Currently there is considerable interest in the study of nonlinear semiconductor and metallic nanoparticles as new light sources in the nanoscale regime. For example, nanoparticles consisting of non-centrosymmetric metallic nanoparticles (MNPs) exhibit two-photon second-harmonic generation (SHG) which can be used for nonlinear optical microscopy. Nanoparticles made of pure noble metals have high electron polarizabilities and produce a giant enhanced local electric field. Strong local fields are particularly important for nonlinear optical processes, such as surface-enhanced Raman scattering and SHG which scale with the power of the applied field. Two-photon photoluminescence has been studied in nanostructured noble metals, and was found to be more sensitive to the local field than single-photon luminescence. SHG in semiconductor nanoparticles such as quantum dots has also been investigated experimentally and theoretically. Two-photon excitation has many advantages over one-photon excitation including higher spatial resolution, deeper penetration and less photo-damage. Nonlinear nanoparticles have applications nanoscale antennae nanoscale lenses and photolithography and two-photon microscopy .

In this project we study the SHG in a quantum dot (QD) and metallic nanoparticle (MNP) hybrid system. The QD-MNP hybrid system is embedded in a host dielectric medium (see figure 1). In this work, silica is used however many other materials could be substituted such as photonic crystals. A schematic diagram for the present system is shown in Figure. Interactions between the MNP and QD are strong when they are in close proximity and their optical excitation frequencies are resonant with each other. Optical excitations in the QD are electron-hole pairs, which are called excitons. The optical excitations in the MNP are the collective oscillations of conduction band electrons, and are called surface plasmon polaritons (SPPs). We consider that the QD in the hybrid system has three discrete excitonic states. Similar QDs have been studied in the literature where coherent population trapping and electromagnetically induced transparency have been observed.

A strong probe field is applied to the hybrid system, which leads to two-photon absorption in the quantum dot and metallic nanoparticle. SHG photons and surface plasmon polaritons are emitted by the quantum dot and metallic particle, respectively. Induced dipoles are created in the QD and MNP due to the two-photon nonlinear effect. Hence both systems are interacting with each other via the dipole-dipole interaction. The density matrix method has been used to evaluate the SHG intensity and the dipole-dipole interaction. It is found that SHG signals from the QD are enhanced by the dipole-dipole interaction and the SHG electric field produced by the MNP. A similar enhancement is also found in SHG signals from the MNP. It has also been found that the SHG signals can be switched on and off by applying a external control field (see figure 2). There is a good agreement between our theory and the findings from recent experimental studies. The present hybrid system can be used to fabricate all optical nano-switching devices.

The higher-order nonlinear process has also gained considerable interest for its efficient enhancement of the harmonic generation process in harmonically resonant heterostructures. A theory of fourth harmonics generations (4HG) and fifth harmonics generations (5HG) is developed for metallic nanohybrids. Theoretical calculations were performed for a triple-layer nanohybrid in an ensemble of Au, Al and CuS metallic nanoparticles. When a probe field is applied to the nanohybrids, the photons would be coupled to the surface charges, and forming the surface plasmon polaritons (SPPs). The applied field would also induce dipoles, and these dipoles interact with each other which causes dipole-dipole interaction (DDI). With the produced SPP and DDI fields, the intensities of the output 4HG and 5HG fields are calculated by using the coupled mode formalism based on Maxwell's equations. The susceptibilities of different metallic nanoparticles are determined by the density matrix method under their localized SPP resonance frequencies. It is found that the 4HG and 5HG intensities depend on the fourth and fifth-order magnetic susceptibility. In the presence of SPP and DDI, the light-matter interaction is significantly enhanced by the coupling of their LSPRs. The output 4HG and 5HG intensities of the Al/Au/CuS triple-layer nanohybrids formed by the coupled LSPRs are calculated and compared with the experimental data, which showed the consistency with the theoretical model. The findings illustrate the effectiveness of producing higher harmonic generations within resonant plasmonic structures.