Self-pulsing laser as oscillator Toda: approximations through elementary functions

A simple model of self-pulsation in lasers is considered. The laser is described by the system of two ordinary differential equations for the number of photons in the cavity and the number of excitations in the active medium, leading to the equation for the oscillator Toda with damping. For the case of strong spiking, the damping is considered as perturbation; the estimates in terms of elementary functions are suggested for the period of pulsation, damping rate, amplitude and phase of pulsation, quasi-energy and the output power. These estimates are compared to the numerical solution and to the experimental data. PACS numbers: 42.60.Rn, 02.30.Hq, 02.30.Mv (Some figures in this article are in colour only in the electronic version) 1.