Both versions are aligned block by block, in reading order: title, the essentials, then paragraph by paragraph. Where the translation merged or split a paragraph, the matching cell stays empty — we never pair two passages by guesswork.
スクリーンに浮かんだ点は、整然としているのに同じ模様を繰り返さない。東京大学、東京科学大学、NTTの研究者らは、数学界を揺らした「ハット型タイル」の配置を実際のナノ構造に移し、光を当てたときの特異な回折を観測した。研究論文はNature Communicationsに掲載された。
The spots that appeared on the screen were orderly without repeating the same pattern. Researchers from the University of Tokyo, Institute of Science Tokyo and NTT transferred the arrangement of the “hat tile,” which shook up the mathematical world, into an actual nanostructure and observed its unusual diffraction when illuminated. The research paper was published in Nature Communications.
発端は、1種類の形だけで平面を隙間なく埋められる一方、全体では同じ模様が周期的に繰り返されないという「アインシュタイン問題」だ。2023年に解としてハット型タイルが発見されたが、その数学的な配置が現実の物理で何を起こすかは分かっていなかった。研究チームは各タイルの重心に点を置き、120度回しても同じ形になる一方、左右反転では重ならない準格子を設計した。
The story began with the “Einstein problem”: whether a plane can be tiled without gaps using only one shape while the overall pattern does not repeat periodically. In 2023, the hat tile was discovered as a solution, but it was unknown what its mathematical arrangement would do in a real physical system. The research team placed a point at the center of each tile and designed a quaslattice that retains the same shape after a 120-degree rotation but does not overlap with its mirror image.
その配置を、NTTの微細加工技術で薄膜に刻んだ。厚さ350nmの窒化シリコン膜に、半導体製造でも使われる電子線リソグラフィなどを用い、半径100nmの円孔を大面積に並べた。緑色の単色レーザーを照射すると、繰り返しのない構造にもかかわらず、回折像にはくっきりしたブラッグピークが現れ、照射位置を動かしてもピークの位置はほとんど変わらなかった。全体として長距離の秩序を持つことを示す結果だという。
The team etched that arrangement into a thin film using NTT’s microfabrication technology. Using electron-beam lithography, a technique also employed in semiconductor manufacturing, they arranged circular holes with a radius of 100 nm over a large area in a 350 nm-thick silicon nitride film. When illuminated with a green monochromatic laser, the structure produced sharp Bragg peaks in its diffraction pattern despite having no repetition, and the positions of the peaks barely changed even when the illumination position was moved. The result indicates that the structure has long-range order overall, according to the team.
さらに、白色レーザーでも緑色レーザーでも、回折像は風車のように一方向へ回った。配置を鏡像にすると回転方向も逆になる。右回りと左回りの円偏光、つまり電場の向きがねじれながら進む光を当て分けると、点の明るさにも差が出た。鏡像と重ならない構造が、光の模様と偏光への応答に反映された形だ。
With both a white laser and a green laser, the diffraction pattern also rotated in one direction like a pinwheel. When the arrangement was changed to its mirror image, the direction of rotation was reversed. When the team separately illuminated the structure with right- and left-handed circular polarization—that is, light whose electric-field direction twists as it travels—the brightness of the spots also differed. The fact that the structure does not overlap with its mirror image was reflected in the light pattern and its response to polarization.
では、具体的に何が変わるのか。 今回の成果は、数学上の非周期タイルを、光を操作する実験可能な素材の設計へ変えたことにある。現時点で示されたのは作製したナノ構造での現象確認で、製品や実用装置ではない。研究チームは今後、メタサーフェスやフォトニック結晶に組み込み、新しい光学応答の応用を探るとしている。
So what specifically changes? The achievement lies in transforming mathematical nonperiodic tiles into a design for an experimentally usable material that manipulates light. What has been demonstrated so far is the confirmation of a phenomenon in a fabricated nanostructure, not a product or practical device. The research team says it will explore applications of new optical responses by incorporating the structure into metasurfaces and photonic crystals.