Transmission line approach to quantifying the resonance and transparency properties of electrically small layered plasmonic nanoparticles

The scattering and transparency properties of layered plasmonic nanoparticles are studied from the perspective of spherical transmission line theory. The advantage of this approach is that the interaction of the nanoparticle with its surroundings can be very conveniently represented as a combination of admittances. In this framework we reformulate the total impedance expression of a spherical nanoparticle, and from this we derive through a compact and intuitive methodology the two conditions that govern the resonance and transparency states of a nanoparticle. These conditions are satisfied when the particle's input admittance becomes inductive and capacitive, respectively. The recursive relations that determine the TM admittance of an electrically small, radially inhomogeneous dielectric sphere are analyzed, and it is demonstrated that any degree of layering can be homogenized by a decomposition into successive binary mixtures. The appropriate material choice results in mixtures that exhibit multiple Lorentzian resonances that are directly mapped to the particle's admittance, due to its small electrical size. Consequently, the particle's admittance exhibits multiple inductive-to-capacitive switchings, and thus the resonance and transparency conditions are satisfied at multiple frequencies. This explains the well-known feature of multiple resonance-transparency pairs observed in the scattering signature of layered plasmonic nanoparticles.