Using the Purcell effect for the modification of third-harmonic generation in a quantum dot near a metallic nanosphere

We study the modification of third-harmonic generation from a quantum dot close to a metallic nanosphere. We show that the strong variation of the spontaneous decay rate of the quantum dot near the metallic nanoparticle can be used for tailoring the third-harmonic generation coefficient of the quantum dot. Specifically, the strong enhancement or suppression of the quantum dot's spontaneous emission rate can strongly modify the third-harmonic generation coefficient of the quantum dot depending on the distance of the quantum dot from the surface of the metallic nanosphere and on the direction of the electric dipole moment of the quantum dot. The alteration of the third-harmonic generation coefficient is also strongly dependent on the quantum dot's pure dephasing rate.