Absorption and scattering of light by metal-dielectric nanoeggs

TL;DR

The paper addresses how geometry and material composition in dielectric-core/metal-shell nanoeggs influence their optical response, particularly surface plasmon resonances. It develops a quasistatic model of two non-concentric spheres, derives a closed-form dimensionless polarizability $\tilde{\alpha}_@$ and corresponding absorption and scattering cross-sections, and decomposes the electron relaxation into bulk, surface, and radiative contributions via $\gamma_{\mathrm{eff}}$. The results reveal geometry- and material-driven shifts and splitting of SPR features, show how the number and position of maxima depend on the offset and size parameters, and provide design guidance for maximizing radiation efficiency across spectral ranges (e.g., Ag in visible, Cu in near-UV). These insights advance the design of plasmonic nanoantennas for sensing, spectroscopy, and photothermal applications, with explicit formulas to guide material and geometric choices.

Abstract

The optical and plasmonic properties of metal-dielectric nanoeggs were investigated in this study. Frequency dependencies of polarizability, absorption and scattering cross-sections, and radiation efficiency were determined. Expressions describing the size-dependent behavior of surface plasmon resonance frequencies were derived. The causes of blue and red shifts in the maxima of polarizability, absorption, and scattering cross-sections as well as variations in their number and amplitude were identified. Recommendations were proposed regarding the use of materials with maximum radiation efficiency in different spectral ranges.

Figures (8)

• Figure 1: Geometry of the problem.
• Figure 2: (Colour online) Frequency dependencies of the real (a) and imaginary (b) parts, as well as the modulus (c) of the dimensionless polarizability for nanoeggs with different inner and outer radii (${\rm{Si}}{{\rm{O}}_2}@{\rm{Ag}}$) $d = 2\,\,{\rm{nm}}$: 1 --- $a = 10\,\,{\rm{nm}}$, $b = 15\,\,{\rm{nm}}$; 2 --- $a = 10\,\,{\rm{nm}}$, $b = 30\,\,{\rm{nm}}$; 3 --- $a = 10\,\,{\rm{nm}}$, $b = 50\,\,{\rm{nm}}$; 4 --- $a = 20\,\,{\rm{nm}}$, $b = 30\,\,{\rm{nm}}$; 5 --- $a = 25\,\,{\rm{nm}}$, $b = 30\,\,{\rm{nm}}$.
• Figure 3: (Colour online) Frequency dependencies of the absorption cross-sections for nanoeggs ${\rm{Si}}{{\rm{O}}_2}@{\rm{Ag}}$: Nanoeggs with different inner and outer radii (a) and silver nanoshells with different dielectric core materials (b) at parameters: $a = 20\,\,{\rm{nm}}$, $b = 30\,\,{\rm{nm}}$, $d = 2\,\,{\rm{nm}}$.
• Figure 4: (Colour online) Frequency dependencies of the absorption cross-sections for nanoeggs: ${\rm{Si}}{{\rm{O}}_2}@{\rm{Me}}$ (a), nanoeggs ${\rm{Si}}{{\rm{O}}_2}@{\rm{Au}}$ and ${\rm{Si}}{{\rm{O}}_2}@{\rm{Cu}}$ at different valency values (b), nanoeggs ${\rm{Si}}{{\rm{O}}_2}@{\rm{Al}}$ at different effective electron masses (c): $a = 20\,\,{\rm{nm}}$, $b = 30\,\,{\rm{nm}}$, $d = 2\,\,{\rm{nm}}$.
• Figure 5: (Colour online) Frequency dependencies of the scattering cross-sections for nanoeggs ${\rm{Si}}{{\rm{O}}_2}@{\rm{Ag}}$ with different inner and outer radii (a) and silver nanoshells with different dielectric cores (b) at parameters: $a = 20\,\,{\rm{nm}}$, $b = 30\,\,{\rm{nm}}$, $d = 2\,\,{\rm{nm}}$.