  Semiconductor quantum dots embedded in photonic-crystal nanostructures have
been the subject of intense study. In this context, quantum dots are often
considered to be simple two-level emitters, i.e., the complexities arising from
the internal finestructure are neglected. We show that due to the intricate
spatial variations of the electric field polarization found in photonic
crystal, the two orthogonal finestructure states of quantum dots in general
both couple significantly to a cavity mode, implying that the two-level
description is not sufficient. As a consequence the emission dynamics and
spectra, which are often recorded in experiments, are modified both in the
weak- and strong-coupling regimes. The proposed effects are found to be
significant for system parameters of current state-of-the-art photonic-crystal
cavities.
