WO2013133175A1 - Three-dimensional meta-material - Google Patents

Abstract

A three-dimensional meta-material (20) includes a plurality of unit cells (10) arranged periodically in three dimensions. Each unit cell (10) is provided with a dielectric resonator (1) disposed at the center thereof, a plurality of rod-shaped conductors (3) disposed so as to encircle the dielectric resonator (1), and a host medium (2) for supporting the dielectric resonator (1) and the rod-shaped conductors (3). In each unit cell (10), the rod-shaped conductors (3) include rod-shaped conductors (3xa-3xd) disposed in an x direction, rod-shaped conductors (3ya-3yd) disposed in a y direction, and rod-shaped conductors (3za-3zd) disposed in a z direction. By arranging the plurality of unit cells (10) periodically in three dimensions, the x-directed rod-shaped conductors are arranged periodically and parallel to each other, the y-directed rod-shaped conductors are arranged periodically and parallel to each other, and the z-directed rod-shaped conductors are arranged periodically and parallel to each other.

Description

3D metamaterial

The present invention relates to a three-dimensional metamaterial that is an artificial structure that includes a plurality of unit cells that have a predetermined shape and a predetermined structure and that are periodically arranged, and in which parameters as an effective medium can be arbitrarily set. The present invention relates to a three-dimensional right / left-handed composite metamaterial.

As prior art of metamaterials, for example, there are inventions of Patent Documents 1 to 6.

The structure of the metamaterial is a microwave circuit, its components and antennas, a flat plate super lens, and near-field light (light with information of structure smaller than the wavelength of the light) that realizes sub-wavelength resolution. It has been studied for applications to optical devices and their components such as field imaging, cloaking technology and the like. The metamaterial can be used for propagating electromagnetic waves or blocking electromagnetic waves by arbitrarily setting parameters as effective media. Furthermore, while a normal medium has a positive effective dielectric constant and a positive effective magnetic permeability (right-handed medium), the metamaterial includes a left-handed medium having a negative effective dielectric constant and a negative effective magnetic permeability. There is something that functions as.

The metamaterial is “right-handed” when the electromagnetic wave propagates through the metamaterial when the electric field vector, magnetic field vector, and wave number vector of the electromagnetic wave have a right-handed relationship. The electromagnetic wave propagating through the right-handed metamaterial becomes a forward wave (forward wave) in which the direction of transmission power of the electromagnetic wave (direction of group velocity) and the direction of flow of the phase plane (direction of phase velocity) are the same direction.

Also, the metamaterial is “left-handed” when the electromagnetic wave propagates through the metamaterial when the electric field vector, magnetic field vector, and wave number vector of the electromagnetic wave have a left-handed relationship. The electromagnetic wave propagating through the left-handed metamaterial becomes a backward wave (reverse wave) in which the direction of the transmission power of the electromagnetic wave and the direction of the flow of the phase plane are opposite.

When the metamaterial is applied to, for example, a microwave circuit or an antenna device, most of the metamaterial is based on a one-dimensional or two-dimensional left-handed metamaterial structure. Recently, an anisotropic / isotropic left-handed structure using a combination of a split ring resonator and a thin wire, a transmission line network, and a dielectric sphere has also been proposed.

Several methods of configuring metamaterials have been proposed, but two typical examples are a resonant metamaterial and a transmission line (non-resonant) metamaterial.

The former resonant metamaterial consists of a combination of magnetic and electrical resonators that respond to the magnetic field and electric field components of an external electromagnetic field, typically a combination of a split ring resonator consisting of a metal strip and a thin wire. Including things. Since this structure uses a strong resonance interaction between the metal structure and light waves or electromagnetic waves, a large change in optical characteristics or electromagnetic characteristics can be obtained with fewer structures and a smaller volume than those that do not use resonance. There is a feature that you can. However, since the effective permittivity or effective permeability exhibits anti-resonance characteristics, the influence of loss becomes very large near the resonance frequency. In other words, the Q value of the resonator greatly affects its characteristics, and light waves or electromagnetic waves are strongly absorbed at the resonance frequency, and the frequency band in which the characteristics change is limited to the vicinity of the resonance frequency.

On the other hand, in the latter transmission line type metamaterial, a structure is configured using the fact that a general electromagnetic wave propagation form can be described by a transmission line model. The conventional one-dimensional right-handed metamaterial structure that allows forward wave propagation has a ladder-type structure in which inductive elements are inserted in series branches and capacitive elements are inserted in parallel branches (shunt branches). The one-dimensional left-handed metamaterial structure has a structure in which a capacitive element is inserted in a series branch and an inductive element is inserted in a parallel branch in order to make negative values of effective dielectric constant and effective permeability. Many of the transmission line type metamaterials do not exhibit anti-resonance characteristics in terms of effective dielectric constant and magnetic permeability, and thus have a feature of lower loss than the above-described resonance type metamaterial. In transmission line type metamaterials, depending on the operating frequency band, right-handed metamaterials, left-handed metamaterials, single negative metamaterials with one of the negative dielectric constant and the positive magnetic permeability and the other positive, effective dielectric constant or transparent Since it operates as a metamaterial with zero magnetic permeability, it is called a right / left-handed composite metamaterial.

The frequency at which the effective permittivity and effective permeability of the right / left-handed composite metamaterial have zero values is generally different. In that case, in the band between the frequency at which the effective dielectric constant becomes zero and the frequency at which the effective magnetic permeability becomes zero, only one of the effective dielectric constant and the effective magnetic permeability has a negative value, and the other Has a positive value. In this band, the electromagnetic wave propagation condition is not satisfied and the band becomes a forbidden band. The right-hand / left-handed composite metamaterial operates as a left-handed metamaterial because the effective permittivity and effective permeability are both negative in the lower band of this forbidden band, and both are positive in the upper band. Works as a metamaterial. When the effective permittivity and the frequency at which the effective magnetic permeability are equal, no forbidden band is formed, and the left-handed transmission band and the right-handed transmission band are continuously connected. Such a metamaterial is referred to as a balanced right-hand / left-handed composite metamaterial, and a non-balanced right-hand / left-handed composite metamaterial is referred to as a non-equilibrium right-hand / left-handed composite metamaterial. The balanced right-hand / left-handed composite metamaterial has the feature that not only a forbidden band does not occur, but also the group velocity does not become zero at a frequency where the phase constant becomes zero, and efficient power transmission is possible.

JP 2006-114489 A JP 2008-244683 A JP 2008-252293 A Special table 2008-503776 Special table 2008-507733 gazette Pamphlet of International Publication WO2010 / 140655A1

In the prior art, when a three-dimensional metamaterial is formed by extending a one-dimensional metamaterial or a two-dimensional metamaterial to three dimensions, isotropic propagation characteristics (dispersion curve or Bloch impedance in all directions) Etc.) were difficult to achieve.

