Arbitrary Total Angular Momentum Vectorial Holography Using Bi-Layer Metasurfaces

Advanced holographic techniques are increasingly demanded for high-capacity and secure information processing. In this context, orbital angular momentum (OAM) stands out as a powerful resource for optical multiplexing, offering access to an unbounded set of orthogonal modes. To harness this potential, metasurfaces, with their considerable ability to control light, have emerged as key platforms for OAM-multiplexed holography. Nevertheless, conventional OAM holography suffers from limited polarization engineering capabilities due to the lack of chirality control in single-layer metasurfaces. Here, we introduce a bi-layer metasurface architecture that realizes total angular momentum (TAM) vectorial holography, where TAM represents the combination of spin angular momentum (SAM, equivalent to polarization) and OAM of light. In contrast to previous approaches, this scheme enables true polarization-OAM multiplexing, facilitating the independent generation of vectorial holographic images for each orthogonal TAM input state. This concept is validated numerically and experimentally, confirming the feasibility of TAM vectorial holography. The proposed scheme can be easily integrated with other recent holography generation approaches, such as vector beam multiplexing and bidirectional holography, thereby further expanding its multiplexing capability. This work establishes a versatile framework for advanced full-vectorial holography, showing how metasurfaces can unlock multiplexing strategies for emerging photonic systems.

💡 Research Summary

The paper introduces a novel holographic platform based on a bi‑layer metasurface that enables full control over total angular momentum (TAM), the combination of spin angular momentum (SAM, i.e., polarization) and orbital angular momentum (OAM). Conventional single‑layer metasurfaces suffer from symmetry‑imposed chirality limitations, which restrict them to either polarization‑multiplexed OAM holography (intensity‑only multiplexing) or OAM vectorial holography (single‑polarization vector design). By stacking two layers of anisotropic elliptical nanoposts, the authors achieve independent tuning of the orientation angles (θ₁, θ₂) and phase delays (φ₁ˣ, φ₁ʸ, φ₂ˣ, φ₂ʸ) of each layer, thereby realizing a unitary Jones matrix that can be programmed to respond differently to any combination of SAM and OAM.

Design is performed by discretizing target intensity, phase, and polarization (Stokes parameters) on a 2‑D lattice and minimizing a loss function that measures the deviation between simulated far‑field patterns and the desired vectorial holograms. A gradient‑descent algorithm, extended to multi‑objective optimization, updates the four design parameters iteratively. The method naturally supports arbitrary numbers of TAM input‑output pairs, allowing simultaneous encoding of several orthogonal TAM states.

Experimentally, four orthogonal TAM states are selected: left‑circular (LC) and right‑circular (RC) polarizations combined with OAM indices l = −2 and l = +2. For each state the metasurface generates three distinct scalar images (e.g., Latin letters, Greek letters, numbers, animal icons), which together form a single vectorial hologram with prescribed intensity and polarization distributions. Numerical simulations yield an average intensity correlation of 0.962 and a Stokes‑parameter cosine similarity of 0.963 across all 12 images; measured results closely match these figures. The overall transmission efficiencies range from 16 % to 20 %, limited primarily by the number of OAM channels encoded.

Beyond static TAM multiplexing, the authors demonstrate vector‑beam‑multiplexed holography. By coherently superposing two TAM states, a generalized vector beam (VB) is formed, which can be represented on a higher‑order Poincaré sphere (HOPS). The bi‑layer metasurface selectively reconstructs the intended vectorial hologram only when the incident VB matches the programmed point on the HOPS, even when the constituent TAM states are deliberately chosen to be as similar as possible while remaining orthogonal. This capability surpasses previous single‑layer approaches that could support only one VB per HOPS.

Finally, the paper discusses integration with other multiplexing schemes, such as bidirectional holography and additional vector‑beam channels, highlighting the scalability of the platform for high‑capacity, secure optical information processing, free‑space communications, quantum photonics, and three‑dimensional display technologies. The work establishes a versatile, experimentally validated framework for full‑vectorial, TAM‑multiplexed holography, opening new avenues for exploiting the infinite dimensionality of OAM together with polarization control.