Optical Fourier Surfaces for Free-Space Computer-Generated Holography

Computer-generated holography can shape electromagnetic fields by encoding wavefront information in nanostructured surfaces. However, despite significant progress, hologram designs for visible and near-infrared wavelengths remain largely limited by fabrication constraints. Most implementations rely on lithographic methods that produce discretized surfaces that do not match the wave nature of light. Further advances would benefit from accurate, continuous (grayscale) control of interfacial profiles, which would allow straightforward design principles from Fourier optics to be applied. In this work, we introduce optical Fourier surfaces as a versatile, intuitive platform for free-space computer-generated holograms. Exploiting these arbitrarily wavy surfaces, we demonstrate three different design strategies for computer-generated holography. First, we use an analytical linear design approach based on sinusoidal lenses and gratings as fundamental holographic building blocks. Second, we enhance diffraction efficiencies through an iterative Fourier-transform algorithm. Finally, we extend our framework with differentiable inverse design, creating wavelength-multiplexed holograms that reconstruct distinct diffraction responses in a predefined image plane. Our results combine advanced thermal scanning-probe lithography with flexible design strategies to create useful structures for photonic applications, particularly in settings where rapid prototyping is crucial.