The inventor of the present application proposed a three-dimensional metamaterial in Patent Document 6. In this three-dimensional metamaterial, a plurality of dielectric layers including a plurality of dielectrics and a host medium that are juxtaposed at a predetermined interval are sandwiched by a pair of conductive mesh plates each having a plurality of holes. In a metamaterial formed by forming a functional layer including a plurality of dielectric resonators corresponding to a dielectric and laminating a plurality of the functional layers, a plurality of shafts of holes and a plurality of dielectric resonators Are arranged so that their axes are coaxial with each other, and electromagnetic waves are propagated in the propagation direction perpendicular to the laminated surface in each functional layer, and the left-handed metamaterial in the propagation direction perpendicular to the laminated surface It is made to operate as. According to the three-dimensional metamaterial of Patent Document 6, it has a small propagation loss and is very easy to manufacture. In each functional layer, the electromagnetic wave is propagated in a propagation direction perpendicular to the laminated surface, and the laminated surface It can be operated as a left-handed metamaterial with respect to the propagation direction perpendicular to

However, the three-dimensional metamaterial disclosed in Patent Document 6 exhibits isotropic propagation characteristics only when the electromagnetic wave has the same polarization direction as the direction of the laminated surface. The three-dimensional metamaterial of Patent Document 6 is effective when the propagation direction and the polarization direction of electromagnetic waves are uniquely determined, but may not be effective when not uniquely determined. Therefore, there is a need for a three-dimensional metamaterial that does not depend on the propagation direction and polarization direction of electromagnetic waves, that is, has isotropic propagation characteristics.

An object of the present invention is to solve the above problems and to provide a three-dimensional metamaterial that can easily realize isotropic propagation characteristics independent of the propagation direction and polarization direction of electromagnetic waves.

The three-dimensional metamaterial according to the present invention is
In a three-dimensional metamaterial including a plurality of unit cells periodically arranged in three dimensions,
Each unit cell includes a dielectric resonator disposed in the center of the unit cell, a plurality of rod-shaped conductors disposed so as to surround the dielectric resonator, and the dielectric resonator and the rod-shaped conductor. A supporting host medium,
In each of the unit cells, the plurality of rod-shaped conductors include at least one first rod-shaped conductor arranged in a first direction and at least one arranged in a second direction different from the first direction. A second bar-shaped conductor, and at least one third bar-shaped conductor disposed in a third direction having a predetermined angle with respect to a surface stretched by the first and second directions,
In the three-dimensional metamaterial configured by periodically arranging the plurality of unit cells three-dimensionally, the first rod-shaped conductors are arranged in parallel and periodically with each other, and the second rod-shaped conductors Are arranged in parallel and periodically with each other, and the third rod-shaped conductors are arranged in parallel and periodically with each other in a three-dimensional metamaterial,
The host medium includes a first substrate having a cavity and a second substrate sandwiching the first substrate, and the first substrate or / and the second substrate include the first rod-shaped conductor or / And a second rod-shaped conductor is formed,
The dielectric resonator is disposed in the cavity of the first substrate and formed in a unit form sandwiched between the second substrates, or formed in a state where two or more layers of the unit form are laminated. It has the said 3rd rod-shaped conductor, It is characterized by the above-mentioned.

In the three-dimensional metamaterial, the shape and dimensions of the unit cell so that the effective permittivity and effective permeability of the three-dimensional metamaterial are both negative with respect to electromagnetic waves having a predetermined frequency incident on the three-dimensional metamaterial. The shape, dimensions, and relative permittivity of the dielectric resonator, the thickness of the rod-shaped conductor, the interval at which the first, second, and third rod-shaped conductors are periodically disposed, and the host medium The relative dielectric constant is set.

In the above three-dimensional metamaterial,
Each unit cell includes a waveguide formed by the plurality of rod-shaped conductors, each unit cell has a predetermined cutoff frequency, and each unit cell is incident on the three-dimensional metamaterial. The effective dielectric constant of the three-dimensional metamaterial is configured to be negative with respect to electromagnetic waves having a frequency lower than the off-frequency,
The dielectric resonator is excited by an electromagnetic wave having a predetermined frequency incident on the dielectric resonator in a resonance form having an electromagnetic field distribution similar to a magnetic dipole moment, and the three-dimensional metamaterial is effective against the electromagnetic wave. The magnetic permeability is configured to be negative.

In the three-dimensional metamaterial, each unit cell is a cube, and the first, second, and third directions are orthogonal to each other.

In the three-dimensional metamaterial, the dielectric resonator has a spherical shape.

In the three-dimensional metamaterial, the dielectric resonator has a cylindrical shape or a polygonal column shape.

In the three-dimensional metamaterial, the dielectric resonator has a cubic shape, a polyhedral shape, or a rhombohedral shape.

In the three-dimensional metamaterial, the rod-shaped conductor has a rectangular cross-sectional shape.

In the three-dimensional metamaterial, the rod-shaped conductor has a circular cross-sectional shape.

In the three-dimensional metamaterial, the first, second, and third rod-shaped conductors intersect each other.

In the three-dimensional metamaterial, at least one of the first, second, and third rod-shaped conductors does not intersect with another rod-shaped conductor.

In the three-dimensional metamaterial, the first, second, and third rod-shaped conductors are electrically connected to each other.

In the three-dimensional metamaterial, at least one of the first, second, and third rod-shaped conductors is not electrically connected to another rod-shaped conductor.

According to the three-dimensional metamaterial according to the present invention, it is possible to provide a three-dimensional metamaterial that can be easily realized with an isotropic propagation characteristic that is independent of the propagation direction and polarization direction of electromagnetic waves.

