The threshold for multilongitudinal-mode emission in inhomogeneously broadened ring lasers is analytically investigated. In the homogeneous limit the multimode instability corresponds to the classical Risken–Nummedal–Graham–Haken instability. It is found that by increasing the inhomogeneous linewidth, the instability threshold is decreased and the growth of high-frequency side modes is favored. In the limit where the population-inversion decay rate γ<sub>∥</sub> is much smaller than the polarization decay rate γ<sub>⊥</sub> (class B lasers), analytical expressions for the instability threshold are found, which are then generalized to three-level lasers for a comparison with experimental results obtained with erbium-doped fiber lasers. It is shown that even in class B lasers a full Maxwell–Bloch description (in opposition to a rate-equations approach) is necessary when the free spectral range of the cavity is less than ∼(γ<sub>∥</sub>/γ<sub>⊥</sub>)<sup>1/4</sup>γ<sub>⊥</sub>.
© 2001 Optical Society of America
(140.3430) Lasers and laser optics : Laser theory
(140.3510) Lasers and laser optics : Lasers, fiber
(140.3560) Lasers and laser optics : Lasers, ring
(190.3100) Nonlinear optics : Instabilities and chaos
Eugenio Roldán, Germán J. de Valcárcel, Fernando Silva, and Franco Prati, "Multimode emission in inhomogeneously broadened ring lasers," J. Opt. Soc. Am. B 18, 1601-1611 (2001)