\\n\\n
Released this past November, the list is based on data collected from the Web of Science and highlights some of the world’s most influential scientific minds by naming the researchers whose publications over the previous decade have included a high number of Highly Cited Papers placing them among the top 1% most-cited.
\\n\\nWe wish to congratulate all of the researchers named and especially our authors on this amazing accomplishment! We are happy and proud to share in their success!
\\n"}]',published:!0,mainMedia:null},components:[{type:"htmlEditorComponent",content:'IntechOpen is proud to announce that 179 of our authors have made the Clarivate™ Highly Cited Researchers List for 2020, ranking them among the top 1% most-cited.
\n\nThroughout the years, the list has named a total of 252 IntechOpen authors as Highly Cited. Of those researchers, 69 have been featured on the list multiple times.
\n\n\n\nReleased this past November, the list is based on data collected from the Web of Science and highlights some of the world’s most influential scientific minds by naming the researchers whose publications over the previous decade have included a high number of Highly Cited Papers placing them among the top 1% most-cited.
\n\nWe wish to congratulate all of the researchers named and especially our authors on this amazing accomplishment! We are happy and proud to share in their success!
\n'}],latestNews:[{slug:"stanford-university-identifies-top-2-scientists-over-1-000-are-intechopen-authors-and-editors-20210122",title:"Stanford University Identifies Top 2% Scientists, Over 1,000 are IntechOpen Authors and Editors"},{slug:"intechopen-authors-included-in-the-highly-cited-researchers-list-for-2020-20210121",title:"IntechOpen Authors Included in the Highly Cited Researchers List for 2020"},{slug:"intechopen-maintains-position-as-the-world-s-largest-oa-book-publisher-20201218",title:"IntechOpen Maintains Position as the World’s Largest OA Book Publisher"},{slug:"all-intechopen-books-available-on-perlego-20201215",title:"All IntechOpen Books Available on Perlego"},{slug:"oiv-awards-recognizes-intechopen-s-editors-20201127",title:"OIV Awards Recognizes IntechOpen's Editors"},{slug:"intechopen-joins-crossref-s-initiative-for-open-abstracts-i4oa-to-boost-the-discovery-of-research-20201005",title:"IntechOpen joins Crossref's Initiative for Open Abstracts (I4OA) to Boost the Discovery of Research"},{slug:"intechopen-hits-milestone-5-000-open-access-books-published-20200908",title:"IntechOpen hits milestone: 5,000 Open Access books published!"},{slug:"intechopen-books-hosted-on-the-mathworks-book-program-20200819",title:"IntechOpen Books Hosted on the MathWorks Book Program"}]},book:{item:{type:"book",id:"945",leadTitle:null,fullTitle:"Global Perspectives on Bronchoscopy",title:"Global Perspectives on Bronchoscopy",subtitle:null,reviewType:"peer-reviewed",abstract:"Bronchoscopy has become an essential part of modern medicine . Recent advances in technology have allowed integration of ultrasound with this tool. The use of lasers along with bronchoscopes has increased the therapeutic utility of this device. Globally an increasing number of pulmonary specialists, anaesthesiologists and thoracic surgeons are using the bronchoscope to expedite diagnosis and treatment. The current volume on bronchoscopy adds to the vast body of knowledge on this topic. The democratic online access to this body of knowledge will greatly increase the ease with which both trainees and expert bronchoscopists can learn more .The contributions from around the world cover the breadth of this field and includes cutting edge uses as well as a section on pediatric bronchoscopy . The book has been an effort by excellent authors and editors and will surely be a often reviewed addition to your digital bookshelf. . In summary, this book is a great testament to the power of collaboration and is a superb resource for doctors in training, ancillary team members as well as practicing healthcare providers who have to perform or arrange for bronchoscopy or the associated procedures.",isbn:null,printIsbn:"978-953-51-0642-5",pdfIsbn:"978-953-51-7011-2",doi:"10.5772/1452",price:119,priceEur:129,priceUsd:155,slug:"global-perspectives-on-bronchoscopy",numberOfPages:254,isOpenForSubmission:!1,isInWos:1,hash:"ec8fbda36bdb3c7a30caf70a437a60e1",bookSignature:"Sai Praveen Haranath and Samiya Razvi",publishedDate:"June 13th 2012",coverURL:"https://cdn.intechopen.com/books/images_new/945.jpg",numberOfDownloads:53818,numberOfWosCitations:4,numberOfCrossrefCitations:4,numberOfDimensionsCitations:14,hasAltmetrics:0,numberOfTotalCitations:22,isAvailableForWebshopOrdering:!0,dateEndFirstStepPublish:"March 23rd 2011",dateEndSecondStepPublish:"April 20th 2011",dateEndThirdStepPublish:"August 25th 2011",dateEndFourthStepPublish:"September 24th 2011",dateEndFifthStepPublish:"January 22nd 2012",currentStepOfPublishingProcess:5,indexedIn:"1,2,3,4,5,6",editedByType:"Edited by",kuFlag:!1,editors:[{id:"108165",title:"Dr.",name:"Sai P.",middleName:null,surname:"Haranath",slug:"sai-p.-haranath",fullName:"Sai P. 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We aimed to compile information from diverse sources into a single volume and to give some real-life examples, extending the appreciation of organic fertilizers that may stimulate new research ideas and trends in relevant fields. The contributions in this field of research are gratefully acknowledged. The publication of this book is of great importance for those researchers, scientists, engineers, teachers, graduate students, agricultural agronomists, farmers and crop producers who can use these different investigations to understand the advantages of using organic fertilizers.",isbn:"978-1-78985-148-9",printIsbn:"978-1-78985-147-2",pdfIsbn:"978-1-78985-089-5",doi:"10.5772/intechopen.77847",price:119,priceEur:129,priceUsd:155,slug:"organic-fertilizers-history-production-and-applications",numberOfPages:144,isOpenForSubmission:!1,hash:"c139030955f06869c7b1c5f1ef9a492b",bookSignature:"Marcelo Larramendy and Sonia Soloneski",publishedDate:"November 20th 2019",coverURL:"https://cdn.intechopen.com/books/images_new/8017.jpg",keywords:null,numberOfDownloads:3120,numberOfWosCitations:0,numberOfCrossrefCitations:2,numberOfDimensionsCitations:9,numberOfTotalCitations:11,isAvailableForWebshopOrdering:!0,dateEndFirstStepPublish:"January 10th 2019",dateEndSecondStepPublish:"January 31st 2019",dateEndThirdStepPublish:"April 1st 2019",dateEndFourthStepPublish:"June 20th 2019",dateEndFifthStepPublish:"August 19th 2019",remainingDaysToSecondStep:"2 years",secondStepPassed:!0,currentStepOfPublishingProcess:5,editedByType:"Edited by",kuFlag:!1,biosketch:null,coeditorOneBiosketch:null,coeditorTwoBiosketch:null,coeditorThreeBiosketch:null,coeditorFourBiosketch:null,coeditorFiveBiosketch:null,editors:[{id:"14764",title:"Dr.",name:"Marcelo L.",middleName:null,surname:"Larramendy",slug:"marcelo-l.