On the quasistatic optimal plasmonic resonances in lossy media
This paper discusses and analyzes the quasistatic optimal plasmonic dipole resonance of a small dielectric particle embedded in a lossy surrounding medium. The optimal resonance at any given frequency is defined by the complex valued dielectric constant that maximizes the absorption of the particle under the quasistatic approximation and a passivity constraint. In particular, for an ellipsoid aligned along the exciting field, the optimal material property is given by the complex conjugate of the pole position associated with the polarizability of the particle. In this paper, we employ classical Mie theory to analyze this approximation for spherical particles in a lossy surrounding medium. It turns out that the quasistatic optimal plasmonic resonance is valid provided that the electrical size of the particle is sufficiently small at the same time as the external losses are sufficiently large. Hence, it is important to note that this approximation can not be used for a lossless medium, and which is also obvious since the quasistatic optimal dipole absorption becomes unbounded for this case. Moreover, it turns out that the optimal normalized absorption cross section area of the small dielectric sphere has a very subtle limiting behavior, and is in fact unbounded even in full dynamics when both the electrical size as well as the exterior losses tend to zero at the same time. A detailed analysis is carried out to assess the validity of the quasistatic estimation of the optimal resonance and numerical examples are included to illustrate the asymptotic results.