Transient statistics in the switch-on of class B lasers.

Abstract

The transient evolution of the output of a single-mode class B laser (SML) after it is switched-on has been characterized from an experimental point of view by the evolution of the output intensity,[1, 2] both in the linear and non-linear regimes. However, from a theoretical point of view the characterization of the transient statistics of a SML beyond the linear regime has not been considered in detail. [3-5] Nevertheless, it has been possible to analyze both the linear and non-linear regimes for class A lasers,[6] showing that the transient statistics during the non-linear regime constitute a mapping of the transient statistics in the linear regime. In this case, an approximate solution for a switch-on event can be constructed (QDT approximation, [7]) which allows to examine the correspondence between the transient statatistics in both regimes. The main difficulty for a SML arises from the fact that no analytical solution of the deterministic rate equations is known, though it has been shown numerically[3, 4] that the QDT approximation succesfully explains the transient statistics in both the linear and non-linear regimes. Accordingly, we expect that the transient statistics in the non-linear regime can be understood as a mapping of the Passage Time (PT) statistics. The reason is that the random PT t* - defined as the time when the intensity reaches a reference value I r – determines both the beginning of a deterministic stage of evolution and the initial conditions for this period,[3-5] which lasts until the vicinity of the asymptotic steady state is reached.