On the relation between the echo-peak shift and Brownian-oscillator correlation function

We show that for systems that exhibit bimodal dynamics in their system-bath correlation function the shift of the stimulated photon-echo maximum as a function of waiting time reflects fairly well the long time part of the correlation function. For early times this correspondence breaks down due to a fundamentally different behaviour of the echo-peak shift in this time domain and because of the effect of finite pulse duration on the echo-peak shift. The method is used to characterize the solvation dynamics in various dye solutions.