Photon-statistics dispersion in excitonic composites

Linear media are predicted to exist whose relative permeability is an operator in the space of quantum states of light. Such media are characterized by a photon statistics-dependent refractive index. This indicates a new type of optical dispersion: the photon-statistics dispersion. Interaction of quantum light with such media modifies the photon number distribution and, in particular, the degree of coherence of light. An excitonic composite - a collection of non-interacting quantum dots - is considered as a realization of the medium with the photon-statistics dispersion. Expressions are derived for generalized plane waves in an excitonic composite and input-output relations for a planar layer of the material. Transformation rules for different photon initial states are analyzed. Utilization of the photon-statistics dispersion in potential quantum-optical devices is discussed.