Abstract

We have considered the output of a longitudinally pumped, heavily doped Er:Yb:Cr:phosphate glass laser. We experimentally observed that the characteristic output-versus-input curve is not linear and exhibits bistability. A theoretical approach, based on a thermal lensing effect that varies depending on whether the laser is on or off, provides an excellent description of the experimental results. In addition, we observed that the laser operates in a self-pulsing, sinusoidal, or cw regime, although the pumping is continuous such as was already observed in erbium-doped fiber lasers. This effect is attributed to the existence of ion pairs acting as saturable absorbers. Unlike for erbium-doped fibers, we demonstrate that the concentration of ion pairs cannot be deduced from the pump transmission through the amplifying medium because of the presence of ytterbium ions.

© 2002 Optical Society of America

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References

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  1. V. P. Gapontsev, S. M. Matitsin, A. A. Isineev, and V. B. Kravchenko, “Erbium glass lasers and their applications,” Opt. Laser Technol. 14, 189–194 (1982).
    [CrossRef]
  2. E. Snitzer and C. G. Young, in Advances in Lasers, A. Levine, ed. (Marcel Dekker, New York, 1968), Vol. 2, p. 191.
  3. V. P. Gapontsev, S. M. Matitsin, and A. A. Isineev, “Channels of energy losses in erbium laser glasses in the stimulated emission process,” Opt. Commun. 46, 226–230 (1983).
    [CrossRef]
  4. R. I. Laming, S. B. Poole, and E. J. Tarbox, “Pump excited-state absorption in erbium-doped fibers,” Opt. Lett. 13, 1084–1086 (1988).
    [CrossRef] [PubMed]
  5. P. Laporta, S. De Silvestri, V. Magni, and O. Svelto, “Diode-pumped cw bulk Er:Yb: glass laser,” Opt. Lett. 16, 1952–1954 (1991).
    [CrossRef] [PubMed]
  6. P. Laporta, S. Longhi, S. Taccheo, and O. Svelto, “Single-mode cw erbium–ytterbium glass laser at 1.5 μm,” Opt. Lett. 18, 31–33 (1993).
    [CrossRef] [PubMed]
  7. P. Laporta, S. Longhi, S. Taccheo, and O. Svelto, “Analysis and modelling of the erbium–ytterbium glass laser,” Opt. Commun. 100, 311–321 (1993).
    [CrossRef]
  8. P. Le Boudec, P. L. François, E. Delevaque, J. F. Bayon, F. Sanchez, and G. Stéphan, “Influence of ion pairs on the dynamical behaviour of Er3+-doped fibre lasers,” IEEE J. Quantum Electron. 25, 501–507 (1993).
    [CrossRef]
  9. F. Sanchez, P. Le Boudec, P. L. François, and G. Stéphan, “Effects of ion pairs on the dynamics of erbium-doped fiber lasers,” Phys. Rev. A 48, 2220–2229 (1993).
    [CrossRef] [PubMed]
  10. J. Daniel, J. M. Costa, P. Le Boudec, G. Stéphan, and F. Sanchez, “Generalized bistability in an erbium-doped fiber laser,” J. Opt. Soc. Am. B 15, 1291–1294 (1998).
    [CrossRef]
  11. W. Koechner, Solid-State Laser Engineering (Springer-Verlag, Berlin, 1999), Chap. 7, p. 416.
  12. H. Kogelnik, “Imaging of optical mode-resonators with internal lenses,” Bell Syst. Tech. J. 44, 455–494 (1965).
    [CrossRef]
  13. C. S. Lee and H. Osada, “Observation of optical bistability due to resonator configuration transition,” Opt. Lett. 10, 232–234 (1985).
    [CrossRef] [PubMed]
  14. P. Le Boudec, M. Le Flohic, P. L. François, F. Sanchez, and G. Stéphan, “Self-pulsing in Er3+-doped fibre laser,” Opt. Quantum Electron. 25, 359–367 (1993).
    [CrossRef]
  15. F. Sanchez, M. Le Flohic, G. Stéphan, P. Le Boudec, and P. L. François, “Quasi-periodic route to chaos in erbium-doped fiber laser,” IEEE J. Quantum Electron. 31, 481–488 (1995).
    [CrossRef]
  16. E. Delevaque, T. Georges, M. Monerie, P. Lamouler, and J. F. Bayon, “Modeling of pair-induced quenching in erbium-doped silicate fibers,” IEEE Photonics Technol. Lett. 5, 73–75 (1993).
    [CrossRef]