-larramendy",fullName:"Marcelo L. Larramendy",profilePictureURL:"https://mts.intechopen.com/storage/users/14764/images/system/14764.jpeg",biography:"Marcelo L. Larramendy, Ph.D., serves as a Professor of Molecular Cell Biology at the School of Natural Sciences and Museum (National University of La Plata, Argentina). He was appointed as Senior Researcher of the National Scientific and Technological Research Council of Argentina. He is a former member of the Executive Committee of the Latin American Association of Environmental Mutagenesis, Teratogenesis, and Carcinogenesis. He is the author of more than 450 contributions, including scientific publications, research communications, and conferences worldwide. He is the recipient of several national and international awards. Prof. Larramendy is a regular lecturer at the international A. Hollaender courses organized by the IAEMS and a former guest scientist at NIH (USA) and the University of Helsinki, (Finland). He is an expert in genetic toxicology and is, or has been, a referee for more than 20 international scientific journals. He was a member of the International Panel of Experts at the International Agency for Research on Cancer (IARC, WHO, Lyon, France) in 2015 for the evaluation of DDT, 2,4-D, and Lindane. Presently, Prof. Dr. Larramendy is Head of the Laboratory of Molecular Cytogenetics and Genotoxicology at the UNLP.",institutionString:"National University of La Plata",position:null,outsideEditionCount:0,totalCites:0,totalAuthoredChapters:"2",totalChapterViews:"0",totalEditedBooks:"17",institution:{name:"National University of La Plata",institutionURL:null,country:{name:"Argentina"}}}],coeditorOne:{id:"14863",title:"Dr.",name:"Sonia",middleName:null,surname:"Soloneski",slug:"sonia-soloneski",fullName:"Sonia Soloneski",profilePictureURL:"https://mts.intechopen.com/storage/users/14863/images/system/14863.jpeg",biography:"Sonia Soloneski has a Ph.D. in Natural Sciences and is an Assistant Professor of Molecular Cell Biology at the School of Natural Sciences and Museum of La Plata, National University of La Plata, Argentina. She is a member of the National Scientific and Technological Research Council (CONICET) of Argentina in the genetic toxicology field, the Latin American Association of Environmental Mutagenesis, Teratogenesis, and Carcinogenesis (ALAMCTA), the Argentinean Society of Toxicology (ATA), the Argentinean Society of Genetics (SAG), the Argentinean Society of Biology (SAB), and the Society of Environmental Toxicology and Chemistry (SETAC). She has authored more than 380 contributions in the field, including scientific publications in peer-reviewed journals and research communications. She has served as a review member for more than 30 scientific international journals. She has been a plenary speaker in scientific conferences and a member of scientific committees. 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From chapter submission and review, to approval and revision, copyediting and design, until final publication, I work closely with authors and editors to ensure a simple and easy publishing process. I maintain constant and effective communication with authors, editors and reviewers, which allows for a level of personal support that enables contributors to fully commit and concentrate on the chapters they are writing, editing, or reviewing. I assist authors in the preparation of their full chapter submissions and track important deadlines and ensure they are met. I help to coordinate internal processes such as linguistic review, and monitor the technical aspects of the process. As an ASM I am also involved in the acquisition of editors. 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Larramendy",coverURL:"https://cdn.intechopen.com/books/images_new/4616.jpg",editedByType:"Edited by",editors:[{id:"14764",title:"Dr.",name:"Marcelo L.",surname:"Larramendy",slug:"marcelo-l.-larramendy",fullName:"Marcelo L. Larramendy"}],productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}},{type:"book",id:"5358",title:"Soil Contamination",subtitle:"Current Consequences and Further Solutions",isOpenForSubmission:!1,hash:"e4d136df9f1658ae17f3ba7b3c992460",slug:"soil-contamination-current-consequences-and-further-solutions",bookSignature:"Marcelo L. Larramendy and Sonia Soloneski",coverURL:"https://cdn.intechopen.com/books/images_new/5358.jpg",editedByType:"Edited by",editors:[{id:"14764",title:"Dr.",name:"Marcelo L.",surname:"Larramendy",slug:"marcelo-l.-larramendy",fullName:"Marcelo L. Larramendy"}],productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}}]},chapter:{item:{type:"chapter",id:"55714",title:"Novel MT/MPO Single-Mode Multifiber Connector Technologies for Optical Fiber Communications",doi:"10.5772/intechopen.68863",slug:"novel-mt-mpo-single-mode-multifiber-connector-technologies-for-optical-fiber-communications",body:'\nThe number of subscribers to broadband services in Japan now exceeds 38 million, and about 29 million subscribers were using fiber-to-the-home (FTTH) services as of September 2016 [1]. The FTTH networks use many various single-mode optical fiber connection technologies. One such connection is a field mountable optical fiber connector (FMC) or field installable connector (FIC), and another type is a manufactured optical fiber connector. The mechanically transferable (MT) or multifiber push-on (MPO) connectors, which belong to the manufactured connectors, are particularly expected to be used in upcoming FTTH networks because these multifiber connectors are superior to single-fiber connectors with high-density optical fiber cable joints [2–6].
\nOptical fiber communication systems have been used in data centers in the USA. Multimode single-fiber connectors such as a little connector (LC) were mainly used previously, and multimode MPO connectors are also used in current data centers. In addition, high precision MPO connectors with single-mode fibers are expected to be used for communicating more information over long distances in huge data centers.
\nThis chapter reports the latest MT/MPO multifiber connector technologies. Current MT/MPO connectors used in Japan and the USA are explained in Section 2, and our developed innovative single-mode multifiber connectors are reported in Section 3. The low insertion-loss and high return-loss angled physical contact (APC)-MPO single-mode multifiber connectors are described in Section 3.1. Next, MT single-mode 84-fiber connectors for realizing higher density multifiber connectors are explained in Section 3.2. Novel optical fiber switches based on MT multifiber connector technology are reported in Section 3.3. These connectors need to be measured and inspected for high precision multifiber connectors. In Section 4, a new inspection technique for MT ferrules and equipment using the technique are introduced. These single-mode multifiber connectors can be used as key technologies for advanced optical fiber communication systems.
