Abstract. This paper presents a study on the physical limitations for radio frequency absorption in gold nanoparticle suspensions. A canonical spherical geometry is considered consisting of a spherical suspension of colloidal gold nanoparticles characterized as an arbitrary passive dielectric material which is immersed in an arbitrary lossy medium. A relative heating coefficient and a corresponding optimal near field excitation are defined taking the skin effect of the surrounding medium into account. For small particle suspensions the optimal excitation is an electric dipole field for which explicit asymptotic expressions are readily obtained. It is then proven that the optimal permittivity function yielding a maximal absorption inside the spherical suspension is a conjugate match with respect to the surrounding lossy material. For a surrounding medium consisting of a weak electrolyte solution the optimal conjugate match can then readily be realized at a single frequency, e.g., by tuning the parameters of a Drude model corresponding to the electrophoretic particle acceleration mechanism. As such, the conjugate match can also be regarded to yield an optimal plasmonic resonance. Finally, a convex optimization approach is used to investigate the realizability of a passive material to approximate the desired conjugate match over a finite bandwidth. The relation of the proposed approach to general Mie theory as well as to the approximation of metamaterials are discussed. Numerical examples are included to illustrate the ultimate potential of heating in a realistic scenario in the microwave regime.

No abstract

Two different versions of an optical theorem for a scattering body embedded inside a lossy background medium are derived in this paper. The corresponding fundamental upper bounds on absorption are then obtained in closed form by elementary optimization techniques. The first version is formulated in terms of polarization currents (or equivalent currents) inside the scatterer and generalizes previous results given for a lossless medium. The corresponding bound is referred to here as a variational bound and is valid for an arbitrary geometry with a given material property. The second version is formulated in terms of the T-matrix parameters of an arbitrary linear scatterer circumscribed by a spherical volume and gives a new fundamental upper bound on the total absorption of an inclusion with an arbitrary material property (including general bianisotropic materials). The two bounds are fundamentally different as they are based on different assumptions regarding the structure and the material property. Numerical examples including homogeneous and layered (coreshell) spheres are given to demonstrate that the two bounds provide complimentary information in a given scattering problem.

No abstract

We introduce the set of quasi-Herglotz functions and demonstrate that it has properties useful in the modeling of non-passive systems. The linear space of quasi-Herglotz functions constitutes a natural extension of the convex cone of Herglotz functions. It consists of differences of Herglotz functions and we show that several of the important properties and modeling perspectives are inherited by the new set of quasi-Herglotz functions. In particular, this applies to their integral representations, the associated integral identities or sum rules (with adequate additional assumptions), their boundary values on the real axis and the associated approximation theory. Numerical examples are included to demonstrate the modeling of a non-passive gain media formulated as a convex optimization problem, where the generating measure is modeled by using a finite expansion of B-splines and point masses.