Plasmon Hybridization Model for a Nanoparticle above a Dielectric Interface: Dielectric Effects, Comparison with the Dimer System, Range of Applicability, and Limits

Abstract

In the presence of a nearby highly reflecting dielectric substrate, the optical response of a metal nanoparticle exhibits a rich multipolar plasmonic structure. For quantifying the multimodal plasmonic response of such hybrid particle/interface systems, the hydrodynamic plasmon hybridization (PH) method has been applied in the simple case of a solid metal sphere (PI-PH model). In this work I extend the formalism described in my previous paper (J. Phys. Chem. C 2014, 118, 28118−28133) to the more general case where underlying dielectric media are present in the whole space (polarizable ionic background and matrix). In the quasistatic limit the method of images allows the PI-PH model to be closely related to the two-sphere dimer PH model. However, because the dynamics of the electron fluid and of the polarization charges in the mirror particle are enslaved to those in the real metal particle, strong differences between both PH models result from the reduction by a factor of two of the number of dynamical variables describing the system. As compared to jellium spheres in vacuum, the PH formalism is much more complex because the induced surface polarization charges in the underlying media contribute to the energetics of the system. In this work a very detailed analytical description of both PH models, allowing a direct numerical implementation, is provided. In the frame of the original and physically transparent method developed in my previous paper, particular emphasis is given to modeling the coupling of the nanosystem with an external applied field. In the presence of underlying dielectric media, I show that the taking into account of the field created by the additional polarization charge distributions induced by the bare applied field is essential for defining the effective external field that is coupled to the nanosystem. The predictions of both PH models are also compared, through absorption and extinction cross-section spectra, to exact results computed in the frame of the multipole expansion method, allowing the range of applicability and limits of both models to be determined. Finally, the PH formalism is shown to be generalizable to deal with underlying dielectric media characterized by complex (that is, absorbing) frequency-dependent permittivities.