\nFigure 1 shows the configuration of a typical FTTH network in Japan. It is mainly composed of an optical line terminal (OLT) in the central office, underground and aerial optical fiber cables, and an optical network unit (ONU) inside a customer’s home and building. The network requires various fiber connections at office, outdoor, and home sites. With the fiber connections at aerial and home sites in particular, field installable connectors or field mountable connectors and mechanical splices are used to fit the best wiring depending on aerial conditions and room arrangement. Field assembly small (FAS) connectors and field assembly (FA) termination connectors are field installable connectors [7–9]. In contrast, manufactured connectors, such as miniature-unit (MU) coupling optical fiber and single-fiber coupling (SC) optical fiber connectors, are used in central offices and homes. MT connectors are also used in central offices for multifiber ribbon joints. MPO connectors are used in customers’ buildings. These MT and MPO connectors are particularly expected to be used in the upcoming FTTH networks with high-density optical fiber cable joints.
\nTypical FTTH network and various optical fiber connections.
Optical fiber communication systems have been used in data centers in the USA. Previously, multimode single-fiber connectors such as an LC connector were mainly used, and multimode MPO connectors are also used in current data centers. This is because multifiber connectors are superior to other single-fiber connectors with high-density optical fiber cable joints. Figure 2 shows examples of optical fiber wiring (a) with LC single-fiber connectors and (b) with MPO multifiber connectors. Optical fiber wiring with the single-fiber connectors is slightly complicated, whereas that with the multifiber connectors is very simple and well ordered. The MPO multifiber connectors are consequently expected to be used in data center networks with high-density optical fiber cable joints. In addition, high precision MPO connectors with single-mode fibers are expected to be used for communicating more information over long distances in huge data centers. Figure 3 shows the structure of the MT multifiber connector [2, 3], which consists of two plastic ferrules with two guide holes, two guide pins, and a clamp spring. The multifibers are positioned in a row between two guide holes. The ferrules are aligned by the two guide pins and two guide holes and then held with the clamp spring to achieve a low connection loss for multifiber ribbon connections. Refractive index matching material is used between the ferrule endfaces to reduce the Fresnel reflection caused by an air-gap [10, 11]. The device is disconnected simply by removing the clamp spring and guide pins. The 4-, 8-, and 16-fiber MT connectors are currently used in the FTTH services in Japan.
\nExample of optical fiber wiring (a) with single-fiber connectors and (b) with multifiber connectors.
MT multifiber connector.
Figure 4(a) shows the endface of an MT ferrule. In the MT ferrule endface, several fiber holes are positioned between two guide holes. The origin O is designated as the middle point of two guide hole centers. Each fiber hole is designed to be arranged with the designated fiber pitch on the basis of the origin. Figure 4(b) shows the fiber hole eccentricity of the MT ferrule. The actual fiber hole positions on the fabricated MT ferrule endface are different from the designated ideal positions because the molds are not perfectly accurate and/or plastic might deform during the MT ferrule fabrication. This large fiber hole eccentricity might result in large insertion loss of an MT connector, so it must be minimized for low insertion-loss MT connectors. Therefore, a technique has been developed to inspect for fiber eccentricities in MT ferrules, which is described in Section 4.
\n(a) Endface and (b) fiber hole eccentricity of MT ferrule.
One application of the MT connector is as a multifiber push-on (MPO) connector [4–6, 12]. Figure 5 shows the structure of the MPO connector, which is composed of two plugs and an adaptor. The plug contains an MT ferrule that has an endface that is obliquely polished with a slight fiber protrusion to enable physical contact. It is important for physical contact type connectors to eliminate an air gap between fiber ends [13–16]. Two guide pins are fitted into two guide holes in one ferrule to align the ferrules. The plug and adaptor are engaged by fitting a pair of elastic hooks into corresponding grooves. This connector provides easy push-pull reconnections without the need for refractive index matching material.
\nMPO multifiber connector.
Figure 6 shows the fabrication process of an MPO plug. First, the mold is fabricated by using high precision mechanical engineering. A high precision mold is used, and an MT ferrule is fabricated from plastic resin. This MT ferrule is a key device for MT/MPO connectors. Next, the multifiber ribbon is installed and fixed with adhesive in the MT ferrule. The MT ferrule containing the multifiber ribbon is then obliquely polished. Finally, an MPO plug houses the obliquely ended MT ferrule with multifibers. This MPO fabrication process contains two steps: ferrule making and connector assembling. Currently, fewer than 10 companies make ferrules, but more than 100 companies assemble connectors. More companies will make ferrules and assemble connectors in the future.
\nFabrication process of MPO plug.
This section reports our innovative multifiber connectors based on MT/MPO connector technologies. Figure 7 shows three target single-mode multifiber connectors. The first is an extremely lower insertion-loss multifiber connector, which is detailed in Section 3.1. The second is a higher density multifiber connector that enables two high-density optical fiber cables to be connected as soon as possible, which is explained in Section 3.2. The third is a functional multifiber connector that enables multifibers to be switched, which is described in Section 3.3.
\nThree targets of single-mode multifiber connector technologies.
We have investigated extremely great performances of multifiber connectors and developed angled physical contact (APC) MPO connectors that have an insertion loss lower than 0.2 dB and return loss higher than 60 dB. This section explains these APC-MPO connectors. To create lower insertion-loss connectors, fiber core offsets from the ideal positions must be decreased. APC-MPO connectors have two types of fiber core offset. One is due to deviation of components and the other is due to shear force caused by compressing two obliquely ended MT ferrules. These two fiber core offsets are detailed below.
\nOptical loss in a fiber connection has four causes: fiber-core offset, fiber-axis tilt, fiber-end separation, and mode field mismatch [17, 18]. With MT connectors, fiber-core offset is the dominant factor generating optical loss, and so we have limited our considerations to this factor. Figure 8 shows four deviations: d1, d2, d3, and d4. d1 is the fiber hole position deviation. d2 is the deviation due to the clearance between a fiber and a fiber hole. d3 is the deviation due to the clearance between a guide pin and a guide hole. d4 is the fiber-core eccentricity [19]. The four deviations dependently affect total fiber core deviation. To realize an insertion loss of lower than 0.2 dB, the total deviation must be less than 0.5 μm.
\nFour deviations resulting in fiber core offset.
