Four-wave mixing theory for two-photon generation of excitons in thin films of Cu₂O

We propose and theoretically investigate a two-photon four-wave mixing experiment to probe for Bose-Einstein condensation of excitons in Cu ₂O thin films. A relatively simple set of equations describing the dynamics of the system is obtained for a particular configuration of the three incident beams, and numerical and approximate analytical solutions are found. When one takes into account the boundary conditions, which result in reflections from the interfaces, the characteristics of the resulting phase-conjugated signal will exhibit Fabry-Perot-type oscillations. For film thicknesses equal to a multiple of a half wavelength in the film the resulting signal is enhanced by more than an order of magnitude relative thicknesses that are an odd multiple of a quarter wavelength. In this case the contribution from accompanying excitonic condensates with wave vectors ±2k is minimal. Therefore, the resulting phase-conjugated signal vs the delay time between the pump and probe pulses yields a direct measure of the time evolution only of the exciton condensate with wave vector k=0.