Two-photon echo method to determine the transverse relaxation time of excitonic molecules

A nonlinear optical method to determine the transverse relaxation time of excitonic molecules by means of two-photon echo is proposed. In the case of two-photon transition such as excitonic molecule one needs three pulses to obtain an echo signal. When the wave-vector and frequency of the three successive pulses are denoted by k 1 ,ω 1 , k 2 ,ω 2 and k 3 ,ω 3 , the two-photon echo can be observed in the direction of 4k 2 -2k 1 -k 3 with frequency 4ω 2 -2ω 1 -ω 3 . Tuning both ω 1 and ω 2 to be two-photon resonant with excitonic molecule, we can satisfy the phase-matching condition rather easily for appropriate values of ω 3 due to the large dispersion of excitonic polaritons. From the correlation trace of the two-photon echo we can determine directly the transverse relaxation time of excitonic molecules.