The integrated photon echo and solvation dynamics

The time-integrated three-pulse photon echo is discussed in terms of the line-shape functions which are shown to be directly related to the solvation dynamics. By using the short-time approximation to the line-shape function, an algebraic form of the three-pulse photon echo signal S_PE (τ, T) is obtained as a function of two delay times, τ and T, between pulses. On the basis of the approximate form of the photon echo signal, the echo peak shift with respect to the second delay time (population evolution period) is derived and found to be linearly proportional to the time-dependent fluorescence Stokes shift function for times greater than the bath correlation time, τ_c. In the case of intermediate inhomogeneous broadening, the asymptotic echo peak shift magnitude is found to be useful in estimating the static inhomogeneous width. To illustrate the theoretical results, an analysis of the echo peak shift measurement of IR144 in a room temperature glass, PMMA, is presented.