JPH0196603A - Hollow optical waveguide - Google Patents

Hollow optical waveguide

Info

Publication number
JPH0196603A
JPH0196603A JP62254403A JP25440387A JPH0196603A JP H0196603 A JPH0196603 A JP H0196603A JP 62254403 A JP62254403 A JP 62254403A JP 25440387 A JP25440387 A JP 25440387A JP H0196603 A JPH0196603 A JP H0196603A
Authority
JP
Japan
Prior art keywords
thin film
polymer resin
waveguide
optical waveguide
layer
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Granted
Application number
JP62254403A
Other languages
Japanese (ja)
Other versions
JP2633866B2 (en
Inventor
Akishi Hongo
晃史 本郷
Kenichi Morosawa
諸沢 健一
Tsuneo Shioda
塩田 恒夫
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Hitachi Cable Ltd
Original Assignee
Hitachi Cable Ltd
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Hitachi Cable Ltd filed Critical Hitachi Cable Ltd
Priority to JP62254403A priority Critical patent/JP2633866B2/en
Publication of JPH0196603A publication Critical patent/JPH0196603A/en
Application granted granted Critical
Publication of JP2633866B2 publication Critical patent/JP2633866B2/en
Anticipated expiration legal-status Critical
Expired - Lifetime legal-status Critical Current

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Classifications

    • GPHYSICS
    • G02OPTICS
    • G02BOPTICAL ELEMENTS, SYSTEMS OR APPARATUS
    • G02B6/00Light guides; Structural details of arrangements comprising light guides and other optical elements, e.g. couplings
    • G02B6/02Optical fibres with cladding with or without a coating
    • G02B6/032Optical fibres with cladding with or without a coating with non solid core or cladding

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  • Physics & Mathematics (AREA)
  • General Physics & Mathematics (AREA)
  • Optics & Photonics (AREA)
  • Optical Fibers, Optical Fiber Cores, And Optical Fiber Bundles (AREA)

Abstract

PURPOSE:To reduce the transmission loss without spoiling flexibility by forming high polymer resin outside a waveguide formed of a thin film and a metallic layer thinly as a waveguide wall on the dielectric thin film. CONSTITUTION:At least one thin metallic film 12 is provided outside at least one dielectric thin film which has small absorptivity in the oscillation wavelength range of laser light in use and the high polymer resin layer 12 which is thick enough to maintain the mechanical strength of the waveguide is formed outside it. Thus, the high polymer resin coating is provided, so even if the waveguide is bent repeatedly or to small curvature, the high polymer resin is rich in flexibility, so its adaptive force to such bending is high and even the hollow optical waveguide formed of an optically thin film is usable while bent to a small radius of curvature. The transmission loss which causes a problem at the time of using the high polymer resin outside is reduced by providing the thin metallic film 12.

Description

【発明の詳細な説明】 [産業上の利用分野1 本発明は誘電体を内装した中空光導波路に係り、特に低
損失でしかも可撓性のある中空光導波路に関するもので
、医療及び工業加工に使用される炭酸ガスレーザ光の伝
送に好適である。
Detailed Description of the Invention [Industrial Application Field 1] The present invention relates to a hollow optical waveguide with a dielectric inside, and in particular to a low-loss and flexible hollow optical waveguide, and is suitable for medical and industrial processing. Suitable for transmitting carbon dioxide laser light used.

[従来の技術] 炭酸ガスレーザは、発振効率が高(大出力を得ることが
できるため、医療用のレーザメスや工業加工用の溶接、
切断等に広く用いられるようになってきている。しかし
、その発振波長が10.6−という赤外領域にあるため
、従来の石英系光ファイバでは損失が大きく、炭酸ガス
レーザ光用導波路として用い゛ることはできない。従っ
て、現在炭酸ガスレーザ光を導く手段としては、数枚の
ミラーを用いた空中伝送方式が主に採用されているが、
これは操作性において極めて不利である。
[Conventional technology] Carbon dioxide lasers have high oscillation efficiency (large output can be obtained), so they are used in laser scalpels for medical purposes, welding for industrial processing,
It has come to be widely used for cutting, etc. However, since its oscillation wavelength is in the infrared region of 10.6 -, conventional silica-based optical fibers have large losses and cannot be used as waveguides for carbon dioxide laser light. Therefore, currently the main method of guiding carbon dioxide laser light is an aerial transmission method using several mirrors.
This is extremely disadvantageous in terms of operability.

