Nonlocal effects in singular plasmonic metasurfaces

A local model of the dielectric response of a metal predicts that singular surfaces, such as sharp-edged structures, have a continuous absorption spectrum and extreme concentration of energy at the singularity. Here, we show that nonlocality drastically alters this picture: The spectrum is now discrete and the energy concentration, though still substantial, is greatly reduced.

Figure 1

Schematic of nonlocality in the singular metasurface. (a) The screening length of a noble metal (gold in this paper) smooths the singularity. (b) The decay length of the longitudinal mode is coordinate dependent, due to the $k$ dependence of the longitudinal permittivity ${\varepsilon }_L$. (c) Dispersion relation at $x=0$ in the slab frame. (d) The coordinate dependence of $k_{px}^2$ on $x$ for the antisymmetric mode at $\omega =0.6{\omega }_p$, where the red point marks the turning point for the SPP wave.

Figure 2

Reflection spectrum of a groove system with $T=10$ nm under normal incidence with different nonlocal parameters $\beta$: (a) $\beta =1.27\times {10}^6$ m/s; (b) $\beta =1.27\times {10}^5$ m/s; (c) $\beta =1.27\times {10}^4$ m/s; (d) $\beta =1.27$ m/s. The blue solid line corresponds to the analytic calculation while the red dashed line to the comsol simulation, which are compared with a calculation without nonlocality (gray line).

Figure 3

Reflection spectrum of a groove system with $\beta =1.27\times {10}^6$ m/s under normal incidence with different periods $T$: (a) $T=10$ nm; (b) $T=50$ nm; (c) $T=100$ nm. The blue solid line corresponds to the analytic calculation while the red dashed line to the comsol simulation.

Figure 4

Electric field profile for a groove system under normal incidence: (a) $\beta =1.27\times {10}^6$ m/s and $T=10$ nm; (b) $\beta =1.27\times {10}^5$ m/s and $T=10$ nm; (c) $\beta =1.27\times {10}^6$ m/s and $T=100$ nm. The first two columns are field contour plots for $E_x$ and $E_y$, and the last two columns are the normal components of an electric field on the interface of the metasurface shown with different scales in the $y$ axis.

Figure 5

$k$ vector and phase change $\varphi$ at the singularity in the metasurface frame: (a) Dispersion relation ($h=T/2$ is the period of this cavity array) and (b) phase change near the singularity for the cavity with different widths $\delta$ (0.001, 0.01, and 0.1 nm).