On the cubic zero-order solution of electromagnetic waves. II. Isolated particles with lossy plasmas

Abstract

Electromagnetic waves are examined for a single isolated nanoparticle, which is composed of lossy plasmonic components and immersed in an unbounded homogeneous dielectric host medium. Wave characteristics thus obtained on resonance play crucial roles as the zero-order solution for periodic structures such as linear particle chains. The dispersion relation with cubic nonlinearity in frequency accounts for radiation damping in addition to dynamic depolarization. It is theoretically analyzed on the parameter plane spanned by the material loss and the plasma frequency. As in the preceding companion paper of Paper I, analysis shows two types of solutions: propagating waves and stationary states. In addition, the temporal attenuation rate exhibits a maximum feature at a certain material loss in confirmation of experimental results. However, physical behaviors of a nanoparticle turn out quite distinct from those illustrated in Paper I. The reasons are that the different mathematical structures are involved, and different geometries require different underlying assumptions. In special, the issue of series convergence in choosing proper solutions will be addressed. In addition, solutions to nanoparticles made of polarizable dielectric materials are found not to exist.