介电常数和磁导率示意图超构表面：0E0>0,H>0绿色和蓝色区域的材料但有微小、超薄的平面周期NO性或准周期结构er060,u<0零折射率材料：黄粉色区域图取自“罗杰，赖耘，零折射率材料的物理与应用，物理，48卷7期，426（2019）”1
1 介电常数和磁导率示意图 超构表面： 绿色和蓝色区域的材料 但有微小、超薄的平面周期 性或准周期结构 零折射率材料：黄粉色区域 图取自“罗杰，赖耘，零折射率材料的物理与应用，物理， 48卷7 期，426 （2019）
第四章超构表面及零折射率材料4.1零折射率材料及其应用4.2超构表面及其应用4.2.1超材料概况4.2.2基于广义snell定律的相位调控4.2.3偏振调控4.2.4介质超构表面4.2.5基于超构表面的光学非线性古英ygu@pku.edu.cn2
2 第四章 超构表面及零折射率材料 4.1 零折射率材料及其应用 4.2 超构表面及其应用 4.2.1 超材料概况 4.2.2 基于广义snell定律的相位调控 4.2.3 偏振调控 4.2.4 介质超构表面 4.2.5 基于超构表面的光学非线性 古英 ygu@pku.edu.cn
natureREVIEW ARTICLEphotonicsHEDONLINE:17JUEY20NIDOE10.103R/N2011年之前：Pastachievementsandfuturechallengesin3D超构材料thedevelopmentofthree-dimensionalphotonicmetamaterials集中于负折射Costas M. Soukoulis2* and Martin Wegener?"Photonic metamaterials are man-made structures composed of tailoredmicro-ornanostructuredmetallodielectric subwavelengthbuildingblocksbGoldDielectricSilverFigure2|3D photonic-metamaterial structures.a, Double-fishnet negative-index metamaterial with several layers'3s,9.2.zx7,b,"Stereoorchiralmetamaterial(seealsoFig.3)fabricatedthroughstackedelectron-beamlithography24-26.2-33,c,Chiralmetamaterialmadeusingdirect-laserwritingandelectroplating38d,Hyperbolic(or'indefinite)metamaterial434madebyelectroplatinghexagonal-hole-arraytemplates49,e,Metal-dielectriclayeredmetamaterial composedofcoupledplasmonicwaveguides,enablingangle-independentnegativenforparticularfrequencies444s.f,SRRsorientedinallthreedimensions,fabricatedusingmembraneprojectionlithographyst.g,Wide-anglevisiblenegative-indexmetamaterialbasedonacoaxialdesignsph,Connectedcubic-symmetrynegative-indexmetamateriallstructureamenabletodirectlaserwritingo.i,Metalcluster-of-clustersvisible-frequencymagneticmetamaterialmadeusing large-area self-assembly?9.j,All-dielectricnegative-indexmetamaterial composedof two setsofhigh-refractive-index3dielectric spheres arranged on a simple-cubic lattice52-s
3 2011年之前： 3D超构材料 集中于负折射 “Photonic metamaterials are man-made structures composed of tailored micro- or nanostructured metallodielectric subwavelength building blocks
NATUREREVIEWSIPHYSICSVOLUME1MARCH20191992019年综述3Dmetamaterials给出了超材料的要点MuamerKadic,2GraemeW.Miltons,MartinvanHecke45andMartinWeqenero?KeypointsMetamaterialsarerationallydesigned compositesmadeoftailored buildingblockswhicharecomposedofoneormoreconstituentbulkmaterials,leadingtoeffectivemediumpropertiesbeyondthoseoftheiringredients..Metamaterialstherebyfulfila long-standing dreamofcondensedmatterphysicstodesignmaterialsonthecomputertoavoidtedioustrial-and-errorproceduresandexcessiveexperimentationAlthoughmany1Dand2Dmodelarchitectureshavebeenconsideredbecauseoftheireaseoffabrication andreduced design complexity.thefull potentialofthemetamaterialconceptisopenedupfor3Dmicrostructuresandnanostructures.lnelectromagnetismandoptics,examplesareeffectivediamagnetismandParamagnetismuptoopticalfrequencies,impedancematchinganddualitynegativerefractiveindices,maximumelectromagneticchirality.perfectopticalabsorptionandnon-reciprocalpropagationofelectromagneticwaveswithoutstaticmagneticfields.Inacousticsandmechanicsparameters,chiralmechaniccompressibility.negativedybroadbandperfectsoundatandhighlynonlinear,multistconstituents.Intransport,examplesarehitheabsolutemobilityandthmaghetoresistances