Department of Electronics and Nanoengineering The present dissertation is devoted to an A V Spatially dispersive important field of applied electromagnetics: -otlaD atki Spatially dispersive metasurfaces. D 1 A r Marreatansguermfaecnets orfe psurebs-ewnatv ae ltewnog-tdhi minecnlussioionnasl 94/102 hcdas metasurfaces 7 y engineered to manipulate incident electromagnetic radiation in a prescribed pS a fashion. The subject of spatially dispersive ait metasurfaces merges such areas of physics yll d Viktar Asadchy and engineering as metamaterials, bi- si p anisotropic media, antenna arrays, and e r s diffraction gratings. Due to the vi e multidisciplinary nature of the subject, m e phenomena and devices resulting from it may at s carry significant implications for applied u r f a electromagnetics from microwaves to optical c e s frequencies. The dissertation presents design and measurement data of several spatially dispersive metasurfaces: Shadow-free gradient reflector and absorber as well as an optical anomalously reflecting grating. ISBN 978-952-60-7559-4 (printed) BUSINESS + 9 ISBN 978-952-60-7558-7 (pdf) ECONOMY H ISSN-L 1799-4934 S ISSN 1799-4934 (printed) ART + T F ISSN 1799-4942 (pdf) DESIGN + M ARCHITECTURE *G Aalto University aA fha DScehpoaortlm oef nEtl eocf tErilceaclt rEonngicinse aenridn gN anoengineering STECCIEHNNCOEL +O GY U otl f www.aalto.fi n ej CROSSOVER vi + re DOCTORAL DOCTORAL s DISSERTATIONS DISSERTATIONS yti 2017 Aalto University publication series DOCTORAL DISSERTATIONS 149/2017 Spatially dispersive metasurfaces Viktar Asadchy A doctoral dissertation completed for the degree of Doctor of Science (Technology) to be defended, with the permission of the Aalto University School of Electrical Engineering, at a public examination held at the lecture hall T2 of the school on 29 September 2017 at 12. Aalto University School of Electrical Engineering Department of Electronics and Nanoengineering Supervising professors Prof. Sergei Tretyakov, Aalto University, Finland Prof. Igor Semchenko, Francisk Skorina Gomel State University, Belarus Preliminary examiners Prof. Mario Silveirinha, Instituto Superior Técnico, Portugal Dr. Dimitrios Sounas, The University of Texas at Austin, USA Opponent Prof. Romain Fleury, École Polytechnique Fédérale de Lausanne, Switzerland Aalto University publication series DOCTORAL DISSERTATIONS 149/2017 © Viktar Asadchy ISBN 978-952-60-7559-4 (printed) ISBN 978-952-60-7558-7 (pdf) ISSN-L 1799-4934 ISSN 1799-4934 (printed) ISSN 1799-4942 (pdf) http://urn.fi/URN:ISBN:978-952-60-7558-7 Unigrafia Oy Helsinki 2017 Finland Abstract Aalto University, P.O. Box 11000, FI-00076 Aalto www.aalto.fi Author Viktar Asadchy Name of the doctoral dissertation Spatially dispersive metasurfaces Publisher School of Electrical Engineering Unit Department of Electronics and Nanoengineering Series Aalto University publication series DOCTORAL DISSERTATIONS 149/2017 Field of research Radio Engineering Manuscript submitted 7 June 2017 Date of the defence 29 September 2017 Permission to publish granted (date) 10 August 2017 Language English Monograph Article dissertation Essay dissertation Abstract Natural materials and substances possess a rich variety of electromagnetic properties over the entire electromagnetic spectrum. Despite this diversity, nature does not equip us with a full set of possible material tools for controlling electromagnetic waves and realizing all physically possible effects. Only the use of artificial, engineered substances can give us full control over electromagnetic properties of materials. For instance, while spatial dispersion effects are weak in natural materials, they can be strongly pronounced in artificially engineered composite materials, metamaterials. Metamaterials consist of inclusions whose dimensions are small but comparable with the operating wavelength, which enables existence of strong spatial dispersion effects in them such as bi-anisotropy, magnet-less magnetism, and gyrotropy. This dissertation is devoted to the young and scantily explored field of spatially dispersive metasurfaces. Metasurfaces represent a two-dimensional arrangement of sub-wavelength inclusions engineered to manipulate in a prescribed fashion incident electromagnetic radiation. The