Log in

Role of field losses on the Risken–Nummedal–Graham–Haken laser instability: application to erbium-doped fibre lasers

  • Regular Paper
  • Published:
Applied Physics B Aims and scope Submit manuscript

Abstract

We analyse the effect of both distributed and localised losses in a laser cavity on the Risken–Nummedal–Graham–Haken multimode instability. For two-level lasers, distributed losses are found to have a negligible influence on the instability conditions as long as they remain below 10 dB, a value hardly ever exceeded under common experimental conditions. If one keeps raising the distributed loss above that value, finally the uniform-field-limit results are recovered: localised loss becomes less and less important, and in the limit does not enter at all. In contrast, for three-level lasers – in particular for erbium-doped fibre lasers – distributed losses are found to have a profound quantitative influence on the instability threshold.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price includes VAT (Germany)

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. H. Risken, K. Nummedal: Phys. Lett. A 26, 275 (1968); J. Appl. Phys. 39, 4662 (1968)

    Google Scholar 

  2. R. Graham, H. Haken: Z. Phys. 213, 420 (1968)

    Google Scholar 

  3. N.D. Milovsky: Phys. Lett. A 33, 492 (1970)

    Google Scholar 

  4. H. Ohno, H. Haken: Phys. Lett. A 59, 261 (1976)

    Google Scholar 

  5. L.A. Lugiato, L.M. Narducci: Phys. Rev. A 32, 1576 (1985)

    Google Scholar 

  6. L.A. Lugiato, L.M. Narducci, E.V. Eschenazi, D.K. Bandy, N.B. Abraham: Phys. Rev. A 32, 1563 (1985)

    Google Scholar 

  7. L.M. Narducci, J.R. Tredicce, L.A. Lugiato, N.B. Abraham, D.K. Bandy: Phys. Rev. A 33, 1842 (1986)

    Google Scholar 

  8. T.W. Carr, Th. Erneux: Phys. Rev. A 50, 724 (1994); Phys. Rev. A 50, 4219 (1994)

  9. D. Casini, G.D. Alessandro, A. Politi: Phys. Rev. A 55, 751 (1997)

    Google Scholar 

  10. H. Fu: Phys. Rev. A 40, 1868 (1989)

    Google Scholar 

  11. E.M. Pessina, G. Bonfrate, F. Fontana, L.A. Lugiato: Phys. Rev. A 56, 4086 (1997)

    Google Scholar 

  12. T. Voigt, M.O. Lenz, F. Mitschke: Proc. SPIE 4429, 112 (2001)

    Google Scholar 

  13. E. Roldán, G.J. de Valcárcel: Europhys. Lett. 43, 260 (1998)

    Google Scholar 

  14. G.J. de Valcárcel, E. Roldán, F. Prati: Opt. Commun. 163, 5 (1999)

    Google Scholar 

  15. E.M. Pessina, F. Prati, J. Redondo, E. Roldán, G.J. de Valcárcel: Phys. Rev. A 60, 2517 (1999)

    Google Scholar 

  16. J.F. Urchueguía, G.J. de Valcárcel, E. Roldán, F. Prati: Phys. Rev. A 62, 041801(R) (2000)

  17. E. Roldán, G.J. de Valcárcel, F. Silva, F. Prati: J. Opt. Soc. Am. B 18, 1601 (2001)

    Google Scholar 

  18. E. Roldán, G.J. de Valcárcel: Phys. Rev. A 64, 053805 (2001)

    Google Scholar 

  19. Ya.I. Khanin: Principles of Laser Dynamics (Elsevier, Amsterdam 1995)

  20. E. Roldán, G.J. de Valcárcel, J.F. Urchueguía, J.M. Guerra: J. Opt. Soc. Am. B 20, 816 (2003)

    Google Scholar 

  21. In [15] the expressions of d0 and γthat correspond to four-level lasers are different to those derived more recently in [20]. The reason for the apparent discrepancy is that the considered relaxation schemes are different in the two cases. For realistic four-level lasers, such as Nd lasers, the appropriate transformation is as given here and derived in [20]

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to E. Roldán .

Additional information

PACS

42.55Ah; 42.65.Sf; 42.60.Mi; 42.55.Wd

Rights and permissions

Reprints and permissions

About this article

Cite this article

Roldán , E., de Valcárcel , G. & Mitschke , F. Role of field losses on the Risken–Nummedal–Graham–Haken laser instability: application to erbium-doped fibre lasers. Appl Phys B 76, 741–748 (2003). https://doi.org/10.1007/s00340-003-1205-8

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00340-003-1205-8

Keywords

Navigation