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Journal of the Optical Society of America B

Quantum theory of the vibronic solid-state laser

Bożena Ratajska-Gadomska, W. Gadomski

Published May 1, 1999• 6 citations
Publisher

Abstract

A quantum-mechanical description of a vibronic multimode standing-wave transition-metal ion laser is presented. The impurity ion levels are coupled both by the radiation field and by the phonons of the host lattice. A dynamic Heisenberg–Langevin set of equations for the material system and the photon and phonon operators, including radiative and nonradiative damping terms and quantum-stochastic forces, has been derived. The numerical solutions of those equations show the crucial role of the phonons in the laser dynamics. The competition between the photons and the phonons leads to regular stable self-pulsation for certain sets of parameters.

DOI
10.1364/josab.16.000848

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A quantum-mechanical description of a vibronic multimode standing-wave transition-metal ion laser is presented. The impurity ion levels are coupled both by the radiation field and by the phonons of the host lattice. A dynamic Heisenberg–Langevin set of equations for the material system and the photon and phonon operators, including radiative and nonradiative damping terms and quantum-stochastic forces, has been derived. The numerical solutions of those equations show the crucial role of the phonons in the laser dynamics. The competition between the photons and the phonons leads to regular stable self-pulsation for certain sets of parameters.
A quantum-mechanical description of a radiation-balanced solid-state laser is presented. The impurity ion levels are coupled both by the phonons of the host lattice and by the radiation field. The set of dynamic Heisenberg-Langevine equations for the material system and the phonon operators has been derived. These equations include radiative and nonradiative damping terms and quantum-stochastic forces. This description could be used for investigation of the influence of phonon dynamics on laser stability.
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.
Coupling between electronic motions and the lattice vibrations, phonons could broaden the spectral bandwidth of the fluorescence spectroscopy by the energy transferring, which was recognized from the beginning of last century and successfully applied in many vibronic lasers. However, the laser performances under electron-phonon coupling were mainly prejudged by the experimental spectroscopy. The multiphonon participated lasing mechanism is still elusive and should be in-depth investigated. Here, a direct quantitative relationship between the laser performance and phonon participating dynamic process was derived in theory. With a transition metal doped alexandrite (Cr 3+ :BeAl 2 O 4 ) crystal, the multiphonon coupled laser performance was manifested in experiments. Associated with the Huang-Rhys factor calculations and hypothesis, the multiphonon participated lasing mechanism with phonon numbers from 2 to 5 was discovered and identified. This work provides not only a credible model for understanding the multiphonon participated lasing, but should also boost the study of laser physics in the electron-phonon-photon coupled systems.
Recently, a new approach to cool optically pumped solid-state lasers by converting the lattice heat into radiation was presented [Laser Phys.18, 430 (2008)]. It relies on a stimulated radiative process occurring in the laser host material. The internal heat gets partially converted through a four-wave mixing process into a radiating optical field. By adopting a Lorentz oscillator model for the field-atom interaction in the laser host, we identified a shortcut to treat the heating and cooling mechanisms going together with the Stokes and anti-Stokes radiation involved in the four-wave mixing. An energy balance between these mechanisms is derived from the differential equation for the material excitation. This balance will ultimately determine the crystal steady-state temperature. This analysis is the first step towards practical engineering implementations of the optical cooling principle for important new laser systems such as the silicon Raman laser and the Cr-ZnSe laser for the mid-IR.
The quantum kinetic equation describing slow atomic motion in laser light is derived by an operational method which provides mathematical expressions with a transparent physical structure. The authors prove in a general way that the coefficients appearing in this equation, which is of a Fokker-Planck type, are simply related to the mean value and to the correlation functions of the Heisenberg radiative force of the semiclassical approach, where the atomic position is treated classically. They derive in particular a new theoretical expression for the damping force responsible for radiative cooling and they interpret it in terms of linear response theory. The authors also obtain a new crossed r-p derivative term, which does not appear in semiclassical treatments, but which they find to be very small in most situations. Finally, all the theoretical expressions derived are valid for any J g to J e transitions and are not restricted to two-level atoms.