Fourier pixels for bidirectional light control

Digital cameras¹ and displays² use picture elements (pixels³) that perform a single function: detecting or emitting light intensity. To exploit the full information content of electromagnetic waves, more advanced elements are required. This has driven the development of multifunctional components that, for example, simultaneously detect and emit intensity^4,5 or extract intensity and spectral information^6-8. However, no pixel exists that both senses and generates optical wavefronts with full control over amplitude, phase and polarization, limiting bidirectional control and feedback of sophisticated light fields. Here we present a route to such pixels by demonstrating a versatile platform of miniaturized diffractive elements based on Fourier optics⁹. We use plasmonic surface waves¹⁰, which propagate coherently¹¹ and efficiently^12-15 across metallic surfaces. When these plasmons are launched towards wavy microstructures¹⁶ designed with simple Fourier analysis, arbitrary and background-free optical wavefronts are generated. Conversely, incoming light can be sensed, and its amplitude, phase and polarization can be fully characterized. By combining or superposing several such components, we create multifunctional 'Fourier pixels' that provide compact and accurate control over the optical field. Our approach, which we extend to photonic waveguide modes, establishes a scalable, universal architecture for vectorially programmable pixels with applications in adaptive optics^17,18, holographic displays^19-21, optical communication^22,23 and quantum information processing²⁴.