Figure 9(a) and (b) shows side views of connected MT ferrules and an MT ferrule endface in an MPO plug. The MPO connector uses MT ferrules obliquely polished at 8 degrees and can provide high return-loss characteristics. In contrast, the shear force occurs in the connected obliquely ended MT ferrules when two MT ferrules are compressed. This shear force leads to the Y offset of connected fibers in the MT ferrule. By considering the Y offset, fiber positions are designed to be previously offset, as shown in Figure 9(b). This offset quantity is dependent on clearance between a guide hole and a guide pin and deformed material of an MT ferrule. The fiber offset must be controlled for low insertion-loss MPO connectors.
\n(a) Side view of connected MT ferrules and (b) MT ferrule endface in MPO plug.
On the basis of the above design, we fabricated three pairs of high precision single-mode 12-fiber APC-MPO connectors by using three different fabrication molds. The fabricated APC-MPO connectors used high precision ferrules with d1 of less than 0.5 μm and severely controlled guide pins and optical fibers with lower d2, d3, and d4. The fabricated APC-MPO connectors also used the controlled Y offset quantity. We measured the insertion losses and return losses using 1.31 μm LD, a power meter, and a backreflection meter. Figure 10 shows histograms of the insertion losses and return losses of the connectors. The average insertion loss was 0.08 dB with a maximum of 0.17 dB. The return losses were greater than 64 dB. Consequently, we have revealed that the fabricated APC-MPO has an excellent performance.
\n(a) Insertion loss and (b) return loss of fabricated high precision APC-MPO connectors.
We have developed a higher density multifiber connector to enable two high-density optical fiber cables to be connected as soon as possible [20–23]. Figure 11(a) and (b) shows the novel high-density preconnectorized cable joint and endface of high-count fiber MT connectors, respectively. The cable joint consists of an arrayed high-count fiber MT connector and a cable joint housing and can connect high-density optical fiber cables such as 2000-fiber cables at one time. When it is connected, each MT connector is aligned with two guide pins and pushed toward the opposite ferrule by a spring. The MT connectors are aligned and connected individually. This structure is the same as those of a conventional MT connector and MPO connector. The connector endface is polished at a right angle. The connectors need an index matching material to eliminate the Fresnel reflection caused by an air gap. We used a conventionally sized 2.5-mm-thick MT ferrule that has guide holes of 4.6 mm in pitch and 0.7 mm in diameter. This is because this type of ferrule is utilized widely in optical cable components such as MPO connectors. The optical fiber ribbons are generally installed into fiber holes of a ferrule. We used a conventional 12-fiber ribbon with a 0.3 thickness and 0.25 fiber pitch to assemble our fabricated connector. By considering the thickness of the fiber ribbon and that of the MT connector ferrule, we figured that seven is the maximum number of fiber ribbons installable in an MT ferrule. Therefore, we decided that 84 (7 rows of 12) is the target number of fibers installed in our high-count fiber MT connector as shown in Figure 11(b).
\n(a) High-density preconnectorized cable joint and (b) high-count fiber MT connector.
On the basis of the above design, we fabricated an 84-fiber MT connector and high-density preconnectorized cable joint for 2000 fiber cables. Figure 12(a) and (b) shows endface photographs of the fabricated high-count fiber MT connector and high-density preconnectorized cable joint, respectively. The high-count fiber MT connector ferrule consists seven rows of 12 fiber ends between the two guide holes and the high-density preconnectorized cable joint has a 4 × 6 array of a high-count 84-fiber MT connector. Consequently, the fabricated high-density preconnectorized cable joint can potentially connect 2016 fiber cables at one time.
\nEndface pictures of (a) fabricated high-count fiber MT connector and (b) high-density preconnectorized cable joint.
The fabricated high-count 84-fiber MT connector was measured at a wavelength of 1.31 μm. We connected six pairs of high-count fiber MT connectors using the same cramp spring as the conventional MT connectors. The average and maximum insertion losses were 0.40 and 1.8 dB, which are slightly larger than the average (0.3 dB) and maximum (1.0 dB) of the conventional 8-fiber MT connectors. This is because the fabricated fiber hole positions of 84-fiber MT ferrules are thought to have a large offset from the designed positions. However, we think that these offsets can be decreased with the same precision as with the conventional MT connector. The assembly of the high-density preconnectorized cable joint must not generate any excess loss. We demonstrate the insertion-loss changes of the 84-fiber MT connectors in the center and the corner of the installed cable joint. Figure 13(a) and (b) shows the measured insertion-loss change of the high-count 84-fiber MT connectors located at the center and corner of the cable joint, respectively. In Figure 13, there is no loss change of the high-count fiber MT connector before and after assembly. Consequently, there turned out to be no excess loss in the cable joint. Although it takes about 20 hours to connect two sets of 2000 single-mode optical fiber cables using a fusion splice, it took about 5 minutes to connect two sets of 2000 single-mode optical fiber cables using the fabricated cable joint. The cross-sectional area of the cable joint was less than one-fifth that of a conventional optical closure. We have found that the fabricated cable joint can significantly reduce the time and space needed to join high-density optical fiber cables.
\nMeasured insertion-loss change of the high-count 84-fiber MT connectors located at (a) center and (b) corner of cable joint.
We have designed new kinds of functional multifiber connectors on the basis of MT connector technologies [24]. One is a device for switching fibers [25], which is described in this section. Figure 14 shows the basic structure and the switching mechanism of the proposed switch. Figure 14(a)–(c), respectively, shows the fiber connection states before, during, and after switching from one fiber to another. First, two guide pins are fixed at the bottom of the guide holes with the elastic materials in the multifiber array, as shown in Figure 14(a). Next, when the conventional MT ferrule is pushed up with a certain force in a perpendicular direction, the two guide pins begin to slide in the same direction because the elastic materials change to the horizontal direction, as shown in Figure 14(b). Finally, two guide pins are fixed at the top of the guide holes in the multifiber array by the restored elastic materials again after two guide pins have finished sliding, as shown in Figure 14(c). Consequently, a certain optical fiber in the conventional MT ferrule can be switched from one optical fiber to another in the multifiber array.
\nBasic switch structure and the switching mechanism (a) before, (b) during, and (c) after switching.
