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 must be altered to that by the spherical Hankel function of the 2nd kind . 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 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.