1998 (1)

1995 (1)

F. Sanchez, M. Le Flohic, G. Stéphan, P. Le Boudec, and P. L. François, “Quasi-periodic route to chaos in erbium-doped fiber laser,” IEEE J. Quantum Electron. 31, 481–488 (1995).
[CrossRef]

1993 (6)

E. Delevaque, T. Georges, M. Monerie, P. Lamouler, and J. F. Bayon, “Modeling of pair-induced quenching in erbium-doped silicate fibers,” IEEE Photonics Technol. Lett. 5, 73–75 (1993).
[CrossRef]

P. Laporta, S. Longhi, S. Taccheo, and O. Svelto, “Analysis and modelling of the erbium–ytterbium glass laser,” Opt. Commun. 100, 311–321 (1993).
[CrossRef]

P. Le Boudec, P. L. François, E. Delevaque, J. F. Bayon, F. Sanchez, and G. Stéphan, “Influence of ion pairs on the dynamical behaviour of Er3+-doped fibre lasers,” IEEE J. Quantum Electron. 25, 501–507 (1993).
[CrossRef]

F. Sanchez, P. Le Boudec, P. L. François, and G. Stéphan, “Effects of ion pairs on the dynamics of erbium-doped fiber lasers,” Phys. Rev. A 48, 2220–2229 (1993).
[CrossRef] [PubMed]

P. Le Boudec, M. Le Flohic, P. L. François, F. Sanchez, and G. Stéphan, “Self-pulsing in Er3+-doped fibre laser,” Opt. Quantum Electron. 25, 359–367 (1993).
[CrossRef]

P. Laporta, S. Longhi, S. Taccheo, and O. Svelto, “Single-mode cw erbium–ytterbium glass laser at 1.5 μm,” Opt. Lett. 18, 31–33 (1993).
[CrossRef] [PubMed]

1991 (1)

1988 (1)

1985 (1)

1983 (1)

V. P. Gapontsev, S. M. Matitsin, and A. A. Isineev, “Channels of energy losses in erbium laser glasses in the stimulated emission process,” Opt. Commun. 46, 226–230 (1983).
[CrossRef]

1982 (1)

V. P. Gapontsev, S. M. Matitsin, A. A. Isineev, and V. B. Kravchenko, “Erbium glass lasers and their applications,” Opt. Laser Technol. 14, 189–194 (1982).
[CrossRef]

1965 (1)

H. Kogelnik, “Imaging of optical mode-resonators with internal lenses,” Bell Syst. Tech. J. 44, 455–494 (1965).
[CrossRef]

Bayon, J. F.

P. Le Boudec, P. L. François, E. Delevaque, J. F. Bayon, F. Sanchez, and G. Stéphan, “Influence of ion pairs on the dynamical behaviour of Er3+-doped fibre lasers,” IEEE J. Quantum Electron. 25, 501–507 (1993).
[CrossRef]

E. Delevaque, T. Georges, M. Monerie, P. Lamouler, and J. F. Bayon, “Modeling of pair-induced quenching in erbium-doped silicate fibers,” IEEE Photonics Technol. Lett. 5, 73–75 (1993).
[CrossRef]

Costa, J. M.

Daniel, J.

De Silvestri, S.

Delevaque, E.

P. Le Boudec, P. L. François, E. Delevaque, J. F. Bayon, F. Sanchez, and G. Stéphan, “Influence of ion pairs on the dynamical behaviour of Er3+-doped fibre lasers,” IEEE J. Quantum Electron. 25, 501–507 (1993).
[CrossRef]

E. Delevaque, T. Georges, M. Monerie, P. Lamouler, and J. F. Bayon, “Modeling of pair-induced quenching in erbium-doped silicate fibers,” IEEE Photonics Technol. Lett. 5, 73–75 (1993).
[CrossRef]

François, P. L.

