JP2008244683A - 3-dimensional left-handed metamaterial - Google Patents

3-dimensional left-handed metamaterial Download PDF

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JP2008244683A
JP2008244683A JP2007080445A JP2007080445A JP2008244683A JP 2008244683 A JP2008244683 A JP 2008244683A JP 2007080445 A JP2007080445 A JP 2007080445A JP 2007080445 A JP2007080445 A JP 2007080445A JP 2008244683 A JP2008244683 A JP 2008244683A
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JP4644824B2 (en
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Atsushi Sanada
篤志 真田
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Yamaguchi University NUC
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Abstract

<P>PROBLEM TO BE SOLVED: To provide a resonant 3-dimensional left-handed metamaterial which functions as a 3-dimensional electromagnetic wave propagation medium and has negative equivalent-permittivity and permeability of the medium. <P>SOLUTION: The 3-dimensional left-handed metamaterial comprises a structure where a cubical unit lattice is repeatedly arranged in three directions perpendicular to each other in a 3-dimensional space. The structure comprises a first lattice composed of aggregation of a first arm part 1 connecting each vertex of the unit lattice to three directions and a second lattice composed of aggregation of a second arm part 2 connecting each central point of the unit lattice to three directions. The first lattice and the second lattice comprise conductor, respectively, and are arranged with a gap so that they do not contact each other. <P>COPYRIGHT: (C)2009,JPO&INPIT

Description

本発明は電磁波を伝播させるための人工的な媒質(メタマテリアル)に関し、詳しくは、3次元の電磁波伝播媒質として機能し、媒質の等価的な誘電率と透磁率の両者が負となる3次元左手系メタマテリアルに関するものである。   The present invention relates to an artificial medium (metamaterial) for propagating electromagnetic waves, and in particular, functions as a three-dimensional electromagnetic wave propagation medium, and is a three-dimensional medium in which both the equivalent permittivity and permeability of the medium are negative. It relates to left-handed metamaterials.

金属、誘電体、磁性体、超伝導体などの小片(単位構造体)を、波長に対して十分短い間隔(波長の10分の1程度以下)で並べることで自然にはない性質を持った媒質を人工的に構成することができる。この媒質を自然にある媒質のカテゴリに比べてより大きいカテゴリに属する媒質と言う意味でメタマテリアル(metamaterials)と呼んでいる。メタマテリアルの性質は、単位構造体の形状、材質およびそれらの配置により様々に変化する。   By arranging small pieces (unit structure) such as metal, dielectric, magnetic material, superconductor, etc. at sufficiently short intervals (less than 1/10 of the wavelength), it has a property that is not natural. The medium can be artificially constructed. This medium is called metamaterials in the sense that it belongs to a category that is larger than the category of natural media. The properties of the metamaterial vary depending on the shape and material of the unit structure and their arrangement.

中でも、等価的な誘電率εと透磁率μとが同時に負となるメタマテリアルは、その電界と磁界と波数ベクトルが左手系をなすことから「左手系媒質(LHM:Left-Handed Materials)」と名付けられた。この左手系媒質を本明細書においては左手系メタマテリアルと呼ぶ。これに対して、等価的な誘電率εと透磁率μとが同時に正となる通常の媒質は「右手系媒質(RHM:Right-Handed Materials)」と呼ばれる。これら誘電率ε、透磁率μと媒質との関係領域は、図1に示すように、誘電率εの正負および透磁率μの正負に応じた第1象限〜第4象限の媒質に分類できる。右手系媒質は第1象限の媒質であり、左手系媒質は第3象限の媒質である。   Among them, metamaterials whose equivalent permittivity ε and permeability μ are negative simultaneously are “left-handed materials (LHM)” because their electric field, magnetic field, and wave vector form a left-handed system. Named. This left-handed medium is referred to as a left-handed metamaterial in this specification. On the other hand, a normal medium in which the equivalent dielectric constant ε and permeability μ are simultaneously positive is called a “right-handed medium (RHM)”. As shown in FIG. 1, the regions related to the dielectric constant ε, the magnetic permeability μ, and the medium can be classified into mediums in the first quadrant to the fourth quadrant corresponding to the positive / negative of the dielectric constant ε and the positive / negative of the magnetic permeability μ. The right-handed medium is a medium in the first quadrant, and the left-handed medium is a medium in the third quadrant.

特に、左手系メタマテリアルは、波の群速度(エネルギーの伝播する速度)と位相速度(位相の進む速度)の符号が逆転している波(バックワード波と呼ばれる)の存在や、また、非伝播領域で指数関数的に減衰する波であるエバネセント波の増幅、等の特異な性質を持つものである。そして、左手系メタマテリアルによるバックワード波を伝送する線路を人工的に構成することができる。このことは、下記の非特許文献1、非特許文献2にも記載されているように公知である。   In particular, left-handed metamaterials have the presence of waves (called backward waves) in which the signs of the wave group velocity (velocity of energy propagation) and phase velocity (velocity of phase advance) are reversed. It has unique properties such as amplification of evanescent waves that are exponentially attenuated waves in the propagation region. And the track | line which transmits the backward wave by a left-handed-type metamaterial can be artificially comprised. This is known as described in Non-Patent Document 1 and Non-Patent Document 2 below.

