Far-field superresolution imaging via k-space superoscillation

In 1873, Ernst Abbe proposed the famous diffraction limit theory, stating that the resolution of an optical system is limited by the light wavelength and numerical aperture. For a long time, the resolution of imaging systems has been constrained by the Abbe-Rayleigh diffraction limit. This means that to obtain higher spatial resolution, optical systems often have to rely on huge physical apertures, just as astronomical telescopes must possess huge mirrors to “see clearly.” Although superresolution fluorescence microscopy, awarded the 2014 Nobel Prize in Chemistry, successfully broke this limit, existing methods still struggle to achieve single-shot deterministic superresolution imaging under far-field, label-free conditions independent of sample characteristics.

In a new paper published in eLight, a team of scientists, led by Associate Professor Yuanmu Yang from the Department of Precision Instrument, Tsinghua University, China, proposed a new far-field label-free superresolution imaging method termed k-space (momentum space) superoscillation. By designing a metalens with topology-optimized responses in both real- and k-space, they disrupt the spatially shift-invariance assumption in classical imaging systems, thereby breaking the diffraction limit. Preliminary microwave experiments verified that this method achieved an imaging resolution more than twice the diffraction limit without post-processing.

These scientists summarize the operational principle of their method: “To surpass the diffraction limit, a potential approach is to design a lens that can focus a plane wave with an incident angle θ to a spot located at 2ftanθ from the optical axis in the focal plane while maintaining the focal spot size.” However, they note that “such a condition cannot be achieved with a conventional local lens with spatially shift-invariant properties.”

“The physics of nonlocal metalens-based superresolution imaging hinges on k-space superoscillation,” they explain. “When the rate of change of the transmitted field within a certain angular range exceeds the theoretical limit determined by the physical aperture, ‘k-space superoscillation’ occurs.” Unlike traditional real-space superoscillation, they emphasize that “this mechanism breaks the diffraction limit without generating image-plane sidebands and demonstrates advantages in field of view, energy efficiency, and robustness against disturbances.”

“Without any post-processing, the local lens resolves two points at a separation distance of 2.90λ,” whereas “the nonlocal metalens resolves two points at a separation distance of 1.38λ,” the scientists noted regarding their experimental results. “This indicates that the resolution of the nonlocal metalens is 2.10 times higher than that of the local lens.” Additionally, the team highlighted that “the experimentally measured focusing efficiency was 2.24%,” which is “significantly higher than real-space superoscillatory systems with comparable superresolution ratios and fields of view.”

“The prototype operating in the microwave domain holds potential for applications such as direction-of-arrival estimation, millimeter-wave imaging, and sky surveys,” the scientists forecast. “The physical mechanism of k-space superoscillation is universal and not limited to specific frequencies.” They added that “with the advancement of nanofabrication technology, physical devices based on this new mechanism can be constructed in the optical domain using cascaded diffractive layer structures.”

END