Fig. 1. Principle of holographic technology. (a) Wavefront recording; (b) Wavefront reconstruction

Fig. 2. Schematic diagram of the Poincare ball

Fig. 3. Scalar holography and vectorial holography. (a) Scalar holography; (b) Vectorial holography - modulation of the polarization state of the incident light; (c) Vectorial holography - modulation of the polarization state of the output light

Fig. 4. Vectorial holography for modulation of the polarization state of incident light. (a) Multi-channel vectorial holography based on birefringent fully dielectric hypersurfaces^[79]; (b) Full-color vectorial holography based on non-interlaced TiO₂ hypersurfaces^[81]

Fig. 5. Vectorial holography for polarization state modulation of incident light. (a) Vectorial holography based on a 6-degree-of-freedom Jones matrix hypersurface^[82]; (b) Vectorial holography based on a dynamically phased and geometrically phased dielectric hypersurface^[83]; (c) Vectorial holography of a bilayer superstructure surface structure combined with a gradient descent algorithm^[84]

Fig. 6. Vectorial holography for the modulation of the polarization state of an output light. (a) Vectorial holography based on a diatomic plasma structural unit^[86]; (b) Vectorial holography based on a dielectric-super surface polarization generator^[87]; (c) Vectorial holography based on control of polarization transfer function^[88]; (d) Vectorial holography based on a pixelated hypersurface with GaN nanopillars^[89]

Fig. 7. Vectorial holography for polarization state modulation of output light. (a) Vectorial holography based on orthogonal circular polarization superposition^[90]; (b) Vectorial holography based on a reflective plasma hypersurface^[91]; (c) Vectorial holography based on a vector Fourier hypersurface^[92]

Fig. 8. Vectorial holography for polarization state modulation of output light. (a) Vectorial holography based on interleaved hypersurfaces^[93]; (b) Nonlinear vectorial holography^[94]

Fig. 9. Color vectorial holography. (a) Vectorial holography based on novel spin-wavelength encoding hypersurface^[95]; (b) Vectorial holography based on the improved Gerchberg-Saxton algorithm^[96]; (c) Full-color complex amplitude vectorial holography based on diatomic plasma cell structures^[44]

Fig. 10. Vectorial holography for polarization state modulation of output light. (a) Vectorial holography based on a novel spin-wavelength-encoded multi-tasking hypersurface^[97]; (b) Full-color vectorial holography with fully polarized channels^[98]; (c) Vectorial holography based on orthogonal circularly polarized light^[99]; (d) Vectorial holography based on pixelated liquid crystal superstructures^[100]

Fig. 11. Three-dimensional vectorial holography. Vectorial holography for machine learning inverse design based on multilayer perceptron artificial neural networks^[101]