そこで、炭酸ガスレーザ光用導波路として赤外ファイバ
の開発が進められている。最近、より大きな電力伝達を
目的として誘電体を内装した金属中空光導波路が提案さ
れ、第3図に示すようなゲルマニウム内装ニッケツル中
空光導波路が試作されティる(H,Hiyagi、A、
tlongo、’/、^izawa、and S、にa
wakami、 Appl、Phys、Lett 43
,430(1983) ) 。コの製造方法はまずエツ
チング可能な母材パイプの外面にゲルマニウム層31を
スパッタリングにより形成し、さらにその外側にニッケ
ル層32をめっきにより形成した後、母材パイプをエツ
チングによって除去して中空領域33を形成し、ゲルマ
ニウム内装ニッケル中空光導波路を得るものである。
Therefore, infrared fibers are being developed as waveguides for carbon dioxide laser light. Recently, a metal hollow optical waveguide with a dielectric inside has been proposed for the purpose of greater power transmission, and a germanium-incorporated nickel hollow optical waveguide as shown in Fig. 3 has been prototyped (H., Hiyagi, A.
tlongo, '/, ^izawa, and S, nia
wakami, Appl, Phys, Lett 43
, 430 (1983)). This manufacturing method first forms a germanium layer 31 on the outer surface of an etched base material pipe by sputtering, further forms a nickel layer 32 on the outside by plating, and then removes the base material pipe by etching to form a hollow region 33. A germanium-incorporated nickel hollow optical waveguide is obtained.

金属層にしみ込む伝送パワーの深さ(スキンデプス)は
十分浅く、光学的には金属層の厚さは0.1p程度あれ
ば十分である。すなわちニッケル層32は伝送損失に関
与していると同時に機械的強度を保つ働きもしている。
The depth (skin depth) of the transmitted power penetrating into the metal layer is sufficiently shallow, and optically it is sufficient if the thickness of the metal layer is about 0.1p. That is, the nickel layer 32 is involved in transmission loss and at the same time serves to maintain mechanical strength.

誘電体に接する金属層としでは、電気めっきによって容
易に厚膜の金属層が得られるという理由で、第3図の従
来例ではニッケルを材料として選んでいる。しかしなが
ら光学的には、金属層はその複索屈折率の絶対値が十分
大きいか、あるいは複素屈折率の虚数部が実数部に比較
し十分大ぎい材料を用いた方が伝送損失は小さくなる。
In the conventional example shown in FIG. 3, nickel is selected as the material for the metal layer in contact with the dielectric because a thick metal layer can be easily obtained by electroplating. However, optically, the transmission loss will be smaller if the metal layer is made of a material whose absolute value of the complex refractive index is sufficiently large or whose imaginary part of the complex refractive index is sufficiently larger than the real part.

この点でニッケルよりも金、銀。Gold and silver than nickel in this regard.

あるいは銅を用いた方が有利である。囚に、波長10.
6−における各金属複素屈折率はNt :  9.1−
j34.8.^u : 17.1−j55.9. Ag
 : 13.5−j75.3. Cu:14、1−js
4.3である。
Alternatively, it is more advantageous to use copper. Prisoner, wavelength 10.
The complex refractive index of each metal at 6- is Nt: 9.1-
j34.8. ^u: 17.1-j55.9. Ag
: 13.5-j75.3. Cu: 14, 1-js
It is 4.3.

