Antiphase dynamics and self-pulsing due to a low-frequency spatial population grating in a multimode laser

We study analytically equations that extend the Tang-Statz-deMars rate equations for a multimode Fabry-Perot laser by including the low-spatial-frequency population grating and the inhomogeneous pumping rate along the cavity axis [Quant. Semiclassic Opt. 5, L17 (1997)]. First, we prove the theorem that is the foundation of the antiphase dynamics: The total intensity transients are characterized by only one frequency, the single-mode relaxation oscillation. Second, we study the three-mode laser operation. in this context, we derive analytic expressions for the steady-state intensities, their linear stability, and the bifurcation points. We prove that strictly multimode solutions display a Hopf bifurcation leading to passive e-switched solutions. Numerically, we have found that these time-periodic regimes may bifurcate to quasiperiodic and chaotic states and that there are many domains of bistability. [S1050-2947(98)07012-7].