FDTD-Solutions高級(jí)培訓(xùn)課件

AdvancedTraining版權(quán)所有，請(qǐng)勿外傳FDTDSolutionsAdvancedTraining版權(quán)所有，請(qǐng)勿外傳FDTD1?2009LumericalSolutions,Inc.OutlineIntroductionAdvancedFeatures:Scriptinglanguage:Structuregroupsandanalysisgroups:Farfieldanalysiswithscripting:Advancedboundaryconditions:Dispersiveandanisotropicmaterials:InteroperabilitywithASAPanduser-definedsources:CoherenceandpolarizationinFDTDParallelComputationCMOSImageSensordetailedapplicationexample:ReviewtheprinciplesofCMOSImageSensorModelingwithFDTD?Modelingmethodsthatcanbeused?CoherenceandpolarizationWorkshopexamplesandPractice?2009LumericalSolutions,In2GoalsLearntheadvancedfeaturesofFDTDSolutions::::::::ScriptingParameterizationofstructuresanddefiningfiguresofmerit(FOM)FarfieldanalysisSymmetric/Anti-SymmetricandBlochboundariesDispersivematerialsInteroperabilitywithASAPDrawcomplexstructureswithscriptingUnderstandhowtoobtainincoherent,unpolarizedresultswithFDTDUnderstandthecapabilitiesofparallelFDTDSolutionsLearnhowtosetupaparallelsimulationStudyaCMOSimagesensordesign

?2009LumericalSolutions,Inc.Goals:ScriptingUnderstandhow3?2009LumericalSolutions,Inc.ScriptingTOPICSThescriptwindowMathematicsInteractingwiththeLayoutEditorAnalyzingsimulationdataScriptfilesandexample?2009LumericalSolutions,In4?2009LumericalSolutions,Inc.Scripting:EditorandpromptRightclickonmenubar(oruseViewmenu)ScriptfileeditorScriptprompt?2009LumericalSolutions,In5?2009LumericalSolutions,Inc.Scripting:MathematicsSimpleMathematics:plotsomesimplefunctions>x=linspace(-10,10,500);>y=sin(x);>plot(x,y,”x”,”y”,”sin(x)”);>y=exp(-x^2/9)*sin(10*x);>plot(x,y,”x”,”y”,”exp(-x^2/9)*sin(10*x)”);>?size(x);?2009LumericalSolutions,In6?2009LumericalSolutions,Inc.Scripting:MathematicsSimpleMathematics(plota2Dgaussian)>x=linspace(-10,10,500);>y=linspace(-10,10,500);>X=meshgridx(x,y);>Y=meshgridy(x,y);>?size(x);>?size(X);>E=exp(-X^2/9–Y^2/4);>image(x,y,E,”x”,”y”,”test2Dimage”);?2009LumericalSolutions,In7x1,ymx2,ymx3ym…xn,ym……………x1,y3x2,y3x3y3…xn,y3x1,y2x2,y2x3y2…xn,y2x1,y1x2,y1x3,y1…xn,y1ymymym…ym……………y3y3y3…y3y2y2y2…y2y1y1y1…y1x1x2x3…xnx1x2x3…xnx1x2x3…xn……………x1x2x3…xnxhaslengthnXhassizenbym?2009LumericalSolutions,Inc.Scripting:MathematicsY=meshgridy(x,y);yhaslengthmYhassizenbymyxyxX=meshgridx(x,y);

E=exp(-X^2/9–Y^2/4);Ehassizenbymyxx1,ymx2,ymx3ym…xn,ym……………x8?2009LumericalSolutions,Inc.Scripting:InteractingwiththeLayoutEditorSomeusefulcommandstosetandgetobjectpropertiessetnamed:setnamed(“Source1”,”x”,1e-6);getnamed:x=getnamed(“Source1”,”x”);?2009LumericalSolutions,In922Scripting:AnalyzingsimulationdataSomeusefuldatamanipulationcommandsgetdata

:retrievesdatafromanymonitorafterthesimulation

:Bydefaultitautomaticallyunfoldsdatawiththecorrectsymmetries whensymmetric/anti-symmetricboundariesareusedshowdata

:Showswhatmonitorsarecurrentlyavailablewithdatashowdata(“monitorname”);

:Showstheavailabledatainthemonitor/sourcecalled“monitorname”