[発明が解決しようとする問題点] 第3図のように金属層を100〜200−の厚さでめっ
きによって形成した中空導波路では、めっき中に発生す
る残留応力のため中空導波路にランダムな曲がりが発生
しゃすく、伝送損失を十分低減することは難しい。また
、繰り返しの曲げに対して導波路が塑性変形を受けやす
く、特にニッケル層を無光沢めっきによって形成した導
波路ではわずかな曲がりでも塑性変形を受け、繰り返し
曲げを行った後では亀裂が発生したり元の直線状態に戻
らなくなる。一方、硬質の光沢めっきを用いた導波路で
は弾性変形の範囲内である程度の曲率で曲げることは可
能だが、曲げ半径が小さくなると破断しやすくなる。い
ずれにせよ金属層を厚く設けた中空光導波路では、十分
小さい曲げ半径でも曲げられる可撓性の優れた中空光導
波路を得ることは難しい。
[Problems to be Solved by the Invention] As shown in Fig. 3, in a hollow waveguide formed by plating a metal layer with a thickness of 100 to 200 mm, random damage occurs in the hollow waveguide due to residual stress generated during plating. It is difficult to sufficiently reduce transmission loss because bending is likely to occur. In addition, waveguides are susceptible to plastic deformation due to repeated bending, and in particular, waveguides with a nickel layer formed by matte plating are subject to plastic deformation even with slight bending, and cracks may occur after repeated bending. or it will not return to its original straight line state. On the other hand, a waveguide using hard glossy plating can be bent to a certain degree of curvature within the range of elastic deformation, but the smaller the bending radius, the more likely it is to break. In any case, with a hollow optical waveguide provided with a thick metal layer, it is difficult to obtain a hollow optical waveguide with excellent flexibility that can be bent even with a sufficiently small bending radius.

このように従来の金属中空光導波路では、金属層が厚く
、そのため十分小さな曲げ半径で導波路を曲げることが
できないという欠点があった。
As described above, conventional metal hollow optical waveguides have a drawback in that the metal layer is thick and therefore the waveguide cannot be bent with a sufficiently small bending radius.

本発明の目的は、前記した従来技術の欠点を解消し、小
さな曲げ半径でも自由に曲げることができる可撓性に優
れた中空光導波路を提供することにある。
An object of the present invention is to eliminate the drawbacks of the prior art described above and to provide a hollow optical waveguide with excellent flexibility that can be freely bent even with a small bending radius.

[問題点を解決するための手段] 本発明の中空光導波路は、使用するレーザ光の発振波長
域で吸収の小さい少なくとも一層の誘電体薄膜の外側に
、さらに少なくとも一層の金属薄膜を設け、その外部に
導波路の機械的強度を保つ厚膜の高分子樹脂層を被覆し
たものである。
[Means for Solving the Problems] The hollow optical waveguide of the present invention further includes at least one metal thin film provided on the outside of at least one dielectric thin film that has low absorption in the oscillation wavelength range of the laser beam used. The waveguide is coated with a thick polymer resin layer that maintains the mechanical strength of the waveguide.

炭酸ガスレーザの発振波長10.6−において、吸収の
小さい好適な誘電体材料としてGe、 ZnS 。
Ge and ZnS are suitable dielectric materials with low absorption at the oscillation wavelength of 10.6 - for the carbon dioxide laser.

Zn5e、  にC1,Ha(Jl、 GaAs、カル
コゲナイドカラス及びフッ化化合物等があげられる。赤
外波帯では電磁波の重要な伝送媒体となりうろこのよう
な物質は全て誘電体としてふるまう。この誘電体薄膜は
一層内装させただけでも伝送損失は何も内装していない
場合よりも2〜3桁程度低減されるが、屈折率の異なる
2種類の誘電体を交互に多層形成すればさらに伝送損失
は低減される。一方誘電体に接する金属層は前述したよ
うに複素屈折率の大きさが十分大きいかあるいは複素屈
折率の虚数部が実数部に比較し十分大きい材料を用いた
方が有利である。本発明では誘電体に接する金属層は薄
膜であるために、金、銀、銅等の好適な金属材料は全て
真空蒸着、スパッタリング、イオンブレーティング、め
っき等によって容易に形成することができる。また、高
分子樹脂の材料としては例えばポリエチレン、テフロン
、ポリイミド、シリコ−ン等の樹脂があげられる。
Examples include Zn5e, C1, Ha(Jl, GaAs, chalcogenide glass, and fluoride compounds. In the infrared band, they become important transmission media for electromagnetic waves. All substances such as scales behave as dielectrics. This dielectric thin film Even if only one layer of dielectric material is installed, the transmission loss will be reduced by two to three orders of magnitude compared to the case where nothing is installed, but if two types of dielectric materials with different refractive indexes are alternately formed in multiple layers, the transmission loss will be further reduced. On the other hand, as described above, it is advantageous to use a material that has a sufficiently large complex refractive index or whose imaginary part is sufficiently large compared to the real part of the metal layer in contact with the dielectric. In the present invention, since the metal layer in contact with the dielectric is a thin film, any suitable metal material such as gold, silver, copper, etc. can be easily formed by vacuum evaporation, sputtering, ion blasting, plating, etc. Examples of the polymer resin material include resins such as polyethylene, Teflon, polyimide, and silicone.

