Radio wave transmission structure

By adjusting the phase difference between electromagnetic waves in a dual-transmissivity structure, the radio wave intensity in the far field is enhanced, addressing the issue of phase cancellation and maintaining communication quality.

WO2025142892A1PCT designated stage expired Publication Date: 2025-07-03SEKISUI CHEMICAL CO LTD
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Patent Information

Application Number
PCT/JP2024/045591
Authority / Receiving Office
WO · WO
Patent Type
Applications
Current Assignee / Owner
Priority Date
2023-12-28
Filing Date
2024-12-24
Publication Date
2025-07-03

AI Technical Summary

Technical Problem

Existing radio wave transmission structures face a deterioration in communication state due to phase cancellation between improved and unimproved parts, leading to reduced radio wave intensity in the far field.

Method used

An electromagnetic wave transmission structure with both difficult-to-transmit and easy-to-transmit portions, where the phase difference between the first and second electromagnetic waves is adjusted to satisfy specific formulas, enhancing radio wave intensity in the far field.

Benefits of technology

The proposed structure improves radio wave intensity in the far field by suppressing phase cancellation, thereby maintaining or enhancing communication quality.

✦ Generated by Eureka AI based on patent content.

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Abstract

The present invention improves radio wave intensity in the far field of a radio wave transmission structure. A radio wave transmission structure 1 has both a hardly transmitting portion 1a through which radio waves are hardly transmitted and an easily transmitting portion 1b through which radio waves are transmitted more easily than the hardly transmitting portion 1a. A phase difference α (rad) between first radio waves transmitted through the easily transmitting portion 1b and second radio waves transmitted through the hardly transmitting portion 1a satisfies the following formula (1) or (2). (1): 2πN - ωt < α < 2πN - ωt + π (2): βsin(ωt + α) + sin(ωt) > 1 where N is integer; ω is angular velocity (an angular velocity that is based on a frequency and that is a numerical value obtained by multiplying 2π by the frequency); t is the time elapsed from when the first radio waves and the second radio waves are made incident on the radio wave transmission structure to when the first radio waves and the second radio waves are emitted therefrom; and β is the ratio of the maximum electric field intensity of the second radio waves to the maximum electric field intensity of the first radio waves
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Description

Radio wave transparent structure

[0001] The present invention relates to a radio wave transparent structure having both a poorly transmitting portion that does not easily transmit radio waves and an easily transmitting portion that allows radio waves to easily transmit.

[0002] Like light, radio waves used in communications are known to refract and scatter at interfaces with different permittivity and permeability. In communications, all objects, such as concrete walls, display panels, and glass, have different permittivity and permeability from air, so the presence of an object (structure) in the path of the radio waves can cause poor communication.

[0003] In response to this, a technique for increasing the radio wave transmittance of a structure is disclosed, for example, in Patent Document 1. In Patent Document 1, a dielectric structure is bonded to the structure and the dielectric constant of the dielectric structure is adjusted to increase the radio wave transmittance of the structure.

[0004] Special Publication No. 2022-511466

[0005] Hisatake. et al., "Asynchronous electric field visualization using an integrated multichannel electro-optic probe", scientific reports, (2020)10:16479, Internet <URL: https: / / doi.org / 10.1038 / s41598-020-73538-7>

[0006] However, the technique of Patent Document 1 has a problem in that when the radio wave transmittance of a part of the structure is improved, the communication state becomes worse the further away from the improved part.

[0007] The present invention has been made in view of the above problems, and an object of the present invention is to improve the radio wave intensity in the far field of a radio wave transparent structure.

[0008] After extensive research, the inventors of the present application have discovered that the cause of the above problem is that radio waves (first radio waves) that have passed through the easy-to-permeate portions of the structure where radio wave permeability has been improved and radio waves (second radio waves) that have passed through the other difficult-to-permeate portions cancel each other out due to a phase difference between the two. Based on this principle, the inventors have discovered that by adjusting the phase difference between the first radio waves and the second radio waves, it is possible to suppress the phenomenon in which the first radio waves are canceled out by the second radio waves, and improve the radio wave intensity in the far field of the structure.

