Competition and bistability of longitudinal modes in a Raman laser.

The Raman laser is an optically pumped three-level laser in which both the pump and the laser field ~frequencies vP and vL , respectively! are far off resonance ~see Fig. 1!. This system is commonly used to produce high gain steady-state lasing emissions in the midto far infrared spectral region @1#. In addition, this system can show a very rich dynamical behavior @2#, including single-mode pulsations and routes to chaos characterized by period doubling and intermittency @3#. The single-mode plane-wave model of the Raman laser has been already studied in great detail, and experimentally accessible parameters for which laser emission can be periodic or chaotic have been found @4–6#. Yet an important experimental evidence, namely, multimode emission, has not been taken into account in previous theoretical analyses. The single-mode model predicts that unstable behavior is associated with large cavity detuning. But as the cavity detuning becomes comparable with the free spectral range of the cavity, another longitudinal mode is likely to be excited. Therefore, the effects of single-mode and multimode instability should be visible under the same parametric conditions. The observation of two dynamical frequencies reported in @7,8# confirms this picture. We start from the standard set of equations for the singlemode Raman laser @6# written in a notation such that all variables and parameters are dimensionless: