Abstract

In 1982, Arecchi et al. [Phys. Rev. Lett. 49, 1217 (1982) [CrossRef]  ] proposed a simple two-level laser model to interpret the first evidence of chaos and generalized multistability in a $Q$-switched ${{\rm{CO}}_2}$ laser. In this framework, laser dynamics is described by means of a set of two ordinary differential equations for the photon number and the population inversion between the two resonant levels. A sinusoidal function accounts for cavity loss modulation. In this work, we first prove the existence of a periodic orbit for the original two-level non-autonomous laser. Then, we transform this model into a four-dimensional autonomous dynamical system to provide a mathematical analysis that confirms the seminal results already obtained. Finally, by replacing the sinusoidal loss modulation with a delayed function of photon number, we confirm the occurrence of chaos and multistability for such a delayed model with delay times of the order of the reciprocal of the modulation frequencies.

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