We discuss the various applications of the proposed optical switch. Figure 15 shows four types of switches. Types a and b are based on the conventional MT ferrule and multifiber array. In type a, two guide pins slide parallel to the multifiber arrangement between two guide holes. With this switch, a fiber from a row in the MT ferrule can be switched from one optical fiber to another in the same row in the multifiber array. In type b, two guide pins slide vertically in relation to the multifiber arrangement with two rows. In this switch, the optical fibers can be switched by the unit of the row. Type c can be inserted and removed between the two endfaces of conventional MT ferrules. With this switch, two guide pins can slide either parallel or vertical to the multifiber arrangement. This switch can be applied to conventional MT connectors and is useful both for installing MT connectors and for existing MT connectors in current optical fiber systems. Type d is an insertion and removal switch in which two guide pins slide vertically in relation to the multifiber arrangement. Therefore, the optical fibers are switched by the unit of the MT ferrule. Consequently, by using the proposed switching method where two guide pins slide in special guide holes, various types of switches with multifiber arrays can be realized for various uses.
\nVarious types of switches. (a) Fiber switch in a row, (b) fiber row switch, (c) insertable and removable switch, and (d) MT ferrule switch.
We fabricated types a and c for an optical switch. The structure and performances of the type-a optical fiber switch are described elsewhere [25]. This section explains the type c optical fiber switch. Figure 16(a) and (b) shows the structure and a photograph of the fabricated multifiber-ribbon switch, which is composed of two MT ferrules and a multifiber array. The multifiber array has a novel guide hole structure in which two guide pins slide vertically to the four-fiber arrangement. The MT ferrules have two rows of four fibers. Figure 17 shows the switching mechanism. In condition A before switching (a), the upper fiber ribbon in MT ferrule 1 is connected to optical fibers in the multifiber array and is also connected to the upper fiber ribbon in MT ferrule 2. When MT ferrule 1 is pushed up manually with a certain force in a perpendicular direction, the two guide pins slide in the opposite direction. In condition B after switching (b), where two guide pins in the multifiber array slide to the 0.25 mm length vertically to the arrangement direction, the lower fiber ribbon in MT ferrule 1 is connected to optical fibers in the multifiber array and is also connected to the upper fiber ribbon in MT ferrule 2. Therefore, the upper fiber ribbon in MT ferrule 1 is switched to the lower fiber ribbon in MT ferrule 1.
\nFabricated fiber-ribbon switch. (a) Structure and (b) photograph of insertable and removable switch.
Switching mechanism of fiber-ribbon switch. (a) Before switching (condition A) and (b) after switching (condition B).
We measured the connection losses of the fabricated multifiber-ribbon switch at a wavelength of 1.3 μm using an LD and an optical power meter. The conventional two MT ferrules and multifiber array are connected with all four guide pins and a special clamp spring. Refractive index matching material is used between the ferrule and the multifiber array endfaces (both connections 1 and 2). Figure 18 shows the measured connection losses. The average connection loss is 1.1 dB. These connection losses are higher than those of the conventional MT connectors because the fabricated fiber positions are thought to have large misalignments of the offset from the designed positions. However, we think that these offset misalignments can be minimized with the same precision as with the conventional MT connector. We also measured the force needed to push the conventional MT ferrule or multifiber array by hand in order to switch fibers. The measured forces were about 9.5 N. Consequently, we revealed that the fabricated switch can provide ease of handling.
\nConnection losses of fabricated fiber-ribbon switch.
To fabricate a high precision multifiber connector, MT ferrules need to be inspected. To shorten the time it takes to measure MT ferrules using conventional inspection equipment, we have created a novel inspection technique that has both fast measurement and low cost features. This section describes the new inspection technique.
\nFigure 19 shows the (a) structure and (b) observation area of conventional inspection equipment for MT ferrules [26]. The conventional equipment consists of a light source, high precision sample stage, an objective lens with 20 times, a charge-coupled device (CCD) camera with 0.4 M pixels, an image processor, and a computer. As shown in Figure 19 (b), the observation area of conventional equipment is 0.2 × 0.17 mm, which corresponds to covering area of a fiber hole. To inspect whole fiber holes and two guide holes on an MT ferrule, the MT ferrule sample must be scanned on the high precision sample stage. Therefore, the conventional inspection equipment takes a long time to measure MT ferrules. We have thus designed and fabricated new inspection equipment to shorten the measurement time.
\n(a) Structure and (b) observation area of conventional inspection equipment for MT ferrules.
Figure 20 shows the (a) structure and (b) observation area of new inspection equipment for MT ferrules [27]. The novel equipment consists of a light source, an objective lens with 1 time, a CCD camera with 10 M pixels, an image processor, and computer. To reduce measurement time, the scanning measurement must be eliminated. Therefore, the objective lens is changed from the conventional 20-time lens to a 1-time lens. Consequently, the observation area is expanded to be covered by the whole endface of an MT ferrule: 6.4 × 4.6 mm. In addition, the new inspection equipment is given a simpler structure and made more cost effective by eliminating the conventional high precision sample stage.
\n(a) Structure and (b) observation area of novel inspection equipment for MT ferrules.
Our goal is to give the new inspection equipment the same measurement accuracy as the conventional equipment: less than 0.1 μm. The measurement accuracy of the new inspection equipment generally worsens because the objective lens is changed. To improve this worsened measurement accuracy, two methods were used. One is to change the pixels of the CCD camera and the other is to use multivalue processing with an image processor.
\nFigure 21 shows a photograph of the fabricated inspection equipment for MT ferrules. The fabricated inspection equipment is simpler and more cost-effective because it does not need a high precision sample stage, a stage driver, or a laser distance meter. We have experimentally demonstrated the multivalue processing using an image processor. Figure 22 shows experimental results for measurement time and accuracy for a 24-fiber MT ferrule. The measurement accuracy is the standard deviation of nine measurements. As the multivalue with the image processor becomes larger, the normalized standard deviation decreases whereas the normalized measurement time increases. These results indicate that there are optimal conditions for both high speed and high accuracy measurement. Figure 23 shows measured fiber hole offsets for the same 24-fiber MT ferrule using the conventional and the fabricated inspection equipment. The offset results for the conventional and fabricated equipment are almost the same. The measured accuracy with the fabricated inspection equipment is less than 0.1 μm, which is as good as that of the conventional inspection equipment. It takes 3 minutes 40 seconds and 11 minutes 30 seconds to measure 24-fiber and 84-fiber MT ferrules using the conventional inspection equipment, respectively. In contrast, it takes 10 seconds each to measure 24-fiber and 84-fiber MT ferrules using the fabricated inspection equipment. Consequently, we reveal that the fabricated inspection technique can measure MT ferrules with high speed, cost effectiveness, and high accuracy.
\nPhotograph of the fabricated inspection equipment for MT ferrules.
Experimental results of measurement time and accuracy to 24-fiber MT ferrule.
