A new class of composite materials, excitonic composite, has been considered by the example of a collection of identical semiconductor quantum dots (QDs). The QD is modeled by a spatially confined exciton interacting with external electromagnetic field. A self-consistent microscopic local-field theory for an isolated arbitrary shaped QD has been developed. A Hamiltonian of the system has been formulated in terms of the acting field with a separate term responsible for the effect of depolarization. Relations between local and acting fields in QD have been derived in the dipole approximation for both strong and weak confinement regimes with the account for pronounced spatial nonlocality of the electromagnetic response in the latter regime. Homogenezation procedures have been carried out for both cases and expressions for the effective dielectric function have been derived. It has been shown that the nonlocality changes components of the polarizability tensor but does not change the general representation of the scattering operators as compared to the strong confinement regime.
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