From tiling to device
The hat tile was found in 2022 by the amateur mathematician David Smith. A single stone covers an infinite surface without repeating any pattern, and its name does not come from Albert Einstein but from the German "ein Stein", that is, one stone. A question left open for more than half a century closed, and what remained in hand was a shape: a tiling rule that never repeats itself.[1]
The team at the University of Tokyo's Institute of Industrial Science turned that rule into a device. They etched a pattern based on the hat's shape into a silicon nitride thin film, shone a laser onto it and read the light coming out of Bragg diffraction. The light arrived mirror-asymmetric, that is, carrying a handedness. Lead author Yuto Moritake states the starting point plainly: "We wanted to see whether this unique shape could also produce any unexpected physical phenomena."[1]
Why that was not expected
Diffraction is normally the business of a regular lattice: repeating spacings steer light into particular angles. In the hat tiling there is no repetition, yet the emerging light shows a directional preference, and the source of that preference appears to be the tile's own asymmetry rather than a regular lattice. The same handedness could also arise from how the pattern was cut at the film's edges; the choice of boundary in a finite patch also breaks symmetry, and separating the two requires repeating the measurement with different cuts.[1]
On the application side the team lists control of laser light polarisation, telecommunications and quantum cryptography. What is actually on the table is a phenomenon rather than a device: a pattern etched into a thin film was shown to give diffracted light a hand. How strong that hand is, how stable, and at which wavelengths it can be selected are the first things anyone building a polarisation controller would measure, and the paper does not supply those three numbers.[1]