この左手系媒質構成の概念に基づき、金属パターンからなる単位セルを周期的に並べてバックワード波を伝播させる線路が提案されている。これまで、その伝送特性が理論的に取り扱われ、この線路が左手系伝送帯域を持つこと、左手系伝送帯域と右手系伝送帯域との間にバンドギャップが生じること、そのバンドギャップ幅は単位セル中のリアクタンスによりコントロールすることができること等が理論的に明らかになっている。これらに関しては、下記の非特許文献3に記載されている。
D. R. Smith, W. J. Padilla, D. C.Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite medium with simultaneouslynegative permeability and permittivity,” Phys. Rev. Lett., vol. 84, no. 18,pp.4184-4187, May 2000 C. Caloz, and T. Itoh,“Application of the transmission line theory of left-handed (LH) materials tothe realization of a microstrip LH line”, IEEE-APS Int'l Symp. Digest, vol. 2,pp. 412-415, June 2002 Atsushi Sanada, Chritophe Calozand Tatsuo Itoh,“Characteristics of the Composite Right/Left-HandedTransmission Lines,” IEEE Microwave and Wireless Component Letters, Vol.14,No.2, pp. 68-70, February 2004
Based on the concept of this left-handed medium configuration, a line for propagating backward waves by periodically arranging unit cells made of metal patterns has been proposed. Up to now, the transmission characteristics have been treated theoretically, this line has a left-handed transmission band, a band gap occurs between the left-handed transmission band and the right-handed transmission band, and the band gap width is unit cell. It has become theoretically clear that it can be controlled by reactance inside. These are described in Non-Patent Document 3 below.
DR Smith, WJ Padilla, DCVier, SC Nemat-Nasser, and S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett., Vol. 84, no. 18, pp.4184-4187, May 2000 C. Caloz, and T. Itoh, “Application of the transmission line theory of left-handed (LH) materials to the realization of a microstrip LH line”, IEEE-APS Int'l Symp. Digest, vol. 2, pp. 412 -415, June 2002 Atsushi Sanada, Chritophe Calozand Tatsuo Itoh, “Characteristics of the Composite Right / Left-HandedTransmission Lines,” IEEE Microwave and Wireless Component Letters, Vol. 14, No. 2, pp. 68-70, February 2004

左手系メタマテリアルは、その構成上から共振型と非共振型に大別できる。最初に作成された左手系メタマテリアルは共振型である。共振型の左手系メタマテリアルは、人工誘電体の誘電率および人工磁性体の透磁率が、共振周波数の近傍でともに負になる領域を使用するものである。このため、左手系媒質として機能する周波数帯域幅が狭いという欠点がある。さらに、共振周波数の近傍周波数を使用するため損失が大きくなるという欠点がある。   Left-handed metamaterials can be broadly classified into resonant and non-resonant types in terms of their configuration. The first left-handed metamaterial created is resonant. The resonance type left-handed metamaterial uses a region where the dielectric constant of the artificial dielectric and the permeability of the artificial magnetic body are both negative in the vicinity of the resonance frequency. For this reason, there exists a fault that the frequency bandwidth which functions as a left-handed-type medium is narrow. Further, since a frequency near the resonance frequency is used, there is a disadvantage that loss is increased.

これに対して、非共振型の左手系メタマテリアルは、通常の媒質における伝送線路の分布定数インダクタンス(L)、分布定数キャパシタンス(C)を逆に配置した伝送線路の特性に基づいている。このような分布定数LCを逆転させた伝送線路においては、前述のバックワード波が伝送され、左手系メタマテリアルとしての性質を持つのである。非共振型の左手系メタマテリアルは、共振型と比較すると、左手系媒質として機能する周波数帯域幅が広く、損失が小さくなるという特徴がある。   In contrast, a non-resonant left-handed metamaterial is based on the characteristics of a transmission line in which the distributed constant inductance (L) and distributed constant capacitance (C) of the transmission line in a normal medium are reversed. In the transmission line in which the distributed constant LC is reversed, the backward wave described above is transmitted and has a property as a left-handed metamaterial. The non-resonant type left-handed metamaterial is characterized in that it has a wide frequency bandwidth functioning as a left-handed medium and a loss as compared with the resonant type.

非共振型の左手系メタマテリアルとしては、集中定数LC素子(チップインダクタ、チップコンデンサ等)を使用した伝送回路や、伝送路に周期的な構造を配置した分布定数型の媒質があった。しかし、集中定数LC素子を使用したものは動作周波数に上限(素子の自己共振周波数以下でのみ動作可能)があるという問題点があり、数GHz以上で動作する左手系メタマテリアルは実現困難であった。また、集中定数LC素子を多数使用するため製作が困難であり、製造コストも高くなる。   Non-resonant left-handed metamaterials include transmission circuits using lumped constant LC elements (chip inductors, chip capacitors, etc.) and distributed constant type media in which a periodic structure is arranged in the transmission line. However, those using lumped-constant LC elements have a problem that the operating frequency has an upper limit (can only operate below the self-resonant frequency of the element), and it is difficult to realize a left-handed metamaterial that operates at several GHz or higher. It was. In addition, since a large number of lumped constant LC elements are used, it is difficult to manufacture and the manufacturing cost increases.

いずれにしても、非共振型の左手系メタマテリアルは、1次元または2次元の電磁波伝播媒質として機能するものに限られていた。3次元の電磁波伝播媒質として機能する非共振型の左手系メタマテリアルはこれまで実現されていない。   In any case, non-resonant left-handed metamaterials are limited to those functioning as a one-dimensional or two-dimensional electromagnetic wave propagation medium. A non-resonant left-handed metamaterial that functions as a three-dimensional electromagnetic wave propagation medium has not been realized so far.

