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

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-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.

Weak superradiance in arrays of plasmonic nanoantennas

“…hand, leads to a shift in the resonance frequency from its value in the electrostatic limit. We note that similar expressions for the dipolar polarizability of spheres and spheroids have been calculated previously from the modified long-wavelength approximation [34] or from Padé approximations of Mie scattering coefficients [36].…”

Resonant Terahertz Light Absorption by Virtue of Tunable Hybrid Interface Phonon–Plasmon Modes in Semiconductor Nanoshells

“…Therefore, peaks in the absorption spectra can be used to identify hybrid phonon-plasmon modes. The peaks in the absorption spectrum can be identified with phonon-plasmon frequencies on the basis of Mie theory [26], extended to the case of concentric shells [55,56]. To apply this theory to the present case of semiconductor nanoshells, we used the following relative dielectric permittivities:…”

Nonlinear Optics in Dielectric Guided-Mode Resonant Structures and Resonant Metasurfaces

“…Figure 2a shows the simulated scattering cross-section from an isolated silicon nanosphere of 150 nm diameter, which is further decomposed into characteristic electric and magnetic resonances. The scattering spectra for a sub-wavelength spherical particle, expressed as scattering efficiency can be expanded as a superposition of characteristic electric and magnetic resonant modes as follows: [7]…”

“…where a i , b i are the electric and magnetic mode coefficients respectively, which are expanded in terms of Bessel, Hankel, Ricatti-Bessel and Ricatti-Hankel functions, x = ka refers to the modified dimension parameter, and m = √ ε 1 µ 1 √ ε host µ host refers to the contrast parameter [7]. Simplified forms of the scattering expansion for specific structures can be found in ref.…”

“…The resonant effects lead to a build-up of electric field inside or in the vicinity of the structure, resulting in enhancement of the nonlinear optical effects being studied. The structures of interest for such studies can be broadly divided into metallic structures which support plasmonic-type resonances, [6] and dielectric structures which support Mie scattering-type resonances [7]. Plasmonic sub-wavelength structures support field localization at its periphery due to localized surface-plasmon resonances with multipolar electric-type characteristics.…”