[0009] In order to solve the above problems, the present invention includes the following aspects. Item 1: A radio wave transparent structure having both a difficult-to-transmit portion that does not easily transmit radio waves and an easy-to-transmit portion that transmits radio waves more easily than the difficult-to-transmit portion, wherein a phase difference α (rad) between a first radio wave that has transmitted through the easy-to-transmit portion and a second radio wave that has transmitted through the difficult-to-transmit portion satisfies the following formula (1) or (2): 2πN-ωt<α<2πN-ωt+π ... (1) β sin(ωt+α)+sin(ωt)>1 ... (2) N: integer ω: angular velocity (angular velocity due to frequency, calculated by multiplying 2π by the frequency) t: time elapsed from when the first radio wave and the second radio wave enter the radio wave transparent structure until they exit the structure β: ratio of the maximum electric field strength of the second radio wave to the maximum electric field strength of the first radio wave Item 2: The radio wave transparent structure according to item 1, wherein the phase difference satisfies formula (1). Item 3: The radio wave transparent structure according to Item 1, wherein the phase difference satisfies the formula (2).

[0010] According to the present invention, it is possible to improve the radio wave intensity in the far field of a radio wave transparent structure.

[0011] (A) is a plan view of the radio wave transparent structure according to the present embodiment, and (B) is a cross-sectional view taken along the line A-A in FIG. 1(A). It is a schematic cross-sectional view of the structure. (A) to (H) are graphs showing the phase difference α (°) and intensity ratio β that satisfy equation (2) for different ωt. (A) to (E) are graphs showing the phase difference α (°) and θ (= ωt) that satisfy equation (2) for different intensity ratios β. (A) and (B) are a schematic front view and a schematic cross-sectional view of the easily permeable portion, respectively.

[0012] Hereinafter, an embodiment of the present invention will be described with reference to the accompanying drawings. Note that the present invention is not limited to the following embodiment, and various modifications are possible without departing from the spirit of the present invention.

[0013] [Structure] Fig. 1(A) is a plan view of a radio wave transparent structure (hereinafter referred to as structure) 1 according to this embodiment, and Fig. 1(B) is a cross-sectional view taken along line A-A in Fig. 1(A). The shape of the structure 1 is rectangular in plan view, but the shape and size of the structure 1 are not particularly limited.

[0014] As shown in Figure 1 (A), the structure 1 has both a difficult-to-permeate region 1a that does not easily transmit radio waves and an easy-to-permeate region 1b that allows radio waves to pass through more easily than the difficult-to-permeate region 1a. In other words, from the perspective of radio wave permeability, the structure 1 is divided into the difficult-to-permeate region 1a and the easy-to-permeate region 1b. Note that the difficult-to-permeate region 1a and the easy-to-permeate region 1b are located on the same plane, but they do not have to be located on the same plane.

[0015] As shown in FIG. 1B , the structure 1 includes a substrate 11 and a metamaterial structure 12 .

[0016] The substrate 11 is an object that divides a building, such as a concrete wall, glass, etc. The thickness and size of the substrate 11 are not particularly limited.

[0017] The metamaterial structures 12 are members that increase the radio wave transmittance of the structure 1, and a plurality of them are provided at intervals on the substrate 11. As a result, the portions of the structure 1 where the metamaterial structures 12 are provided become the easy-to-transmit portions 1b, and the portions where the metamaterial structures 12 are not provided become the difficult-to-transmit portions 1a.

[0018] [Intensity of transmitted radio waves] The intensity of transmitted radio waves through the structure 1 will be described.

[0019] 2 is a schematic cross-sectional view of the structure 1. The first radio wave R1 incident on the difficult-to-penetrate region 1a of the structure 1 is attenuated and passes through the difficult-to-penetrate region 1a. On the other hand, the second radio wave R2 incident on the easy-to-penetrate region 1b of the structure 1 passes through the difficult-to-penetrate region 1a while being repeatedly scattered and reflected inside the metamaterial structure 12 and the substrate 11. In other words, the second radio wave R2 is a combination of scattered radio waves R21, R22, etc. The second radio wave R2 that passes through the easy-to-penetrate region 1b is attenuated less than the first radio wave R1 that passes through the difficult-to-penetrate region 1a.

