MINIMAL EQUATIONS FOR ANTIPHASE DYNAMICS IN MULTIMODE LASERS

We consider two models of multimode lasers: the Tang-Statz-deMars equations modeling a solid-state Fabry-Perot laser [C.L. Tang, H. Statz, and G. deMars, J. Appl. Phys. 34, 2289 (1963)] and the rate equations modeling intracavity second-harmonic generation in a Nd:YAG ring laser (where YAG denotes yttrium aluminum garnet). In both models, the dynamics is dominated by a global coupling of the modes of the electromagnetic field in the cavity. Although the equations for these two problems are fairly different, we prove that a dominant asymptotic approximation can be determined in each case that leads to the same conservative problem. It depends on one parameter, which measures the strength of the global coupling, and admits a class of antiphase periodic solutions.