Advanced Multidimensional Sampling Theory for Flat Optics

Reviewed by Lexie Corner   on February 5, 2025

A research team at POSTECH, led by Professor Junsuk Rho, along with MS/Ph.D. students Seokwoo Kim, Joohoon Kim, Kyungtae Kim, and Minsu Jeong, developed a multidimensional sampling theory for solving problems in flat optics. The study   was published  in  Nature Communications  .  

This study identifies limitations in traditional patterning theories for metasurface design and presents a novel smoothing technique that improves optical performance.

Planar optics, which manipulates light at the nanoscale using nanostructures to shape extremely thin surfaces, enables the development of ultra-compact, high-performance optical devices. Unlike conventional optical systems that rely on bulky lenses and mirrors, planar optics are essential for advancing AR/VR technology and shrinking the size of smartphone cameras, minimizing “camera bulge.”

Metasurfaces, a key application of planar optics, rely on nanostructures to precisely control the phase distribution of light. The 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 have limitations.

Aliasing artifacts appear when the sampling rate is insufficient, leading to optical distortion and reduced throughput. A well-known example is the cartwheel effect in movies, where a spinning wheel appears to move backwards or freezes due to an incorrect frame rate. In metasurface design, aliasing degrades optical accuracy and efficiency.

The Nyquist sampling theorem is traditionally used to predict and reduce aliasing. Although effective in digital signal processing, the POSTECH research team found that the Nyquist theorem does not fully explain 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 requires consideration of the wave nature of light and the complex nanostructure of metasurfaces.

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

Their study showed that the optical performance is significantly affected by the geometric relationship between the spectral characteristics and the nanostructured network of the metasurface. By combining diffractive elements and adjusting the rotation of the grating, the team introduced an antialiasing technique to reduce noise and improve light control.

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

This research opens up new opportunities for the next generation of flat optical devices, including high-NA metals and wide-angle meta-holograms. Our newly developed sampling theory is very versatile, covering wavelengths from microwave to extreme ultraviolet. Short-wavelength ultraviolet optics require very precise fabrication, which makes research in this area very challenging. However, our findings significantly reduce these fabrication requirements and open up new possibilities in ultraviolet metasurfaces  .

Junsuk Rho, profesor, 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.