Taking as a starting point the Liouville equation for the one-body density matrix operator, a general expression for the third-order nonlinear current density responsible for the optical Kerr effect associated with intersubband transitions in a quantum well is derived by use of the perturbative expansion method. The nonlinear current density is related to the local field inside the quantum well via a nonlocal relation. By combining the field-induced nonlinear part of the current density with the Maxwell equation, a nonlinear integral equation for the local field is established. For a two-level quantum well, the integral equation is solved exactly. The nonlinear optical reflectivity, transmittance, and absorbance of the quantum well in turn are obtained. Numerical calculations of the light-induced change of the optical spectra are presented for a Al 0.5 Ga 0.5 As/GaAs/Al 0.5 Ga 0.5 As quantum well. The numerical results show that the optical reflectivity and absorbance decrease, and the transmittance increases as the optical intensity of the incident light is increased. In the case where the quantum-well structure is heavily doped, a notable light-induced red-shift of the location of the resonance peak in the optical spectra stemming from the combined local-field effect and field-induced population redistribution is predicted.
Nonlinear optical response and optical coherence time of excitons localized to quantum islands in a
GaAs∕AlGaAs single quantum well are studied by the three-pulse photon echo technique. At low temperature, the optical coherence time is estimated to be
1.8ns from the decay of the photon echo signal. The decay profile for short time delay shows the strong dependence on the input pulse area of the third pulse. Rabi oscillations are also observed. The oscillations show nonlinear behavior affected by the pre-excited polarization. Such behavior can be qualitatively explained by the local field effect due to the exciton-exciton interaction between the localized excitons.