:Eg:?showdata("source1")showsvariablesin“source1”settingstransmission

:calculatesnormalizedtransmissiongetelectric(andgetmagnetic)

:retrieves:Bydefaultitautomaticallyunfoldsdatawiththecorrectsymmetries

?2009LumericalSolutions,Inc.|E|or|H|22Scripting:A10Scripting:AnalyzingsimulationdataMostelectromagneticfielddatafromthe

simulationsisa3or4dimensionalmatrixExample >Ex=getdata(“Monitor1”,”Ex”);

Ex(i,j,k,m):::::irepresentsthexdimensionjrepresentstheydimensionkrepresentsthezdimension(3Donly)mrepresentsfrequencyortimeThisisafieldquantity,notintensity

?2009LumericalSolutions,Inc.Scripting:Analyzingsimulatio11?2009LumericalSolutions,Inc.Scripting:AnalyzingsimulationdataThepinchfunction:>E=matrix(12,4,1,6);>?size(E);>?size(pinch(E));#removedimension3>?size(pinch(E,2,3));#2nddimension,3rdelementpinchremovesallsingletondimensionspinchwith2arguments,selectsasub-matrix?2009LumericalSolutions,In12?2009LumericalSolutions,Inc.Scripting:AnalyzingsimulationdataAccessingandmanipulatingmatrixelements>>>>x=1:5;?x;x(2:3)=5:6;?x;?2009LumericalSolutions,In13?2009LumericalSolutions,Inc.Scripting:ScriptfilesandexampleCopythefilescripting1.fspandscripting1.lsftoyourmachineOpenscripting1.fspandeditscripting1.lsfWe’llcalculatetransmissionandreflectionasafunctionoftheradiusofadielectricrod?2009LumericalSolutions,In14?2009LumericalSolutions,Inc.Scripting:Scriptfilesandexample##########################################file:scripting1.lsf#Thisfileshowshowtorunmultiplesimulationsusingscripting.#Youshouldopenscripting1.fspbeforerunningthisscript##########################################define10rodradiitouserad=linspace(0.5e-6,3e-6,10);#reserve3matrices,1forTransmission,1forreflection#oneforpoweratsidesT=matrix(length(rad));R=matrix(length(rad));side_power=matrix(length(rad));?2009LumericalSolutions,In15?2009LumericalSolutions,Inc.Scripting:Scriptfilesandexample#startaloopovereachdesiredradiusfor(i=1:length(rad)){#switchtolayoutmodesothatyoucanedittheobjectsswitchtolayout;#switchtothestructurestabtoeditthescatteringrodstructures;#settheradiusoftheobjectnamed"rod"tothedesiredvaluesetnamed("rod","radius",rad(i));#outputwhichsimulationisrunning?"runningsimulation"+num2str(i)+"of"+num2str(length(rad));#runthesimulationrun;#gettransmissionandreflectionT(i)=transmission("transmission");R(i)=abs(transmission("reflection"));side_power(i)=transmission("y2")-transmission("y1");#getthefrequencyatwhichthedatawasrecordedf=getdata("transmission",“f“);#thequotescannotbeuseddirectlyinscript.changeitafterpaste!}#endofthemainloopovertheradius?2009LumericalSolutions,In16?2009LumericalSolutions,Inc.Scripting:Scriptfilesandexample#plotthefinalresultsplot(rad*1e6,R,T,R+T+side_power,"radius(microns)","normalized

power","transmissionandreflectionat"+num2str(c/f*1e6)+" microns");legend("R","T","total");?2009LumericalSolutions,In17?2009LumericalSolutions,Inc.StructuregroupsandanalysisgroupsTOPICSCreatingsimplegroupsUsingscriptcommandsingroupstoparameterizestructuresCreatingadvancedanalysisgroupstocalculatefiguresofmerit?2009LumericalSolutions,In18?2009LumericalSolutions,Inc.StructuregroupsandanalysisgroupsWorkthroughanexamplebasedonthesilver

nanowirescatteringexamplefromthegetting startedThecompletedfileandscriptisinthegroupsfolder(group_example1.fspandgroup_example1.lsf)Copythefilenanowire.fspfiletoyourcomputerandrenamegroup_example.fsp?2009LumericalSolutions,In19StructuregroupsandanalysisgroupsStructuregroup

