Analytical study of linear optical properties of metal nanoparticle trimers: the impact of dipole-dipole interaction on different modes of configuration

In this study, we theoretically investigate the linear properties of a metal nanoparticle (MNP) trimer. Three identical spherical nanoparticles (NPs) whose centers are equidistantly oriented on a same straight line are considered. Using the solid core approximation for NPs and considering interaction between particles through induced electric dipoles, the motion equation of each NP conduction electrons is analytically solved. Some appropriately approximated expressions are derived for the permittivity of each NP based on a Drude-like model, allowing the clear observation of the contribution of inter-particle interaction. Depending on the orientation of the trimer axis and incident laser beam geometry (i.e., orientation of electromagnetic (EM) fields and wave vector of laser beam), three different configurations or modes are considered. The extinction efficiency of each NP as a function of wavelength is plotted, revealing that when the laser electric field is perpendicular to the symmetry axis of the trimer, it increases compared to the case of non-interactional single NP, and its plasmon resonance peak experiences a red shift. For other cases where the electric field of the laser beam is parallel to the trimer axis, the extinction efficiency of each NP decreases, and its peak shifts to the blue. In all cases, the effect of interaction on the optical properties of the middle NP is greater than on the other NPs.