固体材料的宏观光学性质

第四章固体材料的宏观光学性质固体材料的宏观光学性质共60页，您现在浏览的是第1页!OverviewThestudyoftheopticalpropertiesofmaterialsisahugefieldandwewillonlybeabletotouchonsomeofthemostbasicpartsSowewillconsidertheessentialpropertiessuchasabsorption/reflection/transmissionandrefractionThenwewilllookatotherphenomenalikeluminescenceandfluorescenceFinallywewillmentionapplications,inparticularopticalfibresandlasers固体材料的宏观光学性质共60页，您现在浏览的是第2页!NatureoflightLightisanelectromagneticwave:withavelocitygivenbyc

=

1/(00)=3x108m/sInviewofthis,itisnotsurprisingthattheelectricfieldponentofthewaveshouldinteractwithelectronselectrostatically.astronomynotes./light/emanim.gif固体材料的宏观光学性质共60页，您现在浏览的是第3页!GeneraldescriptionofabsorptionBecauseofconservationofenergy,wecansaythatI0=IT+IA+IRIoistheintensity(W/m2)ofincidentlightandsubscriptsrefertotransmitted,absorbedorreflectedAlternativelyT+A+R=1whereT,A,andRarefractionsoftheamountofincidentlightT=IT/I0,etc.Somaterialsarebroadlyclassedastransparent:relativelylittleabsorption

