Metapinhole: Planar Fourier Optics Without Lenses

Abstract

The 4f lens system is a standard Fourier-optics building block for angular control in optical platforms such as spatial light modulators, imaging systems, and data storage devices. This work presents the first nanoscale implementation of an equivalent system, achieving a five-orders-of-magnitude footprint reduction. By engineering the angular scattering response of metagratings, sharp-edge spatial filtering is realized through the interplay of angle-dependent two-dimensional dipolar resonances, Rayleigh anomalies, and Kerker-like dipolar cancellation. The metagrating functions as a high-efficiency low-pass and a controllable high-pass angular filter in transmission. In addition, diffraction-controllable angular invariance across the entire spatial Fourier space enables tunable band-pass filtering in reflection. This lens-free approach provides a compact, alignment-insensitive solution for spatial filtering in electromagnetic regimes where conventional lenses or pinholes are impractical or costly -- such as the terahertz or infrared ranges -- and facilitates spatial filtering for movable beams without complex mechanical adjustments. It also enables unprecedented single-shot multiplexing of diverse spatial filtering functions at distinct central wavelengths, and extends spatial filtering to signals with extremely low coherence lengths.