Light Scattering by a Dielectric Sphere: Perspectives on the Mie Resonances

TLDR: In this paper, the Lorenz-Mie theory is used to describe light scattering by a small spherical particle, a central topic for electromagnetic scattering theory, and some of the basic features of its resonant scattering behavior are covered.

Abstract: 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–Pade 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–Pade 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.