[0020] Here, because radio waves undergo a phase shift when reflected at an interface with different dielectric constants and magnetic permeabilities, the phase of the first radio wave R1 and the phase of the second radio wave R2 generally differ. The inventors of the present application have discovered that the phase difference between the first radio wave R1 and the second radio wave R2 causes them to cancel each other out, and that the closer the phase difference is to 180°, the greater the amount of cancellation between the first radio wave R1 and the second radio wave R2. Prior art does not take this phenomenon into consideration and therefore does not adjust the phase difference. As a result, even if the intensity of the transmitted second radio wave R2 is high near the easy-to-transmit portion 1b of the structure 1, the first radio wave R1 and the second radio wave R2 may cancel each other out in the far field where they mix, resulting in poor communication conditions.

[0021] Therefore, in this embodiment, the phase difference α (rad) between the first radio wave R1 and the second radio wave R2 is adjusted to suppress the phenomenon in which the first radio wave R1 is canceled out by the second radio wave R2, thereby improving the radio wave strength in the far field of the structure. Specifically, the phase difference α satisfies the following formula (1) or (2): 2πN-ωt<α<2πN-ωt+π (1) βsin(ωt+α)+sin(ωt)>1 (2) N: integer ω: angular velocity (angular velocity caused by frequency, calculated by multiplying 2π by the frequency) t: time elapsed from when the first radio wave R1 and the second radio wave R2 enter the structure 1 until they leave the structure 1 β: ratio of the maximum electric field strength of the second radio wave R2 to the maximum electric field strength of the first radio wave R1 (hereinafter referred to as the intensity ratio)

[0022] The process of deriving formula (1) will be described below. The maximum electric field strength of the first radio wave R1 is Esmax, the maximum electric field strength of the second radio wave R2 is Etmax, the electric field strength reaching the far field is γ, the frequency of the first radio wave R1 and the second radio wave R2 is f (Hz), and the time that elapses from when the first radio wave R1 and the second radio wave R2 enter the structure 1 until they leave is t (s). The first radio wave R1 and the second radio wave R2 have the same frequency and are sine waves with the same waveform, so γ = Esmax sin(ωt + α) + Etmax sin(ωt) (3).

[0023] Since β=Esmax / Etmax, Esmax=βEsmax is obtained, and when this is substituted into the equation (3), the following is obtained: γ=βEtmax·sin(ωt+α)+Etmax·sin(ωt) (4).

[0024] If the electric field strength reaching the far field exceeds the electric field strength of the second radio wave R2 regardless of time t, the radio wave strength in the far field is improved compared to when the structure 1 is not provided, thereby solving the problem of the present invention. In this case, γ>Etmax·sin(ωt), and substituting this into equation (4) gives: βEtmax·sin(ωt+α)+Etmax·sin(ωt)>Etmax·sin(ωt) ... (5) Rearranging equation (5) gives: βEtmax·sin(ωt+α)>0. Here, since β>0 and Etmax>0, sin(ωt+α)>0 (6) holds, and when equation (6) holds for all t, the range of the phase difference α (rad) is 2πN-ωt<α<2πN-ωt+π (1), and equation (1) is derived. That is, regardless of the thickness of the structure 1 and the frequencies of the radio waves R1 and R2, the difference between the maximum and minimum values ​​of α is always π.

[0025] The process of deriving equation (2) will be explained below. If the electric field strength reaching the far field exceeds the maximum electric field strength of the second radio wave R2, the radio wave strength in the far field will be improved compared to when the structure 1 is not provided, thereby solving the problem of the present invention. In this case, since γ>Etmax, from equation (4), we obtain βEtmax·sin(ωt+α)+Etmax·sin(ωt)>Etmax ... (5) Dividing both sides of equation (5) by Etmax gives βsin(ωt+α)+sin(ωt)>1 ... (2) and equation (2) is derived.

[0026] As described above, if the phase difference α (rad) between the first radio wave R1 and the second radio wave R2 is adjusted to satisfy the following formula (1) or (2), the radio wave intensity in the far field is improved compared to the case where the structure 1 is not provided, thereby solving the problem of the present invention. 2πN-ωt<α<2πN-ωt+π (1) βsin(ωt+α)+sin(ωt)>1 (2)

[0027] Since ωt in formulas (1) and (2) is determined by the dielectric constant and thickness of the structure 1, the phase difference α and the intensity ratio β can be adjusted depending on the value of ωt. Figures 3(A) to 3(H) are graphs showing the phase difference α (°) and the intensity ratio β that satisfy formula (2) for different ωt. In each graph, the shaded area satisfies formula (2). Note that the pattern of the shaded area in each graph is constant over the entire range of α (-180° to 180°).