:Selectthecircleandcopyit

:Setthenameofonecircleto“l(fā)eft”andtheotherto“right”(onlytwocirclesnow)

:Selectbothcirclesandaddthemtoanewgroup(left-clickyourmouth)

?Namethegroup“dimer”

:Editthegroupandaddproperties

?radius(type=Length)andsetto10nm

?d(type=Length)andsetto10nm

?2009LumericalSolutions,Inc.Structuregroupsandanalysis20StructuregroupsandanalysisgroupsCreateascriptinthegroup(centralbutton)withthe followinglines::::selectall;set(“radius”,radius);setnamed(“l(fā)eft”,”x”,-radius-d/2);setnamed(“right”,”x”,radius+d/2);(note:whenyoucopyandpastetheabovelines,the quotesarenotcorrectinscript,sopleasemodifythem)

?2009LumericalSolutions,Inc.Structuregroupsandanalysis21?2009LumericalSolutions,Inc.StructuregroupsandanalysisgroupsLookattheanalysisgroups:Thegrouphas4monitorsthatmakeaboxaroundtheparticles:Thewidthcanbemodifiedeasily?2009LumericalSolutions,In22?2009LumericalSolutions,Inc.StructuregroupsandanalysisgroupsRunthesimulationandlookatthefielddistributionf=1000THzf=869THz?2009LumericalSolutions,In23?2009LumericalSolutions,Inc.StructuregroupsandanalysisgroupsWecandefineinputparametersandoutputvaluesfortheanalysisgroupobjectInputparametersOutputvalues?2009LumericalSolutions,In24?2009LumericalSolutions,Inc.StructuregroupsandanalysisgroupsThisscriptcalculatesthecrosssection:sigma=power/Is?poweristhenetpowerflowoutofthebox(Watts)?Isistheintensityofthesource(Watts/m):Italsoreturnsthefrequencies(f)andwavelengthinnm(lam)fandlamsigma?2009LumericalSolutions,In25?2009LumericalSolutions,Inc.StructuregroupsandanalysisgroupsConsiderthefinalanalysiswhenusingananalysisobject:Filegroup_example1.lsfUpdatealltheoutputvaluesUsegetdatacommandtogettheoutputvaluesPlottheresults?2009LumericalSolutions,In26?2009LumericalSolutions,Inc.StructuregroupsandanalysisgroupsThefinalresult?2009LumericalSolutions,In27?2009LumericalSolutions,Inc.StructuregroupsandanalysisgroupsStructuregroupandanalysisgroups:Powerfulobjectstoparameterizeyourdesignsandanalysis:Canbesimplegroupingofobjects,orverycomplexstructuresusingscriptingWherecanyougettheseobjects:Downloadfrom/fdtd_online_helpandpasteintoyoursimulation?CopyshortcutisCtrl-C?PasteshortcutisCtrl-V:Emailsupport@forhelpcreatingthemforyourapplication:Createyourown!?2009LumericalSolutions,In28FarfieldanalysisTOPICSGeneralconceptExamples::::Compareprojectiontosimulation,2DProject3DbeamProjectionofperiodicstructurein3DFarfieldfiltering

?2009LumericalSolutions,Inc.Farfieldanalysis:Comparepro29Farfieldanalysis

R=1mFarfields

d=1mmNearfields

?2009LumericalSolutions,Inc.Farfieldanalysis R=1m d=1mm30X

material

ZY

?2009LumericalSolutions,Inc.Z=0Farfieldanalysis

E(x,y,z=0)H(x,y,z=0)

HomogeneousE(x,y,z>0)H(x,y,z>0)X materialZ=0Farfieldanalys31ZYXFarfieldanalysis

IfweknowE(xs,ys,zs)andH(xs,ys,zs)atthesurfaceofthebox,wecancalculateE(x,y,z)andH(x,y,z)outsidethebox,atarbitrarydistance

Homogeneous material?2009LumericalSolutions,Inc.ZYXFarfieldanalysisandH(xs,32

FarField Projection?2009LumericalSolutions,Inc.Examplesimulations:DVDsurfaceoptimization

