Radiation of a point dipole in “spherical semiconductor quantum dot + spherical metal nanoparticle” structure (theory)

Abstract

A model is proposed allowing considering radiation of semiconductor quantum dot (QD) in a vicinity of metal nanoparticle (NP) as radiation of an ensemble of unit cells, from which the QD consists. It is shown that each unit cell of QD can be considered as a separate radiating point dipole. Relations are obtained between the coefficients of multipole expansions of electromagnetic fields in two spherical coordinate systems centered in the semiconductor QD and the metal NP. The relations allow using separately spherical symmetry of the QD and the NP despite the “QD + NP” structure s a whole is not spherically symmetric. It is shown, that contribution of a particular QD unit cell into the total QD radiation is proportional to the value of the envelope exciton wave function in corresponding QD node. Summing contributions from all QD unit cells makes possible to find characteristic radiative and nonradiative times in “QD + NP” structure and evaluate their decrease relatively to that of isolated QD due to resonant excitation of dipole and higher order multipole plasma oscillations in metal NP. For the metal NP not only contribution of free carriers to its dielectric function is taken into account (Drude term) but that of bound carriers too due to possible interband transitions in real metals in the actual frequency range. Besides, to cover the cases of extremely small metal NPs (less then 10 nm in size) a spatial dispersion in NP dielectric function is also accounted.