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.

Performing analog computations with metastructures is an emerging wave-based paradigm for solving mathematical problems. For such devices, one major challenge is their reconfigurability, especially without the need for a priori mathematical computations or computationally-intensive optimization. Their equation-solving capabilities are applied only to matrices with special spectral (eigenvalue) distribution. Here we report the theory and design of wave-based metastructures using tunable elements capable of solving integral/differential equations in a fully-reconfigurable fashion. We consider two architectures: the Miller architecture, which requires the singular-value decomposition, and an alternative intuitive direct-complex-matrix (DCM) architecture introduced here, which does not require a priori mathematical decomposition. As examples, we demonstrate, using system-level simulation tools, the solutions of integral and differential equations. We then expand the matrix inverting capabilities of both architectures toward evaluating the generalized Moore–Penrose matrix inversion. Therefore, we provide evidence that metadevices can implement generalized matrix inversions and act as the basis for the gradient descent method for solutions to a wide variety of problems. Finally, a general upper bound of the solution convergence time reveals the rich potential that such metadevices can offer for stationary iterative schemes.

Novel surface integral equation (SIE) based theory of characteristic mode (TCM) formulations are proposed for homogeneous penetrable bodies. Analytical expressions for the characteristic eigenvalues are presented and good agreement between the numerical and analytical results is observed for both lossless and lossy, as well as for dielectric and magnetodielectric objects. The new formulations, without any postprocessing methods, avoid spurious modes and resonances appearing in existing SIE-based TCM formulations. For lossy objects the obtained eigenvalues are complex. The real part of an eigenvalue is related to the ratio of the reactive and radiated power, as in the original TCM formulation for PEC structures, and the imaginary part gives the ratio between the dissipated and radiated power.

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 electric 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 Padé approximants for the Mie coefficients. The results reveal the existence of a self-regulating radiative damping mechanism for the first magnetic resonance and general resonating aspects for the higher order multipoles. Hence, a systematic way of exploring the scattering response is introduced, sharpening our understanding of the sphere's scattering behavior and its emergent functionalities.

The nonreciprocal magnetoelectric effect, also known as the Tellegen effect, promises a number of groundbreaking phenomena connected to fundamental (e.g., electrodynamics of axion and relativistic matter) and applied physics (e.g., magnetless isolators). We propose a three-dimensional metamaterial with an isotropic and resonant Tellegen response in the visible frequency range. The metamaterial is formed by randomly oriented bi-material nanocylinders in a host medium. Each nanocylinder consists of a ferromagnet in a single-domain magnetic state and a high-permittivity dielectric operating near the magnetic Mie-type resonance. The proposed metamaterial requires no external magnetic bias and operates on the spontaneous magnetization of the nanocylinders. By leveraging the emerging magnetic Weyl semimetals, we further show how a giant bulk effective magnetoelectric effect can be achieved in a proposed metamaterial, exceeding that of natural materials by almost four orders of magnitude.

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 Padé 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.