Optical structures based on the Smith hat produced unusual light patterns that reflected their lack of mirror symmetry and changed with light direction and polarization.
The Smith hat first drew global attention in 2023 because a single tile could cover an entire surface without ever creating a repeating pattern. Now, the same unusual geometry has produced another surprise: when researchers recreated the pattern at the nanoscale and illuminated it with laser light, it generated optical behavior unlike that of conventional quasicrystals.
Researchers from the Institute of Industrial Science, The University of Tokyo, and collaborating institutions built optical structures based on the Smith hat and investigated how they diffract light. Their findings, published in Nature Communications, reveal that the pattern can produce chiral optical responses, meaning the resulting light patterns have a handedness linked to the structure’s lack of mirror symmetry.
The mathematical foundation comes from the long-standing Einstein problem, which asks whether a single tile shape, or “monotile,” can cover a surface in a non-repeating arrangement. Familiar periodic patterns such as honeycombs and checkerboards repeat regularly. An aperiodic monotile, by contrast, can tile all of space without settling into a repeating pattern.
The Smith hat provided the first solution to that problem in 2023. But solving the mathematical puzzle left another question open: What physical properties might emerge from such an unusual arrangement?
“What is especially fascinating about the hat tile is that, although the resulting pattern appears irregular at first glance, it is actually constructed from the honeycomb lattice,” says lead author Yuto Moritake. “We wanted to see whether this unique shape could also produce any unexpected physical phenomena.”
The Smith hat created chiral light patterns
To test that possibility, the researchers used electron-beam lithography to fabricate nanoscale Smith hat patterns on silicon nitride films. They then illuminated the structures with laser light and examined the resulting diffraction, the patterns produced as light interacts with the material.
Instead of the behavior typically associated with conventional quasicrystals, the structures produced distinctive pinwheel-like diffraction patterns. Those patterns directly reflected the chiral character of the aperiodic arrangement.
“We found that the diffraction patterns themselves become chiral because the structure lacks mirror symmetry,” explains senior author Masaya Notomi. “This kind of optical response is fundamentally different from that observed in conventional quasicrystalline materials.”
Light response depended on symmetry
The optical effect was not fixed. Changing the direction or polarization of the incoming light also changed the diffraction pattern.
The researchers found an additional connection between the geometry of the structure and its optical response. When they created real space mirror images of the structures, the resulting optical behavior reversed accordingly, revealing a new form of symmetry-controlled response.
“These results open a new direction of research on the fusion of quasiperiodic order and chirality,” remarks Moritake. “Monotile patterns provide a platform for exploring optical phenomena that emerge from the interplay of symmetry, chirality, and aperiodicity.”
Abstract geometry could shape optical devices
The researchers hope that structures inspired by monotiles could eventually contribute to technologies for manipulating light, controlling polarization, and developing advanced optical devices.
More broadly, the findings show how a mathematical shape originally celebrated for solving an abstract tiling problem can also produce physical behavior that had not been observed in conventional quasicrystalline materials.
Reference: “Chiral diffraction from aperiodic monotile structure” by Yuto Moritake, Masato Takiguchi, Takuma Aihara and Masaya Notomi, 29 July 2026, Nature Communications.
DOI: 10.1038/s41467-026-75023-7
This work was supported by the Japan Society for the Promotion of Science (JSPS) KAKENHI (No. JP20H05641, JP21K14551, JP24K01377, JP24H02232, and JP24H00400).
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2 Comments
Light response depended on symmetry. The optical effect was not fixed. Changing the direction or polarization of the incoming light also changed the diffraction pattern.
VERY GOOD.
The Topological Vortex Theory (TVT) points out that the topological stability of topological spin vortices is the physical root of observer effects: the observation locking of two-dimensional spin vortices can only exhibit left or right rotation, and this “observation selection exclusivity” is an inevitable result of topological charge conservation, rather than a limitation of measurement techniques. The same applies to internationes.
The same applies to interactiones.