Aperiodic metalenses: intrinsically near-achromatic visible focusing with identical nanocylinders

Abstract

Conventional metalenses control light by varying meta-atom geometry, a design strategy that inherently couples phase modulation to structural dimensions and exacerbates chromatic dispersion. Here, we break this paradigm by decoupling phase control from meta-atom geometry. We introduce an aperiodic metalens architecture composed exclusively of structurally identical dielectric nanorods, where full 2-pi phase coverage is achieved solely through local periodicity modulation (i.e., by varying the spacing between adjacent nanorods). We theoretically demonstrate that this geometric invariance yields a linear effective-refractive-index scaling that intrinsically satisfies the dispersive condition required for near-achromatic focusing. Operating in the visible spectrum, we evaluate our polarization-insensitive aperiodic designs across four distinct scenarios: moderate and high numerical aperture configurations (0.4 and 0.8), large scalable apertures, and different constituent materials (Si and TiO2). In all cases, the geometric invariance reveals a passive suppression of dispersive chromatic aberration. Compared with conventional size-variant designs, our aperiodic approach reduces the longitudinal chromatic focal shift by nearly 42% (Si) and 66% (TiO2) at moderate numerical apertures, consistently yielding tighter, near-diffraction-limited focal spots. Furthermore, transitioning to a low-loss TiO2 platform raises the peak focusing efficiency to near 60% while maintaining superior spectral stability. By relying on a fully deterministic analytical formulation and a single, potentially fabrication-tolerant nanostructural building block, this approach offers a highly simplified and scalable route toward next-generation broadband metasurfaces.