Optical Properties of Materials.pdf

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1、file:///C:/DOCUME~1/TSINGH~1/LOCALS~1/Temp/maftemp/1266640...LorentzOscillatorTuesday,February09,20104:15PM(Reading:JDJsection3.5;MarkFox2.2;)Herewefirstlookattheopticalresponseofaparticulartypeofelectronscharacterizedwithaspecificbindingenergytonucleus.Thisbindingenergyismodeledasaspringwit

2、hacharacteristicresonantfrequency.Ignorelocalfieldeffect(whichusuallyappliedforlow‐densitymaterialsuchasgasphasebutingeneralnottrueforsolidstate).TheelectronwillbedrivenbyexternalfieldthroughLorentzforcelaw(ignoringmagneticfieldsince1/csmallerthanE‐field),induceddipolemomentbythiselectronperato

3、mis1of172/19/201011:41PMfile:///C:/DOCUME~1/TSINGH~1/LOCALS~1/Temp/maftemp/1266640...Nearw,theopticalresponseofmaterialisdominatedbythissetsofelectrons.ThereOare,however,otherelectronswhoseresonantfrequenciesarefarawayfromw,andareOconsideredtobeoffresonance.Theircontributioncanbeconsideredm

4、oreorlessconstantoverthenarrowspectralrangenearresonanceofw,andisrepresentedbyaObackgroundterm.Consideringonlythiselectron,thedisplacementfieldbecomesFoxeqs2.15‐2.162of172/19/201011:41PMfile:///C:/DOCUME~1/TSINGH~1/LOCALS~1/Temp/maftemp/1266640...Anomalousdispersion&ResonantAbsorptionMonday

5、,February08,20109:42PMFoxeq.2.183of172/19/201011:41PMfile:///C:/DOCUME~1/TSINGH~1/LOCALS~1/Temp/maftemp/1266640...TheseequationsdescribeasharpatomicabsorptionlinecenteredatwOwithfull‐width‐at‐half‐maximum(FWHM)equaltog,asexplainedbelow.(AdoptedfromFox)Provetheequationsasshownabove(Equation

6、s2.20‐2.21inFox)4of172/19/201011:41PMfile:///C:/DOCUME~1/TSINGH~1/LOCALS~1/Temp/maftemp/1266640...CharacteristicsofLorentzianfunctions:ImaginarypartstronglypeaksatDx=0,andfallstohalfatDx=±g/2.RealpartiszeroatDx=0,positivelypeaksDx=-g/2,negativelypeaksDx=g/2.f1dropsmuchslowerthanf2atx>1.Thi

7、sindicatesthatatlargeoffresonance,theeffectoff1islonglastingwhereasthatoff2onlyoccursnearresonance.Exampleofdielectricbehaviornearasingleresonance.5of172/19/201011:41PMfile:///C:/DOCUME~1/TSINGH~1/LOCALS~1/Temp/maftemp/1266640...Anomalousdispersion:theregionwher