“…Many experimental techniques, such as fluorescence upconversion [1][2][3][4][5][6], femtosecond photon echo [7], two-step excitation [8], time-resolved fluorescence Stokes shifts [9], time-resolved spontaneous emission spectra [10 -15], and femtosecond time-resolved stimulated emission pumping fluorescence depletion spectrum [16,17], have been developed to measure the vibrational relaxation and the solvent effects of mole-cules in solution. Liu et al [18,19] measured experimentally the femtosecond fluorescence depletion spectra (FDSs) of dye molecules in solution and studied the relaxation dynamics of dye molecules. Theoretically, Lin and coworkers [20] studied the effect of vibrational relaxation on the pump-probe stimulated emission and calculated the time constant of vibrational relaxation of Rhodobacter capsulatus.…”