andreflectiontranslucent:lightscatteredwithin

thematerial(seeright)opaque:relativelylittletransmission.tekano.pwp.blueyonder.co.uk/tekano/translucent.jpg固体材料的宏观光学性质共60页，您现在浏览的是第4页!Thus,ifwecanplot-ln(I)againstx,weshouldfindfromthegradientDependingonthematerialandthewavelength,lightcanbeabsorbedbynuclei–allmaterialselectrons–metalsandsmallband-gapmaterials固体材料的宏观光学性质共60页，您现在浏览的是第5页!Ifwethinkofouratom-on-springsmodel,thereisasingleresonancepeak:Butthingsaremoreplexwhentheatomsareconnected–phononsrecalltransverseandlongitudinalopticalphononsf0fabsorption固体材料的宏观光学性质共60页，您现在浏览的是第6页!MolecularmaterialsMaterialssuchasorganic(carboncontaining)solidsorwaterconsistofmoleculeswhicharerelativelyweaklyconnectedtoothermoleculesHence,theabsorptionspectrumisdominatedbyabsorptionsduetothemoleculesthemselvese.g.watermolecule:.sbu.ac.uk/water/images/molecul5.jpg固体材料的宏观光学性质共60页，您现在浏览的是第7页!Sincethebondshavedifferent“springconstants”,thefrequenciesofthemodesaredifferentwhentheincidentilluminationisofawavelengththatexcitesoneofthesemodes,theilluminationispreferentiallyabsorbedThistechniqueallowsustomeasureconcentrationsofdifferentgasspeciesin,forexample,theatmospherebyfittingspectraofknowngasestothemeasuredatmosphericspectra,wecanfigureoutthequantitiesofeachofthegases固体材料的宏观光学性质共60页，您现在浏览的是第8页!ThisstructureformetalsmeansthatalmostanyfrequencyoflightcanbeabsorbedSincethereisaveryhighconcentrationofelectrons,practicallyallthelightisabsorbedwithinabout0.1µmofthesurfaceMetalfilmsthinnerthanthiswilltransmitlighte.g.goldcoatingsonspacesuithelmetsPenetrationdepths(I/I0=1/e)forsomematerialsare:water:32cmglass:29cmgraphite:0.6µmgold:0.15µm固体材料的宏观光学性质共60页，您现在浏览的是第9页!Themetalappears“silvery”sinceitactsasaperfectmirrorOKthen,whyaregoldandcoppernotsilvery?becausethebandstructureofarealmetalisnotalwaysassimpleaswehaveassumedtherecanbesomeemptylevelsbelowEFandtheenergyre-emittedfromtheseabsorptionsisnotinthevisiblespectrumMetalsaremoretransparenttoveryhighenergyradiation(x-&-rays)whentheinertiaoftheelectronsthemselvesisthelimitingfactor固体材料的宏观光学性质共60页，您现在浏览的是第10页!Electronicabsorptioninnon-metalsDielectricsandsemiconductorsbehaveessentiallythesameway,theonlydifferencebeinginthesizeofthebandgapWeknowthatphotonswithenergiesgreaterthanEgwillbeabsorbedbygivingtheirenergytoelectron-holepairswhichmayormaynotre-emitlightwhentheyrelaxECEVEGhole固体材料的宏观光学性质共60页，您现在浏览的是第11页!Semiconductorscanappear“metallic”ifvisiblephotonsareallreflected(likeGe)butthosewithsmallerEg,suchasCdSlookcolouredyellowforCdSwhichabsorbs540nmandaboveTheabovepictureisgoodforpurematerialsbutimpuritiescanaddextraabsorptionfeaturesECEVphononhf1hf2固体材料的宏观光学性质共60页，您现在浏览的是第12页!Refractioninnon-metalsOneofthemostimportantopticalpropertiesofnon-metallicmaterialsisrefractionThisreferstothebendingofalightbeamasitpassesfromonematerialintoanothere.g.fromairtoglassWedefinetheindexofrefractiontobe n=c/vwherecisthespeedoflightinavacuumandvisthespeedoflightinthematerial(whichisingeneralwavelength-dependent)Afamiliarexampleistheprismwherethedifferentamountsofbendingseparatesoutthewavelengths固体材料的宏观光学性质共60页，您现在浏览的是第13页!Sincelightisanelectromagneticwave,theconnectionwithboththedielectricpermittivity()andthemagneticpermeability(µ)isnotsurprisingTheindexofrefractionisthereforeaconsequenceofelectricalpolarization,especiallyelectronicpolarizationHence,theradiationlosesenergytotheelectrons+–固体材料的宏观光学性质共60页，您现在浏览的是第14页!Reflectioninnon-metalsReflectionoccursattheinterfacebetweentwomaterialsandisthereforerelatedtoindexofrefractionReflectivity,R=IR/I0,wheretheI’sareintensitiesAssumingthelightisnormallyincidenttotheinterface:wheren1andn2aretheindicesforthetwomaterialsOpticallensesarefrequentlycoatedwithantireflectionlayerssuchasMgF2whichworkbyreducingtheoverallreflectivitysomelenseshavemultiplecoatingsfordifferentwavelengthsn1n2固体材料的宏观光学性质共60页，您现在浏览的是第15页!ColoursSmalldifferencesinpositioncanleadtolargedifferencesinappearanceForexample,high-puritysingle-crystalAl2O3iscolourlesssapphireIfweaddonly0.5-2.0%ofCr2O3wefindthatthemateriallooksredrubyTheCrsubstitutesfortheAlandintroducesimpuritylevelsinthebandgapofthesapphireTheselevelsgivestrongabsorptionsat:400nm(green)and600nm(blue)leavingonlyredtobetransmitted固体材料的宏观光学性质共60页，您现在浏览的是第16页!TranslucencyEvenafterthelighthasenteredthematerial,itmightyetbereflectedoutagainduetoscatteringinsidethematerialEventhetransmittedlightcanloseinformationbybeingscatteredinternallysoabeamoflightwillspreadoutoranimagewillbeeblurredInextremecases,thematerialcouldbeeopaqueduetoexcessiveinternalscatteringScatteringcanefromobviouscauses:grainboundariesinpoly-crystallinematerialsfineporesinceramicsdifferentphasesofmaterials固体材料的宏观光学性质共60页，您现在浏览的是第17页!Rayleighscatteringalsocausestheskytobeblue.Thereasonforthisisthewavelength-dependenceofRayleighscatteringscatteringgoesasl-4sosincelred~2lbluebluelightisscattered~16timesmorethanredlightThismechanismisofgreattechnologicalimportancebecauseitgovernslossesinopticalfibresformunicationButbeforewegetontofibres,wewillmentionacouplemorebasiceffects固体材料的宏观光学性质共60页，您现在浏览的是第18页!DispersionDispersionisageneralnamegiventothingswhichvarywithwavelengthForexample,thewavelength-dependenceoftheindexofrefractionistermedthedispersionoftheindexAnotherimportantcasearisesbecausethespeedofthewavedependsonitswavelengthIfapulseofwhitelightistransmittedthroughamaterial,differentwavelengthsarriveattheotherendatdifferenttimesthisisalsocalleddispersion固体材料的宏观光学性质共60页，您现在浏览的是第19页!LuminescenceisfurtherdividedintophosphorescenceandfluorescenceFluorescenceandphosphorescencearedistinguishedbytheelectrontransitionsrequiringnochangeorachangeofspin,respectivelyhencefluorescenceisafasterprocessbecausenochangeofspinisrequired,around10-5–10-6sphosphorescencetakesabout10-4–101sThustheenergydiagrammightbelike:E2E1E3phosp.phosp.fluor.incidentflipflip固体材料的宏观光学性质共60页，您现在浏览的是第20页!Influorescentlights,theplasmageneratesUVlight,andafluorescentcoatingonthewallsofthetubeconvertsthistovisiblelighttheselightshaveavisibleflickerbecause(60Hz)-1>10-5sRatherconfusingly,materialsthatdothisaregenerallycalledphosphorsToobtainawhitelight,amixtureofphosphorsmustbeused,eachfluorescingatadifferentwavelengthTVtubesusuallyusematerialsdopedwithdifferentelementstogivethecolours:ZnSdopedwithCu+givesgreenZnS:AggivesblueYVO4:Eugivesred固体材料的宏观光学性质共60页，您现在浏览的是第21页!Obviously,thelossinthecableisimportantbecauseisdeterminesthemaximumuninterruptedlengthofthefibreWeknowthatlossesdependonthewavelengthofthelightandthepurityofthematerialrecallthepenetrationdepthforglasswas~30cmIn1970,1kmoffibreattenuated850nmlightbyafactorof100By1979,1kmoffibreattenuated1.2µmlightbyafactorofonly1.2thislightisinfraredNow,over10kmofopticalfibresilicaglass,thelossisthesameas25mmofordinarywindowglass!固体材料的宏观光学性质共60页，您现在浏览的是第22页!TheRayleighscatteringresultsfromminutelocaldensityvariationswhicharepresentintheliquidglassduetoBrownianmotionandbeefrozenintothesolidThereallycleverpartaboutopticalfibresisthatthelightisguidedaroundbendsinthefibreThisisachievedbytotalinternalreflectionattheboundaryofthefibre固体材料的宏观光学性质共60页，您现在浏览的是第23页!ThelightistransmittedinthecoreandtotalinternalreflectionismadepossiblebythedifferenceintheindexofrefractionbetweenthecladdingandthecoreAsimpleapproachisthe“step-index”design:Themainproblemwiththisdesignisthatdifferentlightraysfollowslightlydifferenttrajectoriesn固体材料的宏观光学性质共60页，您现在浏览的是第24页!Suchbroadeningislargelyeliminatedbyusinga“graded-index”design:ThisisachievedbydopingthesilicawithB2O3orGeO2parabolicallyasshownaboveNow,waveswhichtravelintheouterregions,dosoinalowerrefractiveindexmaterialandtheirvelocityishigher(v=c/n)n固体材料的宏观光学性质共60页，您现在浏览的是第25页!AconvenientfactisthatpoundsemiconductorlaserscanemitIRlightclosetothe1.55µmwavelengthwherethefibreabsorbsleastReferringbacktothesystemdiagram,itwouldbeadvantageoustointegratetheencoderandtransmittersothecircuitsandthelightemittercanbeintegratedThisiswhythereissomuchinterestingettinglightoutofporoussiliconorSipoundswherethinstrandsofmaterialexhibitquantum-mechanicaleffectswhichadjusttheSibandstructuretofacilitateefficientlightemission固体材料的宏观光学性质共60页，您现在浏览的是第26页!LasersLASERstandsforLight

