Geometric amplitude assisted beamforming in transverse-twist metasurfaces

The geometric phase that introduces the phase discontinuities by the twist of individual meta-atoms has attracted intensive interest in designing multifunctional planar metasurfaces. Typically, the twist axis aligns parallel to the plane of incidence, defined as the plane formed by the norm to the boundary surface and the incident wave vector, termed here as the longitudinal axis. So far, the degree of freedom associated with the other two transverse axes perpendicular to the plane of incidence remains rarely explored. This work introduces a geometric amplitude theory to analyze the effects of transverse-twist metasurfaces. Unlike longitudinal twist, transverse twist enables continuous amplitude modulation while maintaining phase invariance. It also achieves asymmetric radiation and prevents cross-polarization conversion. In this finite inhomogeneous array, nonlocal effects from meta-atoms coupling are significantly suppressed. Additionally, two physics-driven optimization algorithms were developed, and experimental verification demonstrates multichannel beamforming in both near- and far-field regions. This approach offers a new degree of freedom for out-of-plane deformation, unlocking new possibilities for reconfigurable beamforming and imaging across the frequency spectrum.