It is a perspective view which shows the structure of the three-dimensional metamaterial 20 which concerns on embodiment of this invention. It is a perspective view which shows the structure of the unit cell 10 which comprises the three-dimensional metamaterial 20 of FIG. FIG. 3 is a horizontal sectional view passing through the center of the unit cell 10 of FIG. 2. It is a perspective view which shows the structure of the unit cell 11 which comprises the three-dimensional metamaterial 20 which concerns on the 1st modification of embodiment of this invention. It is a perspective view which shows the structure of the unit cell 12 which comprises the three-dimensional metamaterial 20 which concerns on the 2nd modification of embodiment of this invention. It is a perspective view which shows the structure of the three-dimensional metamaterial 21 which concerns on the 3rd modification of embodiment of this invention. It is a perspective view which shows the structure of the unit cell 13 which comprises the three-dimensional metamaterial 21 of FIG. It is a disassembled perspective view which shows the structure of the three-dimensional metamaterial 22 which concerns on the 4th modification of embodiment of this invention. It is a perspective view which shows the structure of the board | substrate layer 31 of FIG. FIG. 10 is a cross-sectional view taken along line A-A ′ of FIG. 9. It is a perspective view which shows the structure of the board | substrate layer 32 of FIG. FIG. 12 is a sectional view taken along line B-B ′ of FIG. 11. FIG. 9 is a cross-sectional view illustrating a structure of a three-dimensional metamaterial 22 including substrate layers 31-1, 32-1, 31-2, 32-2, and 31-3 in FIG. It is a graph which shows the dispersion | distribution curve of the three-dimensional metamaterial which concerns on Example 1 of this invention. It is a graph which shows the dispersion | distribution curve of the three-dimensional metamaterial which concerns on Example 2 of this invention. It is a graph which shows the dispersion | distribution curve of the three-dimensional metamaterial which concerns on Example 3 of this invention. It is a figure for demonstrating the expression of the wavenumber area | region which concerns on the three-dimensional metamaterial of embodiment of this invention. It is a perspective view which shows the structure of the three-dimensional metamaterial 10 which concerns on Example 4 of this invention. It is a perspective view which shows the direction defined in the three- dimensional metamaterials 10 and 12 of FIG.18 and FIG.21. It is a graph which shows the dispersion | distribution curve of the three-dimensional metamaterial 10 of FIG. It is a perspective view which shows the structure of the three-dimensional metamaterial 12 which concerns on Example 5 of this invention. It is a graph which shows the dispersion | distribution curve of the three-dimensional metamaterial 12 of FIG. It is a graph which shows the dispersion | distribution characteristic when the rod-shaped conductors 6 placed along three directions orthogonal to each other in the three-dimensional metamaterial according to Example 6 of the present invention are not in direct contact with each other and there is a minute gap. .

Embodiments according to the present invention will be described below with reference to the drawings. In addition, in each following embodiment, the same code | symbol is attached | subjected about the same component.

FIG. 1 is a perspective view showing a structure of a three-dimensional metamaterial 20 according to an embodiment of the present invention. FIG. 2 is a perspective view showing the structure of the unit cell 10 constituting the three-dimensional metamaterial 20 of FIG. The three-dimensional metamaterial 20 in FIG. 1 is configured by periodically arranging the unit cells 10 in FIG. 2 three-dimensionally. Each unit cell 10 is preferably a cube having a side length Lx = Ly = Lz. Each unit cell 10 includes a dielectric resonator 1 disposed in the center of the unit cell 10 and a plurality of rod-shaped conductors 3xa to 3xd, 3ya to 3yd, 3za to 3zd disposed so as to surround the dielectric resonator 1. (Hereinafter collectively referred to as “3”) and a host medium 2 that supports the dielectric resonator 1 and the rod-shaped conductor 3. The dielectric resonator 1 has, for example, a spherical shape with a radius R1, and further has a relative dielectric constant much higher than that of the host medium 2 (for example, relative dielectric constants 1 to 10 of the host medium 2). The dielectric constant of the dielectric resonator 1 is 15 to 110). In each unit cell 10, the rod-shaped conductor 3 includes rod-shaped conductors 3 xa to 3 xd disposed along the x direction, rod-shaped conductors 3 ya to 3 yd disposed along the y direction, and rod-shaped conductors disposed along the z direction. Conductors 3za to 3zd. In a three-dimensional metamaterial 20 configured by periodically arranging a plurality of unit cells 10 in a three-dimensional manner, a plurality of bar conductors in the x direction are periodically arranged in parallel to each other, The rod-shaped conductors are also arranged in parallel and periodically with each other, and the plurality of z-direction rod-shaped conductors are also arranged in parallel with each other and periodically. For example, rod-shaped conductors (such as 3za to 3zd) arranged along the z direction are periodically arranged for each length Lx in the x direction, periodically arranged for each length Ly in the y direction, and In other directions (for example, a direction along the surface including the rod-shaped conductors 3za and 3zd), the electrodes are periodically arranged at predetermined lengths.

In order for the three-dimensional metamaterial 20 to operate as a left-handed metamaterial that is substantially isotropic in the three-dimensional direction, the dielectric resonator 1 is inserted into the unit cell 10 having a negative effective dielectric constant. Thereby, the three-dimensional metamaterial 20 is configured so that both the effective dielectric constant and the effective magnetic permeability thereof are negative with respect to the electromagnetic wave having a predetermined frequency. The configuration principle will be described below.

FIG. 3 is a cross-sectional view in the horizontal direction (direction along a plane parallel to the xy plane) passing through the center of the unit cell 10 in FIG. In FIG. 3, the center unit cell 10 and a part of unit cell adjacent to it are shown. Each of the rod-shaped conductors 3 (only the rod-shaped conductors 3za to 3zd in the z direction are shown in FIG. 3) has, for example, a square cross-sectional shape having a side length L2. The rod-shaped conductors 3za to 3zd are periodically arranged with an interval L1 in the x direction and are periodically arranged with an interval L3 in the y direction. However, as described above, when the unit cell 10 is a cube, L1 = L3. The unit cell 10 is configured as a waveguide in which, for example, in the x direction, a section having a length L2 surrounded by a conductor and a section having a length L1 not surrounded by a conductor are alternately arranged. The effective dielectric constant of the section surrounded by the conductor in this waveguide becomes negative in a frequency region lower than the cutoff frequency of the TE mode. Accordingly, this waveguide is an electromagnetic wave having a frequency lower than the cutoff frequency. For example, when an electromagnetic wave directed in the + x direction arrives as an incident wave, the negative effective dielectric constant ε2 <0 is obtained in the section surrounded by the conductor. And the section not surrounded by the conductor is configured to have a positive effective dielectric constant ε1> 0. At this time, the three-dimensional metamaterial 20 as a whole has an effective dielectric constant of a predetermined value of positive, zero, or negative. Similarly, the unit cell 10 is configured as a waveguide in which sections surrounded by a conductor and sections not surrounded by a conductor are alternately arranged along the y direction and the z direction. These waveguides are electromagnetic waves having a frequency lower than the cut-off frequency, and when an electromagnetic wave directed in the y direction or the z direction arrives as an incident wave, it has a negative effective dielectric constant in a section surrounded by a conductor. The section not surrounded by the conductor is configured to have a positive effective dielectric constant. Also in these cases, the three-dimensional metamaterial 20 as a whole has an effective dielectric constant of a predetermined value of positive, zero, or negative.

