Multidimensional Sampling Theory for Flat Optics

A research team at POSTECH, led by Professor Junsuk Rho, along with M.S./Ph.D. students Seokwoo Kim, Joohoon Kim, Kyungtae Kim, and Minsu Jeong, has developed a multidimensional sampling theory to address challenges in flat optics. The study was published in Nature Communications.

The study identifies limitations in traditional sampling theories for metasurface design and introduces a novel anti-aliasing technique that enhances optical performance.

Flat optics, which manipulates light at the nanoscale using nanostructures to shape ultra-thin surfaces, enables the development of ultra-compact, high-performance optical devices. Unlike conventional optical systems that rely on bulky lenses and mirrors, flat optics is critical for advancing AR/VR technology and reducing the size of smartphone cameras, minimizing the "camera bump."

Metasurfaces, a key application of flat optics, rely on nanostructures to precisely control the phase distribution of light. This process involves sampling, where analog optical signals are converted into discrete data points, similar to how the human brain rapidly processes visual information to create the perception of continuous motion. However, conventional sampling techniques introduce limitations.

Aliasing artifacts occur when the sampling rate is insufficient, leading to optical distortions and reduced efficiency. A well-known example is the wagon-wheel effect in motion pictures, where a spinning wheel appears to move backward or freeze due to inadequate frame rates. In metasurface design, aliasing compromises optical precision and efficiency.

The Nyquist sampling theorem has traditionally been applied to predict and mitigate aliasing. While effective in digital signal processing, the POSTECH research team found that Nyquist’s theorem does not fully account for the optical complexity of metasurfaces. Standard Nyquist theory defines frequency limits for signal processing but does not predict or prevent optical distortions in metasurfaces, which require consideration of both the wave nature of light and the intricate nanostructure of metasurfaces.

To address this limitation, the researchers developed a multidimensional sampling theory that integrates both the wave characteristics of light and the two-dimensional lattice structure of metasurfaces.

Their study demonstrated that optical performance is significantly influenced by the geometric relationship between the spectral profile and the nanostructured lattice of a metasurface. By incorporating diffraction elements and adjusting lattice rotation, the team implemented an anti-aliasing technique to reduce noise and improve light control.

This approach effectively minimized optical noise across a broad wavelength range, from visible light to ultraviolet. It also enabled the development of wide-angle meta-holograms and high-numerical-aperture (NA) metalenses operating in the UV spectrum. The study expands the feasibility of high-resolution ultraviolet and high-NA metasurfaces by redefining the theoretical framework for optical metasurfaces and relaxing fabrication constraints.

This research opens new possibilities for next-generation flat optical devices, including high-NA metalenses and wide-angle meta-holograms. Our newly developed sampling theory is highly versatile, spanning wavelengths from microwaves to extreme ultraviolet. Short-wavelength ultraviolet optics require extremely precise fabrication, making research in this area highly challenging. However, our findings significantly ease these fabrication demands, unlocking new opportunities in ultraviolet metasurfaces.

Junsuk Rho, Professor, Pohang University of Science and Technology

This study was funded by POSCO, Samsung Electronics, the Ministry of Science and ICT, and the National Research Foundation of Korea.

Journal Reference:

Kim, S., et. al. (2025) Anti-aliased metasurfaces beyond the Nyquist limit. Nature Communications. doi.org/10.1038/s41467-024-55095-z