Epsilon-near-zero nanoparticles

In this work we propose epsilon-near-zero (ENZ) nanoparticles formed of metal and dielectric bilayers and employ the effective-medium approach for multilayered nanospheres to study their optical response. We obtain a passive tunable ENZ region by varying the radii of the proposed bilayer nanospheres, ranging from visible to near IR. In addition, we present the absorption and scattering cross section of ENZ nanoparticles using open-source transfer-matrix-based software (stratify). The proposed ENZ nanoparticle is envisioned to be experimentally realized using chemical synthesis techniques.

Figure 1

Schematic representation of the bilayer spherical nanoparticles. Here $a_2$ and $a_1$ represent the inner and outer radii of the sphere. The inner, dark blue, sphere represents the dielectric core (${\mathrm{SiO}}_2$) of the nanoparticle, while the outer, light blue, shell represents the silver coating.

Figure 2

Effective permittivities of different bilayer spheres near their characteristic ENZ wavelengths (a) $a_{2,1}=\{38,40\}$, (b) $a_{2,1}=\{68,70\}$, and (c) $a_{2,1}=\{98,100\}$ nm. Here Re and Im represent the real and imaginary parts of effective permittivity, respectively. Their corresponding ENZ wavelengths are marked with red dashed lines.

Figure 3

Electric field for the bilayer structure, $a_{2,1}=\{98,100\}$ nm at the ENZ wavelength. (a) Actual bilayer structure. (b) Bulk effective-medium structure. (c) Difference of the normalized near-field distribution between (b) and (a). As can be seen from (c), the two simulations are in good agreement with each other in general and they differ only in the vicinity of the surface.

Figure 4

(a) Absorption and (b) scattering cross sections for the bilayered spherical nanoparticles with full permittivity (solid lines) and effective permittivity (dashed lines) for radii $a_{2,1}=\{38,40\}$ nm, $a_{2,1}=\{68,70\}$ nm, and $a_{2,1}=\{98,100\}$ nm. The values in the legend represent the radius values of the inner and outer spherical layers.

Figure 5

The ENZ wavelengths calculated for three different structures of a set of ${\mathrm{SiO}}_2$ layers, with varying thicknesses $d$. The ${\mathrm{SiO}}_2$ inner core and the Ag layers in between are fixed with a radius of $a_2=\left\{98\right\}$ nm and a thickness of 2 nm. The compositions of the multilayer nanospheres are schematically presented with red (${\mathrm{SiO}}_2$) and gray (Ag) circular layers, next to the relevant ${\lambda }_{\text{ENZ}}$ plots, corresponding to two (blue), four (red), and six layers (green), with thickness $d$ values ranging from 10 to 60 nm.