The radiative decays of excited states of transition elements located inside and near core-shell nanoparticles

Abstract Here we discuss the radiative decays of excited states of transition elements located inside and outside of the subwavelength core-shell nanoparticles embedded in dielectric medium. Based on the quantum mechanics and quantum electrodynamics, the general analytical expressions are derived for the probability of the spontaneous transitions in the luminescent centers (emitter) inside and outside the subwavelength core-shell nanoparticle. Obtained expressions holds for arbitrary orientation of the dipole moment and the principal axes of the quadrupole moment of the emitter with respect to the radius-vector r connecting the center of the emitter with the center of the nanoparticle. They have simple form and show how the spontaneous emission in core-shell NPs can be controlled and engineered due to the dependence of the emission rates on core-shell sizes, radius-vector r and permittivities of the surrounding medium, shell, and core.