Aperiodic metalenses with identical nanocylinders: positional phase control and passive chromatic aberration suppression

Conventional metalenses control light by varying meta-atom geometry, a design strategy that inherently couples phase modulation to structural dimensions, contributing to chromatic dispersion. Here, we introduce what we believe is a new design paradigm that decouples phase control from meta-atom geometry. We present an aperiodic metalens architecture composed exclusively of structurally identical, polarization-insensitive dielectric nanorods. In this framework, full 2π phase coverage is achieved solely through local periodicity modulation, that is, by varying the spacing between adjacent nanocylinders. We theoretically demonstrate that this geometric invariance yields a linear dependence of the effective refractive index on the local fill factor, which naturally approaches the dispersive condition required for achromatic focusing. The resulting architecture provides a deterministic, library-free, and analytically tractable approach to metalens design, in which positional degrees of freedom replace geometric variation as the phase-encoding mechanism. An extensive set of full-wave numerical simulations demonstrates the viability of the concept for visible-light focusing, showing that the aperiodic architecture can passively suppress chromatic aberration while maintaining near-diffraction-limited focusing. These results establish geometry-invariant positional phase control as a distinct design framework and provide a simple, reproducible baseline for further dispersion-engineered flat optics.