Fig. 1. (a) Schematic of the OAM-dependent spin splitting. A vertically polarized LG beam is coupled into a graphene metamaterial slab through a CaF2 prism. The two opposite spin components of the transmitted beam will separate along the xt axis. (b) The intensity distributions of the RCP and LCP components of the incident and transmitted beams along the xi and xt axes, respectively. (c) The graphene metamaterial composed of alternating graphene sheets and Al2O3 layers.

Fig. 2. (a) Changes of the normalized OAM-dependent spin splitting Δ/Δup with the incident angle θi and thickness of metamaterial d when w0=180  μm. (b) The dependences of Δ/Δup on θi for w0=90  μm (red color), 225 μm (blue color), and 450 μm (green color). In our calculations, ℓ=1, EF=0.335  eV, d=7.5  μm, and λ=4.509  μm.

Fig. 3. (a) Changes of the spin splitting Δ (red dots) and its upper bounds Δup (blue dots) with the incident OAM ℓ for θi=33° and d=7.5  μm. (b) The normalized spin splitting Δ/Δup changing with the incident angle θi for OAM ℓ=±10 (red color), ±5 (blue color), ±1 (green color), and 0 (black color).

Fig. 4. (a) Dependences of the normalized spin splitting Δ/Δup on the Fermi energy EF for ℓ=−3 and d=7.2  μm (red color), 8.3 μm (blue color), and 9.0 μm (green color). (b) The normalized intensities of the RCP (solid lines) and LCP (dotted lines) components of the transmitted beams along the xt axis for d=8.3  μm and EF=0.275  eV (red color), 0.299 eV (blue color), 0.318 eV (green color), 0.356 eV (pink color), and 0.4 eV (black color).

Fig. 5. Spin splitting Δ changing with the wavelength λ when EF=0.3  eV (red color), 0.335 eV (blue color), 0.38 eV (green color), and 0.45 eV (black color). The inset shows the real part of in-plane permittivity of the graphene metamaterial Re[ϵeff,//] changing with λ for different values of EF.