[作 用] 機械的強度を保つために高分子樹脂を外部に被覆したの
で、繰り返しの曲げや曲率の小さな曲げが加えられても
、高分子樹脂は可撓性に富むため、そのような曲げに対
する適応力が高(、光学的にN膜で構成されている中空
光導波路でも極めて小さい曲げ半径で使用することが可
能となる。
[Function] The exterior is coated with polymer resin to maintain mechanical strength, so even if repeated bending or bending with a small curvature is applied, polymer resin is highly flexible, so it can withstand such bending. It has a high adaptability to the bending radius (even hollow optical waveguides optically composed of N films can be used with extremely small bending radii).

一方、外部を高分子樹脂としたことで問題となる伝送損
失は、誘電体膜の外側に導波路壁としての金属n1lI
を設けることによって低減している。
On the other hand, the problem of transmission loss due to the use of polymer resin for the exterior is that metal n1lI as the waveguide wall is placed outside the dielectric film.
This is reduced by providing .

[実施例] 以下、本発明の実施例を第1図〜第2図を用いて説明す
る。
[Example] Hereinafter, an example of the present invention will be described using FIGS. 1 and 2.

第1図はGeを内装した銀中空光導波路例である。FIG. 1 shows an example of a silver hollow optical waveguide containing Ge.

ここで中空領域14を区画形成する06層11とその上
に設けたAg層12は光学的に導波路壁を構成している
。さらにその外側に高分子樹脂層として耐熱性に優れた
ポリイミド1113をコーティングしている。このポリ
イミド層13は機械的強度を保つためのみの働きをして
おり、光学的には伝送特性に関与せず、光パワーの大部
分は中空領域14に集中する。GeWlllとAO1f
fi12はスパッタリングによって、またポリイミド層
13は浸漬によって形成されている。中空領域14は直
径1.5履で各層の膜厚はGeJlllが0.5JJR
,AQ層12が0、 IJII 、ポリイミドW113
が100−である。06層11の膜厚は伝送損失に太き
(影響し、伝送損失はGeの″膜厚の変化に従って周期
的に変化する。AgN!g12の膜厚さは電磁界のしみ
込む深さ(スキンデプス)以上あれば、狭口的には伝送
損失に大きな影響を及ぼさないが、厚過ぎると曲げによ
って剥離する場合が生じるので0.1−程度が好ましい
Here, the 06 layer 11 defining the hollow region 14 and the Ag layer 12 provided thereon optically constitute a waveguide wall. Furthermore, polyimide 1113, which has excellent heat resistance, is coated on the outside as a polymer resin layer. This polyimide layer 13 functions only to maintain mechanical strength and does not optically affect transmission characteristics, and most of the optical power is concentrated in the hollow region 14. GeWllll and AO1f
The fi 12 is formed by sputtering, and the polyimide layer 13 is formed by dipping. The hollow region 14 has a diameter of 1.5 mm and the thickness of each layer is GeJll of 0.5JJR.
, AQ layer 12 is 0, IJII, polyimide W113
is 100-. The film thickness of the 06 layer 11 has a large effect on the transmission loss, and the transmission loss changes periodically according to changes in the Ge film thickness.The film thickness of the AgN! ) or more does not have a large effect on transmission loss in a narrow sense, but if it is too thick, it may peel off due to bending, so a thickness of about 0.1 is preferable.