Each unit cell 10 has a cut-off frequency (cut-off frequency of the entire unit cell 10) as an effective value depending on the entire structure of the unit cell 10 including the waveguide and other portions. The three-dimensional metamaterial 20 has a zero or positive effective dielectric constant when an electromagnetic wave having a frequency higher than the cutoff frequency of the entire unit cell 10 arrives as an incident wave.

Furthermore, the dielectric resonator 1 has a resonance form with an electromagnetic field distribution similar to the magnetic dipole moment. Here, “an electromagnetic field distribution similar to the magnetic dipole moment” means that a concentric vortex with closed lines of electric force is formed in a plane perpendicular to a certain axis in the dielectric resonator 1. In addition, the magnetic field lines are directed substantially along the axis in the vicinity of the center of the dielectric resonator 1, and the magnetic field lines extend outside the dielectric resonator 1 to form a closed curve. Say. In general, the magnetic field lines are sorenoidal (always closed), and in this case, the magnetic field lines have a distribution that spreads widely outside the dielectric resonator 1. While more electric energy is stored inside the dielectric resonator 1 than magnetic energy, the energy stored by the magnetic field is larger than the energy stored by the electric field outside the dielectric resonator 1. Thus, the coupling between the dielectric resonator 1 and the external electromagnetic field is dominated by magnetic coupling.

In order for the three-dimensional metamaterial 20 to have isotropic propagation characteristics, among the resonance modes of the dielectric resonator 1 having an electromagnetic field distribution similar to the magnetic dipole moment, a first axis having a symmetry axis in the x direction is used. 1 resonance form, a second resonance form having a symmetry axis in the y direction, and a third resonance form having a symmetry axis in the z direction all have substantially the same resonance frequency (ie, three different resonance forms). Mode). When an electromagnetic wave having a frequency near the resonance frequency arrives at the dielectric resonator 1, the dielectric resonator 1 enters a resonance state or a state having an electromagnetic field distribution close to that regardless of the propagation direction of the electromagnetic wave. In addition, the electromagnetic field distribution inside and outside the dielectric resonator 1 at the time of resonance is expressed as one of the three substantially degenerated resonance modes or a combination (linear sum) according to the component of the propagation direction vector of the electromagnetic wave. The In the case of the spherical dielectric resonator 1, the magnetic wall at the boundary (the tangential component of the magnetic field is zero) under the condition that the dielectric constant of the dielectric resonator 1 is sufficiently larger than the dielectric constant of the host medium 2. Assuming that, the resonance mode is approximately calculated. In this simplified model, the electromagnetic field distribution of the dielectric resonator 1 is expressed as a TE ₀₁₁ resonance mode.

In order to operate the three-dimensional metamaterial 20 as a right / left-handed composite metamaterial, when an electromagnetic wave having a predetermined frequency arrives at the dielectric resonator 1, the magnetic field vector of the electromagnetic wave becomes magnetic in the dielectric resonator 1. It is necessary to excite the resonance state of the electromagnetic field distribution similar to the dipole moment. As a result, a positive, zero, or negative effective permeability is realized in the unit cell 10 according to the frequency of the electromagnetic wave. At this time, the three-dimensional metamaterial 20 as a whole has an effective magnetic permeability of a predetermined value of positive, zero, or negative.

The shape and size of the unit cell 10 and the shape, size, and relative dielectric constant of the dielectric resonator 1 are such that the effective dielectric constant and effective permeability of the three-dimensional metamaterial 20 are both negative with respect to an electromagnetic wave having a predetermined frequency. The ratio, the thickness of the rod-shaped conductor 3, the interval at which the rod-shaped conductor 3 is periodically arranged, and the relative dielectric constant of the host medium 2 are determined. At this time, the three-dimensional metamaterial 20 is configured as a left-handed metamaterial that does not depend on the propagation direction and polarization direction of electromagnetic waves, that is, has isotropic propagation characteristics.

Further, the three-dimensional metamaterial 20 is a right-handed metamaterial, a left-handed metamaterial, a single negative metamaterial in which one of the dielectric constant and the magnetic permeability is negative and the other is positive, depending on the operating frequency, the effective dielectric constant or the permeability. It may be configured as a right-hand / left-handed composite metamaterial that operates as a metamaterial with zero magnetic susceptibility.

In addition, the frequency at which the effective permittivity of the three-dimensional metamaterial 20 is zero and the frequency at which the effective permeability is zero are generally different, but by matching these frequencies, the three-dimensional metamaterial 20 can be balanced right-handed / It may be configured as a left-handed composite metamaterial.

The dielectric resonator 1 may be composed of a single dielectric material or a combination of a plurality of dielectric materials.

The dielectric resonator 1 may or may not be in contact with the dielectric resonator 1 of the unit cell 10 adjacent to the unit cell 10 including the dielectric resonator 1.

The host medium 2 is configured by, for example, filling the unit cell 10 with a dielectric having a dielectric constant much lower than that of the dielectric resonator 1. Further, as the host medium 2, at least a part of the inside of the unit cell 10 may be filled with air, or the inside of the unit cell 10 may be filled with a combination of air and a dielectric, or a combination of a plurality of dielectrics. It may be filled.

1 and 2 show a cubic unit cell 10, the shape of the unit cell is not limited to a cube. If a plurality of unit cells can be periodically arranged three-dimensionally to form a three-dimensional metamaterial, a unit cell of an arbitrary shape such as a rectangular parallelepiped, a prism (hexagonal column, etc.), a regular tetrahedron, or a plurality of unit cells Combinations of types of unit cells can be used. In each unit cell, the plurality of rod-shaped conductors are arranged along at least three directions. That is, in each unit cell, the plurality of rod-shaped conductors include at least one first rod-shaped conductor disposed in the first direction and at least one first conductor disposed in a second direction different from the first direction. Two bar-shaped conductors and at least one third bar-shaped conductor disposed in a third direction having a predetermined angle with respect to a surface stretched by the first and second directions. In a three-dimensional metamaterial configured by periodically arranging a plurality of unit cells three-dimensionally, the first rod-shaped conductors are arranged in parallel and periodically with each other, and the second rod-shaped conductors are arranged in parallel with each other. The third rod-shaped conductors are arranged in parallel and periodically with each other. In the three-dimensional metamaterial thus configured, it is possible to easily realize isotropic propagation characteristics that do not depend on the propagation direction and polarization direction of electromagnetic waves. However, for isotropic propagation characteristics, the unit cell preferably has a symmetric shape such as a cube rather than a shape such as a rectangular parallelepiped whose dimensions and the like differ depending on the direction.