[0028] 4A to 4E are graphs showing the phase difference α (°) and θ (=ωt) that satisfy Equation (2) for different intensity ratios β. In each graph, the shaded area satisfies Equation (2). The larger the intensity ratio β, the larger the region of α and θ that satisfies Equation (2). In particular, when the intensity ratio β is 5 or greater, the region of α and θ that satisfies Equation (2) becomes approximately equal to the other regions (the ratio of these regions converges to approximately 1). Therefore, it is preferable to adjust the size and spacing of the easy-to-permeate regions 1b (metamaterial structure 12) so that the intensity ratio β is 5 or greater. The phase difference α (°) can be measured using a commercially available probe antenna and a VNA (vector network analyzer). Furthermore, according to Non-Patent Document 1, the electric field intensity and phase can be measured at any location, so the intensity ratio β can also be derived.

[0029] [Easy-to-Permeate Region] First, the structure of the easy-to-permeate region 1b provided with the metamaterial structure 12 will be described. Figures 5(A) and 5(B) are a schematic front view and a schematic cross-sectional view, respectively, of the easy-to-permeate region 1b. The easy-to-permeate region 1b is configured by laminating a substrate 11, a plurality of metal patterns 3 provided on the substrate 11, and a protective film 14 covering the plurality of metal patterns 3. The protective film 14 is adhered to the substrate 11 via an adhesive layer 13. The metal patterns 3, the adhesive layer 13, and the protective film 14 constitute the metamaterial structure 12.

[0030] 5A, each metal pattern 3 includes a split ring resonator 4 and an enclosing portion 5 that surrounds the split ring resonator 4. The split ring resonator 4 and the enclosing portion 5 are made of a conductor. The enclosing portion 5 is separated from the split ring resonator 4 and is not in contact with the split ring resonator 4.

[0031] With this configuration, the easily permeable portion 1b can have resonance points for radio waves in multiple frequency bands, which is advantageous in that it is possible to have resonance points for radio waves in multiple frequency bands without stacking multiple structures 1, allowing radio waves in multiple frequency bands to pass through a single structure 1, and there are fewer restrictions on the installation location.

[0032] For example, radio waves transmitted from a transmitter are incident on the structure 1. The transmitter is a communication device having a transmitting antenna capable of outputting a radio signal using radio waves as a medium. Examples of transmitters include a fixed base station, a mobile base station, a radio wave transmitter, a wireless terminal, and a local 5G base station.

[0033] The radio waves that have passed through the structure 1 are transmitted to, for example, a receiver inside the building. The receiver is a communication device with a receiving antenna. Examples of receivers include smartphones, mobile phones, tablet devices, laptop computers, portable game consoles, repeaters, radios, and televisions.

[0034] The radio waves that can be transmitted through the structure 1 according to this embodiment are, for example, radio waves in a specific frequency band in which the frequency of the incident wave belongs to any of the ranges of 3 GHz to 5 GHz, 25 GHz to 30 GHz, and 100 GHz to 300 GHz. Among these, it is preferable that the transmission efficiency is set high in the 5 GHz frequency band (3 GHz to 5 GHz, 25 GHz to 30 GHz).

[0035] (Metal Pattern 3) The multiple metal patterns 3 are made of conductors. The multiple metal patterns 3 are formed on the substrate 11. All of the multiple metal patterns 3 are formed in the same shape and have a periodic structure. In other words, one metal pattern 3 represents the smallest unit in the metasurface.

[0036] Examples of methods for forming the metal pattern 3 on the substrate 11 include a method of laminating a thin film, in which the metal pattern 3 is embedded in a thin-film dielectric, on the substrate 11, and a method of forming the metal pattern 3 on the substrate 11 without using a dielectric. Examples of methods for forming the metal pattern 3 on the substrate 11 include the following.

[0037] Photoresist is applied to the substrate 11, covered with a photomask on which the metal pattern 3 is formed, and exposed to ultraviolet light, and the exposed portions are removed with a developer. Next, metal is vapor-deposited on the portions from which the photoresist has been removed, and then the photoresist is removed, thereby forming the metal pattern 3 on the substrate 11. Note that although an example using positive photolithography has been described here, negative photolithography may also be used.