F. Sanchez, M. Le Flohic, G. Stéphan, P. Le Boudec, and P. L. François, “Quasi-periodic route to chaos in erbium-doped fiber laser,” IEEE J. Quantum Electron. 31, 481–488 (1995).
[CrossRef]

P. Le Boudec, P. L. François, E. Delevaque, J. F. Bayon, F. Sanchez, and G. Stéphan, “Influence of ion pairs on the dynamical behaviour of Er3+-doped fibre lasers,” IEEE J. Quantum Electron. 25, 501–507 (1993).
[CrossRef]

P. Le Boudec, M. Le Flohic, P. L. François, F. Sanchez, and G. Stéphan, “Self-pulsing in Er3+-doped fibre laser,” Opt. Quantum Electron. 25, 359–367 (1993).
[CrossRef]

F. Sanchez, P. Le Boudec, P. L. François, and G. Stéphan, “Effects of ion pairs on the dynamics of erbium-doped fiber lasers,” Phys. Rev. A 48, 2220–2229 (1993).
[CrossRef] [PubMed]

Gapontsev, V. P.

V. P. Gapontsev, S. M. Matitsin, and A. A. Isineev, “Channels of energy losses in erbium laser glasses in the stimulated emission process,” Opt. Commun. 46, 226–230 (1983).
[CrossRef]

V. P. Gapontsev, S. M. Matitsin, A. A. Isineev, and V. B. Kravchenko, “Erbium glass lasers and their applications,” Opt. Laser Technol. 14, 189–194 (1982).
[CrossRef]

Georges, T.

E. Delevaque, T. Georges, M. Monerie, P. Lamouler, and J. F. Bayon, “Modeling of pair-induced quenching in erbium-doped silicate fibers,” IEEE Photonics Technol. Lett. 5, 73–75 (1993).
[CrossRef]

Isineev, A. A.

V. P. Gapontsev, S. M. Matitsin, and A. A. Isineev, “Channels of energy losses in erbium laser glasses in the stimulated emission process,” Opt. Commun. 46, 226–230 (1983).
[CrossRef]

V. P. Gapontsev, S. M. Matitsin, A. A. Isineev, and V. B. Kravchenko, “Erbium glass lasers and their applications,” Opt. Laser Technol. 14, 189–194 (1982).
[CrossRef]

Kogelnik, H.

H. Kogelnik, “Imaging of optical mode-resonators with internal lenses,” Bell Syst. Tech. J. 44, 455–494 (1965).
[CrossRef]

Kravchenko, V. B.

V. P. Gapontsev, S. M. Matitsin, A. A. Isineev, and V. B. Kravchenko, “Erbium glass lasers and their applications,” Opt. Laser Technol. 14, 189–194 (1982).
[CrossRef]

Laming, R. I.

Lamouler, P.

E. Delevaque, T. Georges, M. Monerie, P. Lamouler, and J. F. Bayon, “Modeling of pair-induced quenching in erbium-doped silicate fibers,” IEEE Photonics Technol. Lett. 5, 73–75 (1993).
[CrossRef]

Laporta, P.

Le Boudec, P.

J. Daniel, J. M. Costa, P. Le Boudec, G. Stéphan, and F. Sanchez, “Generalized bistability in an erbium-doped fiber laser,” J. Opt. Soc. Am. B 15, 1291–1294 (1998).
[CrossRef]

F. Sanchez, M. Le Flohic, G. Stéphan, P. Le Boudec, and P. L. François, “Quasi-periodic route to chaos in erbium-doped fiber laser,” IEEE J. Quantum Electron. 31, 481–488 (1995).
[CrossRef]

