Multimode Impedance Representation of Scattering, Absorption and Extinction Cross-Sectional Areas for Plasmonic Nanoparticles

In plasmonic nanoparticles, scattering and absorption phenomena are exploited to functionalize them for various applications. Recent research in plasmonic nanoparticles has extended the classic circuit concepts to the optical domain, but under the assumption of only accounting for the fundamental mode (dipole mode) with restrictions placed on the wavelength and size of the nanoparticle. In this paper, we propose an extended approach to the impedance representation of metallic nanoparticles and develop a solution consisting of circuit elements representing their behaviour without any constraints on wavelength, size and material properties. This model offers an intuitive understanding of the qualitative behaviour of a metallic nanoparticle, and rigorously develops an all-mode (i.e., TE_m,n and TM_m,n mode with m = 1 and n varying from 1 → ∞) exact impedance model. The proposed model originates from the rigorous Mie solution. Quantities such as scattering, extinction and absorption cross-sectional areas are derived using voltages, currents and circuit elements and their equivalence is compared with well-known field solutions and full-wave simulations.