Saturation effect on multiphonon relaxation rates of rare earth ions in glasses at high excitation power

An increase of the radiative quantum efficiency with increasing the excitation power is observed for several multiplets of rare earth ions in glasses. The effect of the excited state density on multiphonon relaxation rates is investigated for different rare earth excited states in oxide or fluoride based glasses. The multiphonon relaxation rate follows as usual an exponential gap law with a coefficient depending on the excited state density. A model is proposed to take into account for the saturation of the multiphonon process with increasing the excitation power. This bottleneck effect is related to the specific propagation, in disordered structures, of highly energetic vibrations resulting from the multiphonon process. Application of our model to optical data allows us to derive a phonon diffusion length which is in good agreement with the phonon mean free path estimated from thermal conductivity, heat capacity and sound velocity. Furthermore, the results are compared with the medium range order deduced from the frequency of the boson peak recorded in Raman scattering.