そこで、本発明は、3次元の電磁波伝播媒質として機能し、媒質の等価的な誘電率と透磁率の両者が同時に負の値となる非共振型の3次元左手系メタマテリアルを提供することを目的とする。   Therefore, the present invention provides a non-resonant type three-dimensional left-handed metamaterial that functions as a three-dimensional electromagnetic wave propagation medium, and that both the equivalent permittivity and permeability of the medium have negative values at the same time. Objective.

上記目的を達成するために、本発明の3次元左手系メタマテリアルは、立方体の単位格子を3次元空間の互いに直交する3方向に繰り返し配置した構造の3次元左手系メタマテリアルであって、前記単位格子の各頂点を前記3方向に連結する第1腕部の集合からなる第1格子体と、前記単位格子の各中心点を前記3方向に連結する第2腕部の集合からなる第2格子体とを有する。そして、前記第1格子体および前記第2格子体は、それぞれ導体からなるものであり、かつ、互いに他と接触しないように間隙を持って配置されているものである。   To achieve the above object, the three-dimensional left-handed metamaterial of the present invention is a three-dimensional left-handed metamaterial having a structure in which cubic unit cells are repeatedly arranged in three directions orthogonal to each other in a three-dimensional space, A first lattice body composed of a set of first arms connecting each vertex of the unit lattice in the three directions, and a second lattice composed of a second arm connecting each center point of the unit lattice in the three directions. And a lattice body. The first lattice body and the second lattice body are each made of a conductor, and are arranged with a gap so as not to contact each other.

また、上記の3次元左手系メタマテリアルにおいて、前記第1腕部および前記第2腕部は、両端部の近傍が細く形成され、中央部が太く形成されたものであることが好ましい。   In the three-dimensional left-handed metamaterial, the first arm and the second arm are preferably formed so that the vicinity of both ends is thin and the center is thick.

また、上記の3次元左手系メタマテリアルにおいて、前記第1腕部の中央部の太い部分の断面形状は正方形であり、その1辺の寸法が前記単位格子の1辺の寸法の0.30〜0.49倍であることが好ましい。   In the above three-dimensional left-handed metamaterial, the cross-sectional shape of the thick portion at the center of the first arm is a square, and the dimension of one side is 0.30 to the dimension of one side of the unit cell. It is preferably 0.49 times.

また、上記の3次元左手系メタマテリアルにおいて、前記第1腕部および前記第2腕部は、中央部の太い部分の太さが両端部の細い部分の太さの3倍以上のものであることが好ましい。   Further, in the above three-dimensional left-handed metamaterial, the first arm portion and the second arm portion are such that the thickness of the thick portion at the center is three times or more the thickness of the narrow portions at both ends. It is preferable.

本発明は、以上のように構成されているので、以下のような効果を奏する。   Since this invention is comprised as mentioned above, there exist the following effects.

本発明によれば、3次元の電磁波伝播媒質として機能し、媒質の等価的な誘電率と透磁率の両者が同時に負の値となる非共振型の3次元左手系メタマテリアルを実現することができる。非共振型であるため、左手系媒質として機能する周波数帯域幅が広く低損失である。また、その3次元左手系メタマテリアルを利用してスーパーレンズやスーパーレンズを使用したレンズアンテナや、分散特性を利用したカプラや共振器などの種々の応用機器を実現することができる。   According to the present invention, it is possible to realize a non-resonant type three-dimensional left-handed metamaterial that functions as a three-dimensional electromagnetic wave propagation medium and in which both the equivalent dielectric constant and the magnetic permeability of the medium have negative values at the same time. it can. Since it is non-resonant, it has a wide frequency bandwidth that functions as a left-handed medium and low loss. In addition, using the three-dimensional left-handed metamaterial, various application devices such as a super lens, a lens antenna using a super lens, a coupler and a resonator using dispersion characteristics can be realized.

第1腕部および第2腕部の中央部の太い部分の太さ寸法を単位格子の1辺の寸法の0.30〜0.49倍とすることにより、動作周波数を低下させることができる。換言すれば、電磁波の波長と比較した単位構造体の寸法を小さくでき、左手系メタマテリアルをより均一媒質に近付けることができる。   The operating frequency can be lowered by setting the thickness dimension of the thick part of the central part of the first arm part and the second arm part to 0.30 to 0.49 times the dimension of one side of the unit cell. In other words, the size of the unit structure compared to the wavelength of the electromagnetic wave can be reduced, and the left-handed metamaterial can be brought closer to a uniform medium.

第1腕部および第2腕部の中央部の太い部分の太さを両端部の細い部分の太さの3倍以上とすることにより、動作周波数を低下させることができる。換言すれば、電磁波の波長と比較した単位構造体の寸法を小さくでき、左手系メタマテリアルをより均一媒質に近付けることができる。   The operating frequency can be lowered by setting the thickness of the thick part of the central part of the first arm part and the second arm part to three times or more the thickness of the narrow part of both end parts. In other words, the size of the unit structure compared to the wavelength of the electromagnetic wave can be reduced, and the left-handed metamaterial can be brought closer to a uniform medium.

