Improvement in the Calculation of Anti-Stokes Energy Transfer and Experimental Justification Based on Er 0.01 Yb X Y 1–0.01 -X VO 4 Crystal

The improvement on the calculation of anti-Stokes energy transfer rate is studied in the present work. The additional proportion coefficient between Stokes and anti-Stokes light intensities of quantum Raman scattering theory as compared with the classical Raman theory is introduced to successfully describe the anti-Stokes energy transfer. The theoretical formula for the improvement on the calculation of anti-Stokes energy transfer rate is derived for the first time in this study. The correctness of introducing coefficient exp{ΔE/kT} from well-known Raman scatter theory is demonstrated also. Moreover, the experimental lifetime measurement in Er0.01YbxY1–0.01-x VO4 crystal is performed to justify the validity of our important improvement in the original phonon-assisted energy transfer theory for the first time.