Researchers at the Institute of Industrial Science, The University of Tokyo, have experimentally demonstrated unique chiral optical behavior from the Smith hat monotile, a long-sought aperiodic pattern discovered in 2023. According to lead author Yuto Moritake and senior author Masaya Notomi, the aperiodic structure produces distinctive pinwheel-like diffraction patterns when illuminated by laser light, revealing an optical response fundamentally different from conventional quasicrystalline materials.
Solving the Einstein Problem With Aperiodic Monotiles
The discovery stems from the long-standing Einstein problem, which asks if a single tile shape can cover an entire surface in a nonrepeating pattern. While periodic tilings like checkerboards repeat regularly, an aperiodic monotile covers space without ever producing a repeating arrangement. In 2023, researchers identified the Smith hat as the first such monotile, capturing worldwide attention across the scientific community.
“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,” according to lead author Yuto Moritake. “We wanted to see whether this unique shape could also produce any unexpected physical phenomena.”
Light Reveals Hidden Handedness in Nanoscale Patterns
To test these physical properties experimentally, the team fabricated nanoscale patterns on silicon nitride films using electron-beam lithography. When laser light illuminated the structures, the researchers observed striking pinwheel-like patterns that directly revealed the chiral nature of the aperiodic structure.
“We found that the diffraction patterns themselves become chiral because the structure lacks mirror symmetry,” according to senior author Masaya Notomi. “This kind of optical response is fundamentally different from that observed in conventional quasicrystalline materials.”
Did you know? Unlike periodic structures that repeat regularly, aperiodic monotiles like the Smith hat can tile an infinite plane without ever forming a repeating grid, yet they originate from underlying honeycomb lattices.
Symmetry-Controlled Optical Responses
Further experiments revealed that the diffraction pattern shifts depending on the direction and polarization of the incoming light. Structures mirrored in real space produced corresponding reversals in optical behavior, demonstrating a new form of symmetry-controlled optical 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.”
The research team hopes that these monotile-inspired structures will contribute to technologies involving light manipulation, polarization control, and advanced optical devices. The findings were published in the journal Nature Communications in 2026 under the title “Chiral Diffraction from Aperiodic Monotile Structure” (DOI: 10.1038/s41467-026-75023-7).
Frequently Asked Questions
What is an aperiodic monotile?
An aperiodic monotile is a single tile shape that can cover an infinite surface without ever creating a repeating arrangement, as seen with the Smith hat discovered in 2023.
How did researchers test the Smith hat’s optical properties?
Researchers at The University of Tokyo fabricated nanoscale patterns on silicon nitride films using electron-beam lithography and illuminated them with laser light.
What makes the optical response of the Smith hat unique?
According to senior author Masaya Notomi, the diffraction patterns become chiral because the structure lacks mirror symmetry, creating an optical response fundamentally different from conventional quasicrystalline materials.
What are the potential practical applications of this research?
The findings may help scientists twist light into striking chiral patterns and contribute to technologies involving light manipulation, polarization control, and advanced optical devices.
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