本発明の実施の形態について図面を参照して説明する。図2は、本発明のメタマテリアル3の構成を示す斜視図である。図2では、メタマテリアル3の全体構成を示すために、細部の形状は正確に表示されていない。メタマテリアル3は、立方体の単位格子4(図3、図4参照)を3次元空間の互いに直交する3方向(xyz軸方向)に繰り返し配置した構造となっている。なお、図2は、メタマテリアル3を単位格子4の境界面で切断した状態を表している。図2では、3×3×3=27個の単位格子4のみが表示されているが、実際のメタマテリアルではさらに多数の単位格子4が配列される。   Embodiments of the present invention will be described with reference to the drawings. FIG. 2 is a perspective view showing the configuration of the metamaterial 3 of the present invention. In FIG. 2, in order to show the whole structure of the metamaterial 3, the detailed shape is not displayed correctly. The metamaterial 3 has a structure in which cubic unit cells 4 (see FIGS. 3 and 4) are repeatedly arranged in three directions (xyz axis directions) orthogonal to each other in a three-dimensional space. FIG. 2 shows a state in which the metamaterial 3 is cut at the boundary surface of the unit cell 4. In FIG. 2, only 3 × 3 × 3 = 27 unit cells 4 are displayed, but in an actual metamaterial, a larger number of unit cells 4 are arranged.

図3は、メタマテリアル3を上方(z軸+側)から見た平面図である。単位格子4を二点鎖線で表示しており、単位格子4の頂点41と中心点40も表示している。単位格子4は立方体であり、その各頂点41をxyz軸それぞれの方向に連結する第1腕部1によって第1格子体10(図5参照)が形成されている。すなわち、第1格子体10は、メタマテリアル3内部の各頂点41において6本の第1腕部1が連結されたものである。第1腕部1および第1格子体10は、導体(典型的には金属)からなるものである。   FIG. 3 is a plan view of the metamaterial 3 as viewed from above (z axis + side). The unit cell 4 is indicated by a two-dot chain line, and the vertex 41 and the center point 40 of the unit cell 4 are also displayed. The unit lattice 4 is a cube, and a first lattice body 10 (see FIG. 5) is formed by the first arm portion 1 that connects each vertex 41 in the direction of each xyz axis. That is, the first lattice body 10 is formed by connecting six first arm portions 1 at each vertex 41 inside the metamaterial 3. The 1st arm part 1 and the 1st lattice body 10 consist of conductors (typically metal).

また、隣接する単位格子4の中心点40をxyz軸それぞれの方向に連結する第2腕部2によって第2格子体20(図6参照)が形成されている。第2格子体20も、メタマテリアル3内部の各中心点40において6本の第2腕部2が連結されている。第2腕部2および第2格子体20も、導体(典型的には金属)からなるものである。第1格子体10は全体が導体からなり電気的に接続されている。また、第2格子体20も全体が導体からなり電気的に接続されている。   Moreover, the 2nd grating | lattice body 20 (refer FIG. 6) is formed of the 2nd arm part 2 which connects the center point 40 of the adjacent unit grating | lattice 4 to the direction of each xyz axis | shaft. In the second lattice body 20, six second arm portions 2 are connected at each center point 40 inside the metamaterial 3. The second arm portion 2 and the second lattice body 20 are also made of a conductor (typically metal). The entire first grid 10 is made of a conductor and is electrically connected. Further, the entire second grid 20 is also made of a conductor and is electrically connected.

しかし、第1格子体10と第2格子体20とは、互いに間隙を有し接触しないように配置されている。すなわち、第1格子体10と第2格子体20とは、直流的には絶縁されている。第1格子体10と第2格子体20とは、全体が絶縁体内に埋め込まれてもよいし、その一部が絶縁体によって固定され位置決めされていてもよい。   However, the first lattice body 10 and the second lattice body 20 are arranged so as to have a gap and do not contact each other. That is, the first grid body 10 and the second grid body 20 are insulated in terms of direct current. The first grid body 10 and the second grid body 20 may be entirely embedded in an insulator, or a part thereof may be fixed and positioned by the insulator.

図4は、1つの単位格子4によって切断された第1腕部1および第2腕部2の構成を示す斜視図である。なお、図2および図4において、第2腕部2の切断面はハッチングを付して表示している。図4では、第1腕部1の集合した第1格子体10と、第2腕部2の集合した第2格子体20とが、互いに接触しないように間隙を有して配置されていることが示されている。   FIG. 4 is a perspective view showing the configuration of the first arm portion 1 and the second arm portion 2 cut by one unit lattice 4. 2 and 4, the cut surface of the second arm portion 2 is indicated by hatching. In FIG. 4, the first lattice body 10 in which the first arm portions 1 are gathered and the second lattice body 20 in which the second arm portions 2 are gathered are arranged with a gap so as not to contact each other. It is shown.

図5は、第1腕部1の集合した第1格子体10を上方(z軸+側)から見た平面図である。第1腕部1は、互いに隣接配置された単位格子4の各頂点41をxyz軸それぞれの方向に連結するものである。これらの第1腕部1が集合して第1格子体10を形成している。   FIG. 5 is a plan view of the first lattice body 10 in which the first arm portions 1 are assembled as viewed from above (z axis + side). The 1st arm part 1 connects each vertex 41 of the unit lattice 4 arrange | positioned adjacent to each other in the direction of each xyz axis. These first arm portions 1 are assembled to form a first lattice body 10.

図6は、第2腕部2の集合した第2格子体20を上方(z軸+側)から見た平面図である。第2腕部2は、互いに隣接配置された単位格子4の各中心点40をxyz軸それぞれの方向に連結するものである。これらの第2腕部2が集合して第2格子体20を形成している。   FIG. 6 is a plan view of the second lattice body 20 in which the second arm portions 2 are gathered as viewed from above (z axis + side). The 2nd arm part 2 connects each center point 40 of the unit lattice 4 arrange | positioned adjacent to each other in the direction of each xyz axis. These second arm portions 2 are assembled to form a second lattice body 20.

