A Dynamic Approach to the Lumped Impedance Representation of a Nanoparticle

Recent research on plasmonic nanoparticles have emphasized their use in the circuits and device-based applications by exploiting control of the plasmon resonance. The resonance behavior of the nanoparticles can be explained by its lumped-impedance representation at optical frequencies, which is derived using voltage-current (VI) laws. The VI model uses quasi-static approximation, which is inherently restricted, and can only work well for small radii (R <; 10 nm) nanoparticles. In this paper, an extended approach is proposed by solving for the full dipole equation, including the radiation damping for the dominant mode of the oscillating nanoparticle. The proposed approach employs taking all time-dependent fields of a dipole and introduced the concept of radiation impedance, which can store and absorb radiated power. Closed-form expressions for the quantities, such as internal and external impedances are derived using voltages and currents, giving good understanding of the behavior of a metallic nanoparticle. A comparison with the Mie solution demonstrates that our proposed impedance model extends the range of the impedance model to the larger radii nanoparticles.