and theofmagnitude.Future3Dmaterialprinters!10μm2um1μmpropertiesfromonlyasmalltoday's2DgraphicalprinterFig.2|Gallery of designed3D opticalmetamaterial unit cells andcorresponding experimental realizations.cartridges.alAnarrangementofmetallicsplit-ringreslatorsleadingtoartificialmagnetismb|Afishnetarrangementforuniaxialnegativerefractiveindices.c|AnABAB...ABlaminate,whichisaunitcellusedinmanymetamaterials,including4hyperbolicmetamaterialsd|Helicesprovidingchiralbehaviour,e|Multipleintertwinedhelicesforrecoveringthree-foldrotationalsymmetry.PanelaisadaptedwithpermissionfromREF.Wiley-VCH.PanelbisadaptedfromREE,Springer
4 2019年综述 给出了超材料 的要点
natureFOCUSIREVIEW ARTICLEnanotechnologyPUBLISHEDONLINE:7JANUARY2016|DOI:10.1038/NNANO.2015.304All-dielectricmetamaterialsSaman Jahani andZubin Jacob1.2*超材料的研究集中在：负折射、手性、零折射率材料、双曲材料等方面，但是人们研究超材料是为了在亚波长尺度任意操控光（振幅、相位、偏振），光学超构表面的研究正是达到了此目的Even though metamaterials research started with the quest fornegative-index, zero-index,chiral73 and hyperbolic74media, thegoal of the field has grown into arbitrary control of the amplitude,phase andpolarization of light wavesatthe subwavelength(nano)scale2930.The most promising route to achieve this goal consists of5
5 超材料的研究集中在： 负折射、手性、零折射率材料、双曲材料等方面，但是人们研 究超材料是为了在亚波长尺度任意操控光（振幅、相位、偏 振），光学超构表面的研究正是达到了此目的
4.2超构表面及其应用4.2.1超材料概况4.2.2基于广义snell定律的相位调控4.2.3偏振调控4.2.4介质超构表面4.2.5基于超构表面的光学非线性6
6 4.2 超构表面及其应用 4.2.1 超材料概况 4.2.2 基于广义snell定律的相位调控 4.2.3 偏振调控 4.2.4 介质超构表面 4.2.5 基于超构表面的光学非线性
Metasurface：超表面、超构表面planar,ultrathinmetamaterials、metafilms、周期或准周期thetwo-dimensional eguivalent of metamaterials相比于matematerial，Metasurface具有以下优势：制备更简单？、光损耗更小、更紧凑（体积小）相位等性质的调控不依赖传播长度的累积，从而减少了色散有人把metasurface的到来，叫做“平面光学”时代10多年来研究工作层出不穷（SCI两万多篇）1调控相位振幅和偏振等，结构和原理丰富、应用广泛仅review都超过百篇，侧重点各有不同
7 有人把 metasurface的到来，叫做“平面光学”时代 10多年来研究工作层出不穷（SCI两万多篇），调控相位、 振幅和偏振等，结构和原理丰富、应用广泛 仅review都超过百篇，侧重点各有不同 Metasurface：超表面、超构表面 planar, ultrathin metamaterials、metafilms、周期或准周期 the two-dimensional equivalent of metamaterials 相比于matematerial, Metasurface具有以下优势： 制备更简单？、光损耗更小、更紧凑（体积小） 相位等性质的调控不依赖传播长度的累积，从而减少了色散
SCIENCEVOL33421OCTOBER2011333Light Propagation with PhaseDiscontinuities:Generalized Laws ofReflection and RefractionNanfangatriceGenet2MikhailKatsFrancecoAieta,3JeanPhilippeTetiennFedericoCapasso,1+ZenoGaburro1,5传统光学中，相位的改变来自于光在传播中长度的累积（超构表面）中，提出了新的改变相位的自由度metasurface原理：通过亚波长尺度的结构设计，实现“陡峭的”相位移动AGeneralizedrefraction law:2odosin(o)nt-sin(0,)ni=2元dx0n;p+dΦdx>XGeneralized reflection law:nt020 ddsin(0.)-sin(01) = 2元m; dxB8
8 传统光学中，相位的改变来自于光在传播中长度的累积 metasurface （超构表面）中，提出了新的改变相位的自由度 原理：通过亚波长尺度的结构设计，实现“陡峭的” 相位移动 Generalized refraction law: Generalized reflection law:
Review ArticleVol.4,No.1/January2017/Optica139OpticaRecentadvancesinplanaroptics:fromplasmonicto dielectric metasurfacesPATRICEGENEVET14FEDERICOCAPASSO2*FRANCESCO AIETA3MOHAMMADREZAKHORASANINEJADANDROBERTDEVLIN?co . sin p六%(1)I n, sin O, -n in O,=级装,(b)(a)超构表面的相位移动直观、易于理解9
