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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. Urchueguía, 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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  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.
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  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.
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  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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