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Physical Review A

Model for laser action in vibronic systems

P. Schwendimann, E. Sigmund, Karl Zeile

Published Apr 1, 1988• 17 citations
Publisher

Abstract

The theory of laser action in solid-state systems is reconsidered with emphasis on the role of the interaction between lasing impurity states and lattice vibrations. The influence of a strong electron-phonon coupling on threshold conditions and field dynamics is presented, taking into account the vibronic-level structure, and compared with the usual four-level scheme.

DOI
10.1103/physreva.37.3018

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Physical Review A•Oct 1, 1989•0 citations
The theory of laser action in solid-state systems is reconsidered with emphasis on the role of the interaction between lasing impurity states and lattice vibrations. The influence of a strong electron-phonon coupling on threshold conditions and field dynamics is presented, taking into account the vibronic-level structure, and compared with the usual four-level scheme.
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.
Taking into account the vibronic-level structure in a laser medium, we study the influence of electron-vibration interaction on the field dynamics. Different vibronic transitions are coupled in the medium through this interaction and contribute to the emission from excited states, thus coupling different field modes in the cavity and influencing the field dynamics. A general model is presented and solved in a simple example of four coupled transitions. In particular, the effect of degenerate transitions is stressed.
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.
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.
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.