Applied Physics B

, Volume 79, Issue 2, pp 175–183 | Cite as

Experimental investigation of Risken–Nummedal–Graham–Haken laser instability in fiber ring lasers

  • T. Voigt
  • M.O. Lenz
  • F. Mitschke
  • E. Roldán
  • G.J. de Valcárcel
Article

Abstract

It has been suggested (by Pessina et al. in 1997) that the observed spontaneous mode beating of erbium-doped-fiber ring lasers can be explained as the multimode instability described in 1968 by Risken and Nummedal and by Graham and Haken (the RNGH instability), which is based on Rabi-splitting-induced gain. If true, this would constitute the first ever example of this instability in an actual experiment. We test the hypothesis through a quantitative experimental investigation. We demonstrate that there is indeed a clear, marked onset of the instability, a fact that went unnoticed in all previous experiments because it is very close to the lasing threshold. We intentionally raise cavity loss to better separate onset of lasing and of instability. We obtain quantitative information on the instability onset. An interpretation as the predicted second threshold is reasonable provided inhomogeneous gain line broadening is taken into account. We also observe that instability above its onset exists only intermittently; this may hint at a subcritical bifurcation and noise-driven transitions. In any event, the RNGH mechanism is present, if not in a pure form.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    C.O. Weiss, R. Vilaseca: Dynamics of Lasers (VCH, Weinheim 1991) Google Scholar
  2. 2.
    Ya.I. Khanin: Principles of Laser Dynamics (Elsevier, Amsterdam 1995) Google Scholar
  3. 3.
    P. Mandel: Theoretical Problems in Cavity Nonlinear Optics (Cambridge University Press, Cambridge 1997) Google Scholar
  4. 4.
    O. Svelto: Principles of Lasers (Plenum, New York 1989) Google Scholar
  5. 5.
    H. Risken, K. Nummedal: Phys. Lett. A 26, 275 (1968) CrossRefGoogle Scholar
  6. 6.
    H. Risken, K. Nummedal: J. Appl. Phys. 39, 4662 (1968) CrossRefGoogle Scholar
  7. 7.
    R. Graham, H. Haken: Z. Phys. 213, 420 (1968) Google Scholar
  8. 8.
    F. Fontana, M. Begotti, E.M. Pessina, L.A. Lugiato: Opt. Commun. 114, 89 (1995) Google Scholar
  9. 9.
    E.M. Pessina, G. Bonfrate, F. Fontana, L.A. Lugiato: Phys. Rev. A 56, 4086 (1997) CrossRefGoogle Scholar
  10. 10.
    Q.L. Williams, J. Garcia-Ojalvo, R. Roy: Phys. Rev. A 55, 2376 (1997) CrossRefGoogle Scholar
  11. 11.
    E. Roldán, G.J. de Valcárcel: Europhys. Lett. 43, 255 (1998) CrossRefGoogle Scholar
  12. 12.
    E.M. Pessina, F. Prati, J. Redondo, E. Roldán, G.J. de Valcárcel: Phys. Rev. A 60, 2517 (1999) CrossRefGoogle Scholar
  13. 13.
    T.-M. Voigt, M.O. Lenz, F. Mitschke: Proc. SPIE 4429, 112 (2000) Google Scholar
  14. 14.
    L.A. Lugiato, L.M. Narducci, E.V. Eschenazi, D.K. Bandy, N.B. Abraham: Phys. Rev. A 32, 1563 (1985) CrossRefGoogle Scholar
  15. 15.
    G.J. de Valcárcel, E. Roldán, F. Prati: Opt. Commun. 163, 5 (1999) CrossRefGoogle Scholar
  16. 16.
    E. Roldán, G.J. de Valcárcel, F. Mitschke: Appl. Phys. B 76, 741 (2003) CrossRefGoogle Scholar
  17. 17.
    P. Franco, M. Midrio, A. Tozzato, M. Romagnoli, F. Fontana: J. Opt. Soc. Am. B 11, 1090 (1994) Google Scholar
