Excitonic superradiance to exciton-polariton crossover and the pole approximations

We examine the relationship between atomic and excitonic superradiance in thin and thick slab geometries. We demonstrate that superradiance can be treated by a unified formalism for atoms, Frenkel excitons, and Wannier excitons. It is well known that in sufficiently thick slabs, the normal modes of the system are polaritons, a superposition of the slab exciton, and photon modes. We specifically examine the crossover from superradiance to polariton modes and derive both the crossover slab length and the maximum superradiative decay rate. We show that the exciton and polariton pole approximations, which give simple expressions for superradiance and polariton mode decay rates, give excellent agreement with the exact expressions for the pertinent thicknesses for which the approximations are valid.