Stokes-anti-Stokes correlation in the inelastic scattering of light by matter and generalization of the Bose-Einstein population function

The Stokes and anti-Stokes components in the inelastic scattering of light are related to phonon statistics and have been broadly used to measure temperature and phonon lifetimes in different materials. However, correlation between the components is expected to change the Stokes/anti-Stokes intensity ratio, imposing corrections to the broadly used Bose-Einstein statistics. In this work the excitation power dependence of these scattering processes is theoretically described by an effective Hamiltonian that includes correlation between the Stokes and the anti-Stokes events. The model is used to fit available experimental results in three-dimensional diamond and two-dimensional graphene, showing that the phenomenon can significantly increase in the low-dimensional system under specific resonance conditions. By setting the scientific basis for the Stokes-anti-Stokes correlated phenomenon, the use of the Bose-Einstein population function to determine the inelastic scattering is generalized, providing a model to predict the conversion of optical phonons into heat or light, according to coupling constants and decay rates. The model applies to inelastic scattering in general.