Route to Chaos in a CO₂ Laser with Injected Signal

Abstract

It is well known that the equations for a single-mode laser can be reduced to the Lorenz equations[1] and a chaotic behavior should be seen. However, this type of chaos has never been observed because of the actual values of the parameters in physical systems. Hence, it is necessary to introduce an external modulation[2] or to have a multimode laser where the degrees of freedom are larger than three. In these systems, experimental results have been reported [3–4]. In this communication a transition to chaos by intermittency is numerically shown in a single-mode laser with an injected signal without any modulated parameter. We refer to a CO₂ laser medium where the pressure broadening provides a homogeneous gain line. A CO₂ laser system has a relaxation time (1/γ|| = 10⁻³s) much larger than the dipole decay time (l/γ_┴ = 10⁻⁸s); hence, the single mode dynamics is described by the coupling between two degrees of freedom (rate equations). Introducing an external field whose frequency ω_l is detuned with respect to the cavity resonance ω₀ and the atomic transition frequency ω_c, we have the three degrees of freedom necessary for the onset of chaos.