Light control of optical intersubband absorption and amplification in a quantum well inside a cavity

We give a local-field calculation of the dynamic response of a single quantum well (QW) inside a cavity pumped by a strong light beam. The starting point of our theory is the microscopic Maxwell-Lorentz equation combined with light-induced nonlinear current densities associated with intersubband transitions in the QW system. The frequency- and space-dependent current densities are derived from the density-matrix formalism in a nonperturbative manner. Assuming only the electromagnetic coupling from the pump beam to the probe beam is important, we solve the wave equation exactly for both the pump and probe fields. In turn we determine the probe absorption coefficient of the QW structure. For a GaAs/Al${}_{0.33}$Ga${}_{0.67}$As QW placed between vacuum and a GaAs/AlAs distributed Bragg reflector followed by a GaAs prism, we calculate the probe absorption spectra for different parameters such as the pump frequency, the incident intensity of the pump field, and the cavity quality. Our results show that the optical absorption and amplification for the probe field are strongly dependent of these parameters. It is also demonstrated that it is of importance to take into account the dynamic screening effect for the pump field in the calculation of the probe spectra.