Theory of Laser Action Involving Free Excitons and LO-Phonon-Assisted Transitions

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Abstract
The laser system is described by the equations of motion for the creation operators (amplitude equations) of the excitons in the lowest band, the longitudinal optical phonons, and the photons in the laser mode. These equations include damping, pump, and fluctuation terms. By eliminating the `virtual excitons' with wavevector q=0 one finds the effective amplitude equations for the indirect transitions (A1‐LO line). From these equations quantum mechanical rate equations are derived, whose fluctuation operators have shot‐noise character. The mean stationary rate equations are treated in the limit of a short LO‐phonon lifetime and of a fast relaxation of the excitons into the thermal distribution in the lowest band. For the example of CdS, we calculated the temperature dependence of (a) the maximum gain frequency at threshold, (b) the threshold pump rate Pth, (c) the spectrum of the gain function at threshold, and (d) the output power in the region 0.1≤P/Pth≤2.0, where P is the pump rate. Finally, the light intensities of the A1 line (direct transitions) and of the A1‐LO line are calculated simultaneously in the same pump range. The calculated slopes of the intensity curves are in good agreement with those measured by Nikitine et al. in CdS.