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Soviet Journal of Quantum Electronics

Optical bistability and lasing of crystals containing impurities in the case of an adiabatic electron–phonon interaction

A. P. Saǐko, V. S. Kuz’min

Published Jun 30, 1988• 0 citations
Publisher

Abstract

A theoretical study is made of the threshold conditions for the observation of optical bistability and stimulated emission of zero-phonon lines of crystals containing impurities. A reduction in the electron–photon interaction constant ensures that nonlinear absorption due to a purely electronic transition is attained in a lower saturating field and the lasing threshold rises exponentially as the reciprocal of the Debye–Waller factor. It is shown that there are critical temperatures for the appearance of these effects. Experimental studies of the threshold conditions for lasing and optical bistability make it possible to determine directly the Debye–Waller factor at different temperatures of a crystal.

DOI
10.1070/qe1988v018n06abeh012293

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We continue the discussion of the nonperturbative theory of zero-phonon impurity lines in crystals formulated by Osad’ko and more recently by us. In that paper, a diagrammatic analysis was undertaken which led to analytic results for the thermal width and shift of the zero-phonon line. Here we evaluate these results for two model phonon densities of states: the Debye model for acoustic phonons, and a sharply peaked density of states appropriate for optical phonons. For Debye phonons we find that at low temperatures the standard (perturbative) theory of optical dephasing is qualitatively correct, but at high temperatures it becomes very inaccurate. Moreover, if one of the excited state phonon frequencies tends to zero (a soft mode), then perturbation theory breaks down completely. For optical phonons our results give an Arrhenius temperature dependence for the linewidth and place an upper bound on the value of the preexponential. In paper II of this series we will discuss dephasing by pseudo-local phonons, and in paper III we will compare our results to absorption, photon echo, and hole burning experiments.
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We study the lasing action due to nonlinear interactions of photons with boson elementary excitation, such as phonons and excitons, and point out the distinct features from the conventional laser model described by the two-level model. External feedback by means of cavity mirrors is unnecessary for the lasing action as well as for the increasing absorption optical bistability. It is shown that the Landau theory of the second-order phase transition is applicable to the threshold behaviour of the present mirrorless laser model.