Time-domain adjoint optimization for metalens design toward enhanced broadband efficiency and uniformity

We propose a time-domain adjoint optimization method for achromatic metalens design, achieving high efficiency and near-uniform spectral response. Unlike frequency-domain approaches, which require simulations for each sampled frequency, our method evaluates the entire frequency band continuously with consistent simulation times. Dynamically adjusting design variables and incident pulses during iterations balances performance and spectral uniformity. For a numerical aperture (NA) of 0.99, absolute focusing efficiency improves by 20%-30% over frequency-domain designs, with average efficiency increasing from 27% to 45%. Computational efficiency is demonstrated with 4.98 s per iteration compared to 61.8 s for frequency-domain methods. Scalability analysis shows high versatility across NAs (0.8, 0.6, and 0.4) and lens sizes (6.75 μm-50 μm), maintaining 70%-80% focusing efficiency with linear simulation time growth. This methodological advancement in nanophotonics establishes an efficient framework for designing high-performance optical devices with broad applications in imaging, communications, diagnostics, and precision metrology.