Beyond Group Delay: Fundamental Limits of Achromatic Metasurfaces

Abstract

Achromaticity is one of the most demanding functionalities achievable with a metasurface because it requires reproducing the same optical response over a finite spectral bandwidth rather than at a single wavelength. Although previous studies established aperture-bandwidth limits based on temporal-delay considerations, the role of optical performance on these limits has remained unresolved. Here, we develop a rigorous theoretical framework that explicitly highlights how the optical performance sets the true aperture-bandwidth limit of single interface achromatic metasurfaces, quantifying the fundamental limits through the Strehl ratio. We identified two distinct operating regimes. In the first, the achromaticity conditions are exactly satisfied, guaranteeing diffraction-limited performance across the entire bandwidth. Surprisingly, the maximum achievable aperture in this regime is essentially independent of bandwidth and is instead governed by the ability of practical meta-atoms to simultaneously realize the required phase and dispersion. In the second regime, relaxing the required optical performance allows larger apertures at the cost of a fundamental trade-off between aperture, bandwidth, and optical performance. Numerical validation using a large library of high-transmission GaN meta-atoms confirms the theory and reveals the transition between these regimes. Our framework establishes the fundamental limits of achromatic metasurfaces, providing practical design rules for balancing aperture, bandwidth, and optical performance of achromatic metasurfaces.