Chiral Diffraction from Aperiodic Monotile Lattice

TL;DR

This paper experimentally investigates a new aperiodic monotile lattice using nanophotonics, revealing unique chiral diffraction patterns and polarization effects, thus broadening the understanding of nonperiodic structures beyond quasicrystals.

Contribution

It provides the first experimental diffraction analysis of aperiodic monotile lattices, demonstrating their long-range order and unique polarization-dependent properties.

Findings

Observation of clear Bragg peaks indicating long-range order

Detection of chiral diffraction patterns

Exotic circular polarization dependence not seen in traditional quasiperiodic structures

Abstract

Aperiodic systems such as quasiperiodic systems exhibit unique properties different from periodic structures. In 2023, Smith et al. discovered a new aperiodic structure: a single-shaped tile that can only tile space aperiodically, known as an aperiodic monotile. Although the aperiodic monotile possesses intriguing mathematical properties, its experimental investigation remains unexplored. In this study, we report an experimental investigation of diffraction patterns from a monotile lattice using a nanophotonic platform. We observed clear Bragg peaks, which is evidence of long-range order and a chiral structure of the diffraction patterns. Furthermore, we found exotic behavior in circular polarization dependence, which cannot be observed in conventional quasiperiodic structures. These findings establish the monotile lattice as a novel class of aperiodic systems, expanding the study of nonperiodic structures beyond conventional quasicrystals.