AmplificationbytheStimulated

EmissionofRadiationThekeywordhereis“stimulated”Allofthelightemissionwehavementionedsofarisspontaneousithappenedjustduetorandomlyoccurring“natural”effectsStimulatedemissionreferstoelectrontransitionsthatare“encouraged”bythepresenceofotherphotonsEinsteinshowedthatanincidentphotonwithE≥Egwasequallylikelytocausestimulatedemissionoflightastobeabsorbed.007sdomain./gf_laser.jpg固体材料的宏观光学性质共60页，您现在浏览的是第27页!Sincewegetmorephotonsoutthanweputin,thisisopticalamplificationhencelAserthissystemwasfirstusedtoamplifymicrowavesformunications(maser)SuchaconditioniscalledapopulationinversionThisstimulatedemissioniswhatgivesthelaseritscoherentoutputwhichiswhatmakesitusefulforholography,forexampleClearly,randomspontaneousemission“wastes”electrontransitionsbygivingincoherentoutputsoweminimisethembyusingtransitionsforwhichthespontaneousemissionsareoflowprobabilityso-calledmetastablestates固体材料的宏观光学性质共60页，您现在浏览的是第28页!Soallweneedtomakealaseristoachieve(i)apopulationinversion(ii)enoughphotonstostimulateemissionThefirstisachievedbyfillingthemetastablestateswithelectronsgeneratedbylightfromaxenonflashlampThesecondconditionisachievedbyconfiningthephotonstotravelbackandforthalongtherodofrubyusingmirroredendsnextslideTherubylaserhasanoutputat694.3nm固体材料的宏观光学性质共60页，您现在浏览的是第29页!Inordertokeepthecoherentemission,wemustensurethatthelightwhichpletestheroundtripbetweenthemirrorsreturnsinphasewithitselfHencethedistancebetweenthemirrorsshouldobey2L=NlwhereNisaninteger,listhelaserwavelengthandListhecavitylengthSemiconductorlasersworkinjustthesamewayexceptthattheyachievethepopulationinversionelectricallybyusingacarefullydesignedbandstructure固体材料的宏观光学性质共60页，您现在浏览的是第30页!SummaryWehavelookedathowtheelectronicstructureofatomsandtheirbondingleadstovaryingopticalbehavioursinmaterialsInparticular,propertiessuchasabsorptionandemissionarecloselyrelatedtotheelectronsApplicationsofthisknowledgeincludeanti-reflectivecoatingsforlensesfibre-opticmunicationslasers固体材料的宏观光学性质共60页，您现在浏览的是第31页!Manyoftheelectronicpropertiesofmaterials,informationonthebonding,materialpositionetc.wasdiscoveredusingspectroscopy,thestudyofabsorbedoremittedradiationevidenceforenergylevelsinatomsevidenceforenergybandsandband-gapsphotoelectriceffect固体材料的宏观光学性质共60页，您现在浏览的是第32页!Ifthematerialisnotperfectlytransparent,theintensitydecreasesexponentiallywithdistanceConsiderasmallthicknessofmaterial,xThefallofintensityinxisIsoI=-a.x.Iwhereistheabsorptioncoefficient(dimensionsarem-1)Inthelimitofx0,wegetThesolutionofwhichisI

=

I0

exp(–x)Taking“ln”ofbothsides,wehave:whichisknownasLambert’sLaw(healsohasaunitoflightintensitynamedforhim)固体材料的宏观光学性质共60页，您现在浏览的是第33页!ATOMICABSORPTIONHowthesolidabsorbstheradiationdependsonwhatitis!Solidswhichbondionically,showhighabsorptionbecauseionsofoppositechargemoveinoppositedirectionsinthesameelectricfieldhencewegeteffectivelytwicetheinteractionbetweenthelightandtheatomsGenerally,wewouldexpectabsorptionmainlyintheinfraredbecausethesefrequenciesmatchthethermalvibrationsoftheatoms固体材料的宏观光学性质共60页，您现在浏览的是第34页!ElectronicabsorptionA/~kieran/reuhome/vizqm/figs/hydrogen.gif固体材料的宏观光学性质共60页，您现在浏览的是第35页!Thespectrumofliquidwater.sbu.ac.uk/water/images/watopt.jpg固体材料的宏观光学性质共60页，您现在浏览的是第36页!OpticalpropertiesofmetalsRecallthattheenergydiagramofametallookslike:EFistheenergybelowwhich,at0K,allelectronstatesarefullandabovewhichtheyareemptythisistheFermiEnergyForT>0,EFistheenergyatwhichhalfoftheavailableenergystatesareoccupiedSemiconductorsalsohaveaFermilevelforanintrinsicmaterialEFisinthemiddleofthebandgapnearerEcforn-type;nearerEvforp-typefulllevelsempty

levelsT=0KEF固体材料的宏观光学性质共60页，您现在浏览的是第37页!Sowhathappenstotheexcitedatomsinthesurfacelayersofmetalatoms?theyrelaxagain,emittingaphotonTheenergylostbythedescendingelectronisthesameastheoneoriginallyincidentSothemetalreflectsthelightverywell–about95%formostmetalsmetalsarebothopaqueandreflectivetheremainingenergyisusuallylostasheatIntermsofelectrostatics,thefieldoftheradiationcausesthefreeelectronstomoveandamovingchargeemitselectromagneticradiationhencethewaveisre-emitted=reflected固体材料的宏观光学性质共60页，您现在浏览的是第38页!Reflectionspectraforgoldandaluminumare:blueredgoldreflectslotsofredwavelengthsaluminumspectrumisrelativelyflat.thermo./eThermo/CMA/Images/Various/109Image_12275.gif固体材料的宏观光学性质共60页，您现在浏览的是第39页!Hence,theabsorptioncoefficientsofvarioussemiconductorslooklike:固体材料的宏观光学性质共60页，您现在浏览的是第40页!ImpuritylevelsdivideupthebandgaptoallowtransitionswithenergieslessthanEg