first half of the dissertation contains a theoretical review of the research field essential for understanding of the obtained results outlined in the second half. Presentation of novel results can be broken down into three parts. The first part describes a semi- analytical technique for polarizability extraction of an arbitrary electrically small bi-anisotropic scatterer. Subsequently, the technique was exploited for the design of a novel scatterer with extremely pronounced spatial dispersion of the first order. The second part outlines the key ideas behind two designed spatially dispersive metasurfaces: A resonant gradient reflector and an absorber transparent outside the resonance band. It is demonstrated that such shadow-free operation of the metasurfaces requires spatial dispersion effects. The last part presents the exact synthesis of gradient metasurfaces for ideal wavefront control in reflection and transmission regimes. The fundamental importance of spatial dispersion in such metasurfaces is demonstrated. As a proof of concept, an optical metasurface for perfect anomalous reflection is designed and measured. Keywords spatial dispersion, metamaterials, metasurfaces, bi-anisotropy, gratings ISBN (printed) 978-952-60-7559-4 ISBN (pdf) 978-952-60-7558-7 ISSN-L 1799-4934 ISSN (printed) 1799-4934 ISSN (pdf) 1799-4942 Location of publisher Helsinki Location of printing Helsinki Year 2017 Pages 201 urn http://urn.fi/URN:ISBN:978-952-60-7558-7 Preface Ourrealityislikeagame.Weareallforcedtofollowtherulesofthisgame. WedonotknowwhywearepulledbygravitationtotheEarth,butweknow thatitisoneofthegamerules.Theserulesaretheonlyuniversalrules; theyremainconstantanddonotdependonsocietiesandcivilizations. ThenameofthisgameisPhysics. ThepresentworkwascarriedoutattheDepartmentofElectronicsand NanoengineeringofAaltoUniversity,SchoolofElectricalEngineering. I would like to express my warmest gratitude to my supervisor, Prof. SergeiTretyakov. Withoutyourguidanceandpersistenthelpthisdisser- tation would not have been possible. I very appreciate your numerous scientificadvicesanddiscussionswithyoufromwhichIhavelearntalot. ThereisstillsomuchIcouldlearnfromyou. Itwasagreathonourand privilege for me to workin your group and contribute to its high-quality research. Ilikethefriendlyandinternationalspiritofthegroupaswell asveryimportantseminars. Youmakethecrucialcontributiontobothof them. IwouldliketothankmysecondsupervisoratFranciskSkorinaGomel State University (Belarus), Prof. Igor Semchenko. I am very grateful to you for bringing me to the field of metamaterials and proposing to me several important research directions. You are always ready to support meinbothacademicandpracticalmatters. Thereareseveralotherpeoplewhomadecrucialimpactonmyacadem- icalpath. Firstofall,itismyteacherofphysicsathighschool,Dr. Alexei Pavlov.Hisoutstandingteachingskillsanddeepunderstandingofphysics havedeterminedmyfuture. IthankDr. ValeriiKapshaiandotherexcel- lent professors and lecturers at Francisk Skorina Gomel State Univer- sitywhoprovidedhigh-levelphysicseducationduringmyundergraduate studiesatuniversity.IamverygratefultoProf.SergeiKhakhomovforhis 1 Preface help with multiple practical and academic issues as well as for his good andencouraginghumour. IamalsoindebtedtoProf.MartinWegenerand Mr. AndreasWickbergforprovidingmetheopportunitytolearndifferent nanofabricationandopticalmeasurementtechniquesduringmyresearch visitinKarlsruheInstituteofTechnology. Thelastbutnotleast,Iwould liketothankProf. ConstantinSimovskiandProf. IgorNefedovformulti- pleimportantscientificdiscussionsduringmydoctoralstudies. Iwouldliketoexpressmythankstoallmycollaboratorsandfriends:Dr. Ihar Faniayeu, Dr. Younes Ra’di, Ms. Svetlana Tcvetkova, Dr. Moham- mad Albooyeh, Dr. Ana Díaz Rubio, Dr. Mohammad Sajjad Mirmoosa, Prof. Do-Hoon Kwon, Mr. Amr Elsakka, Dr. Joni Vehmas, Dr. Osama Mirza,Mr. DimitriosTzarouchis,Mr. MikhailOmelyanovich,Mr. Sergei Kosulnikov,Dr. IrinaNefedova,Mr. GrigoriiPtitcyn,Dr. FuLiu,andMr. Xu-Chen Wang. I have so many memories about pleasant and exciting timespentwithyouall. MyspecialgratitudegoestomybestfriendsMr. AndreiBorisenkaandDr. IharFaniayeu. Itisimpossibletodescribehow greatandsupportivetomethesepeoplehavebeenthroughoutmylife. Iwouldliketothankthepreliminaryexaminers,Prof.MarioSilveirinha