この第1腕部1と第2腕部2とは、全く同じ形状に形成されている。また、第1格子体10と第2格子体20に関しても、両者は実は同等の構成である。第1格子体10と第2格子体20とは、互いに構成は同等であり、一方は他方を所定量だけ平行移動した位置に配置されているのである。平行移動のベクトルは単位格子4の中心点40と頂点41とを結ぶベクトルとなる。   The first arm portion 1 and the second arm portion 2 are formed in exactly the same shape. Further, both the first lattice body 10 and the second lattice body 20 are actually the same configuration. The first grid body 10 and the second grid body 20 have the same configuration, and one is arranged at a position where the other is translated by a predetermined amount. The translation vector is a vector connecting the center point 40 and the vertex 41 of the unit cell 4.

図7は、第1腕部1の構成を示す斜視図である。第1腕部1は連結点(頂点41)側が細く形成されており、中央部が太く形成されている。中央部は立方体を形成しており、その立方体の1辺の長さは単位格子4の1辺の長さの1/2より小さい。なお、この図は第1腕部1の形状を示しているが、第2腕部2も全く同じ形状である。   FIG. 7 is a perspective view showing the configuration of the first arm 1. The first arm portion 1 is formed so that the connecting point (vertex 41) side is thin, and the center portion is formed thick. The central part forms a cube, and the length of one side of the cube is smaller than ½ of the length of one side of the unit cell 4. Although this figure shows the shape of the first arm portion 1, the second arm portion 2 has the same shape.

図8は、第1腕部1の各部の寸法を示す平面図である。図示のように、単位格子4の頂点41間の距離(単位格子4の配列ピッチ)を寸法Pとし、第1腕部1の中央部の立方体の各辺の長さを寸法Aとする。そして、第1腕部1の連結点側部分の長さを寸法Bとし、連結点側部分の太さを寸法Cとする。連結点側部分は、断面形状が正方形(1辺の長さが寸法C)の四角柱である。寸法Bは、寸法Pと寸法Aによって次の式1のように表される。   FIG. 8 is a plan view showing dimensions of each part of the first arm part 1. As shown in the figure, the distance between the vertices 41 of the unit cell 4 (the arrangement pitch of the unit cells 4) is defined as a dimension P, and the length of each side of the cube at the center of the first arm 1 is defined as a dimension A. The length of the connection point side portion of the first arm 1 is defined as dimension B, and the thickness of the connection point side portion is defined as dimension C. The connecting point side portion is a quadrangular prism having a square cross section (the length of one side is dimension C). The dimension B is expressed by the following formula 1 by the dimension P and the dimension A.

B=(P−A)/2 ・・・ 式1
また、第1腕部1の中央部の立方体と、第2腕部2の中央部の立方体との間の間隙の大きさを寸法Gとすると、寸法Gは、寸法Pと寸法Aによって次の式2のように表される。式2は、図3から導き出される。
B = (P−A) / 2 Formula 1
If the size of the gap between the center cube of the first arm 1 and the center cube of the second arm 2 is a dimension G, the dimension G depends on the dimension P and the dimension A. It is expressed as Equation 2. Equation 2 is derived from FIG.

G=P/2−A ・・・ 式2
図3に示されるように、第1腕部1の立方体の寸法Aは、単位格子4の配列ピッチの寸法Pの1/2よりもやや小さく設定される。例えば、A=0.4Pとすれば、式1、式2より、B=0.3P,G=0.1Pとなる。なお、図8は第1腕部1の形状・寸法を示しているが、第2腕部2も全く同じ形状・寸法である。
G = P / 2−A Equation 2
As shown in FIG. 3, the dimension A of the cube of the first arm 1 is set slightly smaller than ½ of the dimension P of the arrangement pitch of the unit cell 4. For example, if A = 0.4P, from Equations 1 and 2, B = 0.3P and G = 0.1P. Although FIG. 8 shows the shape and dimensions of the first arm portion 1, the second arm portion 2 has the same shape and dimensions.

以上のようなメタマテリアル3は、隣接する第1腕部1の立方体と第2腕部2の立方体との間にキャパシタンスを持ち、かつ、第1腕部1および第2腕部2の両端連結部によるインダクタンスを持つ。このため、メタマテリアル3が非共振型の左手系メタマテリアルの特性を示すものと考えられる。   The metamaterial 3 as described above has capacitance between the cube of the first arm portion 1 and the cube of the second arm portion 2 that are adjacent to each other, and the both ends of the first arm portion 1 and the second arm portion 2 are connected. Has inductance due to the part. For this reason, it is thought that the metamaterial 3 exhibits the characteristics of a non-resonant left-handed metamaterial.

このようなメタマテリアル3の各部の寸法の実例を示す。第1腕部1および第2腕部2の寸法P:10.0mm、寸法A:4.0mm、寸法B:3.0mm、寸法C:1.0mmとする。このとき、第1腕部1の中央部と第2腕部2の中央部との間の間隙は寸法G:1.0mmとなる。このような寸法・配置のメタマテリアル3は、後述のように5.0〜8.0GHz付近で左手系媒質の特性を示す伝播モードを持つ。なお、この寸法例は一例であり、他の任意の寸法とすることができる。メタマテリアルの寸法・配置を変更すれば、左手系媒質の特性を示す周波数も変化する。   The example of the dimension of each part of such a metamaterial 3 is shown. The dimensions P of the first arm 1 and the second arm 2 are 10.0 mm, the dimension A is 4.0 mm, the dimension B is 3.0 mm, and the dimension C is 1.0 mm. At this time, the gap between the central portion of the first arm portion 1 and the central portion of the second arm portion 2 is a dimension G: 1.0 mm. The metamaterial 3 having such dimensions and arrangement has a propagation mode that exhibits the characteristics of the left-handed medium in the vicinity of 5.0 to 8.0 GHz as will be described later. In addition, this dimension example is an example and it can be set as other arbitrary dimensions. If the dimensions and arrangement of the metamaterial are changed, the frequency indicating the characteristics of the left-handed medium also changes.