Measured fiber hole offsets of same 24-fiber MT ferrule using the conventional and fabricated inspection equipment. (a) X position offset and (b) Y position offset.
This chapter reported the latest mechanically transferable (MT) and multifiber push-on (MPO) multifiber connector technologies.
\nLow insertion-loss and high return-loss angled physical contact (APC)-MPO single-mode multifiber connectors were developed. For these multifiber connectors to achieve a high performance, it is necessary to reduce deviations of all components and to control fiber offset due to shear force caused by compressing two obliquely ended MT ferrules.
\nNext, MT single-mode 84-fiber connectors were developed to realize higher density multifiber connectors. We have developed a novel high-density optical cable joint that has a 24-connector array consisting of new 84-fiber MT connectors. The new cable joining technique significantly shortens the time needed to join the optical fiber cables.
\nNovel optical fiber switches were developed on the basis of MT multifiber connector technology. The switches use a manual guide-pin slide method in special guide holes in a novel multifiber array. The fabricated fiber switches can be easily pushed up at a force of less than 10 N by hand.
\nBecause high precision multifiber connectors need to be measured and inspected, a new inspection technique for MT ferrules was developed and equipment for it was fabricated. The fabricated inspection equipment can measure MT ferrules with high speed, cost effectiveness, and high accuracy.
\nThese single-mode multifiber connectors can be used as key technologies for advanced optical fiber communication systems.
\nThe author thanks Drs. K. Shiraki and T. Kurashima at NTT Access Service Systems Laboratories (ANSL) for their encouragement and helpful suggestions. The author is deeply grateful to R. Koyama, K. Saito, Y. Yamaguchi, and Y. Machida at ANSL for discussing the low insertion APC-MPO connectors and high-density MT connectors; T. Shimizu and C. Fukai at ANSL for discussing the novel optical switch based on MT connector technology; K. Noda and K. Nakashoji for helpful discussions regarding the inspection technique for MT ferrules; and Dr. T Satake at USConec Ltd. for providing the pictures of Figure 2.
\nIn the last decade, microwave quantum electronics received a substantial boost by the advancements in superconducting circuits and dilution refrigerators technologies. These platforms allow experiments to be easily carried out in the mK regime, where the detection and manipulation of signals in the range
Solid state microwave quantum electronics is founded on a building block that has no analogous in quantum optics: the Josephson junction [2]. This, in fact, is a unique nondissipative and nonlinear component that represents the key element of a large series of quantum experiments.
Furthermore, microwave quantum electronics allows the exploration of the so-called ultrastrong coupling regime [3], hard to be reached in quantum optics, and it is worth mentioning that nonlinear resonator can be exploited to access relativistic quantum effects and quantum vacuum effects. To give an example, the Lamb shift [4] effect has been observed in superconducting artificial atom [5], while the dynamical Casimir effect [6, 7] has been promoted by properly engineered superconducting waveguide [8].
From the very beginning, superconducting electronics has been pushed by the strong interest coming from the quantum computation and information community. However, it has been only recently shown that a new concept of 1D metamaterial with embedded several Josephson junctions enables strong photon-photon on-chip interactions [9], allowing experimentalists to engineer dispersion relations that drive the waves traveling along artificial waveguides [10, 11]. These concepts and technologies allow the control and tunability of the wave mixing process. As an example, a weak signal traveling in a metamaterial can interact with a strong pump tone at a different frequency, activating the so-called parametric amplification [12]. The class of devices where these phenomena are promoted is commonly known as traveling-wave Josephson parametric amplifiers (TWJPA) and represents the solid state analogous to optical
It has been shown that TWJPAs can act as quantum parametric amplifiers by reaching the so-called quantum limit [14]. With the purpose of a comparison to the state-of-the-art commercially available low-noise amplifiers, these latter can operate at
The capability to beat the quantum limit is related to the so-called phase-sensitive amplification process, where the metamaterial can operate in degenerate mode (degenerate parametric amplifier, DPA), acting on two waves (signal and idler) at the same frequency (
It should be evident how superconducting electronics not only has demonstrated to be an ideal platform for microwave quantum parametric amplification but also has pushed forward the research field focusing on the generation of nonclassical radiation with attractive potential applications in metrology and quantum information processing.
The theory of a new concept of microwave amplifier was developed by Cullen [12] in 1959. In his paper, Cullen showed a novel mechanism of periodic transfer of power between a pump tone and a signal traveling in a transmission line composed of a voltage dependent capacitance per unit length. A nonlinear component of an RLC circuit can change periodically the resonance frequency of the whole system, leading to a novel way of making broadband amplification, the so-called parametric amplification. In Figure 1, we report two toy models for parametric amplification in mechanical systems with their electrical counterparts.
(a) Sketch of a swing process. An oscillating system at a frequency ωs is excited by parametric amplification via periodical changes of the center of mass position at a frequency ωp=2ωs. (b) LC circuit with variable (nonlinear) C and L components. The case in which the capacitance C is periodically changed in time is the circuit analogous to the mechanical system represented in (a), while the case having an oscillating inductance L mimics the condition sketched in (c), consisting in a torque pendulum with variable inertia momentum [18].
One of the first realizations of Cullen’s idea was made by Mavaddat et al. in 1962 [19]. The signal line was basically a low pass filter, in which the shunt elements were similar varactor diodes. There, the nonlinearity was given by the specific capacitance-voltage relation of the varactor diodes, which is highly nonlinear for relative small voltage values. In this pioneering experiment, a gain of 10 dB and a bandwidth of 3 MHz were shown.
After the theorizing and the subsequent discovery of the Josephson effect [2], it was understood that an easy way to embed a nonlinear component into a transmission line and simultaneously reduce losses was to build a nonlinear inductance made of superconducting material, exploiting a Josephson junction as a source of nonlinearity following the vanguard idea by Sweeny and Mahler [13]. There, the parametric amplifier was modeled by a first-order small-signal theory with the same approach adopted to predict the behavior of GaAsFET transmission line amplifiers. The proposed design consisted of a superconducting thin-film niobium transmission line, composed by a coplanar waveguide integrating a large number of Josephson junctions.
