Fig. 3

Manipulation five parameters (P_R, P_L, γ, Φ_R and Φ_L) of HDPBs. a Conceptual illustration of generating multi-channel perfect HDPBs via cascaded chiral metasurfaces (meta_1 and meta_2). The generated HDPBs are analyzed by RCP/LCP analyzers for RCP/LCP incidences. b Top- and (c) side-view scanning electron microscope images of the fabricated metasurface. Scale bars: 1 μm. d The intensity distributions of HDPBs under RCP/LCP incidences and analyzers with topological charges of l₁ = 7, m₁=-5, n₁ = 7, l₂ = 8, m₂ = 1, n₂ = 4 (left) and l₁ = 7, m₁ = 4, n₁=-5, l₂ = 8, m₂ = 6, n₂ = 8 (right) corresponding to polarization orders P_R of 8 and 3/2, P_L of 7/2 and 7. e The measured intensity profiles of perfect HDPBs with different ellipticities γ of 0.6, 0.8, 1.0 and 1.2. f The generated eight states on the equators of two high-dimensional Poincaré spheres marked by Greek numerals I, II, III and IV. The north and south poles of two high-dimensional Poincaré spheres are indicated by A (C) and B (D) where A (C) represents the state \(\left| {\psi _{R}^{{{l_1}+{l_2}}}} \right\rangle +\left| {{}^{{{\Phi _{21}}}}\psi _{L}^{{{l_1}+{m_2}}}} \right\rangle\) (\(\left| {\psi _{L}^{{{l_1}+{l_2}}}} \right\rangle +\left| {{}^{{{\Phi _{22}}}}\psi _{R}^{{{l_1}+{n_2}}}} \right\rangle\)) while B (D) represents the state \(\left| {\psi _{L}^{{{m_1}+{l_2}}}} \right\rangle +\left| {{}^{{{\Phi _{22}}}}\psi _{R}^{{{m_1}+{n_2}}}} \right\rangle\) (\(\left| {\psi _{R}^{{{n_1}+{l_2}}}} \right\rangle +\left| {{}^{{{\Phi _{21}}}}\psi _{L}^{{{n_1}+{m_2}}}} \right\rangle\)). The rotation angles θ_R and θ_L of annular intensity profiles are related to the azimuth angles Φ_R = Φ₁₁ + Φ₂₂ and Φ_L = Φ₁₂ + Φ₂₁