[0038] The dielectric used here preferably has a relative dielectric constant of 1.5 or more, more preferably 2.5 or more, and even more preferably 3 or more. Examples of the dielectric include acrylic resin, PET (polyethylene terephthalate), and a mixture of acrylic and air.

[0039] Examples of conductors include one or more of silver, gold, copper, platinum, aluminum, titanium, silicone, indium tin oxide, and alloys (e.g., alloys containing nickel, chromium, and molybdenum). Examples of alloys containing nickel, chromium, and molybdenum include various grades of Hastelloy B-2, B-3, C-4, C-2000, C-22, C-276, G-30, N, W, and X.

[0040] The thickness of the metal pattern 3 is preferably 10 nm or more, more preferably 30 nm or more, and even more preferably 100 nm or more. On the other hand, the upper limit of the thickness of the metal pattern 3 is preferably 10 μm or less, more preferably 5 μm or less, and even more preferably 4 μm or less. When the thickness of the metal pattern 3 is 10 nm or more, appropriate radio wave intensity can be ensured.

[0041] Each metal pattern 3 preferably has a side of 15 mm or more, more preferably 20 mm or more, and even more preferably 25 mm or more, while each metal pattern 3 preferably has a side of 50 mm or less, more preferably 40 mm or less, and even more preferably 30 mm or less.

[0042] The distance between adjacent metal patterns 3 is preferably equal to or less than the wavelength of the radio waves to be transmitted. Specifically, it is preferably 20 mm or less, and more preferably 15 mm or less. On the other hand, the distance between adjacent metal patterns 3 may be 0 mm or more, and is preferably 5 mm or more, and more preferably 10 mm or more.

[0043] The metal pattern 3 preferably has a relative dielectric constant of 7 or more. On the other hand, the upper limit of the relative dielectric constant is preferably 10,000 or less.

[0044] As shown in Fig. 5(A), each metal pattern 3 includes a split-ring resonator 4 and an enclosing portion 5 that surrounds each of the split-ring resonators 4 in a one-to-one relationship. The metal pattern 3 may have various shapes depending on the desired frequency band of radio waves for which radio wave permeability is to be increased. Here, the pattern shown in Fig. 5(A) will be described as an example. The metal pattern 3 of this embodiment can increase radio wave permeability in three frequency bands: a frequency band near 2 GHz, a frequency band near 3.4 GHz, and a frequency band near 5.1 GHz.

[0045] (Split-ring resonator 4) The split-ring resonator 4 is a metal microstructure having a structure finer than the wavelength of the target radio waves (electromagnetic waves). The split-ring resonator 4 corresponds to the split-ring resonator in a metasurface (metamaterial) and is also called a split-ring resonator (SRR).

[0046] The split ring resonator 4 according to this embodiment is composed of multiple linear bodies. Each linear body extends thinly. In this embodiment, each linear body is linear. Preferably, each split ring resonator 4 is formed rotationally symmetrically about the center of gravity G1 of the split ring resonator 4. The split ring resonator 4 according to this embodiment has a shape obtained by rotating a figure (a substantially T-shaped figure) consisting of a first linear body 41 extending horizontally from the center of gravity G1 and a second linear body 42 extending vertically from the middle of the first linear body 41 by 90 degrees about the center of gravity G1. In other words, the split ring resonator 4 according to this embodiment has a four-fold symmetry figure.

[0047] The multiple linear bodies are all formed with the same width in the longitudinal direction (same width). The line width is, for example, preferably 10 μm or more, more preferably 1 mm or more, and even more preferably 1.8 mm or more. On the other hand, the line width is preferably 2 mm or less. When the line width of the linear bodies is 2 mm or less, the degree of freedom in designing the metal pattern 3 can be improved. When the line width of the linear bodies is 10 μm or more, the productivity of the metal pattern can be maintained while suppressing costs.

[0048] (Enclosing portion 5) The surrounding portion 5 is provided on the substrate 11 and surrounds the split-ring resonator 4. The surrounding portion 5 is spaced apart from the split-ring resonator 4. The minimum distance L1 from the split-ring resonator 4 to the surrounding portion 5 is preferably 50% or more, more preferably 80% or more, and even more preferably 100% or more of the width (line width) of the linear body of the split-ring resonator 4. The maximum distance L2 from the split-ring resonator 4 to the surrounding portion 5 is preferably less than the wavelength of radio waves in the frequency band for which radio wave transmittance is to be increased.

