Ultra narrowband geometric-phase resonant metasurfaces.

The concept of a geometric phase has sparked a revolution in photonics. Conventional space-variant polarization manipulation in optical systems only results in broadband geometric phases. Recently emerged nonlocal metasurfaces show an ability to compress the operating bandwidth through modulations of wavelength-dependent amplitudes. However, their geometric phases are still broadband and not linear, posing severe challenges to realize ultra narrowband metadevices. Here, we propose and demonstrate the generation of ultra narrowband and spatially variable geometric phases in resonant metasurfaces. We find that an array of perturbed Mie resonators is able to simultaneously preserve its global symmetry and local transformation. Local transformation provides a pixel-level geometric phase, whereas global symmetry yields an ultranarrow operation bandwidth. We further reveal that this geometric phase can be well pinned to the resonant mode by introducing additional perturbations to individually define the phase at nonresonant wavelengths. Consequently, we realize experimentally pixelated phase-gradient metasurfaces and metalenses with record-breaking Q factors and high confidentiality. We believe that our general approach and demonstrated results will open a paradigm of multiplexed metasurfaces and information encryption.