JP6379009B2 - Laminated metamaterial substrate - Google Patents

Description

  The present invention relates to a band elimination substrate technique for obtaining a wide elimination band by periodically arranging resonant elements having the same shape.

  A metamaterial is a structure that is formed by periodically arranging fine structural units that are sufficiently small with respect to the wavelength. Its dielectric constant and permeability can be changed by designing the fine structural units and the periodic length. Applications to lenses, cloaking technology, antenna miniaturization, etc. are expected. An example of a microstructure that makes up a metamaterial is a resonant element, and a metamaterial substrate with two-dimensionally arranged resonant elements has the characteristic of minimizing the transmittance of electromagnetic waves at the resonant frequency. Therefore, it can be applied to a band elimination substrate (see Non-Patent Document 1).

N. R. Han, et. Al., Optics Express, “Broadband multi-layer terahertz metamaterials fabrication and characterization on flexible substrates”, vol. 19, pp. 6990-6997, (2011).

  A metamaterial substrate in which resonant elements are two-dimensionally arranged has band elimination characteristics as described above. However, since the resonance frequency is one point, the elimination band is narrow.

  Therefore, Non-Patent Document 1 proposes a method of widening the removal band by laminating metamaterial substrates in which resonant elements having different shapes are two-dimensionally arranged.

  However, since this method requires a photomask corresponding to the shape type of the resonant element, there is a problem that the manufacturing cost increases, such as a photomask manufacturing process and a replacement process.

  The present invention has been made in view of the above problems, and an object of the present invention is to provide a technique for obtaining a wide removal band by using a resonance element having the same shape as a band removal substrate using a metamaterial substrate. There is.

In order to solve the above-described problems, the present invention provides a laminated metamaterial substrate in which two layers are laminated, and one of the two layers is a substrate having a resonance element having the same shape formed on the substrate. The other layer different from the one layer is formed on the substrate or another substrate with an interlayer distance between the one layer and the same shape as the resonance element. Are regularly arranged in the vertical direction and the horizontal direction of the substrate, and the transmittance of electromagnetic waves incident on the laminated metamaterial substrate is between the resonant element of the one layer and the resonant element of the other layer. The resonance elements of all the stacked layers are configured to have a minimum value at two resonance frequencies, a resonance frequency in a resonating antisymmetric mode and a resonance frequency in a symmetric mode. Have the same dimensions And wherein the door.

  According to the present invention, since the transmittance of the incident electromagnetic wave exhibits a minimum value at two or more resonance frequencies, a wide removal band can be obtained even when the resonance elements having the same shape are used.

It is a figure which shows the utilization form of the lamination | stacking metamaterial board | substrate 1 which concerns on this Embodiment. 2 is an exploded view of a laminated metamaterial substrate 1. FIG. It is a top view of the board | substrate 11 (12) which comprises the lamination | stacking metamaterial board | substrate 1. FIG. 3 is a plan view of a resonant element 2. FIG. 3 is a circuit diagram of a simplified equivalent circuit of a resonant element 2. FIG. It is a figure which shows the frequency characteristic of the transmittance | permeability of the electromagnetic waves which inject into the metamaterial board | substrate of only one layer as a comparative example. It is a figure which shows the frequency characteristic of the transmittance | permeability of the electromagnetic wave W which injects into the lamination | stacking metamaterial board | substrate 1. FIG. Anti symmetric mode of the layered meta-material substrate 1 (omega _-) and is a diagram showing a circulating current in the symmetric mode (omega _+). It is a figure which shows the frequency characteristic of the transmittance | permeability at the time of changing the interlayer distance t. It is a figure which shows two resonance frequencies at the time of changing the gap g and the ring size r. It is a figure which shows the frequency characteristic of the transmittance | permeability at the time of changing the gap g and the ring size r.

  Hereinafter, embodiments of the present invention will be described with reference to the drawings.

  FIG. 1 is a diagram showing a usage pattern of the laminated metamaterial substrate 1 according to the present embodiment. FIG. 2 is an exploded view of the laminated metamaterial substrate 1. FIG. 3 is a plan view of the substrate 11 (12) constituting the laminated metamaterial substrate 1.

