Modulation of a two-mode laser

We analyze a two-mode laser, described by rate equations, whose gain is periodically modulated. The nature of the response varies significantly with the modulation amplitude. We study both the small modulation in which the pump parameter remains always above the lasing threshold for the second mode, and the deep modulation in which the pump parameter is located during part of the cycle between the single-mode and the two-mode thresholds. Apart from the strong McCumber nonlinear resonance at the relaxation oscillation frequency, we describe a rich variety of nonlinear properties such as multistability among periodic and quasi-periodic solutions, and small resonances in the vicinity of the second (and lower) internal frequency. We also identify domains that suggest the occurrence of the traditional routes to chaos