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323Vol．32No．320133COLLEGEPHYSICSMar．20132012－09－232012－10－30No．11104016、．1989—2008．100875．．、．O435．1A1000-0712201303-0049-04、、．．．．．metamaterial．“”、、“”1．．metasurface．2、3-6、7．8．2-8．、910．．．1、、．1112．．910．5032．AB∫BAnrdrnr．∫BAdφr=0．．Φrsrs．Φrs+∫BAk·drk．．．Φrs．θixA、BADBAEB1．k0nisinθidx+Φ+dΦ－k0ntsinθtdx+Φ=01θtΦΦ+dΦdxnintk0=2π/λ0λ0．11．dΦ/dx1ntsinθt－nisinθi=λ02πdΦdx22dΦ/dx．±θi．nt＜niθtc=arcsin±ntni－λ02πnidΦd()x33ntniλ0dΦ/dx．－ntni－λ02πnidΦdx≥－1dΦdx≤－nt+ni2πλ0dΦdx＞－nt+ni2πλ0．nt＞nidΦdx≥nt－ni2πλ0．．A、CAHCAGC2k0nisinθidx+Φ+dΦ－k0nisinθrdx+Φ=04dΦ/dx4sinθr－sinθi=λ02πnidΦdx5θr．5θrθi．3512．θrc=arcsin±1－λ02πnidΦd()x66．nt＞nint＜nini、λ0dΦ/dx．2．．xOzxkiθikrθrktθt3．Eix+Erx=Etx7Eix=Aixe－iωit－kilix+miy+nizErx=Arxe－iωrt－krlrx+mry+nrz+ΦxEtx=Atxe－iωtt－ktltx+mty+ntz+Φxlα、mα、nαki、krkt．z=0txyztωi=ωr=ωt．xy3kimi=krmr=ktmt8kilix=krlrx－Φx=ktltx－Φx9ki=kisinθi0cosθimr=mt=0xOz．lr=sinθrlt=sinθt9ωcnisinθix=ωcnisinθrx－Φx=ωcntsinθtx－Φx1010xωcnisinθi=ωcnisinθr－dΦxdx=ωcntsinθt－dΦxdx11sinθr－sinθi=λ02πnidΦxdx12ntsinθt－nisinθi=λ02πdΦxdx13．．35232θiθr=arcsinsinθi+λ02πnidΦd[]x14θt=arcsinnintsinθi+λ02πntdΦd[]x1536θrcθtc．dΦdx=014151314．．1415、、．．ΦdΦ/dx．．dΦ/dx．dФ/dx．．910V．V．．、、、、．1．“metamaterials”．J20044215-16．2LeeJWSeoMASohnJYetal．InvisiblePlasmonicMeta－materialsThroughImpedanceMatchingtoVacuumJ．OpticsExpress2005132610681-10687．3SaenzEEderraIIkonenPetal．Powertransmissionenhancementbymeansofplanarmeta－surfacesJ．JournalofOpticsAPureandAppliedOptics20079S308-S314．4SaenzEEderraIGonzaloRetal．CouplingReductionbetweenDipoleAntennaElementsbyUsingaPlanarMeta－SurfaceJ．IEEETransactionsonAntennasandProp-agation2009572383-394．5SaenzEEderraIetal．Highlyefficientdipoleantennawithplanarmeta－surfaceJ．ElectronicsLetters20074316850-851．6SaenzlEGonzaloREderraIetal．ResonantMeta－SurfaceSuperstrateforSingleandMultifrequencyDipoleAntennaArraysJ．IEEETransactionsonAntennasandPropagation2008564951-960．7MosallaeiHSarabandiK．AOne－LayerUltra－ThinMe-ta－SurfaceAbsorberJ．IEEEAntennasandPropagationSocietyInternationalSymposium1B2005615-618．8AliciBKTurhanABSoukoulisCMetal．Opticallythincompositeresonantabsorberatthenear－infraredbandapolarizationindependentandspectrallybroadbandconfigurationJ．OpticsExpress2011191514260-14267．9YuNGenevetPKatsMAetal．LightPropagationwithPhaseDiscontinuitiesGeneralizedLawsofReflec-tionandRefractionJ．Science2011334333333-337．10NiXEmaniNKKildishevAVetal．BroadbandLightBendingwithPlasmonicNanoantennasJ．Sci-enceExpress20113356067427-430．11PendryJBSchurigDSmithDR．ControllingElectro-magneticFieldsJ．Science200631257811780-1782．585832uxx=l=htgt、ht．1．M．3．2010．2．M．2．2011．3．M．2．1990．AmethodofsimultaneouslyhomogenizingboundaryconditionsanddifferentialequationYAODuan-zhengSchoolofPhysicsandTechnologyWuhanUniversityWuhanHubei430072ChinaAbstractOneoftheun-determinedfunctionsmethodsforsolvingthedeterministicproblemswithnon-homo-geneousboundaryconditionsbyusingthemethodofvariableseparationhasbeenpresentedwhichcanhomogenizeboundaryconditionsanddifferentialequationsimultaneously．Alsothedeterministicproblemsofthreetypicalkindsofmathematicalphysicalequationswiththefirstthesecondorthethirdtypeofthenon-homogeneousboundaryconditionsarediscussedrespectively．Thespecificconclusionsandthesolvingmodelarepresented．Keywordsmethodofseparationofvariablesnon-homogeneousboundaryconditionswaveequationtrans-portequationLaplaceequationthreekindsofboundaryconditionssecond－orderlinearordinarydifferentiale-quation5212LeonhardtU．OpticalconformalmappingJ．Science200631257811777-1780．13．M．2003270-271310-318．14．M．2008136-138．TwomethodsforgenerallawsofreflectionandrefractionformetasurfacewithphasediscontinuityHANLuWANGZhao-naAppliedOpticsMajorLaboratoryofBeijingDepartmentofPhysicsBeijingNormalUniversityBeijing100875ChinaAbstractConsideringtheabruptphaseshiftattheinterfacebetweenthetwomediathegeneralreflectionandrefractionlawsatthemetasurfacewiththeabruptphaseshiftarederivedbythetwomethodsbasedonFermat'sprincipleandtheboundaryconditionsofcontinuityrespectively．Itisfoundthatthetraditionreflectionandrefrac-tionlawsarethespecialcasesofthegeneralizedreflectionandrefractionlawswhenthephaseshiftgradientisequaltozero．Basedonthegeneralizedlawsofreflectionandrefractiontheoccurrenceconditionsofthetotalinternalre-flectionandthefulltransmissionaregivenandtheeffectoftherefractionindexandthephaseshiftgradientaredis-cussed．Itisshownthatthearbitrarycontrollingoftheelectromagneticwavescanbeeasilyachieved．Keywordsmetasurfacereflectionlawrefractionlawabruptphaseshift