FIG. 4 is a perspective view showing the structure of the unit cell 11 constituting the three-dimensional metamaterial 20 according to the first modification of the embodiment of the present invention. The unit cell 10 in FIGS. 1 and 2 includes the spherical dielectric resonator 1, but may include other shapes of dielectric resonators. The unit cell 11 of FIG. 4 includes a cylindrical dielectric resonator 4 having a radius R2 and a height H1. In the case of the cylindrical dielectric resonator 4, (1) an electromagnetic field distribution similar to a magnetic dipole moment parallel to the axis of symmetry of the cylinder is formed in the vicinity of the TE _01δ resonance mode and its resonance frequency, and (2) HE _In the vicinity of the _11δ resonance mode and its resonance frequency, an electromagnetic field distribution similar to the magnetic dipole moment is formed in the direction perpendicular to the side surface of the cylinder. In this case, since the degree of freedom in determining the direction perpendicular to the side surface of the cylinder is 2, it is assumed here that the two resonance states are degenerated. When the resonance frequencies of (1) and (2) are the same, an electromagnetic field distribution similar to three magnetic dipole moments having symmetric axes in three different directions can be realized at the same frequency. . The diameter (radius R2 × 2) and height H1 of the dielectric resonator 4 are determined to be approximately the same length so that the resonance frequencies of the TE _01δ mode and the HE _11δ mode of the dielectric resonator 4 are degenerated at substantially the same frequency. It is done.

FIG. 5 is a perspective view showing the structure of the unit cell 12 constituting the three-dimensional metamaterial 20 according to the second modification of the embodiment of the present invention. The unit cell 12 of FIG. 5 includes a cubic-shaped dielectric resonator 5 having a side having a length Lc.

Even in the three-dimensional metamaterial using the dielectric resonator 4 of FIG. 4 or the dielectric resonator 5 of FIG. 5, it is not dependent on the propagation direction and polarization direction of electromagnetic waves, that is, isotropic propagation characteristics are easily achieved. Can be realized.

The shape of the dielectric resonator is not limited to a spherical shape, a cylindrical shape, and a cubic shape, and any shape such as a spheroid, a polygonal column, a polyhedron, a rhombohedron, or a combination of a plurality of types of shapes should be used. Can do.

When paying attention to one unit cell, isotropic propagation characteristics are impaired if a dielectric resonator having an asymmetric shape is used. Even when such a dielectric resonator is used, on average, isotropic propagation characteristics are realized by arranging the dielectric resonators in various directions in a plurality of unit cells. be able to. Further, when paying attention to one unit cell, isotropic propagation characteristics are impaired unless the dielectric resonator is arranged at the center of the unit cell. Even if the dielectric resonator is not arranged in the center of the unit cell, the isotropic propagation characteristics can be achieved on average by arranging the dielectric resonator in various different positions in the unit cells. can do.

FIG. 6 is a perspective view showing the structure of the three-dimensional metamaterial 21 according to the third modification of the embodiment of the present invention. FIG. 7 is a perspective view showing the structure of the unit cell 13 constituting the three-dimensional metamaterial 21 of FIG. In FIG. 1 and FIG. 2, the bar conductors 3 in the x direction, the y direction, and the z direction are shown to intersect with each other, but the bar conductors in at least one of these bar conductors 3 are in other directions. It does not have to intersect with the rod-shaped conductor. Moreover, in FIG.1 and FIG.2, although the rod-shaped conductor 3 had a rectangular cross-sectional shape, you may have another cross-sectional shape. The unit cell 13 of this modification has a circular cross-sectional shape having a diameter L4 and includes rod-shaped conductors 6x, 6ya, 6yb, 6za to 6zd (hereinafter collectively referred to as “6”) that do not intersect each other.

Each unit cell 13 includes a dielectric resonator 1 disposed in the center of the unit cell 13, a plurality of rod-shaped conductors 6 disposed so as to surround the dielectric resonator 1, and the dielectric resonator 1 and the rod-shaped conductor. 6 and a host medium 2 that supports 6. In each unit cell 13, the rod-shaped conductor 6 includes a rod-shaped conductor 6x disposed along the x direction, rod-shaped conductors 6ya and 6yb disposed along the y direction, and a rod-shaped conductor 6za disposed along the z direction. ~ 6zd. In a three-dimensional metamaterial 21 configured by periodically arranging a plurality of unit cells 13 in a three-dimensional manner, a plurality of bar conductors in the x direction are periodically arranged in parallel to each other, The rod-shaped conductors are also arranged in parallel and periodically with each other, and the plurality of z-direction rod-shaped conductors are also arranged in parallel with each other and periodically.

In addition, the rod-shaped conductors 6 in the x direction, the y direction, and the z direction may or may not be electrically connected to each other.

Next, an example of a method for producing a three-dimensional metamaterial according to an embodiment of the present invention will be described with reference to FIGS.

FIG. 8 is an exploded perspective view showing the structure of the three-dimensional metamaterial 22 according to the fourth modification of the embodiment of the present invention. The three-dimensional metamaterial 22 includes a plurality of stacked substrate layers 31-1, 32-1, 31-2, 32-2, 31-3,..., 31-N. As will be described later, some of the substrate layers 32-1, 32-2,..., 32- (N-1) (hereinafter collectively referred to as “32”) accommodate the dielectric resonator 1, respectively. The remaining substrate layers 31-1, 31-2, 31-3,..., 31-N (hereinafter collectively referred to as reference numeral “31”) are disposed between the substrate layers 32, respectively. The dielectric resonator 1 is fixed to the cavity of the substrate layer 32 by sandwiching it. 2 is formed as a pattern conductor formed on at least one surface of each of the substrate layers 31 and 32, or is formed as a through-hole conductor penetrating each of the substrate layers 31 and 32. . The number of substrate layers 31 and 32 can be arbitrarily selected in consideration of necessary characteristics. The three-dimensional metamaterial 22 shown in FIG. 8 includes N substrate layers 31 and N−1 substrate layers 32.

FIG. 9 is a perspective view showing the structure of the substrate layer 31 of FIG. FIG. 10 is a cross-sectional view taken along line A-A ′ of FIG. The base material of the substrate layer 31 is formed of a dielectric substrate 41 made of a semi-cured resin such as epoxy or polyimide, and at least one surface of the dielectric substrate 41 (the surface on the + z side in FIGS. 9 and 10), A plurality of pattern conductors 42x extending along the x direction (corresponding to the bar-shaped conductors 3xa to 3xd in the x direction in FIG. 2) and a plurality of pattern conductors 42y extending in the y direction (the y direction in FIG. 2) Grid-like planar electrodes made of a plurality of rod-shaped conductors 3ya to 3yd). Further, at the positions (lattice points) where the pattern conductors 42x and 42y intersect, the through-hole conductors 43 (rod-shaped conductors 3za to 3zd in the z direction in FIG. 2) that penetrate the dielectric substrate 41 are respectively used by using a laser method or a punching method. Corresponding to the above) is formed.

