Conservative-Dissipative Behavior of CO2 Laser with Injected Signal

Abstract

Class B lasers1 are described by the so called rate equations for field intensity and population inversion. A suitable nonlinear transformation shows that such equations are fully equivalent to a Toda oscillator with intensity dependent losses2. More precisely, the dissipative terms are proportional to the square root ε = γ η / k of the ratio between the decay rate γ η of population inversion and k of field intensity. In many physical cases (CO2, Nd-Yag etc.) ϵ is ≪1, and the motion, within a first order approximation, is a conservative one. By extending such approximation to the case of an externally injected laser, we obtain a reversible model, that is, a flow invariant the composition of time reversal and a suitable reflection R of coordinates3. Reversibility implies conservativity only with the further assumption that any trajectory is invariant under R-reflection. In particular we have observed that, for critical values of the external amplitude, global symmetry-breaking (SB) transitions occur. More precisely, finite regions in the phase space change their structure from a conservative to a dissipative one. Consequences of these critical phenomena can also be revealed in the original physical system. In fact, the SB yields a stability of the orbit much stronger than that owed to the dissipative terms here neglected.