Quantum-mechanical-model calculations of radiative properties of a molecular crystal. I. Polaritons and abnormal decays of excitons in one- and two-dimensional systems

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Abstract
An analysis of the interaction of an electronic collective excitation, of dimensions 1 and 2, with the radiation field is presented. The use of translation symmetry in infinite lattices allows us to reduce the interaction problem to a coupling of a discrete matter state to an effective continuum of photons presenting a low-energy edge. The resulting states (radiatively unstable excitons, polaritons) are investigated as a function of the electronic excitation energy relative to the edge of the continuum, with emphasis on the spectral properties and the dynamical regimes in the intermediate region, when the energy of the electronic excitation sweeps the edge of the continuum. Contact with the three-dimensional polariton is made while application to radiative dynamics in layered crystals is suggested.