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

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

  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.

  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.

  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.

  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.

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

  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.

  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.

  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.

  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.

  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.

  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.

  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.

  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.

  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.

  Since this invention is comprised as mentioned above, there exist the following effects.

  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.

  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.

  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.

  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.

  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).

  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.

  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.

  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.

  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.

  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.

  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.

  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.

  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 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 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.

  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.

  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.

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.

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.

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).

  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.

  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.

  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.

  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 .

  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.

  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.

  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.

  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.

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. It is a perspective view which shows the structure of the metamaterial 3 of this invention. It is the top view which looked at metamaterial 3 from the upper part. 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. It is the top view which looked at the 1st lattice object 10 where the 1st arm part 1 gathered from the upper part. It is the top view which looked at the 2nd lattice object 20 where the 2nd arm part 2 gathered from the upper part. 2 is a perspective view showing a configuration of a first arm part 1. FIG. FIG. 3 is a plan view showing dimensions of each part of the first arm part 1. 4 is a graph showing dispersion characteristics of metamaterial 3.

Explanation of symbols

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)

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. 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. 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. 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. .

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