JP2015180939A - 完全なフォトニック、電子又はフォノニックバンドギャップを有する非結晶材料 - Google Patents
完全なフォトニック、電子又はフォノニックバンドギャップを有する非結晶材料 Download PDFInfo
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Abstract
Description
本願で説明した研究は、全米科学財団から助成金番号0606415によって助成されている。アメリカ合衆国政府は、本発明について一定の権利を有する。
I)前記へテロ構造について構造因子を選択するステップと、
II)点の第1点パターンを有する、大きさLのボックスを作図するステップであって、前記複数の点は、並進的に不規則に間隔を空けられており、前記間隔を空けられている複数の点は、平均間隔を有し、前記平均間隔≪Lであるステップと、
III)前記第1点パターンからドロネー三価タイルを作図し、各前記タイルについて重心をプロットして重心点パターンを作成するステップと、
IV)前記重心点パターン内の各重心について、前記タイルの最近接部を特定するステップと、
V)複数の線を作図して、
(i)前記複数の線が、頂点を有する複数のエッジ又は面を規定し、
(ii)前記複数のエッジ又は面の内部には、内部にセル空間を有する超セルを規定し、
(iii)各前記超セルは、前記第1点パターンで特異点を包囲する
ように各前記近接部内の前記重心を接続するステップと、
VI)前記エッジ又は面及び頂点上に第1材料エレメントを配列し、第2材料エレメントを用いて前記セル空間を充填するステップである。
本発明の種々の実施形態の理解を容易にするために、いくつかの用語(この定義セクションでは引用符で強調する場合もある)を以下で定義する。本明細書で定義する用語は(特に指定しない限り)、本発明に関連する分野の当業者に一般に理解される意味を有する。本明細書及び添付する請求項で使用する限り、「一つの」(a, an)及び「その」(the)は、単数形を指すわけではなく、文脈上そうでないことが示されない限り、説明に使用できる具体例の一般的な集合を含む。本明細書の専門用語は、本発明の特定の実施形態を説明するのに使用するが、特定の用語は、請求項で要点を述べたものを除いて、いずれも本発明を限定するものでない。
一態様において、本発明の実施形態は、エネルギー又はエネルギー量を放出、伝送、増幅、検出及び調節する際に使用する構造を設計する方法を提供する。この方法は、光(即ちフォトン)の量、又はそれに相当する電磁波を放出、伝送、増幅、検出又は調節する構造を設計することに特に適合する。この方法は、フォトン、本願でより適切に言うと電磁波に影響を与える周期性依存構造(例えば結晶)が必要とする精度を有しない組立可能な構造に適用可能である。
フォトニックバンドギャップ構造(非結晶構造を含むが、非結晶構造に限定されるわけではない)は、次のように「ステルス」構造について計算してもよい。所望の回転対称性及び並進規則を有する点パターンを選択及びプロットした後、次のステップでは、最大の完全バンドギャップを作成することになる、選択した点パターン周囲の誘電体材料の配置を決定する。出願人は、本明細書で、選択した点パターン(結晶、準結晶、又は不規則超均一であっても)を変形して、並進及び回転対称性を有するが最適に近いフォトニックバンドギャップ構造(絶対最適(absolute optimal)バンドギャップの1%以内)を有しないセルの充填形にするための新規な方法を提供する。この手順は、自由度2に対してのみ変化することを要求するので、プロトコルは、他の方法よりも充分少ない計算資源を使用する。一実施形態において、本発明に係る方法は、以下で説明するように、図2に示す白丸の不規則超均一点パターンから始まる。
Claims (23)
- 凝縮状態又は固体状態で超均一に配列した複数の材料エレメントを含むヘテロ構造を有する製品。
- 前記へテロ構造は、電子、フォトン、フォノン及びスピン波から成る群から選択される励起子と相互作用する請求項1記載の製品。