FIG. 11 is a perspective view showing the structure of the substrate layer 32 of FIG. 12 is a cross-sectional view taken along line B-B ′ of FIG. The base material of the substrate layer 32 is formed of a dielectric substrate 51 made of a semi-cured resin such as epoxy or polyimide, and at least one surface of the dielectric substrate 51 (the surface on the + z side in FIGS. 11 and 12), A plurality of pattern conductors 52x extending along the x direction (corresponding to the bar-shaped conductors 3xa to 3xd in the x direction of FIG. 2) and a plurality of pattern conductors 52y extending along the y direction (the y direction of FIG. 2) Grid-like planar electrodes made of a plurality of rod-shaped conductors 3ya to 3yd). Furthermore, at the positions (lattice points) where the pattern conductors 52x and 52y intersect, the through-hole conductors 53 (rod-shaped conductors 3za to 3zd in the z direction in FIG. 2) that penetrate the dielectric substrate 51 are used by using a laser method or a punching method, respectively. Corresponding to the above) is formed. Further, in the regions surrounded by the pattern conductors 52x and 52y on the dielectric substrate 51, cavities 54 penetrating the dielectric substrate 51 are formed by using a laser method or a punching method, respectively. The dielectric resonators 1 are provided in the cavities 54, respectively.

A hole for providing a through-hole conductor 53 and a hole for a cavity 54 are formed in the dielectric substrate 51 of the substrate layer 32. The diameter of the hole for providing the through-hole conductor 53 is formed smaller than the diameter of the dielectric resonator 1, and the hole of the cavity 54 is formed larger than the diameter of the dielectric resonator 1. Accordingly, if a plurality of dielectric resonators 1 (which is sufficiently larger than the number of cavities 54 in a certain substrate layer 32) are arranged on the dielectric substrate 51 and the dielectric resonator 1 is swept with a squeegee, the dielectric resonators 1 can be loaded into the cavity 54. At this time, since the diameter of the through-hole conductor 53 is smaller than that of the cavity 54, the dielectric resonator 1 does not enter the through-hole conductor 53. When the diameter of the through-hole conductor 53 is larger than that of the cavity 54, the dielectric resonator 1 can be similarly formed by using a suction method device used when installing a solder ball on a circuit board in LSI mounting. Can be loaded into the cavity 54 only.

FIG. 13 is a cross-sectional view showing the structure of the three-dimensional metamaterial 22 including the substrate layers 31-1, 32-1, 31-2, 32-2, and 31-3 in FIG. After the dielectric resonator 1 is loaded in the cavity 54 of the substrate layers 32-1 and 32-2, the positions of the holes (dotted lines in FIG. 13) for providing the through- hole conductors 43 and 53 are aligned as shown in FIG. The substrate layers 31-1, 32-1, 31-2, 32-2, and 31-3 are stacked, and the whole is compressed in the z direction. Since the substrate layers 31 and 32 are in a semi-cured state as described above, they are integrated as a whole by compression. Next, a conductive resin material is inserted into a hole for providing the through- hole conductors 43 and 53 with a squeegee or the like, and heat is applied to the entire body at about 80 to 180 ° C. to finally cure. Further, after loading the dielectric resonator 1 into the cavity 54 of the substrate layers 32-1 and 32-2, the positions of the holes (dotted lines in FIG. 13) for providing the through- hole conductors 43 and 53 are aligned in FIG. As shown, the substrate layers 31-1, 32-1, 31-2, 32-2, and 31-3 are stacked, and then a conductive resin material is placed in a hole for providing the through- hole conductors 43 and 53 with a squeegee or the like. The whole may be inserted and heated and compressed in the z direction. According to this example of the manufacturing method, each dielectric resonator 1 includes the pattern conductors 42x and 42y and the through-hole conductors 43 of the substrate layer 31 and the substrate layer, similarly to being surrounded by the rod-shaped conductor 3 of FIG. Each of the dielectric resonators 1, the pattern conductors 42 x, 42 y, 52 x, 52 y and the through- hole conductors 43, 53 are surrounded by dielectric substrates 41, 51. Supported. Therefore, according to this example of the manufacturing method, as in the three-dimensional metamaterial 20 of FIG. 1, etc., a plurality of unit cells each including the dielectric resonator 1 are periodically arranged in three dimensions. A dimensional metamaterial 22 can be manufactured.

Pattern conductors may be formed on both surfaces of each of the dielectric substrates 41 and 51. In the above description, the through- hole conductors 43 and 53 are formed by inserting a conductive resin material into the holes for providing the through- hole conductors 43 and 53 with a squeegee or the like. Conductive columns may be formed in the holes for providing 43 and 53.

It was confirmed by numerical calculation that the three-dimensional metamaterial of the embodiment described above operates as an isotropic left-handed metamaterial in the three-dimensional direction. Hereinafter, the simulation results will be described with reference to FIGS.

FIG. 14 is a graph showing a dispersion curve of the three-dimensional metamaterial according to Example 1 of the present invention. In Example 1, a simulation was performed on the three-dimensional metamaterial 20 shown in FIGS. The parameters used were the radius R1 of the dielectric resonator 1 = 3.8 mm, the relative dielectric constant ε _DR = 110 of the dielectric resonator 1, the relative dielectric constant ε _r = 1 of the host medium, and the unit cell 10 (cubic shape). The side length L = Lx = Ly = Lz = 9.0 mm, and the side length L2 of the cross section (square) of the rod-shaped conductor 3 was 0.5 mm.

FIG. 17 is a diagram for explaining the representation of the wave number region related to the three-dimensional metamaterial according to the embodiment of the present invention. In the wave number domain (spatial frequency domain) obtained by Fourier transforming the spatial coordinates (x, y, z), each point is represented by a wave vector β = (βx, βy, βz) having components βx, βy, βz. . Furthermore, when the structure of the three-dimensional metamaterial has periodicity, the dispersion curve representing the propagation characteristics has periodicity in the wavenumber region, and the entire region is expressed using a partial region in the wavenumber region called the first Brillouin region. Is done. The origin (βx, βy, βz) = (0, 0, 0) of this wave number region is called “Γ” point. When the electromagnetic wave propagates in the x-axis direction in FIG. 1 and the like, the wave vector has only a βx component, and the boundary point (π / L, 0, 0) of the Brillouin region in that direction is represented as “X”. Similarly, when the electromagnetic wave propagates in the (x, y, z) = (1, 1, 0) direction in FIG. 1 and the like, the components of the wave vector have a relationship of βx = βy and βz = 0, and the direction The boundary point (π / L, π / L, 0) of the Brillouin region is expressed as “M”. Further, when the electromagnetic wave propagates in the (x, y, z) = (1, 1, 1) direction in FIG. 1 and the like, the components of the wave vector have a relationship of βx = βy = βz, and the Brillouin region in that direction The boundary points (π / L, π / L, π / L) are represented as “R”.

