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Journal of the Optical Society of America B

Journal of the Optical Society of America B


  • Vol. 20, Iss. 5 — May. 1, 2003
  • pp: 816–824

Observability of the Risken–Nummedal–Graham–Haken instability in Nd:YAG lasers

Eugenio Roldán, Germán J. de Valcárcel, Javier F. Urchueguı́a, and José M. Guerra  »View Author Affiliations

JOSA B, Vol. 20, Issue 5, pp. 816-824 (2003)

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Multilongitudinal mode instability in ring Nd:YAG lasers is theoretically analyzed. After we review the way in which the standard two-level laser theory applies to this laser we extend the theoretical treatment to include transverse effects. We do this by taking into account the finite transverse section of the active medium and by assuming a Gaussian transverse distribution for the intracavity field. Finally we demonstrate that multimode emission develops whenever the intracavity field waist diameter is almost equal to the active rod diameter. We conclude that continuous-wave diode-pumped Nd:YAG lasers with low cavity losses are good candidates for the observation of the Risken–Nummedal–Graham–Haken instability.

© 2003 Optical Society of America

OCIS Codes
(140.0140) Lasers and laser optics : Lasers and laser optics
(140.3530) Lasers and laser optics : Lasers, neodymium
(190.0190) Nonlinear optics : Nonlinear optics
(190.3100) Nonlinear optics : Instabilities and chaos

Eugenio Roldán, Germán J. de Valcárcel, Javier F. Urchueguía, and José M. Guerra, "Observability of the Risken–Nummedal–Graham–Haken instability in Nd:YAG lasers," J. Opt. Soc. Am. B 20, 816-824 (2003)

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  1. H. Risken and K. Nummedal, “Instability of off resonance mode in lasers,” Phys. Lett. A 26, 275–276 (1968). [CrossRef]
  2. H. Risken and K. Nummedal, “Self-pulsing in laser,” J. Appl. Phys. 39, 4662–4672 (1968). [CrossRef]
  3. R. Graham and H. Haken, “Quantum theory of light propagation in a fluctuating laser-active medium,” Z. Phys. 213, 420–450 (1968). [CrossRef]
  4. C. O. Weiss and R. Vilaseca, Dynamics of Lasers (VCH, Weinheim, Germany, 1991).
  5. E. M. Pessina, G. Bonfrate, F. Fontana, and L. A. Lugiato, “Experimental observation of the Risken–Nummedal–Graham–Haken multimode laser instability,” Phys. Rev. A 56, 4086–4093 (1997). [CrossRef]
  6. E. Roldán and G. J. de Valcárcel, “On the observability of the Risken–Nummedal–Graham–Haken multimode instability in erbium-doped fiber lasers,” Europhys. Lett. 43, 255–260 (1998). [CrossRef]
  7. E. M. Pessina, F. Prati, J. Redondo, E. Roldán, and G. J. de Valcárcel, “Multimode instability in ring fibre lasers,” Phys. Rev. A 60, 2517–2528 (1999). [CrossRef]
  8. T. Voigt, M. O. Lenz, and F. Mitschke, “Risken–Nummedal–Graham–Haken instability finally confirmed experimentally,” in International Seminar on Novel Trends in Nonlinear Laser Spectroscopy and High-Precision Measurements in Optics, S. N. Bagaev, V. N. Zadkov, and S. M. Arakelian, eds., Proc. SPIE 4429, 112–115 (2001). [CrossRef]
  9. F. Mitschke, Universität Rostock, Rostock, Germany (personal communication, 2002).
  10. E. Roldán, G. J. de Valcárcel, F. Silva, and F. Prati, “Multimode emission in inhomogeneously-brodened ring lasers,” J. Opt. Soc. Am. B 18, 1601–1611 (2001). [CrossRef]
  11. E. Roldán and G. J. de Valcárcel, “Multimode instability in inhomogeneously broadened class-B ring lasers: beyond the uniform field limit,” Phys. Rev. A 64, 053805 (2001). [CrossRef]
  12. E. Roldán, G. J. de Valcárcel, and F. Mitschke, “Localized and distributed intracavity losses and the Risken–Nummedal–Graham–Haken instability,” Appl. Phys. B (to be published).
  13. L. A. Lugiato and M. Milani, “Effects of Gaussian-beam averaging on laser instabilities,” J. Opt. Soc. Am. B 2, 15–17 (1985). [CrossRef]
  14. C. P. Smith and R. Dykstra, “Lorenz-like chaos in a Gaussian mode laser with radially dependent gain,” Opt. Commun. 117, 107–110 (1995). [CrossRef]
  15. J. F. Urchueguía, G. J. de Valcárcel, and E. Roldán, “Laser instabilities in a Gaussian cavity mode with Gaussian pump profile,” J. Opt. Soc. Am. B 15, 1512–1520 (1998). [CrossRef]
  16. J. F. Urchueguía, G. J. de Valcárcel, E. Roldán, and F. Prati, “Transverse effects in ring fibre laser multimode instabilities,” Phys. Rev. A 62, 041801 (2000). [CrossRef]
  17. In principle there could be a small inhomogeneous contribution to the gain line caused by the proximity of some Nd ions to the sparing defects in the YAG crystal. But such inhomogeneous broadening has not been reported as far as we know, and thus the assumption of pure homogeneous broadening is a good approximation.
  18. A slightly different model was derived in Ref. 7 because equal relaxation rates for the two lasing levels were assumed. This is not a realistic approximation for Nd:YAG lasers, and thus the model given here corrects that of Ref. 7. The present derivation follows Ref. 19.
  19. Ya. I. Khanin, Principles of Laser Dynamics (Elsevier, Amsterdam, 1995).
  20. T=1−R, where R is the fraction of light exiting the medium that is reinjected by the cavity into the medium after one round trip. 0≤R≤1 by definition, and the uniform field limit requires that R→1, i.e., that T→0.
  21. W. Koechner, Solid State Laser Engineering, Vol. X of Springer Series in Optical Sciences (Springer, New York, 1976).
  22. In practice this means that the detuning between a longitudinal mode and the gain line, which at most equals half of the cavity’s free spectral range Δω, must be much smaller than the width of the gain line γ; i.e., Δω≡πc/Lc≪γ. With the given parameters for Nd:YAG lasers we have Δω/γ~10−4, so the inequality is safely verified.
  23. P. Mandel, Theoretical Problems in Cavity Nonlinear Optics (Cambridge U. Press, Cambridge, 1997).
  24. A. G. Fox and T. Li, “Modes in a maser interferometer with curved and tilted mirrors,” Proc. IEEE 51, 80–89 (1963). [CrossRef]
  25. A. E. Siegman, Lasers (Oxford U. Press, Oxford, 1986).
  26. J. Arnaud, “Degenerate optical cavities,” Appl. Opt. 8, 189–195 (1969). [CrossRef] [PubMed]
  27. J. R. Tredicce, E. J. Quel, A. M. Ghazzawi, C. Green, M. A. Pernigo, L. M. Narducci, and L. A. Lugiato, “Spatial and temporal instabilities in a CO2 laser,” Phys. Rev. Lett. 62, 1274–1277 (1989). [CrossRef] [PubMed]
  28. D. Dangoisse, D. Hennequin, C. Leppers, E. Iouvergneaux, and P. Glorieux, “Two-dimensional optical lattices in a CO2 laser,” Phys. Rev. A 46, 5955–5958 (1992). [CrossRef] [PubMed]
  29. Lamp pumping is not considered because thermal lensing effects make effective pumping more that 1.5 times above threshold impossible, whereas pumping at least 9 times above threshold is required for observing instability.

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