図9に、上記の寸法・配置によるメタマテリアル3の分散特性を示す。これは図3、図4の単位格子4においてx,y,z軸方向に周期境界条件を与えて計算した有限要素法による電磁界シミュレーション結果である。x軸方向の波数をkx、y軸方向の波数をky、z軸方向の波数をkzとすると、伝搬定数βは、β=(kx 2+ky 2+kz 21/2である。図5の横軸のΓ、X、MおよびRはそれぞれ波数(kx,ky,kz)空間上の高対称点すなわち点Γ(0,0,0)、点X(π/P,0,0)、点M(π/P,π/P,0)、点R(π/P,π/P,π/P)である。ただし、πは円周率、Pは単位格子4の配列ピッチである。 In FIG. 9, the dispersion characteristic of the metamaterial 3 by said dimension and arrangement | positioning is shown. This is an electromagnetic field simulation result by the finite element method calculated by giving periodic boundary conditions in the x, y, and z axis directions in the unit cell 4 of FIGS. wave number k x the x-axis direction, wave number k y in the y-axis direction, when the wave number of the z-axis direction and k z, propagation constant beta is, β = (k x 2 + k y 2 + k z 2) 1/2 It is. In FIG. 5, Γ, X, M, and R on the horizontal axis are high symmetry points in the wave number (k x , k y , k z ) space, that is, point Γ (0, 0, 0), point X (π / P, 0, 0), point M (π / P, π / P, 0), and point R (π / P, π / P, π / P). However, (pi) is a circumference and P is the arrangement pitch of the unit cell 4.

Γ−X区間はβをkx=0→π/Pかつky=kz=0なる関係で変化させた区間を、X−M区間はβをkx=π/P,ky=0→π/P,kz=0なる関係で変化させた区間を示す。また、M−R区間はβをkx=ky=π/P,kz=0→π/Pなる関係で変化させた区間を、およびR−Γ区間はβをkx=ky=kz,kx=π/P→0なる関係で変化させた区間をそれぞれ示す。 The Γ-X section is a section in which β is changed in a relationship of k x = 0 → π / P and k y = k z = 0, and the X-M section is β is k x = π / P, k y = 0. → Indicates a section changed in a relationship of π / P, k z = 0. In the M-R section, β is changed in a relationship of k x = k y = π / P, k z = 0 → π / P, and in the R-Γ section, β is changed to k x = k y = P. The sections changed by the relationship k z , k x = π / P → 0 are shown.

また図9の縦軸は周波数fである。この分散曲線のΓ−X区間およびR−Γ区間中の任意の点において、点Γから引いた直線の傾きに2πを乗じたもの2πf/β(=ω/β;ωは角周波数)は位相速度(vp)を示し、またこの点における接線の傾きに2πを乗じたもの2π∂f/∂β(=∂ω/∂β)は群速度(vg)を示す。 The vertical axis in FIG. 9 is the frequency f. 2πf / β (= ω / β; ω is an angular frequency) obtained by multiplying the slope of the straight line drawn from the point Γ by 2π at any point in the Γ-X section and the R-Γ section of the dispersion curve is a phase. indicates the speed (v p), also 2π∂f / ∂β (= ∂ω / ∂β ) multiplied by 2π to the gradient of the tangent at this point shows the group velocity (v g).

本分散曲線のΓ−X区間およびR−Γ区間において、βの絶対値が増加するに従って周波数が低くなる領域を持つ伝播モードがある。例えば、Γ−X区間の下から2番目のモードがそうである。これらの領域では群速度と位相速度との符号が異なるバックワード波が伝播することが分かる。これは、この領域でメタマテリアル3が左手系媒質の特性となっていることを示すものである。すなわち、この伝播モードにおいてはメタマテリアル3が5.0〜8.0GHz付近で左手系媒質の特性を示す。   In the Γ-X section and the R-Γ section of the dispersion curve, there is a propagation mode having a region where the frequency decreases as the absolute value of β increases. For example, this is the second mode from the bottom of the Γ-X section. It can be seen that backward waves with different signs of group velocity and phase velocity propagate in these regions. This indicates that the metamaterial 3 has the characteristics of a left-handed medium in this region. That is, in this propagation mode, the metamaterial 3 exhibits the characteristics of the left-handed medium around 5.0 to 8.0 GHz.

以上のメタマテリアル3において、第1腕部1および第2腕部2の両端部の連結点側部分の形状は断面が正方形の四角柱としているが、断面形状はどのようなものでもよく円や任意の多角形とすることもできる。また、連結点側部分の太さ(断面寸法)は小さくするほど左手系媒質として動作する周波数が低下し、メタマテリアル3がより均質媒質として機能することが分かっている。具体的には、中央部の太さ(寸法A)が両端部の太さ(寸法C)の3倍以上であることが好ましい。   In the metamaterial 3 described above, the shape of the connecting point side portions at both ends of the first arm portion 1 and the second arm portion 2 is a quadrangular prism with a square cross section. It can also be an arbitrary polygon. In addition, it is known that the frequency of operating as a left-handed medium decreases as the thickness (cross-sectional dimension) of the connecting point side portion decreases, and the metamaterial 3 functions as a more homogeneous medium. Specifically, it is preferable that the thickness (dimension A) of the central portion is three times or more the thickness (dimension C) of both ends.