FourierTransform FarFieldExamplesimulations33?2009LumericalSolutions,Inc.FarfieldbyscriptingcommandsThescriptingfarfieldcommandsaremoreextensiveoptionsthantheGUIWe’lltryGUIandscriptedfarfieldprojectionsbyworkingthroughexamples?2009LumericalSolutions,In34?2009LumericalSolutions,Inc.Simplefarfieldexample1Copyfarfield1.fspandopenitgaussiansourcefullprofilemonitornearpowermonitor2farpowermonitorstimemonitor?2009LumericalSolutions,In35?2009LumericalSolutions,Inc.Simplefarfieldexample1RunthesimulationPlotEzvst|Ez(t)|^2Image|Ez(w)|^2overspace?2009LumericalSolutions,In36?2009LumericalSolutions,Inc.Simplefarfieldexample1ToplotfarfielddatawiththeGUI,choose“farfield”here(choose“near”monitor)?2009LumericalSolutions,In37?2009LumericalSolutions,Inc.Simplefarfieldexample1Thefarfieldprojectionsettingscanbemodifiedhere?2009LumericalSolutions,In38?2009LumericalSolutions,Inc.Simplefarfieldexample1Results?2009LumericalSolutions,In39?2009LumericalSolutions,Inc.Simplefarfieldexample1Let’sseewhatwecandowithscriptingCopythefilefarfield1.lsftoyourcomputerandopenitwiththescripteditorItfirstrecreatestheresultsfromtheGUI?2009LumericalSolutions,In40?2009LumericalSolutions,Inc.Simplefarfieldexample1Next,itcompares“FDTD”–thefieldsrecordedatthemonitorcalled“farx”and“projected”–thefieldprojectedfromthemonitor“near”tothesamelocationasmonitor“farx”(approximately15microns):Scriptfunction“farfieldexact”allowsforprojectionsovershortdistancesErrorsarefromnumerical

dispersionanddiscretization?2009LumericalSolutions,In41?2009LumericalSolutions,Inc.Simplefarfieldexample1ConsiderthephasesoftheprojectedandcalculatedtermsThedifferenceisduetogriddispersion,whichisanisotropicRemember:infieldmonitorsthefieldsarecomplex(infrequencydomain)?2009LumericalSolutions,In421kyy22wt1kxx11kzzwckkkckGriddispersionDispersionrelationinFDTDwehaveThefarfieldprojectionassumesthatw=ck

?2009LumericalSolutions,Inc.2

2ctsin2xsin2ysin2zsin2

t0 x0Wheny0 z0

222xyz1kyy22wt1k43?2009LumericalSolutions,Inc.Simplefarfieldexample1Wehaveseenthesescriptingcommandsfarfield2dfarfieldanglefarfieldexact2dNow,let’sconsider3D...?2009LumericalSolutions,In44?2009LumericalSolutions,Inc.Simplefarfieldexample2Opentheexamplefarfield2.fspandrunit,plotthefarfieldwiththesesettings?2009LumericalSolutions,In45?2009LumericalSolutions,Inc.Simplefarfieldexample2Let’sconsiderscripting,runfarfield2.lsf.WecanrecreatetheGUIplotlikethis?2009LumericalSolutions,In46?2009LumericalSolutions,Inc.Simplefarfieldexample2Polarization

:Cartesioncoordinates

:Spherical(polar)coordinatesCartesianPolar?2009LumericalSolutions,In47Simplefarfieldexample2Thecommandfarfieldvector3disusedto

obtainvectorialfarfieldinformationabs(Ex)

abs(Ey)?2009LumericalSolutions,Inc.abs(Ez)Simplefarfieldexample2abs(48Simplefarfieldexample2Thecommandfarfieldpolar3disusedtoobtain

vectorialfarfieldinformationinpolar(spherical)

coordinates.Wecanseethatthepolarizationangleis indeed15degrees,assetinthesourcesettings.abs(Er)

abs(Etheta)?2009LumericalSolutions,Inc.abs(Ephi)Simplefarfieldexample2abs(49?2009LumericalSolutions,Inc.Simplefarfieldexample2WeplotonlythephaseofEtheta,andEphi.