In FIG. 14, “Γ−X” indicates a dispersion curve when the propagation direction of the electromagnetic wave is from the origin to the point (1, 0, 0) (+ x direction) in the xyz coordinates shown in FIG. “−M” indicates a dispersion curve when going from the origin to the point (1, 1, 0), and “Γ-R” shows a dispersion curve when going from the origin to the point (1, 1, 1). When the propagation direction of the electromagnetic wave is “Γ-X”, the propagation characteristic does not depend on the polarization direction. When the propagation direction of the electromagnetic wave is “Γ-M”, the dispersion curve of horizontal polarization (polarization direction parallel to the xy plane) and the dispersion curve of vertical polarization (polarization direction perpendicular to the xy plane) are obtained. It was. When the propagation direction of the electromagnetic wave is “Γ-R”, the propagation characteristic does not depend on the polarization direction.

The dispersion curve in FIG. 14 was obtained from eigenvalue calculation. β represents the phase constant of the three-dimensional metamaterial (note that the phase constant β corresponds to the component of the wave vector β). FIG. 14 shows that the dispersion characteristic is isotropic near the Γ point. It was also found that the dispersion curve in the left-handed mode ranges from about 3.8 to 4.2 GHz and operates with a bandwidth of about 400 MHz.

FIG. 15 is a graph showing a dispersion curve of a three-dimensional metamaterial according to Example 2 of the present invention. In Example 2, the side length L of the unit cell 10 (cubic shape) L = 11.0 mm, the side length L2 of the cross-section (square) of the rod-shaped conductor 3 = 0.4 mm, and the relative permittivity ε _{r of the} host medium = 2.2 was used and the other parameters were the same as those used in Example 1. According to FIG. 15, the dispersion characteristic of the balanced right / left-handed composite metamaterial was obtained.

FIG. 16 is a graph showing a dispersion curve of a three-dimensional metamaterial according to Example 3 of the present invention. In Example 3, a simulation was performed on the three-dimensional metamaterial 21 shown in FIGS. 6 and 7. The parameters used were as follows: the radius R1 of the dielectric resonator 1 = 3.8 mm, the relative permittivity ε _DR = 110 of the dielectric resonator 1, the relative permittivity ε _r = 2.2 of the host medium, the unit cell 10 (cube The side length L of the shape) was 11.0 mm, and the cross-section (circular) diameter L4 of the rod-shaped conductor 6 was 0.5 mm. In the three-dimensional metamaterial 21 shown in FIG. 6, the dielectric resonator 1 cannot be arranged so as to be equidistant from all the rod-like conductors 6 as shown in FIG. 7. Since the resonance frequency varies depending on the difference in distance between the dielectric resonator 1 and the rod-shaped conductor 6, the frequency satisfying the phase constant β = 0 differs depending on the mode. FIG. 16 is a dispersion curve of “Γ-X”, and shows dispersion curves for two modes (polarization A and polarization B) having orthogonal polarization directions. According to FIG. 16, it can be seen that even if the bar conductors 6 in the x, y, and z directions do not intersect each other, the propagation characteristics do not change so much from the case where they intersect (FIG. 15).

The three-dimensional metamaterial of the present invention is configured not only to operate at a frequency on the order of several GHz as shown in Examples 1 to 3, but also to operate at a frequency of several MHz or a frequency of several THz. Is also possible.

18 is a perspective view showing a configuration of the three-dimensional metamaterial 10 (FIG. 2) according to the fourth embodiment of the present invention, and FIG. 19 is defined in FIG. 18 and the three- dimensional metamaterials 10 and 12 in FIG. It is a perspective view which shows a direction. FIG. 20 is a graph showing a dispersion curve of the three-dimensional metamaterial 10 of FIG. By appropriately adjusting the structural parameters, a balanced CRLH transmission characteristic without a band gap is obtained between the right-handed mode and the left-handed mode as shown in FIG. The left-handed transmission band shown is widened to about 250 MHz. The parameters used for the calculation are R1 = 3.8 mm, ε _DR = 110, L = 8.32 mm, t = 0.6 mm, and ε _r = 2.2. Of the two types of Γ-M curves, a broken line indicates a case where the polarization direction is in the z direction, and a solid line indicates a case where the polarization direction is parallel to the xy plane.

FIG. 21 is a perspective view showing the configuration of the three-dimensional metamaterial 12 (FIG. 5) according to the fifth embodiment of the present invention. FIG. 22 is a graph showing a dispersion curve of the three-dimensional metamaterial 12 of FIG. Each direction is defined as in FIG. As is apparent from FIG. 22, a balanced CRLH structure having no band gap between the right-handed mode and the left-handed mode can be designed by appropriately adjusting the structural parameters. The structural parameters used in the numerical calculation are Lc = 6 mm, ε _DR = 110, L = 8.45 mm, t = 0.8 mm, and ε _r = 2.2. Of the two types of Γ-M curves, the solid line indicates the case where the polarization direction is in the z direction, and the broken line indicates the case where the polarization direction is parallel to the xy plane.

FIG. 23 shows dispersion characteristics when the bar-shaped conductors 6 placed along three directions orthogonal to each other in the three-dimensional metamaterial according to Example 6 of the present invention are not in direct contact with each other and there is a minute gap. It is a graph. Here, it was assumed that there is a gap of 50 μm between the rod-shaped conductor 6 and the rod-shaped conductor 6. As can be seen from FIG. 23, the major difference from the case where no gap is given is that a new mode is generated by giving a gap, and the right-handed left / handed system mode that originally existed is coupled in a region having a large phase constant. It is a point that is shaped. However, in the vicinity of the frequency where the normalized phase constant βL / π is 0, the right-handed mode RH and the left-handed mode LH exist as usual (see 101 and 102 in FIG. 23), and show CRLH characteristics. It was. The structural parameters used in the numerical calculation are as follows: the radius R1 of the spherical dielectric resonator 1 = 3.8 mm, ε _DR = 110, L = 11.0 mm, L2 / 2 = 0.5 mm, ε _r = 2.2. It is.

