  We formulate a full quantum mechanical theory of the interaction between
electromagnetic modes in photonic crystal slabs and quantum well excitons
embedded in the photonic structure. We apply the formalism to a high index
dielectric layer with a periodic patterning suspended in air. The strong
coupling between electromagnetic modes lying above the cladding light line and
exciton center of mass eigenfunctions manifests itself with the typical
anticrossing behavior. The resulting band dispersion corresponds to the
quasi-particles coming from the mixing of electromagnetic and material
excitations, which we call photonic crystal polaritons. We compare the results
obtained by using the quantum theory to variable angle reflectance spectra
coming from a scattering matrix approach, and we find very good quantitative
agreement.
