Light emission by point dipole located inside spherical (semiconductor) particle in the vicinity of a spherical metal particle

Abstract

Proposed in this work is a theoretical model that enables to correctly calculate light emission characteristics of a hybrid nanosystem formed by a spherical semiconductor quantum dot (QD) and spherical metal nanoparticle (NP) when QD is excited by light. The QD that emits mainly dipole-type electromagnetic (EM) field can not be considered as a point dipole at small separation distances between QD and NP (of the same order as the QD size). However, only the “point dipole” concept of QD is used in all currently known theoretical models of hybrid nanosystems. Correspondingly, unlike a simulated “point dipole + spherical metal NP”, the real hybrid nanosystem is nonspherical as a whole. In this work: i) relations have been obtained between the coefficients of EM field multipole expansions in two spherical coordinate systems with their origins in semiconductor QD and metal NP. As a result, spherical symmetry of semiconductor QD and metal NP can be used separately to solve the equations related to boundary conditions at their surfaces; ii) it has been shown that EM field emitted by QD can be represented as a sum of contributions of all crystal unit cells forming QD and that each unit cell can be considered as an emitting point dipole. The contribution of a particular unit cell to the total EM field is determined by the exciton wave function; iii) to be closer to the real situation, the contribution εib(ω) of interband transitions to the NP permittivity has been taken into account in the visible spectral range.