We have developed a theory for the photoluminescence (PL) and scattering cross section of a core–shell hybrid, where the core is the metallic nanoparticle and the shell is made of an ensemble of quantum emitters. A probe field is applied to calculate the scattering cross section of the core–shell hybrid. The surface plasmon polariton field in the metallic nanoparticle is calculated by solving the Maxwell equations in the quasi-static approximation. Dipoles are induced in the ensemble of quantum emitters because of the probe field and surface plasmon polariton field. Therefore, the dipole of one quantum emitter interacts with dipoles of other quantum emitters in the ensemble, and hence, there is the dipole–dipole interaction (DDI) between quantum emitters. We discovered an anomalous DDI, which is induced by the surface plasmon polaritons. It is shown that the strength of the DDI can be controlled by the surface plasmon polariton frequency, and it plays a dominant role in the phenomenon of the PL and scattering cross section. The surface plasmon polariton field can also interact with excitons of the quantum emitters via the exciton-surface plasmon polariton interaction. Using the density matrix method, the PL and scattering cross section are evaluated. It is found that the spectrum of the PL and the scattering cross section splits from one peak into two peaks mainly because of the strong coupling between the excitons and anomalous DDIs. It means that the PL and scattering spectrums can be switched ON (one peak) and OFF (two-peaks). This finding is consistent with the experimental data of the PL and scattering cross section of the J-aggregate and silver core–shell hybrid. We have found that the splitting and height of the two peaks can be increased or decreased by controlling mainly the strength of the anomalous DDI. The anomalous DDIs can be controlled by applying an external pulse pressure and pulse control laser. Hence, the present findings can be used for fabricating nanosensors and nanoswitches for applications in nanotechnology and nanomedicines.

We developed a theory for the fluorescence (FL) for quantum emitter and double metallic nanoshell dimer hybrids using the density matrix method. The dimer is made from two identical double metallic nanoshells, which are made of a dielectric core, a gold metallic shell and a dielectric spacer layer. The quantum emitters are deposited on the surface of the spacer layers of the dimers due to the electrostatic absorptions. We consider that dimer hybrids are surrounded by biological cells. This can be achieved by injecting them into human or animal cells. The surface plasmon polaritons (SPP) are calculated for the dimer using Maxwell's equations in the static wave approximation. The calculated SPP energy agrees with experimental data from Zhai et al (2017 Plasmonics 12 263) for the dimer made from a silica core, a gold metallic nanoshell and a silica spacer layer. We have also obtained an analytical expression of the FL using the density matrix method. We compare our theory with FL experimental data from Zhai et al (2017 Plasmonics 12 263) where the FL spectrum was measured by varying the thickness of the spacer layer from 9 nm to 40 nm. A good agreement between theory and experiment is found. We have shown that the enhancement of the FL increases as the thickness of the spacer layer decreases. We have also found that the enhancement of the FL increases as the distance between the double metallic nanoshells in the dimer decreases. These are interesting findings which are consistent with the experiments of Zhai et al (2017 Plasmonics 12 263) and can be used to control the FL enhancement in the FL-based biomedical imaging and cancer treatment. These interesting findings may also be useful in the fabrication of nanosensors and nanoswitches for applications in medicine.