Anomalous size dependence of degenerate four-wave mixing due to double resonance of internal field and third-order susceptibility

The degenerate four-wave mixing (DFWM) of weakly confined excitons in a mesoscopic thin film is studied by means of the nonlocal theory of nonlinear response, where the self-consistency between the induced polarization and the radiation field is considered. As a result, it is elucidated that the DFWM signal is greatly strengthened due to the double resonance of the internal field and the energy denominators of χ⁽³⁾, affecting both the incident and signal beams, and that the enhanced nonlinear response is originated from the transition associated with the nondipole type polarization pattern. The result clearly shows that the consideration of the nonlocal and self-consistent description of the response field is essential, which is in a striking contrast to the nonlinear response described in the long wavelength approximation.