P. Le Boudec, P. L. François, E. Delevaque, J. F. Bayon, F. Sanchez, and G. Stéphan, “Influence of ion pairs on the dynamical behaviour of Er3+-doped fibre lasers,” IEEE J. Quantum Electron. 25, 501–507 (1993).
[CrossRef]

P. Le Boudec, M. Le Flohic, P. L. François, F. Sanchez, and G. Stéphan, “Self-pulsing in Er3+-doped fibre laser,” Opt. Quantum Electron. 25, 359–367 (1993).
[CrossRef]

F. Sanchez, P. Le Boudec, P. L. François, and G. Stéphan, “Effects of ion pairs on the dynamics of erbium-doped fiber lasers,” Phys. Rev. A 48, 2220–2229 (1993).
[CrossRef] [PubMed]

Le Flohic, M.

F. Sanchez, M. Le Flohic, G. Stéphan, P. Le Boudec, and P. L. François, “Quasi-periodic route to chaos in erbium-doped fiber laser,” IEEE J. Quantum Electron. 31, 481–488 (1995).
[CrossRef]

P. Le Boudec, M. Le Flohic, P. L. François, F. Sanchez, and G. Stéphan, “Self-pulsing in Er3+-doped fibre laser,” Opt. Quantum Electron. 25, 359–367 (1993).
[CrossRef]

Lee, C. S.

Longhi, S.

P. Laporta, S. Longhi, S. Taccheo, and O. Svelto, “Analysis and modelling of the erbium–ytterbium glass laser,” Opt. Commun. 100, 311–321 (1993).
[CrossRef]

P. Laporta, S. Longhi, S. Taccheo, and O. Svelto, “Single-mode cw erbium–ytterbium glass laser at 1.5 μm,” Opt. Lett. 18, 31–33 (1993).
[CrossRef] [PubMed]

Magni, V.

Matitsin, S. M.

V. P. Gapontsev, S. M. Matitsin, and A. A. Isineev, “Channels of energy losses in erbium laser glasses in the stimulated emission process,” Opt. Commun. 46, 226–230 (1983).
[CrossRef]

V. P. Gapontsev, S. M. Matitsin, A. A. Isineev, and V. B. Kravchenko, “Erbium glass lasers and their applications,” Opt. Laser Technol. 14, 189–194 (1982).
[CrossRef]

Monerie, M.

E. Delevaque, T. Georges, M. Monerie, P. Lamouler, and J. F. Bayon, “Modeling of pair-induced quenching in erbium-doped silicate fibers,” IEEE Photonics Technol. Lett. 5, 73–75 (1993).
[CrossRef]

Osada, H.

Poole, S. B.

Sanchez, F.

J. Daniel, J. M. Costa, P. Le Boudec, G. Stéphan, and F. Sanchez, “Generalized bistability in an erbium-doped fiber laser,” J. Opt. Soc. Am. B 15, 1291–1294 (1998).
[CrossRef]

F. Sanchez, M. Le Flohic, G. Stéphan, P. Le Boudec, and P. L. François, “Quasi-periodic route to chaos in erbium-doped fiber laser,” IEEE J. Quantum Electron. 31, 481–488 (1995).
[CrossRef]

P. Le Boudec, P. L. François, E. Delevaque, J. F. Bayon, F. Sanchez, and G. Stéphan, “Influence of ion pairs on the dynamical behaviour of Er3+-doped fibre lasers,” IEEE J. Quantum Electron. 25, 501–507 (1993).
[CrossRef]

P. Le Boudec, M. Le Flohic, P. L. François, F. Sanchez, and G. Stéphan, “Self-pulsing in Er3+-doped fibre laser,” Opt. Quantum Electron. 25, 359–367 (1993).
[CrossRef]

F. Sanchez, P. Le Boudec, P. L. François, and G. Stéphan, “Effects of ion pairs on the dynamics of erbium-doped fiber lasers,” Phys. Rev. A 48, 2220–2229 (1993).
[CrossRef] [PubMed]

Stéphan, G.

