Analytical vectorial light-field engineering with fixed-meta-atom interferometric metasurfaces.

Optical metasurfaces have become an important platform for achieving multifunctional light field manipulation. However, conventional metasurface-based light field modulation schemes mostly rely on computational solvers for complex equations and iterative searches of the meta-atom parameter library, which lacks convenience and flexibility in design and implementation. Our work proposes an analytically designed four-meta-atom interferometric metasurface. Through the interference effect among four fixed-dimension meta-atoms, it can independently regulate the amplitude and phase of two orthogonal linear polarization channels. Unlike previous analytical formulations based on the Jones matrix, our method explicitly reveals the internal polarization evolution of the interferometric meta-molecule in the linear polarization basis, thereby providing a direct geometric interpretation of the rotation-angle solutions. For verification, we numerically demonstrate two representative devices: a four-channel metasurface array integrating near-field nanoprinting and far-field holography, and a dual-channel interferometric vortex beam generator capable of generating superimposed vortex beams. The proposed method is concise, efficient, and theoretically extendable to other wavelength bands, and provides a feasible route for designing multifunctional and multi-channel optical devices.