andDr. DimitriosSounas,forthoroughexaminationofthisthesis. DuringthisthesisworkIhavereceivedfinancialsupportfromtheAalto ELECDoctoralSchool,NokiaFoundation,andFoundationforAaltoUni- versity Science and Technology. All this support is gratefully acknowl- edged. IaddressmywarmestgratitudetomydearparentsNatalliaandSergei, auntElena,brotherIlia,andcousinEkaterinafortheirunboundedkind- ness and love to me, persistent support and presence in my life. Family isofthehighestimportancetome. Myspecialthanksgoestomygrand- motherLyudmilawhowasanexampleofhighestmoralityforme. Finally, I wish to express my sincere thanks to my sweetheart wife Huyen. Ourmeetinghasdividedmylifeintotwoparts: Incomplete“be- fore”andveryhappy“after”. Espoo,August16,2017, ViktarAsadchy 2 Contents Preface 1 Contents 3 ListofPublications 5 Author’sContribution 7 ListofAbbreviations 11 ListofSymbols 12 1. Introduction 18 I Researchfield 22 2. Frequencydispersion 24 3. Spatialdispersion 27 3.1 MacroscopicMaxwell’sequations . . . . . . . . . . . . . . . . 27 3.2 First-orderspatialdispersionandbi-anisotropy . . . . . . . 29 3.3 Second-orderspatialdispersionandartificialmagnetism . . 31 3.4 Spatialdispersionofhigherorders . . . . . . . . . . . . . . . 33 3.5 Constituentsofbi-anisotropicmaterials . . . . . . . . . . . . 34 3.6 Classificationofbi-anisotropicmaterials . . . . . . . . . . . . 37 3.7 Timeinversionandnon-reciprocityinelectrodynamics . . . 41 3.8 Spatialinversionandnon-reciprocalbi-anisotropicmaterials 44 3.9 Constraintsonmaterialparameters . . . . . . . . . . . . . . 49 3.10 Wave propagation in bi-anisotropic materials and extreme bi-anisotropy . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 3 Contents 4. Metamaterialsandroleofspatialdispersion 58 4.1 Negativerefraction . . . . . . . . . . . . . . . . . . . . . . . . 58 4.2 Sub-wavelengthfocusingandtransformationoptics . . . . . 61 4.3 Wiremedia . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 4.4 Braggscatteringandelectromagneticcrystals . . . . . . . . 65 4.5 Metasurfaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68 4.6 Homogenizationmodelsofmetasurfaces . . . . . . . . . . . . 74 II Results 78 5. Singlebi-anisotropicinclusions 80 5.1 Polarizabilitiesextractiontechniques. . . . . . . . . . . . . . 80 5.1.1 Author’scontribution . . . . . . . . . . . . . . . . . . . 82 5.2 Purelybi-anisotropicscatterers . . . . . . . . . . . . . . . . . 84 5.2.1 Author’scontribution . . . . . . . . . . . . . . . . . . . 85 6. Spatiallydispersivemetasurfacesandtheirapplications 88 6.1 Shadow-freegradientreflectors . . . . . . . . . . . . . . . . . 88 6.1.1 Author’scontribution . . . . . . . . . . . . . . . . . . . 90 6.2 “Invisible”absorbers . . . . . . . . . . . . . . . . . . . . . . . 92 6.2.1 Author’scontribution . . . . . . . . . . . . . . . . . . . 94 6.3 Exactsynthesisofmetasurfacesforwavefrontcontrol . . . . 95 6.3.1 Author’scontribution . . . . . . . . . . . . . . . . . . . 97 7. Conclusions 102 Bibliography 103 Publications 114 4 List of Publications Thisthesisconsistsofanoverviewandofthefollowingpublicationswhich arereferredtointhetextbytheirRomannumerals. I V.S.Asadchy,I.A.Faniayeu,Y.Ra’di,andS.A.Tretyakov. Determining polarizability tensors for an arbitrary small electromagnetic scatterer. PhotonicsandNanostructures: FundamentalsandApplications,12,is- sue4,(298–304)(invitedpaper),August2014. II M.Albooyeh,V.S.Asadchy,R.Alaee,S.M.Hashemi,M.Yazdi,M.S.Mir- moosa, C. Rockstuhl, C.R. Simovski, and S.A. Tretyakov. Purely bian- isotropicscatterers. PhysicalReviewB,94,issue24,245428(1–7),De- cember2016. III V.S. Asadchy, Y. Ra’di, J. Vehmas, and S.A. Tretyakov. Functional metamirrorsusingbianisotropicelements.PhysicalReviewLetters,114, issue9,095503(1–5),March2015. IV V.S. Asadchy, M. Albooyeh, and S.A. Tretyakov. Optical metamirror: all-dielectricfrequency-selectivemirrorwithfullycontrollablereflection phase. Journal of the Optical Society of America B, 33, issue 2, (A16– A20)(invitedpaper),February2016. V V.S.Asadchy,I.A.Faniayeu,Y.Ra’di,S.A.Khakhomov,I.V.Semchenko, and S.A. Tretyakov. Broadband reflectionless metasheets: frequency- selective transmission and perfect absorption. Physical Review X, 5, issue3,031005(1–10),July2015. 5