J. Daniel, J. M. Costa, P. Le Boudec, G. Stéphan, and F. Sanchez, “Generalized bistability in an erbium-doped fiber laser,” J. Opt. Soc. Am. B 15, 1291–1294 (1998).
[CrossRef]

F. Sanchez, M. Le Flohic, G. Stéphan, P. Le Boudec, and P. L. François, “Quasi-periodic route to chaos in erbium-doped fiber laser,” IEEE J. Quantum Electron. 31, 481–488 (1995).
[CrossRef]

P. Le Boudec, P. L. François, E. Delevaque, J. F. Bayon, F. Sanchez, and G. Stéphan, “Influence of ion pairs on the dynamical behaviour of Er3+-doped fibre lasers,” IEEE J. Quantum Electron. 25, 501–507 (1993).
[CrossRef]

P. Le Boudec, M. Le Flohic, P. L. François, F. Sanchez, and G. Stéphan, “Self-pulsing in Er3+-doped fibre laser,” Opt. Quantum Electron. 25, 359–367 (1993).
[CrossRef]

F. Sanchez, P. Le Boudec, P. L. François, and G. Stéphan, “Effects of ion pairs on the dynamics of erbium-doped fiber lasers,” Phys. Rev. A 48, 2220–2229 (1993).
[CrossRef] [PubMed]

Svelto, O.

Taccheo, S.

P. Laporta, S. Longhi, S. Taccheo, and O. Svelto, “Single-mode cw erbium–ytterbium glass laser at 1.5 μm,” Opt. Lett. 18, 31–33 (1993).
[CrossRef] [PubMed]

P. Laporta, S. Longhi, S. Taccheo, and O. Svelto, “Analysis and modelling of the erbium–ytterbium glass laser,” Opt. Commun. 100, 311–321 (1993).
[CrossRef]

Tarbox, E. J.

Bell Syst. Tech. J. (1)

H. Kogelnik, “Imaging of optical mode-resonators with internal lenses,” Bell Syst. Tech. J. 44, 455–494 (1965).
[CrossRef]

IEEE J. Quantum Electron. (2)

P. Le Boudec, P. L. François, E. Delevaque, J. F. Bayon, F. Sanchez, and G. Stéphan, “Influence of ion pairs on the dynamical behaviour of Er3+-doped fibre lasers,” IEEE J. Quantum Electron. 25, 501–507 (1993).
[CrossRef]

F. Sanchez, M. Le Flohic, G. Stéphan, P. Le Boudec, and P. L. François, “Quasi-periodic route to chaos in erbium-doped fiber laser,” IEEE J. Quantum Electron. 31, 481–488 (1995).
[CrossRef]

IEEE Photonics Technol. Lett. (1)

E. Delevaque, T. Georges, M. Monerie, P. Lamouler, and J. F. Bayon, “Modeling of pair-induced quenching in erbium-doped silicate fibers,” IEEE Photonics Technol. Lett. 5, 73–75 (1993).
[CrossRef]

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

Opt. Commun. (2)

V. P. Gapontsev, S. M. Matitsin, and A. A. Isineev, “Channels of energy losses in erbium laser glasses in the stimulated emission process,” Opt. Commun. 46, 226–230 (1983).
[CrossRef]

P. Laporta, S. Longhi, S. Taccheo, and O. Svelto, “Analysis and modelling of the erbium–ytterbium glass laser,” Opt. Commun. 100, 311–321 (1993).
[CrossRef]

Opt. Laser Technol. (1)

V. P. Gapontsev, S. M. Matitsin, A. A. Isineev, and V. B. Kravchenko, “Erbium glass lasers and their applications,” Opt. Laser Technol. 14, 189–194 (1982).
[CrossRef]

Opt. Lett. (4)

Opt. Quantum Electron. (1)

P. Le Boudec, M. Le Flohic, P. L. François, F. Sanchez, and G. Stéphan, “Self-pulsing in Er3+-doped fibre laser,” Opt. Quantum Electron. 25, 359–367 (1993).
[CrossRef]

Phys. Rev. A (1)

