Analytical investigation of second harmonic generation in metal nanoparticle trimers using dipole approximation

In this theoretical study, we investigate the generation of second harmonics (SH) during the interaction of a laser beam with a metallic nanoparticle (MNP) trimer. Utilizing a classical electrodynamics framework, we explore the nonlinear interactions between the laser beam fields and nanoparticles (NPs), accounting for dipole-dipole interactions among the particles. Analytical expressions are derived to quantify the impact of these interactions on SH radiation power for two distinct polarizations of the laser beam. Our findings indicate that when the laser electric field is aligned parallel to the trimer's symmetry axis, there is a significant enhancement in SH radiation power compared to a single non-interacting NP, accompanied by a red-shift in the plasmon resonance peak. Conversely, when the laser electric field is perpendicular to the trimer axis, the SH radiation power from each NP decreases, and the plasmon resonance peak experiences a blue-shift. Additionally, we examine the influence of particle size and interparticle separation on SH generation. These results provide valuable insights into the role of interparticle interactions in enhancing nonlinear optical processes in NP assemblies, with potential implications for the design of nanophotonic devices.