Asymptotic dispersion engineering for ultra-broadband meta-optics

Dispersion decomposes compound light into its monochromatic components, which is detrimental to broadband imaging but advantageous for spectroscopic applications. Metasurfaces provide a unique path to modulate the dispersion by adjusting structural parameters on a two-dimensional plane. However, conventional linear phase compensation does not adequately match the meta-unit's dispersion characteristics with required complex dispersion, hindering at-will dispersion engineering over a very wide bandwidth particularly. Here, we propose an asymptotic phase compensation strategy for ultra-broadband dispersion-controlled metalenses. Metasurfaces with extraordinarily high aspect ratio nanostructures have been fabricated for arbitrary dispersion control in ultra-broad bandwidth, and we experimentally demonstrate the single-layer achromatic metalenses in the visible to infrared spectrum (400 nm~1000 nm, NA = 0.164). Our proposed scheme provides a comprehensive theoretical framework for single-layer meta-optics, allowing for arbitrary dispersion manipulation without bandwidth restrictions. This development is expected to have significant applications in ultra-broadband imaging and chromatography detection, among others.