F. Sanchez, P. Le Boudec, P. L. François, and G. Stéphan, “Effects of ion pairs on the dynamics of erbium-doped fiber lasers,” Phys. Rev. A 48, 2220–2229 (1993).
[CrossRef] [PubMed]

Other (2)

W. Koechner, Solid-State Laser Engineering (Springer-Verlag, Berlin, 1999), Chap. 7, p. 416.

E. Snitzer and C. G. Young, in Advances in Lasers, A. Levine, ed. (Marcel Dekker, New York, 1968), Vol. 2, p. 191.

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Figures (9)

Fig. 1
Fig. 1

Simplified energy-level diagram of the Er–Yt system, showing the laser transition, the pump levels, and the relaxation processes.

Fig. 2
Fig. 2

Experimental setup: 1, pump laser diode; 2, 6, optical isolators; 3, aspheric lens; 4, Er:Yb:Cr:glass high-reflection coated at the laser wavelength; 5, concave mirror with radius of curvature Rc; 7, optical filter cutting the pump signal; 8, photodiode or powermeter.

Fig. 3
Fig. 3

Experimental output-power-versus-input power curve for cavity length D=99 mm and Rc=100 mm. Squares (circles), data measured with increasing (decreasing) input power Pin.

Fig. 4
Fig. 4

Stability diagram of the plano–concave cavity, including a thermal lens of focal length fth against the plane mirror. Hatched zones denote that the cavity is unstable.

Fig. 5
Fig. 5

Experimental output-power-versus-input-power curve for D>Rc. Squares (circles) indicate data measured with increasing (decreasing) input power Pin.

Fig. 6
Fig. 6

Graphic illustration of optical bistability in the Pout-versus-Pin curve. This behavior, which is due to a stable–unstable cavity transition that results from thermal lensing, is different depending on whether the laser is on or off.

Fig. 7
Fig. 7

Results of the theoretical modeling, showing good agreement with the experimental observations of Fig. 3.

Fig. 8
Fig. 8

Cross relaxation in ion pairs.

Fig. 9
Fig. 9

Evolution of laser output versus time for several increasing pump powers.

Equations (24)

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

fth=A/PH,
g1=1-Dfth,
g2=1-DRc.
0<g1g2<1.
1feff=1fth+1fL.
N2Y(R)t=σYNYF(R)-kN2Y(R)NE(R),
N2E(R)t=kN2Y(R)[NE-N2E(R)]-σEcρ(R)hν[2N2E(R)-NE]-N2E(R)τE,
qt=σEc Va ρ(R)hν[2N2E(R)-NE]dR-1τc V ρ(R)hν dR,
N2Y(r)=σYNYF(r)kNE,
N2E(r)=σYNYF(r)+(σEc/hν)NEρ(r)1/τE+σYNYF(R)/NE+2σEc/hν[ρ(r)],
W024 12σEcτc Dd+NE2=0G0(r) σYNYF(0)Gp(r)+(σEc/hν)NEρ(0)G0(r)1/τE+σY(NY/NE)F(0)Gp(r)+2σEc/hν[ρ(0)G0(r)]rdr,
Pin=hνp 02π dθ 0 F(0)Gp(r)rdr=πWp22hνpF(0),
Pout=Dτc 02π dθ 0ρ(0)G0(r)rdr=πW02D2τcρ(0),
N2Yt=σYN1YF-kN2YNs-kN2YNs*-2kN2YNp-2kN2YNp*,
Ns*+Ns=(1-2x)NE,
Np*+Np=xNE.
N1Y=kNEσYF+kNE,
fth=A/PH,
PH=Pa+Pb.
Pa=2πhνakd0N2Y(r)[NE-N2E(r)]rdr,
Pb=2πhνbkd 0 N2Y(r)N2E(r)rdr.
N2Y(r)=σYNYF(r)kNE.
N2E(r)=σYNYτEF(r)1+σYNYτEF(r)/NE(laseroff),
N2E(r)=σYNYτEF(r)+(σEc/hν)NEτEρ(r)1+σYNYτEF(r)/NE+(2σEcτE/hν)ρ(r)×(laseron).

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