Correction and verification of dispersion and loss of plasmons on metal nano-spheres

Rigorous verification has been performed on numerical and theoretical analyses of the dispersion and the loss of plasmonic resonance on Ag and Au nano-spheres. It is shown that the widely believed transcendental equation obtained from the Mie theory, which has been originally derived for dielectric spheres, must be modified for the analysis of metal nano-spheres whose permittivity has a negative real part; i.e., assumption of the field outside a sphere by the spherical Hankel function of the 1st kind h ⁽¹⁾ must be altered to that by the spherical Hankel function of the 2nd kind h ⁽²⁾. The complex resonance frequencies of the metal nano-spheres obtained both theoretically and numerically agree very well after the correction, whereas the solutions to the original equation in terms of h ⁽¹⁾ fail, in particular, for the imaginary part. It is a fundamental and important problem; the analysis of metal spheres enables reliable clarification of the appropriate analysis methods and conditions not only from a dispersive nature (real part of the resonance frequency) but also from a dissipative nature (imaginary part of the resonance frequency). The plasmon resonance is then analyzed for various topologies of multiple-sphere clusters, and their resonance states have been characterized from the spectra in infrared to ultraviolet range.