TABLE OF CONTENTS In the previous chapter, the fundamental mechanism of laser dynamics was considered, which is the coherent interaction of laser field with the active medium inside the cavity. This mechanism works also in multimode lasers where it leads to Risken-Nummedal-Graham-Haken instability of stationary oscillations, which is analogous to the Lorenz instability in single-mode lasers. However, in multimode lasers the dynamic behaviour is more often determined by nonlinear mode interaction.
Solutions
There are several varieties of the rate-equation laser models. In this section we consider the simplest of these models, which take into account only additive saturation of the laser medium by lasing modes. The nonstationary processes in such lasers are limited by relaxation oscillations that form the set of low-frequency eigenoscillations of the model
The rate equations can be generalized to describe a multimode laser following the procedure proposed in [316]. Unfortunately, the conditions of their validity remain unknown. Inequalities (3.12) now become insufficient, since there are intermode beat frequencies in the envelope field spectrum if many nondegenerate modes are excited simultaneously. In a nonlinear system, such as the laser, the beats lead to a combination coupling between modes, which is absent in the rate-equation model. Therefore it is advisable to move carefully along the whole route from the general nonadiabatic system to the rate equations [289, 317, 318].
First of all, adding to Eq. (3.1) some...
