Fig. 2. Design principles for the twisted bi-layer metasurfaces.

a Resonant energies of the coupled modes in the bi-layer metasurface in dependence on the interlayer distance. b Dipole representation of the anti-symmetric and symmetric coupled modes of the bi-layer metasurface. c, d Resonance chirality maps of the anti-symmetric and symmetric hybrid modes in twisted bi-layer metasurfaces with varied twist angle θ and interlayer distance H. Gray area in (d) indicates the range of interlayer distances at which the symmetric mode strongly hybridizes with the higher-order modes. e−g Reflection spectra of the bi-layer metasurfaces that operate in the near-field, intermediate, and far-field coupling regimes, respectively. The circle, square, and cross signs correspond to structure parameters (H = 50 nm, θ = 20^o), (H = 280 nm, θ = 45^o), and (H = 530 nm, θ = 45^o) shown in (a−d).