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 k₁,ω₁, k₂,ω₂ and k₃,ω₃, the two-photon echo can be observed in the direction of 4k₂-2k₁-k₃ with frequency 4ω₂-2ω₁-ω₃. Tuning both ω₁ and ω₂ to be two-photon resonant with excitonic molecule, we can satisfy the phase-matching condition rather easily for appropriate values of ω₃ 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.