Polarization-insensitive broadband achromatic metalens with implicit pupil apodization and focal sharpening

Overcoming the severe efficiency penalties associated with focal spot optimization in flat optics remains a fundamental challenge. Here, we demonstrate a polarization-insensitive broadband achromatic metalens (BAML) that combines achromatic focusing with a self-evolved nonuniform pupil-amplitude distribution. By employing a complex-plane joint optimization framework based on TiO₂/SiO₂ composite cross meta-atoms, the optimized metalens develops smooth Toraldo-like transmission depressions without requiring an additional lossy amplitude mask. The designed BAML (NA ≈ 0.387) maintains robust achromatic focusing across the 640-840 nm spectrum under the investigated polarization states. Across this bandwidth, the best-focus full-width at half-maximum (FWHM) is on average approximately 4.92% smaller than the conventional Airy-reference estimate, while maintaining an average focusing efficiency of 55.65%. The nonuniform pupil transmission is therefore interpreted as an implicit pupil-shaping feature that participates in the formation of the optimized focal profile under finite-aperture propagation, rather than as the sole origin of the FWHM difference. This complex-field strategy provides a route toward high-efficiency broadband achromatic metalenses with jointly engineered pupil transmission and focal characteristics.