Mitigating sampling-induced performance limitations in high-NA metalenses via transfer-learning-enabled nonlocal...

From a spatial sampling perspective, the breakdown of the locally periodic approximation (LPA) in high-numerical-aperture (NA) metalenses arises from aliasing caused by undersampling and from strong inter-element coupling in the peripheral region. Here, we propose a transfer-learning-enabled nonlocal inverse-design framework that captures short-range inter-element interactions while maintaining computational tractability. The framework is validated by designing and simulating focusing metalenses with NAs from 0.85 to 0.95. Compared with conventional LPA-based designs under identical constraints, the optimized metalenses show substantially higher focusing efficiency and better phase fidelity. At NA = 0.85, the focusing efficiency increases from 33.9% to 44.5%, accompanied by a 32% decrease in phase root-mean-square error. Although the efficiency remains bounded by the effective Nyquist-like sampling limit of the discrete lattice, the nonlocal framework converts inter-element coupling from a parasitic perturbation into a designable degree of freedom, thereby mitigating phase errors and suppressing scattering losses. These results establish nonlocal inverse design as a viable strategy for improving efficiency and phase fidelity in high-NA metalenses near the sampling limit.