Time-reversal Inverse-designed Metasurfaces for On-demand Resonance Tailoring and Dispersion Engineering

Metasurfaces, endowed with sophisticated spectral tuning capabilities such as broadband optical resonance tailoring and dispersion engineering, play an indispensable role in a range of applications, including optical sensing, filtering, pulse shaping, and integrated optics. However, due to issues such as spectral non-uniform discrete sampling and multi-objective optimization, it remains a significant challenge to design freeform metasurfaces with sophisticated optical spectral responses using traditional frequency-domain topology optimization methods. Here, a straightforward but effective time-domain topology optimization method based on time-reversal for inverse design of broadband resonance and dispersion metasurfaces is proposed. By incorporating time-reversal symmetry and Green's function symmetry, the time-causal gradient of the figure of merit from the metasurfaces' forward and adjoint time-domain pulse responses is extracted. This strategy enables the entire response spectrum of metasurfaces to be captured simultaneously in a single simulation, instead of calculating that of metasurfaces at each frequency individually, thus circumventing the problem of multi-wavelength multi-objective optimization. As a proof-of-concept demonstration, two freeform broadband EIT resonant metasurfaces with different Q factors (2971 and 131) over a bandwidth of 100 nm are demonstrated, as well as a freeform broadband dispersion metasurface exhibiting anomalous group delay dispersion of -12 fs(2) over a 128 nm bandwidth. This research paves the way for arbitrary design of optical resonance and dispersion in metasurfaces and may find exciting applications in metaoptics, integrated optics, and nanophotonics.