固体物理基础讲座：光子晶体

学术讲座之光子晶体Photoniccrystal光子晶体(photoniccrystal)

周期性结构调制，波的运动产生色散，形成带结构，带隙之间的波禁止通过，称为禁带。电子的运动

光子的运动？光子晶体:在高折射率材料的某些位置周期性出现低折射率的材料.这种光的折射率指数的周期性变化产生了光带隙结构，控制着光在晶体中的运动。1987年提出概念:E.Yablonovitch(PRL58,2059)S.John(PRL58,2486)1990年理论预言第一个有完整光子带隙的三维光子晶体

(PRL65,3152)1991年实验制备第一个有完整光子带隙的三维光子晶体

(PRL67,2295)

光子晶体多为人工设计,自然界也有:蛋白石、蝴蝶翅膀OpalButterflyTraditionalmulti-layerfilm三维光子晶体二维光子晶体PhotonicCrystals:

PeriodicSurprisesinElectromagnetismStevenG.JohnsonMIT18871987PhotonicCrystalsperiodicelectromagneticmediawithphotonicbandgaps:“opticalinsulators”(needamorecomplextopology)PhotonicCrystalsperiodicelectromagneticmediawithphotonicbandgaps:“opticalinsulators”magicalovenmittsforholdingandcontrollinglightcantraplightincavitiesandwaveguides(“wires”)PhotonicCrystalsperiodicelectromagneticmediawithphotonicbandgaps:“opticalinsulators”magicalovenmittsforholdingandcontrollinglightcantraplightincavitiesandwaveguides(“wires”)PhotonicCrystalsperiodicelectromagneticmediaButhowcanweunderstandsuchcomplexsystems?Adduptheinfinitesumofscattering?Ugh!Image:/lattice/struk/a4.htmlTheMotherof(almost)AllBandgapsThediamondlattice:fcc(face-centered-cubic)withtwo“atoms”perunitcell(primitive)afcc=most-sphericalBrillouinzone+diamond“bonds”=lowest(two)bandscanconcentrateinlinesRecipeforacompletegap:frequency(c/a)TheFirst3dBandgapStructureK.M.Ho,C.T.Chan,andC.M.Soukoulis,Phys.Rev.Lett.

65,3152(1990).11%gapoverlappingSispheresMPBtutorial,

/mpbforgapatl=1.55µm,spherediameter~330nm光子晶体制备5µmdissolvelatexspheres6-layer[001]silicadiamondlattice4-layer[111]silicadiamondlattice5µm[F.Garcia-Santamaria

etal.,Adv.Mater.

14(16),1144(2002).]Layer-by-LayerLithography•Fabricationof2dpatternsinSiorGaAsisveryadvanced(think:PentiumIV,50milliontransistors)So,make3dstructureonelayeratatime…inter-layeralignmenttechniquesareonlyslightlymoreexoticNeeda3dcrystalwithconstantcross-sectionlayersALayeredStructure(diamond-like:rods~“bonds”)ABC[S.G.Johnsonetal.,Appl.Phys.Lett.

77,3490(2000)]Upto~27%gapforSi/airholelayerMakingRods&HolesSimultaneouslysubstratetopviewsideviewSiMakingRods&HolesSimultaneouslysubstrateAAAAAAAAAAAAAAAAAAAAAAAAAexpose/etchholesMakingRods&HolesSimultaneouslysubstrateAAAAAAAAAAAAAAAAAAAAAAAAAbackfillwithsilica(SiO2)&polishMakingRods&HolesSimultaneouslysubstrateAAAAAAAAAAAAAAAAAAAAAAAAAdepositanotherSilayerlayer

1MakingRods&HolesSimultaneouslyBBBBBBBBBBBBBBBBBBBBBsubstratelayer

1AAAABBBBAAAAAAAAAAAAAAAAAAAAAdigmoreholesoffset&overlappingMakingRods&HolesSimultaneouslyBBBBBBBBBBBBBBBBBBBBBsubstratelayer

1AAAABBBBAAAAAAAAAAAAAAAAAAAAAbackfillMakingRods&HolesSimultaneouslyBBBBBBBBBBBBBBBBBBBBBCCCCCCCCCCCCCCCCCCCCCCCCsubstratelayer

1layer

2layer

3AAAABBBBCCCCAAAAAAAAAAAAAAAAAAAAAAAAAetcetera(dissolvesilicawhendone)oneperiodMakingRods&HolesSimultaneouslyBBBBBBBBBBBBBBBBBBBBBCCCCCCCCCCCCCCCCCCCCCCCCsubstratelayer

