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In the present article the classical problem of electromagnetic scattering by a single homogeneous sphere is revisited. Main focus is the study of the scattering behavior as a function of the material contrast and the size parameters for all electric and magnetic resonances of a dielectric sphere. Specifically, the Pad\'e approximants are introduced and utilized as an alternative system expansion of the Mie coefficients. Low order Pad\'e approximants can give compact and physically insightful expressions for the scattering system and the enabled dynamic mechanisms. Higher order approximants are used for predicting accurately the resonant pole spectrum. These results are summarized into general pole formulae, covering up to fifth order magnetic and forth order electric resonances of a small dielectric sphere. Additionally, the connection between the radiative damping process and the resonant linewidth is investigated. The results obtained reveal the fundamental connection of the radiative damping mechanism with the maximum width occurring for each resonance. Finally, the suggested system ansatz is used for studying the resonant absorption maximum through a circuit-inspired perspective., Comment: 8 pages, 4 figures

The theory of characteristic modes (TCMs) based on the surface integral equation (SIE) formalism is presented for the analysis of plasmonic nanostructures. With TCM, excitation-independent characteristic solutions of the underlying electromagnetic field problem are obtained. Both single and multiple particle nanostructures are analyzed using the conventional SIE approach and the TCM formalism. By comparing these results, the modes that are responsible of the observed scattering and absorption characteristics can be identified. These solutions can be further utilized in the design and tuning nanoantenna configurations for specific application purposes.

We theoretically investigate whether a dielectric sphere can mimic the behavior of an equivalent surface impedance sphere and we discuss some of the of emergent properties, such as cloaking (minimum scattering) and maximum absorption conditions.

The surface integral equation (SIE) method, discretized with the method of moments, is a well-established methodology for the scattering analysis of subwavelength plasmonic nanoparticles. SIEs are usually discretized with low-order basis functions that preserve the normal continuity of the surface currents across the edges arising in the meshed boundary, such as Rao-Wilton-Glisson (RWG) functions. However, the plasmonic enhancement modeling on sharp-edged particles is an extremely challenging task, especially due to the singular fields exerted at sharp corners, exposing a slow (or no) convergence in the computation of the scattering and absorption spectra. In this paper, we propose an alternative discretization strategy based on a discontinuous basis function set in conjunction with a volumetric-tetrahedral testing scheme. We demonstrate the potential of the proposed discretization scheme by studying scattering and absorption spectra of three canonical plasmonic polyhedra, i.e., a hexahedral, an octahedral, and a tetrahedral silver inclusion. The results expose an improved accuracy and faster convergence in both far-field and near-field regions when compared to the standard RWG implementation. The proposed discretization scheme can offer faster and more accurate routes towards the exploration and design of the plasmonic resonant spectrum of sharp-edged nanoparticles and nanoantennas.

With analytical (generalized Mie scattering) and numerical (integral-equation-based) considerations we show the existence of strong resonances in the scattering response of small spheres with a lossless impedance boundary. With increasing size, these multipolar resonances are damped and shifted with respect to the magnitude of the surface impedance. The electric-type resonances are inductive and the magnetic ones capacitive. Interestingly, these subwavelength resonances resemble plasmonic resonances in small negative-permittivity scatterers but occur in two families unlike the only-electric multipoles in the plasmonic case. The fundamental dipolar mode is also analyzed from the point of view of surface currents and the effect of the change of the shape into a nonspherical geometry. For dissipative impedance scatterers, maximum absorption is shown to result in the matched-impedance case.

In this work the polarizability of a subwavelength core-shell sphere is considered, where the shell exhibits a radially inhomogeneous permittivity profile. A mathematical treatment of the elec- trostatic polarizability is formulated in terms of the scattering potentials and the corresponding scattering amplitudes. As a result, a generalized expression of the polarizability is presented as a function of the radial inhomogeneity function. The extracted general model is applied for two particular cases, i.e., the well-known power-law profile and a new class of permittivity profiles that exhibit exponential radial dependence. The proposed analysis quantifies in a simple manner the inhomogeneity effects, allowing the direct implementation of naturally or artificially occurring permittivity inhomogeneities for a wide range of applications within and beyond the metamaterial paradigm. Furthermore, the described analysis open avenues towards the phenomenological and first-principles modeling of the electrodynamic scattering effects for graded-index plasmonic par- ticles at the nanoscale. Finally, such description can be readily used either for the benchmarking of novel computational methods incorporating inhomogeneous materials or for inverse scattering purposes., 21 pages, 4 figures

IB054. The general mathematical treatment for the electrostatic polarizability will be presented in terms of scattering potentials. The case of a power-law profile and a new class of permittivity profiles that exhibit an exponential-radial dependence are considered. The presented theoretical results can open multiple avenues towards the exploration/implementation of scatterers with more exotic permittivity profiles for RF/optics and remote sensing applications.

Using Mie scattering, we derive the characteristic modes of both conducting and dielectric spheres. The results also provide a physically clear interpretation of the imaginary part of the characteristic eigenvalues for lossy objects in general.

The use of the theory of characteristic modes for the study of plasmonic eigenstates of rounded hexahedral and octahedral nanoscatterers is proposed and presented. After a brief study of electrostatic modes in an hexahedral structure follows the corresponding characteristic mode analysis. The analysis reveals the existence, for the first time, of highly symmetric dark modes on the surface of a rounded cube, enhancing our views on the triggered scattering mechanisms for single nanoparticles.

TPID5200891TCMSIE. These solutions can provide important insights into the fundamental scattering and radiation properties of arbitrary structures that can be difficult and time consuming to achieve with conventional scattering analysis techniques. TCM has been found to be a particularly powerful tool in antenna design. It can enable systematic and intuitive antenna analysis with increased physical understanding and lead to antenna configurations with enhanced properties.

