Core-shell nanospheres under visible light: Optimal absorption, scattering, and cloaking

Discovering peak-performing components, under certain structural and material constraints, is vital for the efficient operation of integrated systems that incorporate them. This becomes feasible by comprehensive scanning of the parametric space for one of the simplest classes of three-dimensional particles used in visible-light metasurface applications: the core-shell nanosphere. For each combination of actual media picked from a long list, the highest-scoring nanoparticles in terms of absorbance, scattering, and cloaking are recorded, while their near-field visualizations unveil the resonance mechanisms that make them so special. The reported results offer additional degrees of freedom in modeling collective meta-atom interactions and contribute to the photonic inverse design by providing the upper limits in the performance for particles of a basic geometry.

Figure 1

(a) The structural model of a core-shell nanosphere illuminated by a plane wave of visible light. (b) Typical variation of absorbed/scattering power metric $P/P_{\mathrm{inc}}$ with respect to aspect ratio $a/b$ and optical size $b/{\lambda }_0$ for fixed materials and wavelength. (c) Typical variation of maximum $P/P_{\mathrm{inc}}$ as a function of operational wavelength ${\lambda }_0$ for fixed materials.

Figure 2

Typical spatial distribution of the normalized magnitude of (a) total electric field $\left|\mathbf{E}\right|$ and (b) total magnetic field $\left|\mathbf{H}\right|$ on the $(z,x)$ plane for most core-shell designs of Table 1. The specific outputs belong to Cu/GaP nanospheres at ${\lambda }_0=640$ nm. The arrows show the direction of the in-plane components of the corresponding fields.

Figure 3

Typical spatial distribution of the normalized magnitude of (a) total electric field $\left|\mathbf{E}\right|$ and (b) total magnetic field $\left|\mathbf{H}\right|$ on the $(z,x)$ plane for most shell-core designs of Table 2. The specific outputs belong to a GaP/Au nanosphere at ${\lambda }_0=700\mathrm{nm}$. The arrows show the direction of the in-plane field components of the corresponding fields.

Figure 4

Normalized absorbed power $P_{\mathrm{abs}}/P_{\mathrm{inc}}$ as a function of operational wavelength ${\lambda }_0$ for the best designs picked from (a) Table 1, corresponding to nanospheres with metallic core and dielectric coat, and (b) Table 2, corresponding to nanospheres with dielectric core and metallic coat.

Figure 5

(a, b) Spatial distribution of the normalized magnitude of the total electric field $\left|\mathbf{E}\right|$ for (a) typical homogeneous dielectric sphere maximal scattering design (AlSb alone at ${\lambda }_0=700$ nm) and (b) optimal particle with silver core and GaP shell (at ${\lambda }_0=485$ nm). The arrows show the direction of the in-plane electric field vector. (c, d) Normalized absorbed power $P_{\mathrm{scat}}/P_{\mathrm{inc}}$ as a function of operational wavelength ${\lambda }_0$ for certain designs picked from Tables 3 and 4.

Figure 6

(a, b) The radiation patterns $\left[r^2{p}_{\mathrm{scat}}(r,\theta ,\phi )/P_{\mathrm{inc}}\right]$ for spherical nanoparticles of the same external radius: homogeneous metallic (blue), homogeneous dielectric (green), and cloaked core-shell (red). (c, d) The respective near-field spatial distributions of $\left|\mathbf{E}\right|$; the arrows represent the in-plane vector of electric field. Panels (a) and (c) correspond to the Ag/GaP pair (at ${\lambda }_0=645\mathrm{nm}$) and panels (b) and (d) to the $\mathrm{Ag}/{\mathrm{TiO}}_2$ combination (at ${\lambda }_0=525\mathrm{nm}$) of Table 5.

Figure 7

The variation of $P_{\mathrm{scat}}/P_{\mathrm{inc}}$ with respect to operational wavelength ${\lambda }_0$ for several optimally cloaked nanoparticles picked from Table 5 working at different colors of the visible spectrum. Asymmetric (Fano) resonances [7] occur.