また、第1腕部1の中央部と第2腕部2の中央部との間の間隙の寸法Gは、小さい方が左手系媒質として動作する周波数が低下し、メタマテリアル3がより均質媒質として機能することが分かっている。具体的には、G≦0.2Pであることが好ましい。すなわち、中央部立方体の寸法Aは、式2より、A≧0.3Pであることが好ましい。メタマテリアル3の製造しやすさを考慮に入れれば、0.01P≦G≦0.2Pの範囲、すなわち0.3P≦A≦0.49Pの範囲が実用範囲と考えられる。   Further, the smaller the dimension G of the gap between the central portion of the first arm portion 1 and the central portion of the second arm portion 2, the lower the frequency at which it operates as a left-handed medium, and the metamaterial 3 is more homogeneous. Is known to function as. Specifically, it is preferable that G ≦ 0.2P. That is, the dimension A of the central cube is preferably A ≧ 0.3P according to Equation 2. Taking into account the ease of manufacture of the metamaterial 3, the range of 0.01P ≦ G ≦ 0.2P, that is, the range of 0.3P ≦ A ≦ 0.49P is considered as the practical range.

単位格子4は直交3軸(xyz軸)方向に等間隔で周期的に配置されていることが望ましい。しかし、単位格子4の位置および内部構造各部の寸法が厳密に正確な周期性を持っていなくとも、左手系メタマテリアルとしての特性を示し、ある程度の範囲での位置ずれおよび寸法誤差は許容される。   It is desirable that the unit cells 4 are periodically arranged at regular intervals in the orthogonal three-axis (xyz-axis) direction. However, even if the position of the unit lattice 4 and the dimensions of each part of the internal structure do not have strictly accurate periodicity, it shows the characteristics as a left-handed metamaterial, and positional deviation and dimensional errors within a certain range are allowed .

以上のように、本発明によれば、3次元の電磁波伝播媒質として機能し、媒質の等価的な誘電率と透磁率の両者が同時に負の値となる非共振型の3次元左手系メタマテリアルを実現することができる。非共振型であるため、左手系媒質として機能する周波数帯域幅が広く低損失である。   As described above, according to the present invention, a non-resonant type three-dimensional left-handed metamaterial that functions as a three-dimensional electromagnetic wave propagation medium and has both negative values of equivalent dielectric constant and magnetic permeability of the medium at the same time. Can be realized. Since it is non-resonant, it has a wide frequency bandwidth that functions as a left-handed medium and low loss.

なお、本発明の実施の形態においては、第1腕部1と第2腕部2の中央部に立方体形状の太い部分を形成しているが、これらの太い部分は必ずしも立方体でなくともよく、例えば直方体などでもよい。さらに、第1腕部1と第2腕部2の中央部に太い部分を形成せずに、全体を同じ太さとしてもよい。ただし、全体を同じ太さにした場合には、左手系媒質として機能する領域が減少することがあり、太さの範囲にも制限が加わる。   In the embodiment of the present invention, a thick portion of a cube shape is formed at the center of the first arm portion 1 and the second arm portion 2, but these thick portions may not necessarily be a cube, For example, a rectangular parallelepiped may be used. Further, the first arm portion 1 and the second arm portion 2 may have the same thickness as a whole without forming a thick portion at the center. However, if the entire thickness is the same, the area that functions as the left-handed medium may be reduced, and the thickness range is also limited.

以上のような、3次元左手系メタマテリアルの応用例としては、媒質が負の屈折率となることを利用したレンズがある。この負屈折率レンズは結像した像の分解能が波源の大きさ以下となり、いわゆるスーパーレンズとして動作する。スーパーレンズとは、分解能が波の回折限界(波長程度)を超えて高くなるレンズである。通常の右手系媒質によるレンズでは、結像の分解能は波の回折限界によって波源の波長よりも大きくなってしまう。3次元左手系メタマテリアルの応用例としては、さらに、上記のスーパーレンズによる短波長領域での高分解能フォトリソグラフィや、負屈折率を利用したビーム走査アンテナ、分散特性を利用したカプラや共振器など種々のデバイスが考えられる。   As an application example of the three-dimensional left-handed metamaterial as described above, there is a lens using the fact that the medium has a negative refractive index. This negative refractive index lens operates as a so-called super lens because the resolution of the formed image is less than the size of the wave source. A super lens is a lens whose resolution exceeds the wave diffraction limit (about the wavelength). In a lens using a normal right-handed medium, the resolution of imaging is larger than the wavelength of the wave source due to the wave diffraction limit. Examples of applications of three-dimensional left-handed metamaterials include high-resolution photolithography in the short wavelength region using the super lens described above, beam scanning antennas using negative refractive index, couplers and resonators using dispersion characteristics, etc. Various devices are conceivable.

本発明によれば、3次元の電磁波伝播媒質として機能し、媒質の等価的な誘電率と透磁率の両者が同時に負の値となる非共振型の3次元左手系メタマテリアルを実現することができる。また、その3次元左手系メタマテリアルを利用してスーパーレンズやスーパーレンズによる高分解能フォトリソグラフィや、分散特性を利用したカプラや共振器などの種々の応用機器・デバイスを実現することができる。   According to the present invention, it is possible to realize a non-resonant type three-dimensional left-handed metamaterial that functions as a three-dimensional electromagnetic wave propagation medium and in which both the equivalent dielectric constant and the magnetic permeability of the medium have negative values at the same time. it can. In addition, by using the three-dimensional left-handed metamaterial, it is possible to realize various applied devices and devices such as a super lens, high resolution photolithography using a super lens, and a coupler and a resonator using dispersion characteristics.

