Improvement in the calculation of anti-Stokes energy transfer and experimental justification based on Er_0.01Yb_xY_1-0.01-xVO₄ 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 expΔE / kT from well-known Raman scatter theory is demonstrated also. Moreover, the experimental lifetime measurement in Er_0.01Yb_xY_1-0.01-xVO₄ crystal is performed to justify the validity of our important improvement in the original phonon-assisted energy transfer theory for the first time.