As described in detail above, according to the three-dimensional metamaterial according to the present invention, it is possible to easily realize isotropic propagation characteristics that do not depend on the propagation direction and polarization direction of electromagnetic waves.

The three-dimensional metamaterial according to the present invention includes a microwave circuit, its components and antennas (a wide-angle beam scanning antenna, a minute antenna, etc.), a flat super lens, a negative refractive flat lens, a near-field imaging having sub-wavelength resolution, and cloaking. It can be applied to optical devices such as technology and its components.

As an application example of the present invention, there is a solution to radio interference by cloaking technology. In cities, radio waves are irregularly reflected due to the construction of high-rise buildings, and there are many problems that signal propagation errors of video equipment and communication equipment increase. By surrounding a target object (high-rise building) with a metamaterial and optimizing the transmission characteristics of the electromagnetic wave in it, the target object can be bypassed by the electromagnetic wave, diffuse reflection is reduced, and the radio wave environment is improved (radio wave cloaking) ).

Also, there is an example that uses a stopband, which is a transition region between the left-handed system and the right-handed system, and is used to block or attenuate electromagnetic waves. This effect is effective in application to a mobile phone equipped with a plurality of wireless systems and digital circuits under severe mounting conditions. For example, in current mobile phones, 800 MHz band, 1500 MHz band, and 2 GHz band are used for telephones, 1.57 GHz is used for GPS, 470 to 710 MHz band is used for one-segment TV, and electronic money is used. The 13.56 MHz band is used to support such applications, and a plurality of antennas corresponding to the respective frequency bands are arranged in a narrow space of the casing of the mobile phone. In a small housing, communication performance deteriorates due to electromagnetic interference between antennas. In addition, unnecessary radiation of a clock signal from a circuit in the vicinity of these antennas is received as noise by the antenna, which causes a reduction in communication quality. Under such severe mounting conditions, it is effective to use a metamaterial to control electromagnetic waves for each frequency and reduce mutual interference.

1, 4, 5 ... dielectric resonators,
2 ... Host medium,
3, 3xa to 3xd, 3ya to 3yd, 3za to 3zd, 6x, 6ya, 6yb, 6za to 6zd ... rod-shaped conductors,
10 to 13 unit cell,
20-22 ... 3D metamaterial,
31, 32, 31-1, 32-1, ..., 31-N ... substrate layer,
41, 51 ... dielectric substrate,
42x, 42y, 52x, 52y ... pattern conductors,
43, 53 ... through-hole conductors,
54 ... hollow.

Claims (13)

1. In a three-dimensional metamaterial including a plurality of unit cells periodically arranged in three dimensions,
   Each unit cell includes a dielectric resonator disposed in the center of the unit cell, a plurality of rod-shaped conductors disposed so as to surround the dielectric resonator, and the dielectric resonator and the rod-shaped conductor. A supporting host medium,
   In each unit cell, the plurality of rod-shaped conductors include at least one first rod-shaped conductor arranged in a first direction and at least one arranged in a second direction different from the first direction. A second bar-shaped conductor, and at least one third bar-shaped conductor disposed in a third direction having a predetermined angle with respect to a surface stretched by the first and second directions,
   In the three-dimensional metamaterial configured by periodically arranging the plurality of unit cells three-dimensionally, the first rod-shaped conductors are arranged in parallel and periodically with each other, and the second rod-shaped conductors Are arranged in parallel and periodically with each other, and the third rod-shaped conductors are arranged in parallel and periodically with each other in a three-dimensional metamaterial,
   The host medium includes a first substrate having a cavity and a second substrate sandwiching the first substrate, and the first substrate or / and the second substrate include the first rod-shaped conductor or / And a second rod-shaped conductor is formed,
   The dielectric resonator is disposed in the cavity of the first substrate and formed in a unit form sandwiched between the second substrates, or formed in a state where two or more layers of the unit form are laminated. A three-dimensional metamaterial comprising the third rod-shaped conductor.
2. The shape and dimensions of the unit cell and the dielectric resonator so that the effective dielectric constant and effective permeability of the three-dimensional metamaterial are both negative with respect to an electromagnetic wave having a predetermined frequency incident on the three-dimensional metamaterial. The shape, size, and relative dielectric constant, the thickness of the rod-shaped conductor, the interval at which the first, second, and third rod-shaped conductors are periodically arranged, and the relative dielectric constant of the host medium are set. The three-dimensional metamaterial according to claim 1, wherein
3. Each unit cell includes a waveguide formed by the plurality of rod-shaped conductors, each unit cell has a predetermined cutoff frequency, and each unit cell is incident on the three-dimensional metamaterial. The effective dielectric constant of the three-dimensional metamaterial is configured to be negative with respect to electromagnetic waves having a frequency lower than the off-frequency,
   The dielectric resonator is excited by an electromagnetic wave having a predetermined frequency incident on the dielectric resonator in a resonance form having an electromagnetic field distribution similar to a magnetic dipole moment, and the three-dimensional metamaterial is effective against the electromagnetic wave. The three-dimensional metamaterial according to claim 2, wherein the three-dimensional metamaterial is configured to have a negative magnetic permeability.
4. The three-dimensional metamaterial according to any one of claims 1 to 3, wherein each unit cell is a cube, and the first, second, and third directions are orthogonal to each other.
5. The three-dimensional metamaterial according to any one of claims 1 to 4, wherein the dielectric resonator has a spherical shape.
6. The three-dimensional metamaterial according to any one of claims 1 to 4, wherein the dielectric resonator has a cylindrical shape or a polygonal column shape.
7. The three-dimensional metamaterial according to any one of claims 1 to 4, wherein the dielectric resonator has a cubic shape, a polyhedral shape, or a rhombohedral shape.
8. The three-dimensional metamaterial according to any one of claims 1 to 7, wherein the rod-shaped conductor has a rectangular cross-sectional shape.
9. The three-dimensional metamaterial according to any one of claims 1 to 7, wherein the rod-shaped conductor has a circular cross-sectional shape.
10. The three-dimensional metamaterial according to any one of claims 1 to 9, wherein the first, second, and third rod-shaped conductors intersect each other.
11. 10. The 3 according to claim 1, wherein at least one of the first, second, and third rod-shaped conductors does not intersect with another rod-shaped conductor. Dimensional metamaterial.
12. The three-dimensional metamaterial according to any one of claims 1 to 9, wherein the first, second, and third rod-shaped conductors are electrically connected to each other.
13. 10. At least one of the first, second, and third rod-shaped conductors is not electrically connected to other rod-shaped conductors, according to any one of claims 1 to 9 The described three-dimensional metamaterial.

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