MINIMAL EQUATIONS FOR ANTIPHASE DYNAMICS IN MULTIMODE LASERS

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