Theoretical study of the nonlinear optical effects in tunable plasmon–exciton hybrid nanosystems: third- and fifth-order optical processes

The purpose of the present work is to study the nonlinear optical properties of the hybrid nanostructure molecules consisting of a semiconductor quantum dot modelled as a two-level system in the proximity of two metal nanoparticles or a plasmonic nanomaterial such as a plasmonic nanoshell using the density matrix formalism and applying the rotating wave approximation. We discuss the third- and fifth-order nonlinearities of the semiconductor quantum dot in the plexcitonic hybrid configurations, because the nonlinear refractive index and nonlinear absorption coefficient, which led to a variety of fascinating applications, are related to the third- and fifth-order processes. It is shown that the nonlinear optical susceptibilities are significantly altered due to the presence of two metallic nanoparticles or a plasmonic nanoshell than a simple hybrid system made of a single metal nanoparticle coupled with a semiconductor quantum dot. We also show that in addition to the quantum dot size which causes a significant shift in the optical spectra that leads to the change of the nonlinear absorption coefficient and refractive index, the electric field polarization and the distance between nanoparticles strongly affect the spectrum position and the magnitude of the third- and fifth-order nonlinear optical response. Finally, a comparison of the nonlinear optical response of the quantum dot for three hybrid configurations including metal nanoparticle–quantum dot–metal nanoparticle, metal nanoshell–quantum dot and a single metal nanoparticle–quantum dot is presented.