- 前記へテロ構造は、完全バンドギャップを有する請求項2記載の製品。
- 前記バンドギャップは、TE偏光に最適化し、またTM偏光に最適化している請求項3記載の製品。
- 前記へテロ構造は、平面内の超均一点パターンで、互いに間隔を空けて配列した複数の点から得られる請求項3記載の製品。
- 前記へテロ構造は、アジマス対称性を有する請求項5記載の製品。
- 前記点パターンは、空間内に配列している請求項5記載の製品。
- 前記へテロ構造は、多面体を有する請求項7記載の製品。
- 前記へテロ構造は、準結晶対称性を示す請求項1記載の製品。
- 前記へテロ構造は、並進等方的である請求項1記載の製品。
- 前記へテロ構造の前記材料エレメントは格子を有し、
前記格子は、複数の交差線によって規定される複数のセルを有し、
前記線は、セルエッジを規定し、
前記交点は頂点を規定し、
各前記セルにおいて多角形セル空間が規定される請求項1記載の製品。 - 前記格子は、複数の多面体セルを有し、
各前記セルは、多面体セル空間をそこで規定する複数の多角形セル面を有する請求項11記載の製品。 - 前記エッジ、頂点及び面の上には第1材料エレメントが
配列され、
前記多面体セル空間は、第2材料エレメントで充填されている請求項12記載の製品。 - 前記第1材料エレメントは、前記第2材料エレメントよりも大きい誘電率を有する請求項13記載の製品。
- 前記第1材料エレメントはシリコンを含み、前記第2材料エレメントは空気を含む請求項14記載の製品。
- 前記第1材料エレメントは、前記エッジ又は前記面の上に有限の厚さで配列し、各前記頂点は、有限の厚さ及び有限の半径を有する円柱の重心と一致する請求項15記載の製品。
- 完全バンドギャップを有する超均一へテロ構造の作成方法であって、
I)前記へテロ構造について構造因子を選択するステップと、
II)大きさLのボックスを作図するステップであって、前記ボックスは複数の点からなる第1点パターンを有し、前記複数の点は、並進的に不規則に間隔を空けられており、前記間隔を空けられている複数の点は、平均間隔を有し、平均間隔≪Lの関係があるステップと、
III)前記第1点パターンからドロネー三価タイルを作図し、各前記タイルについて重心をプロットして重心点パターンを作成するステップと、
IV)前記重心点パターン内の各重心について、前記タイルの最近接部を特定するステップと、
V)複数の線を描いて、
a)前記複数の線が、頂点を有する複数のエッジ又は面を規定し、
b)前記複数のエッジ又は面の内部には、セル空間を有する超セルが規定され、
c)各前記超セルは、前記第1点パターン内の特異点を包囲するように各前記近接部内の前記重心を接続するステップと、
VI)前記エッジ又は面及び頂点の上に第1材料エレメントを配列することと、前記セル空間を第2材料エレメントで充填することと、複数の前記超セルから前記へテロ構造を組み立てることとにより、ヘテロ構造を構成するステップとを含む方法。 - 前記第1点パターンは、ペンローズタイルの頂点を有する請求項17記載の方法。
- 前記第1点パターンは、ブリルアンゾーン内で構造因子S(k)が正確にゼロへ向かうような波数kの割合を決定するパラメータχを有し、χが増加するに従って、kcはχが臨界値χcに達するまで増加し、χc未満では、前記不規則パターンは長距離並進秩序を達成する請求項17記載の方法。
- 前記第1材料エレメントは、前記第2材料エレメントより大きい誘電率を有する請求項17記載の方法。
- 前記第1材料エレメントはシリコンを含み、前記第2材料エレメントは空気を含む請求項17記載の方法。
- 前記第1材料エレメントは、前記エッジ又は前記面の上に有限の厚さで配列し、各前記頂点は、有限の厚さ及び有限の半径を有する円柱の重心と一致する請求項21記載の方法。
- 前記重心点パターンは、半径Rの球形サンプリングウインドウ内で、分散<NR 2>−<NR>2∝Rpの関係を示し、p<dである請求項22記載の方法。
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