  The laminated metamaterial substrate 1 includes substrates 11 and 12, and the resonant elements 2 having the same shape are periodically formed in two dimensions on the substrates 11 and 12.

  When the resonant element 2 of the substrate 11 is referred to as a layer, and the resonant element 2 of the substrate 12 is also referred to as a layer, the stacked metamaterial substrate 1 is a stacked metamaterial substrate in which two layers are stacked, A plurality of resonance elements 2 having the same shape formed on one substrate 11 are provided, and the other layer is formed on another substrate 12 with an interlayer distance t between one layer and a plurality of resonance elements 2 having the same shape. Is.

  For example, the surface (front surface) having the metal pattern of the substrate 12 is in contact with the surface (back surface) having no metal pattern in the substrate 11. In this case, the interlayer distance t is equal to the substrate thickness, for example, 150 μm.

  The laminated metamaterial substrate 1 is a band removal substrate, and each layer (each substrate) is also referred to as a metamaterial substrate.

  The resonant elements 2 are formed by a metal pattern on the substrate, and are arranged regularly (for example, at equal intervals) in the vertical and horizontal directions of the substrate. The material of the metal pattern is, for example, copper, but other materials may be used. Since the resonant elements 2 have the same shape, two identical substrates may be manufactured and used as the substrates 11 and 12. Therefore, the photomask of the substrate can be shared, and the manufacturing process and the like can be reduced.

  In addition, you may make it the surfaces (back surfaces) without a metal pattern contact. Alternatively, a metal pattern may be provided on the front and back of the substrate 11 to make the substrate 12 unnecessary.

  k is an axis indicating the traveling direction of the electromagnetic wave W, H is an axis indicating the direction of the magnetic field change of the electromagnetic wave W, E is an axis indicating the direction of the electric field change of the electromagnetic wave W, and the same applies to other drawings.

  The laminated metamaterial substrate 1 is configured to reduce the transmittance only in a partial band (referred to as a removal band) of the entire frequency band of the incident electromagnetic wave W.

  FIG. 4 is a plan view of the resonant element 2. FIG. 5 is a circuit diagram of an equivalent circuit of the resonant element 2.

  The resonant element 2 has, for example, a ring-shaped metal pattern, and a gap g is formed at the center. The laminated metamaterial substrate 1 is coupled to the electromagnetic wave W by the gap g functioning as a capacitance C and the ring-shaped part functioning as an inductance L.

  When the gap g is wide, the capacitance C is small, and the resonance frequency shifts in the direction of high frequency.

  If the ring size r, which is the length of one side of the ring-shaped portion, is large, the inductance L is large and the resonance frequency is shifted in the direction of low frequency.

  When the arrangement direction of the resonance elements 2 and the E-axis direction (direction of electric field change) are parallel, a circular current flows through the resonance element 2 due to the asymmetry in the pattern of the resonance element 2, and resonance occurs at the resonance frequency. Generated and has removal characteristics.

  As described above, the resonance element 2 may have another shape as long as it has a ring shape, a gap g is formed, and resonance occurs due to a circulating current flowing by the incident electromagnetic wave W.

  FIG. 6 is a diagram illustrating frequency characteristics of the transmittance of electromagnetic waves incident on a metamaterial substrate having only one layer as a comparative example.

  Here, the gap g is 200 μm, the ring size r is 700 μm, the size of the unit structure including the resonant element 2 and the base portion serving as the base (hereinafter referred to as the unit structure size) is 800 μm, and the thickness of the metal pattern The thickness was 18 μm. The relative dielectric constant of the substrate was 2.2. The arrangement direction of the resonance elements 2 and the E-axis direction (direction of electric field change) are parallel, and the substrate surface and the k-axis direction (traveling direction of electromagnetic waves) are perpendicular. Under such conditions, the transmittance of electromagnetic waves was obtained by simulation. For simplification of calculation, it is assumed that the metal pattern is inside the dielectric substrate having a relative dielectric constant of 2.2, and the analysis space at the time of simulation has a relative dielectric constant of 2.2.