Light scattering by subwavelength spheres exhibiting a radially inhomogeneous permittivity are presented. The theoretical model for power-law, exponential, and Drude-like inhomogeneous profiles are discussed, generalizing the concept of polarizability for graded-index nanoparticles.

This presentation focuses on the electromagnetic scattering characteristics of spheres with surface defined by the impedance boundary condition. The results include resonances that are very strong and sharp for small subwavelength particles, and analogous to the localized surface plasmons.

Light scattering by a subwavelength sphere exhibiting a radially inhomogeneous permittivity profile is considered here. A generalization of the polarizability for radially inhomogeneous sphere is given in terms of a so-called inhomogeneity factor. The special case of an inhomogeneous Drude profile unveils a series of scattering peculiarities, motivating further discussion for the implementation of spheres with graded-index plasmonic profiles.

This article presents and discusses the general features and aspects regarding the electromagnetic scattering by a small core-shell plasmonic sphere. First, the thickness effects on the plasmonic resonances are presented in the electrostatic (Rayleigh) limit, utilizing the MacLaurin expansion of the Mie coefficients of hollow scatterers. Several aspects regarding the core effects are given, illustrating the enabling mechanisms and peculiarities of its resonant scattering response on it electrostatic limit. The electrodynamic aspects of the scattering process are revealed through the newly introduced Pad\'e expansion of the Mie coefficients. Additionally we expose how the core material affects the dynamic mechanisms, such as the dynamic depolarization and radiative damping. The described method can be expanded for other type of resonances and canonical shapes, while the general characteristics presented here are expected to stimulate further studies regarding the functionalities of the core-shell scatterers., Comment: 8 pages, 3 figures, under review to IEEE TAP

In this extended paper we discuss the directive scattering characteristics of small dielectric spheres. Particularly, a recently introduced heuristic method utilizing the Pade approximants of the Mie coefficients is presented. With this method the resonant conditions of the magnetic multipole resonances are extracted. We expand the described method for exploring the Kerker radiation conditions, i.e., maximum forward and backscattering, for the case of a dielectric, non-magnetic sphere. The presented and results enhance our physical intuition of the triggered mechanisms and can be readily used as guidelines for the design of Huygens sources and other all-dielectric composites.

A classical way for exploring the scattering behavior of a small sphere is to approximate Mie coefficients with a Taylor series expansion. This ansatz delivered a plethora of insightful results, mostly for small spheres supporting localized plasmonic resonances. However, many scattering aspects are still uncharted, especially with regards to magnetic resonances. Here, an alternative system ansatz is proposed based on the Pad\'e approximants for the Mie coefficients. The result reveal the existence of a self-regulating radiative damping mechanism for the first magnetic resonance and new general resonating aspects for the higher order multipoles. Hence, a systematic way of exploring the scattering behavior is introduced, sharpening our understanding about the sphere's scattering behavior and its emergent functionalities., Comment: 10 pages, 2 figures

Light scattering by a small spherical particle, a central topic for electromagnetic scattering theory, is here considered. In this short review, some of the basic features of its resonant scattering behavior are covered. First, a general physical picture is described by a full electrodynamic perspective, the Lorenz–Mie theory. The resonant spectrum of a dielectric sphere reveals the existence of two distinctive types of polarization enhancement: the plasmonic and the dielectric resonances. The corresponding electrostatic (Rayleigh) picture is analyzed and the polarizability of a homogeneous spherical inclusion is extracted. This description facilitates the identification of the first type of resonance, i.e., the localized surface plasmon (plasmonic) resonance, as a function of the permittivity. Moreover, the electrostatic picture is linked with the plasmon hybridization model through the case of a step-inhomogeneous structure, i.e., a core–shell sphere. The connections between the electrostatic and electrodynamic models are reviewed in the small size limit and details on size-induced aspects, such as the dynamic depolarization and the radiation reaction on a small sphere are exposed through the newly introduced Mie–Padé approximative perspective. The applicability of this approximation is further expanded including the second type of resonances, i.e., the dielectric resonances. For this type of resonances, the Mie–Padé approximation reveals the main character of the two different cases of resonances of either magnetic or electric origin. A unified picture is therefore described encompassing both plasmonic and dielectric resonances, and the resonant conditions of all three different types are extracted as functions of the permittivity and the size of the sphere. Lastly, the directional scattering behavior of the first two dielectric resonances is exposed in a simple manner, namely the Kerker conditions for maximum forward and backscattering between the first magnetic and electric dipole contributions of a dielectric sphere. The presented results address several prominent functional features, aiming at readers with either theoretical or applied interest for the scattering aspects of a resonant sphere.

The scattering properties of a lossless isotropic dielectric sphere as a function of its relative permittivity are studied and presented. The analytically calculated extinction efficiency spectrum reveal several regions of particular interest, such as plasmonic and dielectric resonances. Additional details about the resonant properties are illustrated from a Poynting streamline perspective. As a result, different aspects of resonant spheres from microwave to optical regime are given physical interpretation, revealing emerging functionalities for plasmonic-dielectric engineered applications.

The resonant plasmonic properties of small dual rounded nanoscatterers are numerically investigated. A set of silver (Drude-like) hexahedral and octahedral structures are studied and compared with a reference spherical particle through a numerical surface integral equation technique. Surface, near-field, Poynting field, and streamline distributions are presented illustrating novel plasmonic features arising from the complex shapes of the nanoparticles, while several designing rules are described. These qualitative observations can be used appropriately toward sensing, sorting, harvesting, and radiation control applications.