Nonlocal theory of the intersubband optical Kerr effect in a semiconductor quantum well

Abstract

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 Al0.5Ga0.5As/GaAs/Al0.5Ga0.5 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.