Single-layer liquid-crystal macro-pixel architecture for complex-amplitude modulation

Liquid crystals (LCs) offer controllable and reconfigurable molecular orientation and high-efficiency geometric-phase modulation, making them attractive for compact wavefront engineering. However, most existing LC devices only provide single-parameter modulation of light, such as geometric-phase or amplitude control. Achieving complex amplitude modulation through the single-layer LC structure would substantially increase functionality and integration yet remains challenging. Here, we demonstrate a single-layer LC macro-pixel architecture that enables deterministic complex-field synthesis by solely programming the in-plane orientation angles of LC molecules. Coherent interference between two diagonal molecule pairs provides decoupled, continuous amplitude and full 0-2π phase control. As the proof of concept, we design and verify two representative complex-amplitude LC devices in experiments: a multifocal lens that generates multiple axial foci with prescribed positions and relative intensities and a complex-amplitude hologram. These results establish a compact and scalable route toward complex-field synthesis in single-layer LC platforms, enabling high-quality light control, such as in 3D holography imaging.