Optical nonlinearities in multiple quantum wells: Generalized Elliott formula

Excitonic nonlinearities due to plasma effects in quantum-well structures under quasistationary excitation can be reproduced by appropriate many-body treatments, which usually require numerical calculations that may become computationally intensive. An alternative approach is based on analytical approximations; however, this has not been examined carefully so far. In this paper we present the analytical calculation of the optical properties of quasi-two-dimensional, type-I semiconductor quantum wells, at varying plasma densities and accounting for one conduction band and two valence subbands. This has been developed based on the two-dimensional version of the Elliott formula and on some analytical approximations already known in part. The obtained analytical results are scalable to a considerable range of constituent materials and of quantum-well thicknesses. These results are compared with the numerical solutions achieved within a more complete many-body approach, based on the Bethe-Salpeter equation, and with experimental results obtained in a pump-probe experiment. The comparison provides general guidelines on the accuracy and on the limitations of the analytical approach applicable to the case of quasi-two-dimensional excitons when multisubband and finite-size effects are included.