber laser. II. Steady-state analysis of length-dependent polarization effects,” Appl. Phys. B 70, 33–43 (2000).
[CrossRef]

T. Chartier, B. Meziane, F. Sanchez, G. Stephan, and P. L. François, “Optical feedback effects in Nd-doped fiber lasers with broadband spectra,” Appl. Opt. 35, 2016–2022 (1996).
[CrossRef] [PubMed]

F. Sanchez and G. Stephan, “General analysis of instabili-ties in erbium-doped fiber lasers,” Phys. Rev. E 53, 2110–2122 (1996).
[CrossRef]

Schirrmacher, A.

P. Glas, M. Naumann, A. Schirrmacher, L. Däweritz, and R. Hey, “Self-pulsing versus self-locking in cw pumped neodymium doped double-clad fiber laser,” Opt. Commun. 161, 345–358 (1999).
[CrossRef]

Stephan, G.

T. Chartier, F. Sanchez, and G. Stephan, “General model for a multimode Nd-doped fiber laser. II. Steady-state analysis of length-dependent polarization effects,” Appl. Phys. B 70, 33–43 (2000).
[CrossRef]

F. Sanchez and G. Stephan, “General analysis of instabili-ties in erbium-doped fiber lasers,” Phys. Rev. E 53, 2110–2122 (1996).
[CrossRef]

T. Chartier, B. Meziane, F. Sanchez, G. Stephan, and P. L. François, “Optical feedback effects in Nd-doped fiber lasers with broadband spectra,” Appl. Opt. 35, 2016–2022 (1996).
[CrossRef] [PubMed]

Taylor, J. R.

Zheludev, N. I.

P. Petropoulos, H. L. Hofferhaus, D. J. Richardson, S. Dhanjal, and N. I. Zheludev, “Passive Q-switching of fiber lasers using a broadband liquefying gallium mirror,” Appl. Phys. Lett. 74, 3619–3621 (1999).
[CrossRef]

P. Petropoulos, S. Dhanjal, D. J. Richardson, and N. I. Zheludev, “Passive Q-switching of an Er3+:Yb3+ fiber laser with a fibrised liquefying gallium mirror,” Opt. Commun. 166, 239–243 (1999).
[CrossRef]

Zhu, Y.

Appl. Opt. (1)

Appl. Phys. B (1)

T. Chartier, F. Sanchez, and G. Stephan, “General model for a multimode Nd-doped fiber laser. II. Steady-state analysis of length-dependent polarization effects,” Appl. Phys. B 70, 33–43 (2000).
[CrossRef]

Appl. Phys. Lett. (1)

P. Petropoulos, H. L. Hofferhaus, D. J. Richardson, S. Dhanjal, and N. I. Zheludev, “Passive Q-switching of fiber lasers using a broadband liquefying gallium mirror,” Appl. Phys. Lett. 74, 3619–3621 (1999).
[CrossRef]

J. Appl. Phys. (1)

W. W. Rigrod, “Gain saturation and output power of optical masers,” J. Appl. Phys. 34, 2602–2609 (1963).
[CrossRef]

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

Opt. Commun. (2)

P. Glas, M. Naumann, A. Schirrmacher, L. Däweritz, and R. Hey, “Self-pulsing versus self-locking in cw pumped neodymium doped double-clad fiber laser,” Opt. Commun. 161, 345–358 (1999).
[CrossRef]

P. Petropoulos, S. Dhanjal, D. J. Richardson, and N. I. Zheludev, “Passive Q-switching of an Er3+:Yb3+ fiber laser with a fibrised liquefying gallium mirror,” Opt. Commun. 166, 239–243 (1999).
[CrossRef]

Opt. Lett. (2)

Phys. Rev. E (1)

F. Sanchez and G. Stephan, “General analysis of instabili-ties in erbium-doped fiber lasers,” Phys. Rev. E 53, 2110–2122 (1996).
[CrossRef]

Rev. Mod. Phys. (1)

J. D. Crawford, “Introduction to bifurcation theory,” Rev. Mod. Phys. 63, 991–1037 (1991).
[CrossRef]

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Figures (3)

Fig. 1
Fig. 1

Laser with a nonlinear mirror. The input mirror is Rmax=100%.

Fig. 2
Fig. 2

Evolution of the normalized losses relative to laser intensity.

Fig. 3
Fig. 3

Temporal evolution of the laser with a nonlinear mirror. (a) Stable self-pulsing operation obtained for r=3; the frequency is ∼100 kHz. (b) Output pulse for the same pumping ratio; the pulse width is ∼70 ns.

Equations (13)

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

d˙=-a1d+Λ-id,
i˙=-γ(i)i+Aid,
γ(i)=1-{tanh(sith)+tanh[s(i-ith)]},
d¯=a1r/Aa1+i¯,
(a1+i¯){1- tanh(sith)- tanh[s(i¯-ith)]}-a1r=0.
δd˙δi˙=Lδdδi,
L=-a1-i¯-d¯Ai¯si¯cosh2[s(i¯-ith)].
scosh2[s(i¯-ith)]-1i¯a1.
d˙=-a1d+Λ-id,
i˙=-i+Ri+Aid,
R˙=-a2(R-{tanh(sith)+tanh[s(i-ith)]}),
a2(a1+i¯)(a1+a2+i¯)
+a1ri¯-a22si¯cosh2[s(i¯-ith)]=0.

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