  Under this condition, the transmittance exhibits one minimum value at about 70 GHz (resonance frequency). That is, since the frequency at which resonance occurs is one, the removal band is a narrow band.

FIG. 7 is a diagram illustrating the frequency characteristics of the transmittance of the electromagnetic wave W incident on the laminated metamaterial substrate 1. FIG. 8 is a diagram illustrating the circulating currents in the antisymmetric mode (ω ₋ ) and the symmetric mode (ω ₊ ) in the laminated metamaterial substrate 1.

  In FIG. 7, the solid line is for the laminated metamaterial substrate 1, and the broken line is for only one layer shown in FIG.

  Also in the laminated metamaterial substrate 1, the gap g was 200 μm, the ring size r was 700 μm, the unit structure size was 800 μm, and the thickness of the metal pattern was 18 μm. The relative dielectric constant of the substrate was 2.2. The interlayer distance t was 150 μm. Under such conditions, the transmittance of electromagnetic waves was obtained by simulation. For simplification of calculation, it is assumed that the metal pattern is inside the dielectric substrate having a relative dielectric constant of 2.2, and the analysis space at the time of simulation has a relative dielectric constant of 2.2.

Under this condition, the transmittance exhibits a minimum value at two frequencies, the resonance frequency of resonance in the antisymmetric mode (ω ₋ ) and the resonance frequency of resonance in the symmetric mode (ω ₊ ). The band also has a low transmittance due to the coupling of the two resonance modes. In other words, the removal band is wider than in the case of only one layer.

  When the resonant elements 2 of the substrates 11 and 12 are mutually coupled, a circulating current flows through each resonant element 2.

As shown in FIG. 8A, in the antisymmetric mode (ω ₋ ), the direction of the circulating current flowing through the resonant element 2 of the substrate 11 and the direction of the circulating current flowing through the resonant element 2 of the substrate 12 are different from each other. Therefore, repulsive force is generated between the substrates.

As shown in FIG. 8B, in the symmetric mode (ω ₊ ), the direction of the circulating current flowing through the resonant element 2 of the substrate 11 is the same as the direction of the circulating current flowing through the resonant element 2 of the substrate 12. Therefore, attractive force is generated between the substrates.

Due to the generation of repulsive force and attractive force, an energy difference is formed between the antisymmetric mode (ω ₋ ) and the symmetric mode (ω ₊ ). The difference in resonance frequency in FIG. 7 is considered to be due to this energy difference.

  FIG. 9 is a diagram showing the frequency characteristics of transmittance when the interlayer distance t is changed.

  The figure shows each transmittance when the interlayer distance t is 50 μm, 250 μm, 500 μm, and 1000 μm, and the transmittance when there is only one layer. The gap g was 200 μm, the ring size r was 700 μm, the unit structure size was 800 μm, and the thickness of the metal pattern was 18 μm. The relative dielectric constant of the substrate was 2.2. For simplification of calculation, it is assumed that the metal pattern is inside the dielectric substrate having a relative dielectric constant of 2.2, and the analysis space at the time of simulation has a relative dielectric constant of 2.2.

  The transmittance when the interlayer distance t is 1000 μm exhibits a minimum value at two resonance frequencies, but the frequency difference is small.

  However, when the interlayer distance t is shorter than the unit structure size, the frequency difference becomes wider as the interlayer distance t becomes shorter. This is because the energy difference is increased.

  FIG. 10 is a diagram showing two resonance frequencies when the gap g and the ring size r are changed.

The interlayer distance t was 150 μm. The spacing between the resonant frequency in the antisymmetric mode (ω ₋ ) and the resonant frequency in the symmetric mode (ω ₊ ) corresponds to the bandwidth of the rejection band, which changes the ring size r. The change is greater when the gap g is changed than when the gap is changed.

On the other hand, the frequency at the midpoint between the resonance frequency in the antisymmetric mode (ω ₋ ) and the resonance frequency in the symmetric mode (ω ₊ ), that is, the center frequency of the removal band, which changes the gap g When the ring size r is changed, the change is greater than when the ring size is changed.

