Fig. 2

Principle and demonstration of multi-momentum meta-transformer. a Geometry of the designed unit cell structure representing one pixel in the meta-transformer, with the periodicity of 325 nm. The TiO₂ nano-fin parameters are w = 80 nm, l = 250 nm, and h = 600 nm. The in-plane rotating angle φ of nano-fin will introduce the geometric phase of 2φ for the incident beam with RCP. b Measured conversion efficiency of the meta-transformer. The conversion efficiency is defined as the optical power of the transmitted light with opposite CP divided by the incident optical power. c Design principle of OAM meta-transformer. Under the illumination of vortex beam 1 (l⁽¹⁾ = −5) with RCP, the transmitted beam with opposite CP carries the total phase profile \(\psi _{{\mathrm{OAM}} = - 5}\left( {x_0,y_0} \right) + \psi _{{\mathrm{meta}}}\left( {x_0,y_0} \right)\) and reconstructs “apple” pattern in the observation plane. When using vortex beam 2 (l⁽²⁾ = 5) with RCP, the total phase profile of the transmitted beam is \(\psi _{{\mathrm{OAM}} = 5}\left( {x_0,y_0} \right) + \psi _{{\mathrm{meta}}}\left( {x_0,y_0} \right)\), which causes the reconstructed pattern change to a spider-shaped pattern. d Simulated (top) and measured (bottom) reconstructed patterns by vortex beam 1 (l⁽¹⁾ = −5) (left) and vortex beam 2 (l⁽²⁾ = 5) (right). Scale bar: 20 μm. e Design principle of LM meta-transformer. Under the illumination of right circularly polarized beam with \({\mathrm{LM}} = k_0^{\left( {\mathrm{R}} \right)}\hbar\), the transmitted beam with opposite CP carry the dispersionless phase profile of metasurface ψ_meta (x₀, y₀). Due to the convolution of \({\mathbf{U}}_{{\mathbf{inc}}}\left( {x_0,y_0} \right)exp\left( {i\psi _{{\mathrm{meta}}}\left( {x_0,y_0} \right)} \right)\) and impulse response \(h\left( {x,y,z,k_0^{\left( {\mathrm{R}} \right)}} \right)\), the transmitted beam reconstructs patterns at the observation plane. Because the impulse response h is k₀-dependent, by changing LM of incidence, the reconstructed images “R”, “G” and “B” components can be shifted to one identical plane (z = Z₀). f Simulated (top) and experimental (bottom) reconstruction of three-primary color holograms at the imaging plane. Scale bar: 20 μm. The original “spider” image was obtained from PNG image website