誘電率ε、透磁率μの正負領域と媒質との関係を示す図である。It is a figure which shows the relationship between the positive / negative area | region of dielectric constant (epsilon), and magnetic permeability (mu), and a medium. 本発明のメタマテリアル3の構成を示す斜視図である。It is a perspective view which shows the structure of the metamaterial 3 of this invention. メタマテリアル3を上方から見た平面図である。It is the top view which looked at metamaterial 3 from the upper part. 1つの単位格子4によって切断された第1腕部1および第2腕部2の構成を示す斜視図である。FIG. 3 is a perspective view showing a configuration of a first arm part 1 and a second arm part 2 cut by one unit lattice 4. 第1腕部1の集合した第1格子体10を上方から見た平面図である。It is the top view which looked at the 1st lattice object 10 where the 1st arm part 1 gathered from the upper part. 第2腕部2の集合した第2格子体20を上方から見た平面図である。It is the top view which looked at the 2nd lattice object 20 where the 2nd arm part 2 gathered from the upper part. 第1腕部1の構成を示す斜視図である。2 is a perspective view showing a configuration of a first arm part 1. FIG. 第1腕部1の各部の寸法を示す平面図である。FIG. 3 is a plan view showing dimensions of each part of the first arm part 1. メタマテリアル3の分散特性を示すグラフである。4 is a graph showing dispersion characteristics of metamaterial 3.

符号の説明Explanation of symbols

1 第1腕部
2 第2腕部
3 メタマテリアル
4 単位格子
10 第1格子体
20 第2格子体
40 中心点
41 頂点
DESCRIPTION OF SYMBOLS 1 1st arm part 2 2nd arm part 3 Metamaterial 4 Unit lattice 10 1st lattice body 20 2nd lattice body 40 Center point 41 Vertex

Claims (4)

立方体の単位格子(4)を3次元空間の互いに直交する3方向に繰り返し配置した構造の3次元左手系メタマテリアルであって、
前記単位格子(4)の各頂点を前記3方向に連結する第1腕部(1)の集合からなる第1格子体(10)と、
前記単位格子(4)の各中心点を前記3方向に連結する第2腕部(2)の集合からなる第2格子体(20)とを有し、
前記第1格子体(10)および前記第2格子体(20)は、それぞれ導体からなるものであり、かつ、互いに他と接触しないように間隙を持って配置されているものである3次元左手系メタマテリアル。
A three-dimensional left-handed metamaterial having a structure in which cubic unit cells (4) are repeatedly arranged in three directions orthogonal to each other in a three-dimensional space,
A first lattice body (10) composed of a set of first arm portions (1) connecting the vertices of the unit lattice (4) in the three directions;
A second lattice body (20) comprising a set of second arm portions (2) connecting the center points of the unit lattice (4) in the three directions;
The first grid body (10) and the second grid body (20) are each made of a conductor and are arranged with a gap so as not to contact each other. Metamaterial.
請求項1に記載した3次元左手系メタマテリアルであって、
前記第1腕部(1)および前記第2腕部(2)は、両端部の近傍が細く形成され、中央部が太く形成されたものである3次元左手系メタマテリアル。
The three-dimensional left-handed metamaterial according to claim 1,
The first arm part (1) and the second arm part (2) are three-dimensional left-handed metamaterials in which the vicinity of both end parts is formed thin and the center part is formed thick.
請求項2に記載した3次元左手系メタマテリアルであって、
前記第1腕部(1)の中央部の太い部分の断面形状は正方形であり、その1辺の寸法が前記単位格子(4)の1辺の寸法の0.30〜0.49倍である3次元左手系メタマテリアル。
The three-dimensional left-handed metamaterial according to claim 2,
The cross-sectional shape of the thick part at the center of the first arm (1) is a square, and the size of one side is 0.30 to 0.49 times the size of one side of the unit cell (4). 3D left-handed metamaterial.
請求項1〜3のいずれか1項に記載した3次元左手系メタマテリアルであって、
前記第1腕部(1)および前記第2腕部(2)は、中央部の太い部分の太さが両端部の細い部分の太さの3倍以上のものである3次元左手系メタマテリアル。
It is the three-dimensional left-handed metamaterial according to any one of claims 1 to 3,
The first arm part (1) and the second arm part (2) are three-dimensional left-handed metamaterials in which the thickness of the thick part at the center is more than three times the thickness of the narrow part at both ends. .
JP2007080445A 2007-03-27 2007-03-27 3D left-handed metamaterial Active JP4644824B2 (en)

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KR101042212B1 (en) 2009-01-15 2011-06-20 숭실대학교산학협력단 Wireless energy transferring/receiving device and wireless energy transferring/receiving system
US8669833B2 (en) 2009-06-05 2014-03-11 National University Corporation Kyoto University of Technology Three-dimensional metamaterial having function of allowing and inhibiting propagation of electromagnetic waves
JP2012089785A (en) * 2010-10-22 2012-05-10 Sumitomo Metal Mining Co Ltd Interfering radio-wave shield or absorber
US8780010B2 (en) 2011-02-23 2014-07-15 Semiconductor Technology Academic Research Center Metamaterial provided with at least one spiral conductor for propagating electromagnetic wave
US9418785B2 (en) 2011-11-29 2016-08-16 Samsung Electronics Co., Ltd. Wireless power transmission system with enhanced magnetic field strength
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