  18. 18.
    K. Tamura, H.A. Haus, E.P. Ippen: Electron. Lett. 28, 2226 (1992) Google Scholar
  19. 19.
    F. Fontana, E. Pessina: private communication Google Scholar
  20. 20.
    G.P. Agrawal: Nonlinear Fiber Optics (Academic, San Diego 1995) Google Scholar
  21. 21.
    E. Roldan, G.J. de Valcárcel, F. Silva, F. Prati: J. Opt. Soc. Am. B 18, 1601 (2001) Google Scholar
  22. 22.
    F. Prati, E.M. Pessina, E. Roldán, G.J. de Valcárcel: Opt. Commun., in print Google Scholar
  23. 23.
    E. Roldán, G.J. de Valcárcel: Phys. Rev. A 64, 053805 (2001) CrossRefGoogle Scholar
  24. 24.
    Equations (14) and (30) in [23] can be applied to three-level lasers by substituting α in (30) by α/(1+W)1/2 and by taking into account that r in (14) relates to W through (16) in [23]. This does not take into account distributed losses. In order to take them into account, the relation between r and W is not that of (16) in [23] but W=[G0+(1+u)(γd+|lnR|)r]/[G0-(1+u)(γd+|lnR|)r], where u=γinh is the inhomogeneous to homogeneous broadening ratio. The lasing threshold occurs at r=1. Notice that the symbol r entering the above equation does not have the same meaning as the one used in the present article: in [23], and in the above equation, r represents the normalized pump in a two-level laser Google Scholar
  25. 25.
    J.F. Urchueguia, G.J. de Valcárcel, E. Roldán, F. Prati: Phys. Rev. A 62, 041801(R) (2000) CrossRefGoogle Scholar
  26. 26.
    M.J. Guy, J.R. Taylor, R. Kashyap: Electron. Lett. 31, 1924 (1995) CrossRefGoogle Scholar
  27. 27.
    J.L. Zhang, C.Y. Yue, G.W. Schinn, W.R.L. Clements, J.W.Y. Lit: IEEE J. Lightwave Technol. 14, 104 (1996) CrossRefMATHGoogle Scholar
  28. 28.
    D.I. Chang, M.J. Guy, S.V. Chernikov, J.R. Taylor, H.J. Kong: Electron. Lett. 32, 1786 (1996) CrossRefGoogle Scholar
  29. 29.
    H. Fu: Phys. Rev. A 40, 1868 (1989) CrossRefGoogle Scholar
  30. 30.
    T.W. Carr, Th. Erneux: Phys. Rev. A 50, 724 (1994); Phys. Rev. A 50, 4219 (1994) CrossRefGoogle Scholar
  31. 31.
    The reader may wonder why we have not tried to test this hypothesis by numerical integration of the model in [23]. As discussed elsewhere [22, 33], the numerical integration for class B lasers is extremely difficult because of the enormous stiffness of the problem. In fact, the first numerical integrations of the Maxwell–Bloch equations with inhomogeneous broadening in the uniform-field limit have been carried out only very recently [22], and much work needs to be done in this direction. In any case, there is numerical evidence that, with inhomogeneous broadening, the RNGHI can also be subcritical (F. Prati, Universitá dell’Insubria, private communication) Google Scholar
  32. 32.
    A. Amon, M. Nizette, M. Lefranc, T. Erneux: Phys. Rev. A 68, 023801 (2003) CrossRefGoogle Scholar
  33. 33.
    G.J. de Valcárcel, E. Roldán, F. Prati: J. Opt. Soc. Am. B 20, 825 (2003)Google Scholar

Copyright information

© Springer-Verlag 2004

Authors and Affiliations

  • T. Voigt
    • 1
  • M.O. Lenz
    • 1
  • F. Mitschke
    • 1
  • E. Roldán
    • 2
  • G.J. de Valcárcel
    • 2
  1. 1.Fachbereich PhysikUniversität RostockRostockGermany
  2. 2.Departament d’ÒpticaUniversitat de ValènciaBurjassotSpain

Personalised recommendations