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Physical review. B, Condensed matter

Laserlike self-excitation of phonons by an inhomogeneously broadened three-level system

Wolfgang Grill, L. Hirschbiegel

Published Jun 15, 1985• 2 citations
Publisher

Abstract

An inhomogeneously broadened three-level electronic system related to impurity ions embedded in a crystal with anisotropic phonon modes is considered. It is shown that such a system can sustain laserlike self-excitation under a steady-state condition, depending on the crystal properties. The anisotropy of the phonons is represented by two sets of modes which are distinguished by their lifetimes. Laserlike self-excitation has been shown to be impossible for isotropic systems. This and the influence of crystal properties on the self-excitation in anisotropic systems are discussed.

DOI
10.1103/physrevb.31.8148

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An inhomogeneously broadened three-level electronic system related to impurity ions embedded in a crystal with anisotropic phonon modes is considered. It is shown that such a system can sustain laserlike self-excitation under a steady-state condition, depending on the crystal properties. The anisotropy of the phonons is represented by two sets of modes which are distinguished by their lifetimes. Laserlike self-excitation has been shown to be impossible for isotropic systems. This and the influence of crystal properties on the self-excitation in anisotropic systems are discussed.
A model consisting of a distribution of three-level systems (defects or ionic impurities) in a lattice characterized by a given phonon spectrum is considered in detail. Equations determining the temporal behavior of such a system in an electromagnetic field are analyzed. A steady-state solution describing three-level saturation in the system is achieved. The possibility of the stimulated emission of phonons is considered. It is shown that laserlike self-excitation of phonons cannot be realized, though phonon flux enhancement may be achieved provided certain conditions are fulfilled.
The possibility of stimulated emission of coherent phonons by impurities (ions) embedded in a crystal is considered. It is shown that when the ions with homogeneously broadened levels are subjected to an electromagnetic field, the frequency Ω of which is larger than an eigenfrequency of the ion ω21, at the Raman frequency ωq=Ω−ω21, a coherent stimulated emission of phonons may emerge. The absorption rate of the pumping electromagnetic field has a singularity near the threshold of the phonon self-excitation.
The equations, determining temporal behavior of coupled electronic and phonon subsystems in the electromagnetic field, are analyzed. The steady state solution describing saturation of the three level in such a system is achieved. It is shown that laser-like self-excitation of phonons cannot be obtained though essential phonon enhancement may be gained provided certain conditions are fulfilled. Field induced transparency is predicted between first two levels when the field saturates ground and highest levels, and the concentration of ions is high.
Herewith we present the quantum theory of the vibronic laser, which is based on the crucial role played by the host crystal phonons in the laser dynamics. In the solid state transition-metal ion laser the operation takes place between the vibronically broadened electronic levels of the gain center, thus the laser action is accompanied by the creation or annihilation of the host lattice phonons. The nonequilibrium coherent phonons, produced in the process of the nonradiative energy transition from the photoexcited impurity ion, pump the energy level, from whivh the laser action takes place. One can say that the laser photons are produced at the cost of lattice phonons. This is the reason why the coherent phonons strongly influence the character of the laser action and govern the complicated laser dynamics. In the laser equations, derived by us, the number of coherent phonons is treated as one of dynamical variables coupled with the number of photons. In solution we observe the eect of energy pulling between photons and phonons. Phonons follow all forms of the photon dynamics including self-pulsations and chaotic dynamics.
When the coupling between two ions associated in pair exceeds a given value, the excitation of both ions of the pair is impossible when using a single narrow laser. This double excitation was obtained with two lasers of different wavelengths. A narrowing of the inhomogeneous broadened lines is observed which gives information on the strain field in the crystal. From the difference between the wavelengths, the order of magnitude of the coupling is deduced and compared with phonon assisted transfer rates.