Statistics of the transient frequency modulation in the switch-on of a single-mode semiconductor laser

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Abstract
The variations of the optical frequency during the switch-on of a single-mode semiconductor laser diode have been studied. Our model relies on stochastic rate equations, and therefore a meaningful description of the laser frequency in the presence of both noise and transient evolution is difficult. The relation between an approximately instantaneous frequency that we calculate numerically and experimentally measured frequencies is discussed. We analyze the frequency variations during switch-on processes and the statistical properties of the nearly instantaneous frequency that we chose as the most reasonable to calculate. The range of the frequency chirp during the first pulse of the intensity is stochastic, but it is correlated with the switch-on time, and therefore its statistical properties can be deduced from those of the first-passage-time distribution. The correlations permit a single discriminator to select a subset of pulses with similar peak intensities, delay times, and chirp ranges. In addition, there are significant differences between the averaged quantities and results for a single switch-on.