Mean-field polariton theory for asymmetric quantum wells

We present a simple method to compute the optical properties of quantum wells of any shape, using microscopic calculations of the electronic states. Near the exciton resonances simple expressions for the polariton states and the radiative lifetimes are obtained as functions of the in-plane wave vector ${\mathit{K}}_{\mathrm{?}}$. The cases of a GaAs/${\mathrm{Al}}_{\mathit{x}}$ ${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$As/AlAs asymmetric well and of double wells are considered; the results relate to those of the symmetric well. The computed splitting between the Z mode and the T mode is shown to depend mostly on the thickness, in fair agreement with experiments by Fröhlich et al. Polaritons associated with crossed excitons involving pairs of subbands forbidden in the symmetric case are found, and are shown to give rise to additional structure in the reflectivity.