Rebinationcanbeeitherradiative(photon)ornon-radiative(phonon)dependingonthetransitionprobabilitiesPracticalp-ndiodesusuallycontainasmallamountofimpuritytohelprebinationbecauseSihasarelativelylowrebination“efficiency”forthesamereasonthatSiisinefficientatgeneratinglight固体材料的宏观光学性质共60页，您现在浏览的是第41页!Refractionisalsovitalforotherapplications,suchas:opticalfibres–keepsthelightinsemiconductorlaser–keepsthelightintheamplifyingcavityofthelaserGiventhatwhereµandµ0(=µrµ0)arethepermeabilityofthematerialandfreespace,respectively(amagneticproperty)andeande0(=ere0)arethepermittivityofthematerialandfreespace,respectively(anelectrostaticproperty)Wefindthatn=√(µrer)(≈√erformanymaterials)固体材料的宏观光学性质共60页，您现在浏览的是第42页!SinceE=hv/,anddoesn’tchange,thevelocitymustbesmallerinthematerialthaninfreespacesinceweloseEtotheatoms,vmustalsodecreaseElectronicpolarizationtendstobeeasierforlargeratomssonishigherinthosematerialse.g.glass:n~1.5leadcrystal:n~2.1(whichmakesglassesandchandeliersmoresparkly!)ncanbeanisotropicforcrystalswhichhavenon-cubiclattices固体材料的宏观光学性质共60页，您现在浏览的是第43页!SpectraSowehaveseenthatreflectionandabsorptionaredependentonwavelengthandtransmissioniswhat’sleftover!Thusthethreeponentsforagreenglassare:CallisterFig.21.8固体材料的宏观光学性质共60页，您现在浏览的是第44页!Thespectraforrubyandsapphirelooklike:Asimilartechniqueisusedtocolourglassesorpotteryglazebyaddingimpuritiesintothemoltenstate:Cu2+:blue-green,Cr3+:greenCo2+:blue-violet,Mn2+:yellow.valleydesign./images//~jtalbot/glossary/photopumping.gif固体材料的宏观光学性质共60页，您现在浏览的是第45页!Inhighlypurematerials,scatteringstilloccursandanimportantcontributionesfromRayleighscatteringThisisduetosmall,randomdifferencesinrefractiveindexfromplacetoplaceInamorphousmaterialssuchasglassthisistypicallyduetodensityorpositionaldifferencesintherandomstructureIncrystals,latticedefects,thermalmotionofatomsetc.alsogiverisetoRayleighscattering固体材料的宏观光学性质共60页，您现在浏览的是第46页!固体材料的宏观光学性质共60页，您现在浏览的是第47页!LuminescenceLuminescenceisthegeneraltermwhichdescribesthere-emissionofpreviouslyabsorbedradiativeenergyCommontypesarephoto-,electro-,andcathodo-luminescence,dependingonwhethertheoriginalincidentradiationwaslightofadifferentwavelength–e.g.fluorescentlightelectricfield–e.g.LEDelectrons–e.g.electronguninacathoderaytube(CRT)Thereisalsochemo-luminescenceduetochemicalreactionswhichmaketheglowingringsseenatfairgrounds!固体材料的宏观光学性质共60页，您现在浏览的是第48页!Iftheenergylevelsareactuallyarangeofenergies,then:Sothelightemittedbyfluorescenceisoflongerwavelengththantheincidentlightsincetheenergyissmallerandphosphorescentlightistypicallylongerwavelengththanfluorescentlightphononemission

~10-12sperhopfluorescence,~10-5s固体材料的宏观光学性质共60页，您现在浏览的是第49页!OpticalfibresFibre-optictechnologyhasrevolutionisedtelemunicationsowingtothespeedofdatatransmission:equivalentto>3hrsofTVpersecond24,000simultaneousphonecalls0.1kgoffibrecarriessameinformationas

30,000kgofcoppercableOwingtoattenuationinthecable,transmissionisusuallydigitalandthesystemrequiresseveralsections:encoderconversiontoopticalrepeaterdetectiondecoder