Polarization-controlled selective excitation of Mie resonances in a dielectric nanoparticle on a coated substrate

Spherical high-index nanoparticles with low material losses support sharp high-$Q$ electric and magnetic resonances and exhibit a number of interesting optical phenomena. Developments in fabrication techniques have enabled further study of their properties and the investigation of related optical effects. After deposition on a substrate, the optical properties of a particle change dramatically due to mutual interaction. Here, we consider a silicon spherical nanoparticle on a dielectric one-layered substrate. At normal incidence of light, the layer thickness controls the contribution of the nanoparticle's electric and magnetic multipoles to the subsequent optical response. We show that changing the polarization of incident light at a specific excitation angle and layer thickness leads to switching between the multipoles. We further observe a related polarization-driven control over the direction of the scattered radiation.

Figure 1

Geometry of the system. $\theta$ denotes angle of incidence. ${\theta }^{\prime }$ and $\phi$ are stand for direction of scattered radiation in a solid angle $d\mathrm{\Omega }$. $\alpha$ indicates the direction of polarization with values of $0^{\circ }$ and ${90}^{\circ }$ for TM and TE, respectively.

Figure 2

(a) Scattering efficiency map for normal incidence in $\lambda$–$h_l$ axis. Dashed lines marks wavelengths of the ED and MD. White lines show layer thicknesses for special cases. (b) Selectivity, calculated from the scattering efficiency map along the dashed lines. $h_l$ axis is common with (a). Red and purple lines shows extreme values of selectivity with the ED/MD dominance in scattering, respectively.

Figure 3

Scattering efficiencies for different layer thicknesses. $Q{}_{\text{sca}}$ axis is common for all panels. (a) Scattering for the simultaneous enhancement (orange) and suppression (dark blue) of the ED and MD. For comparison, $Q{}_{\text{sca}}$ for the particle in free space is added. (b, c) Scattering efficiencies with the ED and MD domination regimes. Thin red and blue dashed lines shows Fano fitting curves for the ED and MD, respectively. Insets shows fields distribution at the corresponding resonances.

Figure 4

Selectivity variation for different angle of incidence and the layer thicknesses. A white dot shows that for $h_l$= 430 nm and $\theta ={75}^{\circ }$ a switch of polarization from TE to TM leads to selectivity alter equals to $-1.3$. At these paremeters, inset shows the selectivity tuning when polarization angle $\alpha$ is rotated.

Figure 5

Scattering efficiency maps as a function of the incidence angle for (a) TE and (c) TM polarization for $h_l$ = 430 nm. Normalized components of electric and magnetic fields for (b) TE and (d) TM polarization. Components of electric and magnetic fields are chosen at the wavelengths of the ED and the MD resonances, respectively.

Figure 6

Scattering spectra of Si nanoparticle on layer with $h_l$ = 430 nm and angle of incidence $\theta ={75}^{\circ }$ for different orientations of polarization $\alpha$. Dashed line represents wavelength of the MQ.

Figure 7

Differential scattering cross-section for (a, c, e) TE and (b, d, f) TM polarization of the excitation and $h_l$ = 430 nm and $\theta ={75}^{\circ }$. White dots indicate the direction of incident radiation.

Figure 8

Diagrams of the negative angle scattering (red curve) and the upward scatterings (blue curve) of Si nanoparticle on layer with $h_l$ = 430 nm and angle of incidence $\theta ={75}^{\circ }$. Data are taken from Figs. 7 and 7.

Figure 9

Scattering efficiency for the spherical silicon nanoparticle on different substartes.

Figure 10

DSCS patterns for the spherical silicon nanoparticle, placed on the silicon substrate with the silica layer with the thickness of 430 nm. The particle is irradiated by TE polarized light at the wavelength $\lambda =520$ nm. (a) One, (b) two, and (c) five multipoles are taken into account for the simulation.