Broadband achromatic silicon metalens integrated with silicon nitride waveguide across the RGB spectrum

Metasurfaces integrated with photonic integrated circuits are essential for efficient guided-wave to free-space coupling. Conventional metalenses suffer from chromatic aberration in broadband visible systems. While recent studies have explored visible-band integration or achromatic designs separately, a waveguide-compatible achromatic metalens covering the full visible spectrum remains challenging. We propose and demonstrate a CMOS-compatible waveguide-integrated achromatic metalens operating across the RGB band under a compact aperture and moderate numerical aperture, designed via zone-multiplexed optimization with particle swarm optimization and detour phase modulation. Simulations show an average focal length of 32.53 µm with only 2.78% variation, offering a scalable solution for on-chip optics applicable to AR/VR, spectrometers, and quantum photonics.