In the cutting-edge realm of nanophotonics, researchers have unveiled a transformative concept known as “Fourier pixels,” revolutionizing the control of light on a subwavelength scale. At the heart of this innovation is the intricate generation and manipulation of surface plasmon polaritons (SPPs), which are electromagnetic waves confined at metal-dielectric interfaces. Unlike conventional pixels that simply modulate intensity or color, Fourier pixels enable precise wavefront shaping by diffracting guided optical waves, unlocking unprecedented functionalities including bidirectional light control and polarization sensitivity.
Central to the operation of a Fourier pixel is the generation of SPPs via sinusoidal gratings patterned on metallic surfaces. Light incident on these gratings couples efficiently into SPP modes when momentum-matching conditions—dictated by the grating period and diffraction order—are satisfied. This coupling condition ensures the in-plane wavevector of photons complements the grating momentum, enabling concurrent excitation of SPPs at multiple wavelengths under specific incidence angles. The launched SPPs then propagate along the plane of the interface, serving as coherent reference waves of complex amplitude and phase.
The transformative aspect of these pixels lies in an engineered “Fourier element” that interacts with the traveling plasmonic wave, sculpting the optical wavefront into any desired complex-valued function. This is achieved by modulating a structured surface height profile, which imparts controlled phase shifts onto the SPP. Leveraging an inverse design methodology, the researchers derived analytical expressions to relate the desired output wavefront to the required nanoscopic surface modulation of the Fourier element. Crucially, the theoretical framework hinges on a scalar diffraction model wherein the optical transmission function of the Fourier element approximates a phase-only modulation for shallow topographies, simplifying fabrication and enhancing efficiency.
Mathematically, the local phase modulation introduced by the Fourier element is linearly proportional to the nanometric height variations of the surface. By carefully tailoring these nanoscale features, it is possible to achieve arbitrary complex output wavefronts projected at far-field or intermediate planes. For far-field patterns, the Fraunhofer diffraction formalism is applied, enabling computational backpropagation of target intensity distributions to the sample plane. This computational approach facilitates the inverse engineering of Fourier pixel designs, allowing high-fidelity generation of desired optical functionalities from compact, subwavelength-scale devices.
The conceptual design naturally extends into polarized light control by considering vectorial SPPs launched along orthogonal directions. Here, each polarization component is described by an associated complex wavefront, and the Fourier element functions as a transparency matrix operating on these vector fields. By independently modulating the phase profiles for each polarization channel, the pixels realize sophisticated polarization multiplexing capabilities, offering a pathway toward integrable polarization sensors or advanced display technologies that manipulate spatial polarization distributions on demand.
Experimentally, these Fourier pixels were fabricated through state-of-the-art thermally assisted scanning probe lithography (TSPL) using poly(phthalaldehyde) resist as a scaffold. The intricate grayscale height profiles were realized with nanometer precision, then transferred into plasmonic silver films or dielectric films via a careful lift-off and etching process. The resulting structures exhibited highly controlled sinusoidal grating arrays combined with topographic Fourier elements supporting efficient SPP excitation and modulation. Advanced optical characterization confirmed the pixels’ capability to focus light efficiently, with coupling efficiencies exceeding 70% under optimized conditions.
An in-depth efficiency analysis revealed dependencies on wavelength and grating amplitude, highlighting plasmonic loss mechanisms intrinsic to silver at shorter optical wavelengths. The incorporation of apodization via an exponential decay profile in the Fourier element further enhanced performance by suppressing undesired back reflections and outscattering, thereby improving coupling and focusing fidelity. When multiple grating harmonics corresponding to different colors were superimposed to enable multiwavelength operation, modest efficiency trade-offs were observed due to enhanced diffraction and scattering modes.
To rigorously extract the full polarization state of incident light impinging on the pixels, the authors implemented robust Stokes polarimetry schemes utilizing the vectorial nature of SPP excitation. By decomposing incoming light fields into orthogonal components and carefully engineering the phase relationships, the Fourier pixels performed deterministic mapping from complex input polarization states to measurable intensity signals, facilitating on-chip polarization analysis compatible with miniaturized photonic circuits.
Complementing optical phase retrieval algorithms, the research introduced a noise-tolerant phase reconstruction approach for large phase profiles by solving a Poisson equation in the spatial Fourier domain. This method mitigates error accumulation inherent in direct integration of phase gradients, providing stable and accurate recovery of continuous phase maps essential for precise device characterization and feedback in iterative design loops.
Overall, the development of Fourier pixels represents a paradigm shift in light-matter interaction at the nanoscale, merging advanced fabrication, rigorous optical theory, and computational inverse design. These devices open avenues for integrated photonic systems with deterministic bidirectional control of light beams, enabling novel applications in microscopy, communication, sensing, and display technologies. The seamless fusion of guided plasmonic waves with diffractive surface elements demonstrates how Fourier optics principles can be miniaturized and harnessed in compact, multifunctional pixel architectures. This foundational work lays a roadmap for future multifunctional metasurface arrays and reconfigurable photonic networks with enhanced control over amplitude, phase, and polarization of light.
Subject of Research: Nanophotonic Fourier pixels for bidirectional and polarization-sensitive light control
Article Title: Fourier pixels for bidirectional light control
Article References:
Glauser, Y.M., Vonk, S.J.W., Seda, D.B. et al. Fourier pixels for bidirectional light control. Nature (2026). https://doi.org/10.1038/s41586-026-10681-7
Image Credits: AI Generated