9 超构表面的相位移动 直观、易于理解
SymmetricmodeAntisymmetricmodeFig.2.(A)Calculated phaseand amplitudeofABscatteredlightfromastraightrodantennamadeofaperfectelectricconductor(20).Thevertical dashed1.01.0lineindicates the first-orderdipolar resonance ofphase.amplitudetheantenna.(B)AV-antenna supports symmetric波长8umandantisymmetricmodes,which areexcited,remspectively,bycomponents ofthe incident.fieldalong80.510.52s and a axes.The angle between the incident po-Colarization and the antenna symmetry axis is 450共振金属结构The schematic current distribution is represented0.00.0bycolorsontheantenna(blueforsymmetricand0.20.40.60.81.0red for antisymmetric mode),with brighter colorrepresenting larger currents,The direction of cur-rentflowis indicatedbyarrowswithcolorgradient.AmplitudePhase ShiftDF(C)V-antennascorrespondingtomirrorimagesof(normalized)(degree)1.81.8180thosein(B).Thecomponents ofthescattered elec-E4E0.9tric field perpendicular to the incident field in (B)1.61.6E135EV0.8and (Ohavea tphasedifference.(D and E)An-901.41.40.7alytically calculated amplitude and phase shift of0O0.6the cross-polarized scattered light for V-antennas8121.2450.5consistingof gold rods witha circularcrosssectionI051.00.421.0andwithvariouslenqthhandanqlebetweenthe00.3rodsAat=8um(20).Thefourcirdesin(D)and-450.80.8d(E) indicate the values of h and Aused in exper-SoP0.20.6900.6iments.The rod geometry enables analytical cal-0.1culations of the phase and amplitudeof thescattered13s0.40.4020406080100120140160180020406080100120140160180liqht,withoutrequiningtheextensivenumerical (degree) (degree)simulations needed to compute the same quan-titiesforflat"antennas witha rectangular cross-->Asection,asusedintheexperiments.TheopticalLLLTET1properties of a rodand"flat"antenna of the same20-Xlength are quantitatively very similar,when theErod antenna diameter and the"flat"antenna40GC厂width and thickness are much smaller than thelength(20).(F)Schematicunitcelloftheplasmonic30interface fordemonstrating the generalized laws ofLLLITIreflection and refraction. The sample shown in Fig. 3Ais created by periodically translating in the x-y planethe unit cell. The antennas are designed to haveequal scattering amplitudes and constant phaseN10differenceA=r/4betweenneighbors.(G)Finitedifferencetime-domain(FDTD)simulationsofthescattered electric field for the individual antennascomposingthearrayin(F).Plotsshowthescat-10teredelectricfieldpolarizedinthexdirectionforr/8T/43r/8T/25T/83F/47r/80y-polarized planewaveexcitation at normal in-xcidencefromthesiliconsubstrate.Thesiliconprinciple, the anomalously refracted beam resutting from the superposi-substrate is locatedatz0.Theantennasare equallyspaced at asub-wavelengthseparationF/8, whereis theunit cell length.Thetilted redtion of these spherical waves is thena planewave thatsatisfies thegeneralized Snell's law (Eq.2) with a phasegradient ldpldxl = 2r/T alongstraightlinein(G)istheenvelopeoftheproiectionsofthesphericalwavesthe interface.scatteredbytheantennasontothex-zplane,OnaccountofHuygens's1021OCTOBER2011333SCIENCEVOL334
10 波长8 um 共振金属结构