  Therefore, the ring size r may be set according to a desired center frequency (frequency at the center of the removal band), and the gap g may be set according to the width of the desired removal band. That is, even if the shape of the resonant element 2 is the same, the laminated metamaterial substrate 1 having various removal bands can be obtained by changing the gap g and the ring size r.

  FIG. 11 is a diagram showing the frequency characteristics of transmittance when the gap g and the ring size r are changed.

  The interlayer distance t is common at 150 μm, but by changing the gap g and the ring size r, various stacked metamaterial substrates 1 having different removal bands and different center frequencies can be obtained.

(Modification)
In the above embodiment, the number of layers is two, but the number of layers may be three or more. By increasing the number of layers, the number of resonance modes increases and the number of resonance frequencies can be increased. Thereby, a removal zone | band can be expanded compared with the case where the number of layers is two. Further, the transmittance can be further lowered in the band where the removal band is overlapped.

  Further, when the number of layers is increased, the interlayer distance t becomes a plurality, so that a plurality of interlayer distances t may have different values.

  Further, the arrangement of the layers of the laminated metamaterial substrate may be manufactured by shifting each other in the in-plane direction in which the resonant elements are arranged. For example, when one of the two layers of the laminated metamaterial substrate is laminated while being shifted in the H direction in FIG. 1, the frequency difference between the two resonance modes increases as the deviation increases.

  Further, by providing a capacitive element (component) in the gap g portion of the resonance element 2, the capacitance C of the gap g portion can be changed even if the gap g portion has the same shape. By making the capacitance of the capacitive element variable, the capacitance of the gap g can be changed even after the laminated metamaterial substrate 1 is manufactured, so that the removal band can be changed even after the manufacturing.

  Further, by providing an inductance element (component) in the ring-shaped part, the inductance L of the ring-shaped part can be changed even if the ring shape is the same. By making the inductance of the inductance element variable, the inductance of the ring-shaped portion can be changed even after the laminated metamaterial substrate 1 is manufactured, so that the removal band can be changed even after the manufacture.

  Also, by changing parameters such as capacitance C and inductance L, the frequency band that is the difference between the highest resonance frequency and the lowest resonance frequency or the center frequency that is the intermediate frequency between the highest resonance frequency and the lowest resonance frequency is changed. Can be made.

1 Laminated Metamaterial Substrate 2 Resonant Elements 11 and 12 Substrate (Metamaterial Substrate)
g Gap r Ring size t Interlayer distance W Electromagnetic wave

Claims (4)

A laminated metamaterial substrate in which two layers are laminated,
In one of the two layers, the same-shaped resonant elements formed on the substrate are regularly arranged in the vertical and horizontal directions of the substrate,
The other layer, which is different from the one layer, is formed on the substrate or another substrate with an interlayer distance between the one layer, and a resonant element having the same shape as the resonant element is arranged in the vertical and horizontal directions of the substrate. Placed
The resonance frequency in the antisymmetric mode and the resonance frequency in the symmetric mode in which the transmittance of the electromagnetic wave incident on the laminated metamaterial substrate resonates between the resonance element of the one layer and the resonance element of the other layer. Are configured to exhibit local minimum values at two resonance frequencies of
The laminated metamaterial substrate, wherein the resonant elements of all the laminated layers have the same shape and the same dimensions. Comprising three or more layers,
It is configured to exhibit a minimum value at a number of resonance frequencies equal to the number of resonance modes obtained by one or more antisymmetric modes and one or more symmetrical modes generated between the resonance elements of each layer. The laminated metamaterial substrate according to claim 1. The laminated metamaterial substrate according to claim 1, wherein at least one of a capacitive element and an inductance element is provided in the resonant element. At least one of the capacitive element and the inductance element is a variable element, and by changing a parameter, a frequency band that is a difference between the highest resonance frequency and the lowest resonance frequency or an intermediate between the highest resonance frequency and the lowest resonance frequency. 4. The laminated metamaterial substrate according to claim 3, wherein a center frequency that is a frequency of the frequency is changed.

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