なお、第1図の実施例では金属層に内装される誘電体と
してGeのみを用いたが211類の誘電体、例えばGe
とZn5eを交互に冬目内装すればさらに低損失な導波
路を得ることができる。
In the embodiment shown in FIG. 1, only Ge was used as the dielectric material included in the metal layer, but a dielectric material of class 211, such as Ge
If Zn5e and Zn5e are alternately coated, a waveguide with even lower loss can be obtained.

また、第1図においてへg層は0.1−と薄いためポリ
イミドl1113を浸漬によってコーティングするとき
06層11及びA47層12に傷がつく危険性がある。
In addition, since the Heg layer in FIG. 1 is as thin as 0.1, there is a risk that the 06 layer 11 and the A47 layer 12 will be damaged when coating with polyimide 1113 by dipping.

これを避sするため第2WJに示すように、06層21
上の^QFIJ22とポリイミドw324との間に、例
えばnt層23を介在させると効果的である。Xi層2
3は無電解めっきあるいは^QFIA22を電極として
用いた電気めっきによって容易に形成できる。
To avoid this, as shown in the second WJ, 06 layer 21
It is effective to interpose, for example, the nt layer 23 between the upper QFIJ 22 and the polyimide w 324. Xi layer 2
3 can be easily formed by electroless plating or electroplating using QFIA22 as an electrode.

めっきによって形成された1層23はAg層22に極め
て強靭に付着し、ポリイミドをコーティングするとき、
^QWJ22及びGeff 21を保護する。但しこの
場合、あまり厚すぎると可撓性を損うのでx+m 23
の膜厚は数p程度にする必要がある。なお、25は中空
領域である。
One layer 23 formed by plating adheres extremely strongly to the Ag layer 22, and when coating with polyimide,
^Protect QWJ22 and Geff 21. However, in this case, if it is too thick, the flexibility will be lost, so x + m 23
It is necessary to make the film thickness of about several micrometers. Note that 25 is a hollow area.

[発明の効果] 本発明によれば次のような優れた効果が得られる。[Effect of the invention] According to the present invention, the following excellent effects can be obtained.

(1)  薄膜で構成した導波路の外部に高分子樹脂を
用いて機械的強度をもたせているため、光導波路は可撓
性に富み、際めで小さい曲げ半径でも曲げることができ
る。
(1) Since a polymer resin is used on the outside of the thin film waveguide to provide mechanical strength, the optical waveguide is highly flexible and can be bent even with a small bending radius.

■) また、誘電体膜薄膜上に導波路壁としての金属層
を薄く形成しているため、可撓性を損うことなく、伝送
損失を低減することができる。特に金属層を金、銀、銅
で形成すれば、伝送損失を一層低減できる。
(2) Furthermore, since a thin metal layer is formed as a waveguide wall on the thin dielectric film, transmission loss can be reduced without impairing flexibility. In particular, if the metal layer is made of gold, silver, or copper, transmission loss can be further reduced.

【図面の簡単な説明】[Brief explanation of the drawing]

第1図は本発明の一実施例を示すポリイミド樹脂によっ
て゛被覆されたゲルマニウム内装銀中空先導波路の横断
面図、第2図は本発明の他の実施例を示し、銀層とポリ
イミド層との間にニッケル層を介在させたゲルマニウム
内装銀中空光導波路の横断面図、第3図は従来のゲルマ
ニウム内装ニッケル中空先導波路の横断面図である。 図中、11.21はGe1l (誘電体1111)、1
2.22はAQ層(金a薄151)、23はXi層、1
3.24G;Lポリイミド1121(1e分子樹脂層)
、14.25は中空領域である。
FIG. 1 is a cross-sectional view of a germanium-incorporated silver hollow guiding waveguide coated with polyimide resin, showing one embodiment of the present invention, and FIG. FIG. 3 is a cross-sectional view of a conventional germanium-equipped nickel hollow optical waveguide with a nickel layer interposed therebetween. FIG. In the figure, 11.21 is Ge1l (dielectric 1111), 1
2.22 is AQ layer (gold a thin 151), 23 is Xi layer, 1
3.24G; L polyimide 1121 (1e molecular resin layer)
, 14.25 is a hollow region.

