Quantum Theory of a Basic Light-Matter Interaction

Quantum field-theoretical methods are applied to the problem of determining how the exciton-lattice interaction affects the dispersion of an electromagnetic field associated with the exciton-radiation interaction. An exact solution for the retarded Green's function of the radiation field is calculated for a quantum model consisting of three interacting boson fields-photon, exciton, and phonon. The classical Green's function of a damped-harmonic-oscillator model of a dielectric is shown to be a special case of this quantum Green's function. Two sets of dispersion relations are derived; one set has well-defined energy, the other has well-defined momentum. Results of the theory clearly suggest that the exciton-lattice interaction is capable of literally damping out the "polariton" effects associated with the exciton-radiation interaction in the field solutions with well-defined energy. A Poynting theorem based on the classical model is also derived which includes effects of both spatial dispersion and damping.