A study of two-photon florescence in metallic nanoshells

A theory of the two-photon florescence for a metallic nanoshell in the presence of quantum emitters has been developed. The metallic nanoshell is made of a metallic nanosphere as a core and a dielectric material as a shell. An ensemble of quantum emitters is deposited on the surface of the dielectric shell. A probe field is applied to study the two-photon process in the metallic nanoshell. Surface plasmon polaritons are created at the interface between the core and shell due to coupling between probe photons and surface plasmons present at the surface of the metallic nanosphere. The intensity of the surface plasmon polariton field is huge when the probe photon energy is in resonance with the polariton resonance energy. Induced electric dipoles are created in each quantum emitter due to the surface plasmon polariton field and the probe field. Dipoles in quantum emitters interact with each other via the dipole-dipole interaction. The dipole-dipole interaction is calculated using the many-body theory and mean field approximation. It is found that the dipole-dipole interaction has new term which is induced by the surface plasmon polariton field. An analytical expression of the two-photon florescence is derived in the presence the dipole-dipole interaction. Our theory predicts that the intensity of the two-photon florescence is enhanced in the presence of quantum emitters relative to the florescence of the metallic nanoshell in isolation. Physics behind the enhancement is the presence of the dipole-dipole interaction between the ensemble of quantum emitters. It is also found that as the concentration of quantum emitters increases, the dipole-dipole field also increases. This in turn, increases the two-photon florescence as function of the concentration. Finally, we have compared our theory with experiments of a metallic nanoshell which is made for Au nanosphere core and the SiO₂ shell. The metallic nanoshell is surrounded by various concentrations of Cadmium-Selenium quantum dots as quantum emitters. A good agreement between theory and experiment is found.