Resonances in small scatterers with impedance boundary

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 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 magnetic ones capacitive. Interestingly, these subwavelength resonances resemble plasmonic resonances in small negative-permittivity scatterers and dielectric resonances in small high-permittivity scatterers. 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 non-spherical geometry

Lower Bounds to Quality Factor of Small Radiators through Quasistatic Scattering Modes

The problem of finding the optimal current distribution supported by a small radiator yielding the minimum quality ($Q$) factor is a fundamental problem in electromagnetism. $Q$ factor bounds constrain the maximum operational bandwidth of devices including antennas, metamaterials, and open optical resonators. In this manuscript, a representation of the optimal current distribution in terms of quasistatic scattering modes is introduced. Quasi-electrostatic and quasi-magnetostatic modes describe the resonances of small plasmonic and high-permittivity particles, respectively. The introduced representation leads to analytical and closed form expressions of the electric and magnetic polarizability tensors of arbitrarily shaped objects, whose eigenvalues are known to be linked to the minimum $Q$. Hence, the minimum $Q$ and the corresponding optimal current are determined from the sole knowledge of the eigenvalues and the dipole moments associated with the quasistatic modes. It is found that, when the radiator exhibits two orthogonal reflection symmetries, its minimum $Q$ factor can be simply obtained from the $Q$ factors of its quasistatic modes, through a parallel formula. When an electric type radiator supports a spatially uniform quasistatic resonance mode, or when a magnetic type resonator supports a mode of curl type, then these modes are guaranteed to have the minimum $Q$ factor

Plasmonic properties and energy flow in rounded hexahedral and octahedral nanoparticles

The resonant plasmonic properties of small dual rounded nano-scatterers are numerically investigated. A set of Drude-like, silver 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 towards sensing, sorting, harvesting, and radiation control applications

Resonant Scattering Particles - Morphological characteristics of plasmonic and dielectric resonances on spherical and polyhedral inclusions

The presented thesis concerns the study of the single particle scattering mechanisms and the corresponding morphological dependencies, specifically targeted for light-matter control applications. The initial part focuses on aspects regarding the most fundamental electromagnetic scattering problem, i.e., single homogeneous sphere in the small size limit domain. The analytical solutions for the corresponding electrostatic and electrodynamic problem are implemented with emphasis to the plasmonic and dielectric resonant domains and their corresponding size-dependent dynamic mechanisms. A novel analytic methodological approach is introduced for extracting the resonant pole distribution, the maximum resonant absorption condition, and other scattering features. This part of the thesis summarize the first article trilogy (Publications I-III). Employed with the intuition that the aforementioned physical results provide, the second part of this thesis explores certain morphological aspects through theory of the superquadric surfaces. These surfaces allow the continuous deformation of a sphere towards other shapes, such as the superguadric hexahedron and octahedron, and the five regular polyhedra i.e., the Platonic solids. The required scattering quantities are numerically extracted via a surface integral equation me-thodology, and the main results are presented in the second article trilogy presented in Publications IV-VI. The main contribution of this thesis is the disclosure of a series of resonant effects and peculia-rities that can be utilized for the design of resonant nanoparticles with on-demand functionalities. The presented results can be immediately exploited by theoretical and experimental communities, either as reference and benchmarking results, or as stepping stone for further theoretical studies in the field of electromagnetic scattering

Analytical Study of Light Scattering Characteristics of Radially Inhomogeneous Subwavelength Spheres

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.Peer reviewe

Polarizability of Radially Inhomogeneous Subwavelength Spheres

In this work the polarizability of a subwavelength core-shell sphere is considered, where the shell exhibits a radially inhomogeneous permittivity profile. The mathematical treatment of the electrostatic 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 to be dependent of the radial inhomogeneity function. The extracted general model is applied for two particular cases, i.e., a 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. Specifically, a special case of symmetric-antisymmetric resonant plasmonic degeneracy is identified and shown for the case of a core-shell spherewith a power-law permittivity profile. This degeneracy could be used for the experimental identification of inhomogeneity-induced effects or for applications where a strong coupling resonant regime is required. Furthermore, the described analysis opens avenues towards the phenomenological and first-principles modeling of the electrodynamic scattering effects for graded-index plasmonic particles at the nanoscale. Finally, such a description can be readily used either for the benchmarking of novel computational methods incorporating inhomogeneous materials or for inverse scattering purposes.Peer reviewe

Unveiling the scattering behavior of small spheres

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.Peer reviewe

Study of Plasmonic Resonances on Platonic Solids

In this study we discuss the plasmonic subwavelength scattering resonances of five regular polyhedra, that is, the Platonic solids tetrahedron, hexahedron, octahedron, dodecahedron, and icosahedron. A brief discussion regarding their geometrical characteristics and the numerical method used in the study is given. All results are compared with the benchmark case of a sphere, in order to observe how the geometry of the solid affects the spectral characteristics. The principal finding is that the shift of the main dipole resonance exhibits a solid vertex hierarchical order; in other words, the position of the resonance correlates with the solid angle of the vertex of the given solid. This is in contrast with the hedra-hierarchical order found for the electrostatic dielectric response of these solids. These results can create new avenues for applications and devices that require plasmonic particles with on-demand functionalities.Peer reviewe

Properties of Hybridized Modes in Core-Shell Scatterers

The character of resonances in plasmonic core-shell structures is analyzed. In particular, the focus is on the behavior of the weaker (antibonding) resonance. Using the residue expansion of the polarizability, it is shown that to maximize the effect of the antibonding resonance, the ratio of the core radius to the whole sphere radius should be 0.596. The polarizability-based results are compared with full Mie scattering calculations showing fair agreement up to size parameters x=1/3.Peer reviewe