NONLOCAL THEORY OF THE INTERSUBBAND OPTICAL KERR-EFFECT IN A SEMICONDUCTOR QUANTUM-WELL

Taking as a starting point the Liouville equation for the one-body den sity matrix operator, a general expression for the third-order nonline ar current density responsible for the optical Kerr effect associated with intersubband transitions in a quantum well is derived by use of t he perturbative expansion method. The nonlinear current density is rel ated to the local field inside the quantum well via a nonlocal relatio n. By combining the field-induced nonlinear part of the current densit y with the Maxwell equation, a nonlinear integral equation for the loc al field is established. For a two-level quantum well, the integral eq uation is solved exactly. The nonlinear optical reflectivity, transmit tance, and absorbance of the quantum well in turn are obtained. Numeri cal calculations of the light-induced change of the optical spectra ar e presented for a Al0.5Ga0.5As/GaAs/Al0.5Ga0.5As quantum well. The num erical results show that the optical reflectivity and absorbance decre ase, and the transmittance increases as the optical intensity of the i ncident light is increased. In the case where the quantum-well structu re is heavily doped, a notable light-induced red-shift of the location of the resonance peak in the optical spectra stemming from the combin ed local-held effect and field-induced population redistribution is pr edicted.