Cooperative frequency locking and stationary spatial structures in lasers

We investigate the spontaneous emergence of transverse patterns in lasers by using both the standard two-level model and the so-called cubic approximation, which is generally valid in the threshold regions. The stationary intensity configurations fall into two distinct classes. The first includes solutions of the single-mode type with the frequency and spatial structure of one of the transverse resonances. The solutions of the second group involve the simultaneous oscillation of several cavity modes, operating in such a way as to produce a stationary intensity profile. The stationary character of these multimode configurations emerges from the fact that the transverse modes of the resonator lock onto a common frequency during the nonlinear transient. We call this phenomenon cooperative frequency locking.