Giant lateral optical forces on Rayleigh particles near hyperbolic and extremely anisotropic metasurfaces

We report a dramatic enhancement of the lateral optical forces induced on electrically polarizable Rayleigh particles near hyperbolic and extremely anisotropic metasurfaces under simple plane-wave illumination. Such enhancement is enabled by the interplay between the ultraconfined surface plasmons supported by these structures and the out-of-plane polarization spin acquired by the particle. The resulting giant lateral forces appear over a broad frequency range and may open unprecedented venues for routing, trapping, and assembling nanoparticles.

Figure 1

Lateral optical forces induced on an electrically polarizable Rayleigh particle located in free space at a distance $z_0$ over an anisotropic metasurface characterized by a conductivity tensor $\overline{\mathbf{\sigma }}$ (a) Schematic of the configuration. The particle scatters an incoming plane wave, exciting directional and confined surface plasmons—with wave vector ${\mathbf{k}}_{\mathbf{spp}}$ and Poynting vector ${\mathbf{S}}_{\mathbf{spp}}$—and experiencing a lateral recoil force ${\mathbf{F}}_{\mathrm{t}}$ (b) Lateral optical forces induced on the particle vs its distance above isotropic (black line; with ${\sigma }_{xx}={\sigma }_{yy}=i10\mathrm{mS}$), $\sigma$-near zero (red line; ${\sigma }_{xx}=i10\mathrm{mS},{\sigma }_{yy}=-i0.1\mathrm{mS}$), and hyperbolic (blue line; ${\sigma }_{xx}=i10\mathrm{mS},{\sigma }_{yy}=-i10\mathrm{mS}$) metasurfaces. Results are normalized with respect to the free-space scattering force ${\mathbf{F}}_0$ (see SM [56]). (c) Absolute magnitude of the normalized Poynting vector on the isotropic (top) and hyperbolic (bottom) metasurfaces. The particle is located at $z_0=1\mu \mathrm{m}$, has a radius $r=15\mathrm{nm}$, relative permittivity ${\varepsilon }_p=3$, and is illuminated by a TM plane wave at 8 THz coming from ${\theta }_i={35}^0$ and ${\varphi }_i=0^0$.

Figure 2

Influence of the metasurface topology on the lateral optical forces induced on a Rayleigh particle located 40 nm above the MTS and illuminated by a RHCP plane wave. (a) Forces induced on the particle vs the MTS conductivity along the $y$ axis, ${\sigma }_{yy}$, for a fixed ${\sigma }_{xx}=i10\mathrm{mS}$ (b) Contributions to the lateral optical force: radiation pressure (${\mathbf{F}}_{\mathrm{t}}^0$, magenta) and interaction force (${\mathbf{F}}_{\mathrm{t}}^{\mathrm{S}}$, black). (c),(d) Isofrequency contours of the A, B, C, and D metasurfactopologies shown in (a). (e) Lateral forces vs the conductivity components of a lossless anisotropic metasurface. Results are normalized with respect to the free-space scattering force ${\mathbf{F}}_0$ (see SM [56]). Other pameters are as in Fig. 1.

Figure 3

Influence of the polarization of an cident plane wave on the lateral optical forces induced on a Rayleigh particle located 40 nm above a lossless anisotropic metasurface. (a) Particle polarization helicity with respect to the $x$ direction [see Fig. 1]. Results are plotted vs the MTS conductivity along the $y$ axis, ${\sigma }_{yy}$, for a fixed ${\sigma }_{xx}=i10\mathrm{mS}$ (b) Lateral forces induced on the particle when it is located above isotropic (black; with ${\sigma }_{xx}={\sigma }_{yy}=i10\mathrm{mS}$), $\sigma$-near zero (red; ${\sigma }_{xx}=i10\mathrm{mS},{\sigma }_{yy}=-i0.1\mathrm{mS}$), and hyperbolic (blue; ${\sigma }_{xx}=i10\mathrm{mS},{\sigma }_{yy}=-i10\mathrm{mS}$) metasurfaces. The incoming plane wave has an axial ratio equal to 1 and polarization states that follows a circular trajectory on the Poincaré sphere. Other parameters are as in Fig. 1.

Figure 4

Lateral optical forces on a Rayleigh particle located 25 nm above nanostructured silver [34]. (a) 3D schematic, showing an incident RHCP plane wave coming from ${\theta }_i={35}^0$ and ${\varphi }_i=0^0$. Superimposed field plot illustrates the $y$ component of the magnetic field excited on the structure (not to scale) at 612 THz due to the scattering process. (b) Lateral optical forces induced on the particle, normalized with respect to the power radiated by the particle when it is polarized in free space, plotted vs frequency. Results obtained when the particle is located above bulk silver [54] are included for comparison purposes. (c) Absolute magnitude of the normalized Poynting vector on the metasurface at the operation frequencies shown in (b). The particle has a radius $r=15$ nm and relative permittivity ${\varepsilon }_p=3$. The metasurface dimensions are $W=120$ nm, $H=80$ nm, and $L=180$ nm.