[0049] The surrounding portion 5 is formed in a quadrangular shape. However, the surrounding portion 5 may be, for example, a triangular shape, a pentagonal shape, a hexagonal shape, a circular shape, an elliptical shape, etc. It is preferable that the surrounding portion 5 is continuous in the circumferential direction.

[0050] In this specification, "continuous" includes not only a state in which the wire is continuous without being divided in the circumferential direction, but also a state in which the wire is mostly continuous (with a small separation in one portion). A small separation falls within the continuous category if it is 5% or less of the circumferential length.

[0051] The line width of the surrounding portion 5 is preferably the same over the entire length. In this embodiment, the line width of the surrounding portion 5 is the same as the width of the linear members of the split-ring resonator 4, but may be smaller than the width of the linear members of the split-ring resonator 4.

[0052] (Protective Film 14) The protective film 14 can protect the metal patterns 3 by covering the multiple metal patterns 3. The protective film 14 has a size corresponding to the substrate 11 in a plan view. Examples of the protective film 14 include films made of synthetic resins. Examples of synthetic resins include one or more selected from the group consisting of PET (polyethylene terephthalate), COP (cycloolefin polymer), polyethylene, polypropylene, polyvinyl chloride, polystyrene, polymethyl methacrylate, polyester, polyformaldehyde, polyamide, polyphenylene ether, vinylidene chloride, polyvinyl acetate, polyvinyl acetal, AS resin, ABS resin, acrylic resin, fluororesin, nylon resin, polyacetal resin, polycarbonate resin, polyamide resin, and polyurethane resin.

[0053] The protective film 14 preferably contains fluorine. The protective film 14 containing fluorine can prevent transmission of ultraviolet rays, and therefore can protect the plurality of metal patterns 3 from ultraviolet rays.

[0054] The thickness of the protective film 14 is preferably 5 μm or more, more preferably 10 μm or more, and even more preferably 15 μm or more, while the upper limit of the thickness of the protective film 14 is preferably 100 μm or less, more preferably 50 μm or less, and even more preferably 25 μm or less.

[0055] The protective film 14 is adhered to the substrate 11 via an adhesive layer 13. The adhesive layer 13 may be made of, for example, a synthetic resin or a rubber adhesive sheet. Examples of synthetic resins include acrylic resin, silicone resin, and polyvinyl alcohol resin.

[0056] [Additional Notes] Although the embodiments of the present invention have been described above, the present invention is not limited to the above-described embodiments, and various modifications are possible without departing from the spirit of the present invention.

[0057] In the above embodiment, the structure 1 forms the easy-to-permeate region 1b by adding the metamaterial structure 12 onto the substrate 11, but there is no particular limitation as long as the structure has both the difficult-to-permeate region 1a and the easy-to-permeate region 1b.

[0058] REFERENCE SIGNS LIST 1 Structure (radio wave-transmitting structure) 1a Difficult-to-transmit portion 1b Easy-to-transmit portion 3 Metal pattern 4 Split-ring resonator 11 Base material 12 Metamaterial structure 13 Adhesive layer 14 Protective film 41 First linear body 42 Second linear body R1 First radio wave R2 Second radio wave

Claims

1. A radio wave transmission structure having a difficult transmission portion that hardly transmits radio waves and an easy transmission portion that transmits radio waves more easily than the difficult transmission portion, wherein a phase difference α (rad) between a first radio wave transmitted through the easy transmission portion and a second radio wave transmitted through the difficult transmission portion satisfies the following formula (1) or (2): 2πN - ωt < α < 2πN - ωt + π... (1) βsin(ωt + α) + sin(ωt) > 1... (2) N: integer ω: angular velocity (angular velocity caused by frequency, which is a value obtained by multiplying the frequency by 2π) t: time elapsed from when the first radio wave and the second radio wave are incident on the radio wave transmission structure until they are emitted β: ratio of the maximum electric field strength of the second radio wave to the maximum electric field strength of the first radio wave 2. The radio wave transmission structure according to claim 1, wherein the phase difference satisfies formula (1).

3. The radio wave transmission structure according to claim 1, wherein the phase difference satisfies formula (2).

Citation Information

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