The first realization of a traveling-wave parametric amplifier embedding a series of Josephson junctions was possible due to the PARTS process developed at IBM [9]. Exploiting niobium/aluminum technology, Yurke et al. [20] reported the construction and characterization of a coplanar waveguide, in which the central trace was composed by an array of 1000 Josephson junctions. The experiment was there performed in reflection mode, by terminating one end of the device with a short, leading to a relative high gain of 16 dB but a narrow bandwidth of 125 MHz and a noise temperature of 0.5 ± 0.1 K. The mismatch between the theoretical model and the experimental data has resulted in the understanding of a lack of a complete description of the physics behind this device when working in a small-signal regime. The study of the collective behavior of groups of Josephson junctions forming a transmission line has been an active field of study of several theoretical works [21, 22]. Subsequently, the use of numerical analysis [23] helped in clarifying how wave propagation acts inside this kind of transmission line, giving information on cutoff propagation, dispersive behavior, and shock-wave formation. An analytical model of a Josephson traveling-wave amplifier of greater complexity was developed by Yaakobi et al. [24]. There, a transmission line made of a series of capacitively shunted Josephson junctions was considered.
One of the main limitations concerning the maximum achievable gain, common to all the TWJPAs concepts, is represented by the phase mismatch between the different tones into the line. In particular, it has to be noticed that even though the incoming waves can be in phase, photon-photon interactions between different tones (cross-phase modulation) or the same tone (self-phase modulation) lead to a modification of the phase of the traveling tones themselves. Indeed, quantum mechanically speaking, the power transport between the pump and the signal waves takes place through a photon energy conversion between the pump and the signal. This means that for an efficient energy exchange, conservation of both energy and momentum needs to take place. The latter condition is the corpuscular analogous to the phase matching requirement between the different electromagnetic waves. An engineering solution to overcome this problem is represented by the so-called resonant phase matching (RPM) [11]. O’Brien et al. analyzed this method theoretically on a simple transmission line made of a series of Josephson junctions capacitively shunted to ground operating in the so-called 4-wave mixing (4WM) regime. In their model, they shunted the transmission line with several LC resonators with a resonance frequency slightly above the pump tone. Doing this, they were able to show the rise of a stop band in the dispersion relation, which is able to re-phase the pump with the signal tones by changing the pump wave vector, favoring the wave mixing.
O’Brien’s design was realized not long after [10] using Al technology. In their design, the unit cell of the transmission line was composed by three single nonlinear Josephson cells, the shunt capacitor was made using low-loss amorphous silicon dielectric and a resonator was placed after each group of 17 unit cells. The device showed a maximum gain of 12 dB over a 4 GHz bandwidth centered on
A similar design was adopted by Macklin et al. [14] to prove experimentally the capability of a TWJPA combined with the RPM technique to be used as a reliable tool for qubits readout. In this paper, the TWJPA, based on Nb technology and a different RPM periodicity, was first characterized, showing a gain of 20 dB over a 3 GHz bandwidth. Moreover, the quantum efficiency of the amplifier was tested when coupled with a 3D transmon qubit, leading to an efficiency value of
Another option to solve the mismatch problem was suggested by Bell and Samlov [26], who proposed a self-phase matching transmission line embedding a series of asymmetric superconducting quantum interference devices (SQUIDs). The remarkable feature of this design is that it does not need any resonant circuit to achieve phase matching. This TWJPA is indeed able to tune the nonlinearity of its SQUIDs just through the use of an external magnetic field. Zhang et al. realized that this design [27] proves the wide tunability on positive and negative values of the Kerr nonlinearity by a magnetic flux and its capability to assist phase matching in the 4WM process. The 4WM process is intrinsically affected by phase mismatch because it takes origin from a cubic (Kerr-like) nonlinearity of the current-phase relation of the SQUIDs composing the TWJPA, getting unwanted effects from self-phase and cross-phase modulations.
Zorin showed [28] that by embedding a chain of rf-SQUIDs into a coplanar waveguide, it is possible to tune both the second and third order nonlinearities of their phase-current relation. This is a totally a novel approach to the TWJPA, since the possibility to use a quadratic term as a source of nonlinearity, allows to work in the 3-Wave Mixing regime (3WM), as theorized by Cullen 57 years before. It is well-known that 3WM has several advantages when compared to 4WM. Firstly, it allows to operate with a minimal phase mismatch. Secondly, it requires a lesser pump power to achieve the same amplification per unit length. Eventually, it separates signal and idler from pump tones, easing the engineering of the experimental setup by removing the requirement of heavy filtering in the middle of the amplification band. A proof of principle based on the Zorin’s layout [29] showed a gain reaching 11 dB over a 3 GHz bandwidth.
A step forward in controlling the metamaterial nonlinearities was attempted by Miano et al. [30] achieving an independent tune of both second and third order terms in the current-phase relation by adjusting the bias current in some inductive circuits surrounding the transmission line. This technology takes the name of symmetric traveling-wave parametric amplifier (STWPA), its peculiarity arising from the symmetric arrangement of the rf-SQUIDs that compose the transmission line. This device concept represents the state-of-the-art in the field, allowing the exploration a wide portion of the control parameters space, leading to a maximum estimated gain of 17 dB and a 4 GHz bandwidth.
In the last decade, different theoretical models have been developed to predict the behavior of an electric transmission line containing an array of Josephson junctions, employed as nonlinear elements. In this section, we will focus on those models developed to predict the behavior of a TWJPA in the particular case of a 4WM process, under undepleted degenerate pump approximation (i.e., assuming that the power held by the pump wave is at first approximation constant and larger than the one owned by the signal and the idler). We will firstly focus on the classical theory proposed by Yaakobi et al. in 2013 [24] and O’Brien et al. in 2014 [11], in which the behavior of the transmission line is derived imposing the current conservation in the system. This starting assumption leads to the definition of a partial differential nonlinear equation that can be turned into a system of coupled mode equations, providing the expression of the amplitude of the pump, signal, and idler tones along the transmission line. Subsequently, we will discuss two different quantum approaches for the description of the parametric amplifier dynamics. The first one, proposed by Grimsmo and Blais in 2017 [31], exploits a Hamiltonian based on continuous-mode operators to derive, in an interaction picture frame, a device’s output field. The second one instead, proposed by van der Reep in 2019 [32], derives a system of coupled mode equations for the creation and annihilation quantum operators starting from a Hamiltonian based on discrete-mode operators.
The theories presented in this chapter will be based on a series of simplifying assumptions, whose experimental realization could be difficult to be obtained. For instance, in a real device, the undepleted pump approximation is hardly respected along the entire extension of the device because, along the line, the pump tone transfers a non-negligible amount of energy to the signal and idler one. The depletion effects, resulting in a reduction of the gain and of the dynamics-range of the amplifier, have been studied both in a classical and quantum frame [28, 33].
