Reaching the highest efficiency of spin Hall effect of light in the near-infrared using all-dielectric metasurfaces

The spin Hall effect of light refers to a spin-dependent transverse splitting of light at a planar interface. Previous demonstrations to enhance the splitting have suffered from exceedingly low efficiency. Achievements of the large splitting with high efficiency have been reported in the microwave, but those in the optical regime remain elusive. Here, an approach to attain the large splitting with high efficiency in the near-infrared is proposed and experimentally demonstrated at 800 nm by using a dielectric metasurface. Modulation of the complex transmission of the metasurface leads to the shifts that reach 10λ along with efficiencies over 70% under two linear polarizations. Our work extends the recent attempts to achieve the large and efficient spin Hall effect of light, which have been limited only to the microwave, to the optical regime.

A nontapered dielectric metasurface can yield better performances ( Supplementary Fig. 1). We optimize a nontapered metasurface that has |t s | = |t p | = 1 and ϕ = π at 800 nm ( Supplementary  Fig. 1a). At a small incident angle, the nontapered metasurface has the high transmittance and the phase difference ϕ of π at 800 nm simultaneously, which is the best condition for the large SHEL with high efficiency. (The sharp enhancement of the shift near θ i = 17 • ( Supplementary Fig. 1f  Efficiency Exp.
However, the reactive ion etching process during fabrication causes a taper angle α = 5

S3
The shift and efficiency of the both tapered and nontapered metasurfaces at θ i = 5 • are summarized in Supplementary Table 1. These results indicate that reducing the taper angle by optimization of etching process can enhance the shift by more than two-folds.  The results of multipole expansion analysis of the metasurface under normal incidence are presented in Supplementary Fig. 3 for better understanding. The metasurface exhibits a strong magnetic dipole Mie resonance ( Supplementary Fig. 3c, dashed), as proved by circulating displacement current density and strong magnetic field localization ( Supplementary Fig. 4).   [5] present maximum values in the given parameter space. Ref.
[2] and ref. [3] show results at θ i = 6 • and at two wavelengths at which the experiments were performed. The shifts and efficiencies in ref. [6] are evaluated at 0.99θ B for H-polarization and at θ B for V -polarization. The slight deviation from θ B is introduced to avoid a singularity of shift at θ B .
The shifts and efficiencies in our work and previous work [1][2][3][4][5][6] are compared in Supplementary  Table 2. Besides the lossless ENZ material [5], which is not feasible, there has been only one previous demonstration that enhances the shift and efficiency simultaneously, but its operating regime is restricted to the microwave [1]. Other studies in the visible exhibit lower efficiencies. It clearly proves that our work is the first demonstration of efficient and large SHEL in the optical wavelengths. The large SHEL with high efficiency can be also achieved in reflection type by exploiting a dielectric metasurface with different dimensions (Supplementary Fig. 5).

Supplementary Note 6. Weak measurement
The main manuscript contains experimental results obtained by the Stokes polarimetry setup. For completeness, this section provides a shift experimentally measured using the weak measurement. The setup parameters and results of the weak measurements are summarized in Supplementary  Table 3 Supplementary Table 3. Setup parameters and results of the weak measurement. β is the relative angle between the postselection polarizer and the orthogonal axis with respect to the preselection polarizer, i.e., the postselection state is cos β, sin β , and A is an amplification factor.
The shift measured using the weak measurement technique agrees well with the results from the Stokes polarimetry setup as shown in Supplementary Fig. 6. Note that the effect of the shift at the back surface of the substrate is considered as δ V ± = ±(δ V sub + δ V tp ts ), where δ V ± is the experimentally measured shift, δ V sub is the shift at the back surface of the substrate, δ V is the shift at the metasurface, and t p and t s are Fresnel coefficients at the back surface [7]. The shift at the back surface is two orders of magnitude smaller than the shift at the metasurface and hence gives a negligible change.

Supplementary Note 7. Optical properties of the hydrogenated amorphous silicon
Experimentally measured permittivity of the hydrogenated amorphous silicon [8] is shown in Supplementary Fig. 7.