Power dependence of Klyshko's Stokes-anti-Stokes correlation in the inelastic scattering of light

Abstract

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 are expected to change the Stokes/anti-Stokes intensity ratio, imposing corrections to the broadly used Bose-Einstein statistics. Here 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 for reasoning 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.

Quantum Mechanical Description of Raman Scattering from Molecules in Plasmonic Cavities

“…(2) Γ,Γ (ω S , ω aS ) for small Ω. We note these results are consistent with those recently reported by Kasperczyk et al 53 from measurements of the Stokes and anti-Stokes pairs emitted from a thin layer of diamond and by Parra-Murillo et al 54 from the theoretical analysis of the Raman scattering.…”

“…Γ,Γ (ω S , ω aS ) ∝ 1/S(ω S ) ∝ Ω −2 dependence, as the rate of coincidences in the detection is determined by the anti-Stokes emission S(ω aS ). 53,54 The results in Fig. 4(a) show this evolution of the correlation for large incident power.…”

“…Γ,Γ (ω S , ω aS , τ = 0) defined by the joint probability of detecting a pair of photons, simultaneously reaching the Stokes (SD, see schematics in Fig. S4) and anti-Stokes detectors (aSD), normalized by the probabilities of the SD and aSD detections Recently, Kasperczyk et al 53 and Parra-Murillo et al, 54 have analyzed an idealized version of such detection setup, in which the detection probabilities P (S) and P (aS) are proportional to the respective intensities of the Raman intensities S(ω S ) and S(ω aS ), respectively. They showed that if all anti-Stokes photons are produced as part of correlated pairs of Stokes and anti-Stokes photons emitted from the cavity (as represented pictorially in Fig.…”

Raman Studies of Carbon Nanostructures

“…The term explicitly dependent on the excitation laser power (P L ) accounts for the Stokes-anti-Stokes-correlated scattering. The constant C SaS depends on fundamental constants, such as coupling and decay rates (74), and it measures the importance of the Stokes-anti-Stokes event. Equation 6 is an approximation valid when n 0 γ /γ C , where γ and γ C are the decay rates for the scattered photons and phonons, respectively.…”

“…This specific sample was engineered to exhibit resonance with the anti-Stokes photon emission. The data are fit with Equation 6, and the tBLG data are dominated by the Stokes-anti-Stokes term (74). The Stokes-anti-Stokes term is also dominant in the diamond data shown by open circles (73,74).…”