A Compact Quasi-Static Model for Magnetic Dipole Resonance in Metallic Nanoparticles With Large Radii

Magnetic resonance in metallic nanoparticles has garnered significant attention from scientists for its promising applications in medical diagnostics, data storage technologies, and the development of advanced metamaterials. The behavior of these applications is driven by the interaction of metallic nanoparticles with electromagnetic fields, thus creating electric and magnetic dipole resonances. In nanoparticles with small radii ( $radius \lt 40$ nm), the response is primarily governed by the electric dipole resonance and can be described by the simplified quasi-static approximation model. However, the magnetic resonance in metallic nanoparticles occurs at significantly larger radii, and its current understanding is limited to the Mie solution and numerical field solvers. These methods provide little insight into the underlying mechanisms of the magnetic dipole resonance. In this paper, we developed a compact series resonance model for magnetic dipole resonance using the quasi-static approximation ( $radius \ll wavelength$ ) and linear circuit theory. The scattering cross-section efficiency, along with the spherical and fringe impedance, are calculated using current and voltage expressions. The simulation results closely align with those of the Mie solution. The quasi-static model now enables the voltage and current approach to effectively model larger nanoparticles (40 nm $\lt ~radius~\lt ~90$ nm), whereas it was initially restricted to nanoparticles less than 40 nm radius. The proposed work enhances understanding and is valuable for large-scale all-photonic applications involving magnetic resonance in metallic nanoparticles.