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ACOUSTICS2008/2904 The role of coherent phonons in the vibronic laser

W. Gadomski, Bożena Ratajska-Gadomska

Published Jan 1, 2008• 0 citations

Abstract

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.

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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.

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.

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.

An atom, bounded to the surface of a crystal; absorbs photons from a strong incident laser field and subsequently emits phonons into the solid. In this paper we study the influence of the laser linewidth on this photon–phonon conversion process. The appearance of coherences obscures the interpretation of the equation of motion in terms of transition rates and prohibits the derivation of a master equation in the transient region. The absorbed energy from the driving field, which is assumed to be resonant with a set of two levels only, results from the work done by the external field on the transition dipole. In the steady state, the energy absorption from the radiation field equals the energy emission in the phonon field. It is shown that in this long-time limit the coherences can be expressed in terms of the populations, and hence the system is again described by a masterlike equation. Specific aspects of the finite laser bandwidth are pointed out.

The dynamics in a GaAs-type quantum dot induced by excitation with Gaussian laser pulses of arbitrary duration are calculated in the density matrix formalism using the correlation expansion. In particular the back-action of nonequilibrium phonons, i.e., the coherent phonon amplitude and the nonequilibrium phonon occupation, on the electronic two-level system are studied. We find that especially for long pulses and low temperatures nonequilibrium phonons play an important role and cannot be neglected.