In all of these models, a lossless electrical circuit composed by the repetition of an elementary cell, whose structure is shown in Figure 2, is taken into account. In order to standardize the notations, we assume that the Josephson junctions embedded in the transmission line are identical (i.e., they have the same critical current
Electrical equivalent representation of a repetition of Josephson junctions embedded in a transmission line. The junctions are modeled as an LC resonant circuit. The length of the unitary cell length is represented by a.
where
where
Furthermore, we define
where
The energy stored in the n-th Josephson junction can be expressed, using the definitions given in Eqs. (1) and (2), as
under the assumption that
where
Finally, we assume identical coupling capacitances
In this subsection, we will present the main steps for the derivation of the classical model presented in [11, 24]. Under proper assumption, this model allows to determine analytically the amplitude of the signal’s and idler’s waves along the transmission line.
Expressing the current flowing through each branch of the circuit presented in Figure 2 in terms of absolute phases
where the last term derives from the first-order approximation of the nonlinear behavior of the Josephson’s inductance.
Assuming the length a of the elementary cell is much smaller than the wave lengths of the propagating waves
In this way, it is possible to define a nonlinear differential equation for the continuous absolute phase
In the case of a weakly nonlinear medium, the dispersion law can be derived from Eq. (9), considering the left-hand side being equal to zero and imposing a plane-wave solution
The solutions of Eq. (9) can be expressed, as shown by O’Brien et al. [11], in the form of a superposition of three waves (pump, signal, and idler) whose amplitudes are complex functions of the position along the line:
The case of a 4WM process with a degenerate pump can be taken into account by imposing the frequency matching condition
where
while the coupling constants
Expressing the complex amplitudes
it can be demonstrated that, working under the undepleted pump approximation
where
The total gain of an amplifier, composed by the repetition of
A standard method to treat quantum superconducting circuits is represented by the lumped element approach [34]. In this latter, the Hamiltonian of the quantum circuit is straightforwardly derived from its classical counterpart by promoting fields to operators and properly imposing commutating relations. In this view, one can proceed by deriving the Lagrangian of a TWJPA composed by the repetition of N unitary cells, under first nonlinear order approximation, as
where
where
where
From Eq. (21), one can easily derive the Euler-Lagrange equation whose form, for
The Hamiltonian of the system can be derived from the Lagrangian by taking into account
where the term
This Hamiltonian can be converted to its quantum form promoting the field
In direct analogy with Eq. (11), one can express the flux operator in terms of continuous-mode functions [34], such as
where the subscript
(where the zero-point energy, which does not influence the dynamics of the amplifier, has been omitted).
Using the expansion of
In the expressions of these contributions, the fast rotating terms and the highly phase mismatched left-moving field have been neglected:
describes the cross-phase modulation,
describes the broadband squeezing, and
describes the self-phase modulation.
The function
Assuming the nonlinear Hamiltonian
where
Working in the monochromatic degenerate pump limit
and
where
Similar to the previous classical treatment, one can introduce the co-rotating framework by replacing the field operators with
In this framework, one can derive the following differential equation
and
where
where
If a state moves inside a TWJPA of length
An alternative approach for the derivation of the quantum dynamics of a TWJPA is the one proposed in [32]. In this model, the quantum Hamiltonian for a 4WM parametric amplifier is expressed as the integral, along an arbitrary quantization length
under the assumption that
Therefore, the quantum Hamiltonian of the system can be expressed, with an approximation to the first nonlinear order, as
where
(here
Before defining the flux operator, it is necessary to define an effective inductance
Using the telegrapher’s equation [37], the discrete-mode current operator, under slowly varying amplitude approximation (
Therefore, the flux operator can be expressed as
The recursive relation deriving from Eq. (49) can be solved iteratively. Exploiting a power series expansion of the sine function and considering just the first order of interaction, it results that
where
Substituting Eqs. (46) and (50) in Eq. (45), and limiting the expression to the first nonlinear order, the Hamiltonian for a 4WM amplifiers turns up
where
Neglecting the constant zero-point energy and assuming a strong degenerate classical pump (as shown in [36])
it is possible to approximate the Hamiltonian in Eq. (52) to the second order in
where
represents the quantum self-phase modulation (when
Starting from the Hamiltonian
In [32], the hypothesis under which the classical coupled mode equations Eqs. (12) and (13) can be obtained from Eqs. (57) and (58) is described in detail.
Moving to a co-rotating frame (
where
whose solutions are
where the exponential complex gain factor is defined as
If a state spends a time
To make the results of this last treatment, in which the operators are expressed as a function of the time, comparable with the previous ones, in which the operators are expressed as a function of the space coordinate, we need to take into account the phase velocity of the tones. It turns out that:
where
The three exponential complex gain factors (
Comparison of total phase mismatches (Ψi) and exponential complex gain factors (gi) predicted by the three treatments presented in Section 3. For these calculations, typical constructive parameters have been assumed: a=50μm, Ic=5μA, CJ=300fF, and C0=35fF, in such a way that the characteristic impedance is Z≈50Ω. Furthermore ωp/2π=6GHz and Ip=Ic/2. In the insets, the differences between the quantum predictions and the classical ones are presented.
It is important to observe that in Eqs. (17), (41), and (61), the last term is always equal to zero in the case of a zero initial idler amplitude. In such a case, and under the hypothesis of a perfect phase matching (
In the present chapter, we have presented the state-of-the-art of the experimental evidences in the field of Josephson junctions-based traveling-wave metamaterials through a historical review in Section 2. Moreover, in Section 3, we have reported three different theoretical approaches for the prediction of a TJWPA dynamics, in the particular case of a 4WM process. Assuming similar simplifying hypothesis, like the use of a classical undepleted degenerate pump, the presence of slowly varying fields along the transmission line and approximating the nonlinearities of the system up to the first order, a similar expression for the signal amplitude (or field annihilation/creation operators in the case of quantum theories) expressed in a co-rotating frame, is derived in the three treatments. Although the results of the quantum theories are similar to the classical ones, the description of the system dynamics with a quantum theory grants the possibility to evaluate photon-number distributions, squeezing effects and averages, standard deviations or higher-order moments of the measurements operators, taking into account the commutation relations between operators explicitly. For instance, detailed calculations of the output state of a TWJPA in the case of a single-photon input state and in the case of a coherent input state are presented in [32].
The author would like to thank Luca Callegaro for the stimulating discussion. This work was partially funded by the Joint Research Project PARAWAVE of the European Metrology Programme for Innovation and Research (EMPIR). This project has received funding from the EMPIR program co-financed by the Participating States and from the European Unions’ Horizon 2020 research and innovation program.
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