A Time-Varying Approach to Circuit Modeling of Plasmonic Nanospheres Using Radial Vector Wave Functions

摘要

Recent research has demonstrated the use of plasmonic nanoparticles (e.g., a silver or a gold nanosphere) as circuit elements. In these metallic nanoparticles, an electromagnetic wave at optical frequencies excites conduction electrons resulting in a plasmon resonance. The derived values of circuit components are based on the observation that the small size of the particle compared to the wavelength leads to lumped-impedance representations under the quasi-static approximation. In this paper, we show that circuit representations based on quasi-static approximations can often result in large errors for typical nanosphere sizes. To remedy this issue, we present a new approach based on time-varying fields, which uses vector wave functions to explicitly derive accurate resonance frequency and impedance expressions for these metallic nanospheres at and around the plasmon resonance. In particular, the proposed approach accurately predicts the dependence of the resonance frequency on the size of the nanoparticle and yields more accurate expressions for the equivalent $L$ and $C$ lumped elements compared to the quasi-static model. The new impedance approach is still compatible with the process of cascading nanoparticles in series and parallel combinations to synthesize more complex nanocircuits. A comparison with Mie and full-wave finite-element simulation results demonstrates that our model provides accurate closed-form expressions, thereby extending the range of the impedance representation to larger radii nanoparticles.