  We present a simple extension of the semi-classical model for a two-level
system in a cavity, in order to incorporate multiple polarized transitions,
such as those appearing in neutral and charged quantum dots (QDs), and two
nondegenerate linearly polarized cavity modes. We verify the model by exact
quantum master equation calculations, and experimentally using a neutral QD in
a polarization non-degenerate micro-cavity, in both cases we observe excellent
agreement. Finally, the usefulness of this approach is demonstrated by
optimizing a single-photon source based on polarization postselection, where we
find an increase in the brightness for optimal polarization conditions as
predicted by the model.