1layer

2layer

3AAAABBBBCCCCAAAAAAAAAAAAAAAAAAAAAAAAAetceteraoneperiodholelayersMakingRods&HolesSimultaneouslyBBBBBBBBBBBBBBBBBBBBBCCCCCCCCCCCCCCCCCCCCCCCCsubstratelayer

1layer

2layer

3AAAABBBBCCCCAAAAAAAAAAAAAAAAAAAAAAAAAetceteraoneperiodrodlayersAMoreRealisticSchematic[M.Qi,H.Smith,MIT]e-beamFabrication:TopView[M.Qi,H.Smith,MIT]e-beamFabrication:SideViews

(cleavingworstsample)[M.Qi,H.Smith,MIT]X-rayInterferenceLithographyTheGoodLargearea:upto10x10cm!Cheap($50kvs.$500kfore-beam)[M.Qi,H.Smith,MIT]TheUglyLayeralignmentstilltrickyFromRectangulartoHexagonal[M.Qi,H.Smith,MIT]TheWoodpileCrystalanearlierdesign:(¤tlymorepopular)[K.Hoetal.,SolidStateComm.

89,413(1994)][H.S.Sözüer

etal.,J.Mod.Opt.

41,231(1994)]Upto~17%gapforSi/air(diamond-like,“bonds”)[FiguresfromS.Y.Linetal.,Nature394,251(1998)]1.25PeriodsofWoodpile[S.Y.Linetal.,Nature394,251(1998)]gap(4“log”layers=1period)“UVStepper:”e-beammaskat~4xsize+UVthroughmask,focusedonsubstrateGood:highresolution,massproductionBad:expensive($20million)http:///media/photonic.htmSi1.25PeriodsofWoodpile@1.55µm[S.Y.Linetal.,Nature394,251(1998)]gap(4“log”layers=1period)1.3µm180nmSi“It’sonlywafer-thin.”[S.Nodaetal.,Science

289,604(2000)][M.Python]WoodpileGapfrom1.3–1.55µm[S.Nodaetal.,Science

289,604(2000)]AMetalPhotonicCrystal[J.G.Flemingetal.,Nature

417,52(2002)]StartwithSiwoodpileinSiO2…dissolveSiwithKOH…fillwithTungstenviachemicalvapordeposition(CVD)(onthinTiNlayer)dissolveSiO2

withHF…enoughlayer-by-layeralready!ATwo-PhotonWoodpileCrystal[B.H.Cumpston

etal.,Nature

398,51(1999)](muchworkonmaterialswithlowerpower2-photonprocess)Difficulttopologies•Arbitrarylattice•No“mask”•Fast/cheapprototyping[fig.courtesyJ.W.Perry,U.Arizona]One-Photon

HolographicLithography[D.N.Sharpetal.,Opt.Quant.Elec.

34,3(2002)]absorptivematerialFourbeamsmake3d-periodicinterferencepattern(1.4µm)k-vectordifferencesgivereciprocallatticevectors(i.e.periodicity)beampolarizations+amplitudes(8parameters)giveunitcellOne-Photon

HolographicLithography[D.N.Sharpetal.,Opt.Quant.Elec.

34,3(2002)]hugevolumes,long-rangeperiodic,fcclattice…backfillforhighcontrast10µmOne-Photon

HolographicLithography[D.N.Sharpetal.,Opt.Quant.Elec.

34,3(2002)]5µm1µm1µm[111]cleavages[111]closeupsimulatedstructuretitaniainversestructureMass-productionII:Colloidsmicrospheres(diameter<1µm)silica(SiO2)sedimentbygravityintoclose-packedfcclattice!(evaporate)Mass-productionII:Colloidshttp://www.icmm.csic.es/cefe/InverseOpalsfccsolidspheresdonothaveagap……butfccsphericalholesinSidohaveagapInfiltrationsub-microncolloidalspheresTemplate(syntheticopal)3DRemoveTemplate“InvertedOpal”completebandgap~10%gapbetween8th&9thbandssmallgap,upperbands:sensitivetodisorderInverse-OpalPhotonicCrystal[Y.A.Vlasov

etal.,Nature

414,289(2001).]Inverse-OpalBandGapgoodagreementbetweentheory(black)&experiment(red/blue)[Y.A.Vlasov

etal.,Nature

414,289(2001).]10μm(a)(b)(c)(e)50μmd1~30ºd2D1D2L(d)1μm200nmOriginalbutterflyThecylindricalmainribsareL1.6μminlengthd1diameter100nmD1interdistance60nmd2diameterof20nmD250nmfromeachother.Recta