Modulation of four-wave mixing in exciton–biexciton quantum dot-metal nanospheroid hybrid nanosystems

We study the four-wave mixing of a semiconductor quantum dot featuring a cascaded exciton–biexciton system in the vicinity of a gold spheroidal nanoparticle, assuming the interaction of the system with a strong pump field and a weak probe field both polarized along the interparticle axis. We express the density matrix equations in a rotating frame under the dipole approximation and apply a perturbative expansion to evaluate the element related to the four-wave mixing optical process. Next, we investigate the dependence of the spectral characteristics on the geometrical parameters of the metal nanoparticle (MNP), considering various interparticle distances, under one-photon, two-photon, or combined resonance conditions. To interpret the emergence of the observed spectral features, we further develop a dressed-state framework and analyze the results based on the theory of plasmonic metaresonances, providing a transparent physical understanding of the underlying exciton–plasmon resonance mechanisms.