Continuum model of strong light-matter coupling for molecular polaritons

Strong coupling between light and matter generates hybrid polariton modes. We present a continuum formalism that expresses the polariton modes in terms of light and matter densities of states (DOS). We derive exact expressions for the light and matter DOS for a planar cavity containing a strongly dispersive dielectric. We show that these DOS depend exclusively on the linear response of the cavity components, i.e., the reflectance of the mirrors and the susceptibility of the dielectric. We further show that, within the strong coupling regime, the light and matter DOS are well-approximated by coupled mode theory. Altogether, our continuum formalism offers a unified treatment of polaritons that connects the framework of light-matter coupling with that of linear dispersion.