Metasurface Holography on a Relative-Phase Manifold for Stable and High Fidelity Tweezer-Array Generation

We present a new holographic approach for generating large scale, polarization resolved optical tweezer arrays. By analyzing the ideal Jones fields that realize a target pattern, we identify that the fundamental degrees of freedom are the relative phases of the individual tweezers, rather than the full spatial phase profile. Leveraging this insight, we formulate a reverse projection optimization that adjusts only a small set of phase parameters to approximate the ideal operator within the physical constraints of a metasurface. This produces significantly higher fidelity and robustness than Gerchberg_Saxton type algorithms. Experimentally, we demonstrate H, V, L, and R polarized tweezer arrays using a single layer metasurface. A key advantage of our method is its phase stability, yielding strong resistance to optical aberrations and enabling coherent global phase modulation such as forming vortex tweezer lattice, without degrading trap quality. This framework provides a conceptually clear and experimentally powerful route for scalable optical field synthesis.