Claims (4)

【特許請求の範囲】[Claims] (1)使用するレーザ光の発振波長域で吸収の小さい誘
電体薄膜が中空領域を区画形成し、上記誘電体薄膜の外
方に金属薄膜を設け、その外部に導波路の機械的強度を
保つ厚膜の高分子樹脂層を有することを特徴とする中空
光導波路。
(1) A dielectric thin film with low absorption in the oscillation wavelength range of the laser beam to be used defines a hollow region, and a metal thin film is provided outside the dielectric thin film to maintain the mechanical strength of the waveguide. A hollow optical waveguide characterized by having a thick polymer resin layer.
(2)上記誘電体薄膜はGe、ZnS、ZnSe、KC
l、NaCl、GaAs、カルコゲナイドガラス、フッ
化化合物のいずれかよりなる1層構造の薄膜、またはこ
れらの任意の組合わせよりなる多層構造の薄膜である特
許請求の範囲第1項記載の中空光導波路。
(2) The above dielectric thin film is made of Ge, ZnS, ZnSe, KC.
The hollow optical waveguide according to claim 1, which is a single-layer structure thin film made of any one of L, NaCl, GaAs, chalcogenide glass, or a fluoride compound, or a multilayer structure thin film made of any combination thereof. .
(3)上記金属薄膜のうち、誘電体薄膜に接する金属薄
膜は、金、銀、銅のいずれかよりなる特許請求の範囲1
項又は第2項記載の中空光導波路。
(3) Among the metal thin films, the metal thin film in contact with the dielectric thin film is made of gold, silver, or copper as claimed in claim 1.
The hollow optical waveguide according to item 1 or 2.
(4)上記高分子樹脂層はポリエチレン、テフロン、ポ
リイミド、シリコーンの樹脂のいずれかよりなる特許請
求の範囲第1項、第2項又は第3項記載の中空光導波路
(4) The hollow optical waveguide according to claim 1, 2, or 3, wherein the polymer resin layer is made of polyethylene, Teflon, polyimide, or silicone resin.
JP62254403A 1987-10-08 1987-10-08 Hollow optical waveguide Expired - Lifetime JP2633866B2 (en)

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Cited By (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
JPH03184003A (en) * 1989-12-14 1991-08-12 Hitachi Cable Ltd Dielectric-containing metallic hollow optical waveguide
JP2003021782A (en) * 2001-07-06 2003-01-24 Marumo Denki Kk Projection lens device and spot light equipped therewith
JP2009524835A (en) * 2006-01-30 2009-07-02 ザ ユニバーシティ オブ シドニー Fiber optic dosimeter
JP2017146357A (en) * 2016-02-15 2017-08-24 住友電気工業株式会社 Hollow optical fiber, endoscope device, and method of manufacturing hollow optical fiber
EP3534194A4 (en) * 2016-11-30 2020-07-01 Pioneer Corporation Electromagnetic wave transmission cable

Citations (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
JPS61217005A (en) * 1985-03-18 1986-09-26 コヒーレント・インコーポレイテッド Hollow waveguide
JPS61206903U (en) * 1985-06-17 1986-12-27

Patent Citations (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
JPS61217005A (en) * 1985-03-18 1986-09-26 コヒーレント・インコーポレイテッド Hollow waveguide
JPS61206903U (en) * 1985-06-17 1986-12-27

Cited By (6)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
JPH03184003A (en) * 1989-12-14 1991-08-12 Hitachi Cable Ltd Dielectric-containing metallic hollow optical waveguide
JP2003021782A (en) * 2001-07-06 2003-01-24 Marumo Denki Kk Projection lens device and spot light equipped therewith
JP2009524835A (en) * 2006-01-30 2009-07-02 ザ ユニバーシティ オブ シドニー Fiber optic dosimeter
JP2017146357A (en) * 2016-02-15 2017-08-24 住友電気工業株式会社 Hollow optical fiber, endoscope device, and method of manufacturing hollow optical fiber
EP3534194A4 (en) * 2016-11-30 2020-07-01 Pioneer Corporation Electromagnetic wave transmission cable
US11018403B2 (en) 2016-11-30 2021-05-25 Pioneer Corporation Electromagnetic wave transmission cable including a hollow dielectric tube surrounded by a foamed resin member having different expansion ratios at different regions therein

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