Initial condition effects on the time dependence of the signal in transient grating experiments

Transient grating and Ronchi ruling experiments, which constitute a powerful observational tool for the investigation of the motion of excitons in molecular crystals, are usually interpreted in terms of an analysis which assumes the initial density matrix of the exciton to be random. This assumption cannot be verified clearly on the basis of currently available experimental data. Recent work has shown that if the assumption is relaxed or changed, significant deviations can occur in the evolution of the signal. Interpretation of the experiments and extraction of exciton motion parameters could therefore be in serious error at least in principle. We carry out a detailed analysis of this initial condition effect on the theoretically predicted signal, present specific time dependences for the signal, and conclude that, at the present state of technology and experimentation, initial condition effects are negligible for most systems studied so far including pure anthracene crystals at 20 K and 10 K for which the motion is known to be quite coherent. The usual theory is therefore quite adequate in such situations. For pure anthracene at 1.8 K, we find that the effects of the deviations from a random initial density matrix are on the borderline of being discernible and, with improved experimentation, might be measurable in the future.