:Notethatthepphaseshiftindicatesachangein sign.angle(Etheta)angle(Ephi)?2009LumericalSolutions,In50?2009LumericalSolutions,Inc.Simplefarfieldexample3Nowwe’llconsiderarealfarfieldexample.ThediffractionpatternfromgratingofholesetchedontoanSOIwafer200nmthick,illuminatedat1.3-1.4mmfromthebackside.We’llassumetheSiO2hasaconstantindexof1.4andtheSihasaconstantindexof3.5.Copythefilefarfield3.fsptoyourcomputerandrunit.?2009LumericalSolutions,In51?2009LumericalSolutions,Inc.Simplefarfieldexample3DesiredplotsfromGUIsignalsvstimetransmissionandreflectionatasafunctionofwavelengthfarfieldat1.3mm(230.61THz)for1periodfarfieldat1.3mmfor5x5periods:Gaussianillumination:tophatillumination?2009LumericalSolutions,In52Periodicstructures:simulationandfarfieldprojectionsThefilefarfield5.fspillustrateshowfarfield

projectionscanbeusedonperiodicstructuresPeriodicstructures:simulatio53farE0Periodicstructures:simulationandfarfieldprojectionsOneperiodThesimulationisoneunitcellbutcorrectlyrepresentsan infiniteperiodicstructureilluminatedbyaplanewaveThefarfieldprojectiononlyprojectsthefieldfrom1period. Thereforewehavesubstantialdiffractionandgenerallyseea

verybroadfunctioninthefarfieldEfarProjectioncomesonlyfrom1periodItiscutbyarectangularfunctionfromtheinfinitestructure!farE0Periodicstructures:54ePeriodicstructures:simulationandfarfieldprojectionsAssumeperiodicityforthefarfieldprojectionsNowweareprojectingmultipleperiods(assume5inthisfigure)Use“tophat”illuminationwhen

:yourexperimenthasafinitenumberofperiodsilluminatedbya largebeamAsthenumberofperiodsincludedintheprojectionincreases,

weseethediffractedordersbegintoappear.Thebeamsget narrowerasthenumberofperiodsincreases.

5periods

2m2i(kkB)ma

farEm

farEePeriodicstructures:simula55fare

meE

farEm2m5/2i(kkB)ma

Periodicstructures:simulationandfarfieldprojectionsAssumeperiodicityforthefarfieldprojectionsNowweareprojectingmultipleperiodswithagaussianweighting(widthof5periodsinthisfigure)Use“gaussian”illuminationwhen::yourexperimenthasalargenumberofperiodsilluminatedbyafinitesizedbeamThewidthofthebeammuststillbelargecomparedtoperiodAsthenumberofperiodsincludedintheprojectionincreases,weseethediffractedordersbegintoappear.Thebeamsgetnarrowerasthenumberofperiodsincreases.

5periodsfare eE far2m56SimulationsofperiodicstructuresThegratingscriptfunctionsNowweareprojectinganinfinitenumberofperiodsWeseethetotalfarfield projectionbecomesaseriesofdeltafunctionsatallthevaluesofkthatmeettheBraggcondition.Simulationsofperiodicstruct57FarfieldfilteringAdvancedfarfieldfilteringtoremoveripplesfromfinitetruncationofthefield.::Openthefileinterface2d.fspandruninterface2d.lsf.Youseethefollowingcurveof|E|2at1mdistancevsangleDipolesourceclosetomaterialinterface

?2009LumericalSolutions,Inc.FarfieldfilteringAdvancedf58?2009LumericalSolutions,Inc.FarfieldfilteringModifythescriptfiletoset:rerun_simulations=0;:farfieldfilter(0);Nowweget?2009LumericalSolutions,In59?2009LumericalSolutions,Inc.FarfieldfilteringThedifferenceisthatthenearfieldistruncatednear theedgesofthesimulation:farfieldfilter(a);

Filteraba=a/(a+b)

a+bshoulder?2009LumericalSolutions,In60?2009LumericalSolutions,Inc.FarfieldDVDexampleTheGettingStartedDVDexampleshowsfarfieldscriptingrunningmultiplesimulations?2009LumericalSolutions,In61Symmetric/Anti-SymmetricandBlochboundaryconditionsSymmetric/Anti-Symmetricboundaryconditions:Reducememory/timeforsymmetricstructures:Advanced:reducememory/timeforperiodicstructuresPeriodicboundaryconditions:Reducememory/timeforperiodicstructuresBlochboundaryconditions:Reducememory/timeforperiodicstructures:Angledplanewaveincidence?2009LumericalSolutions,Inc.Symmetric/Anti-SymmetricandB62Symmetric/Anti-SymmetricandBlochboundaryconditionsNonzerocomponentsoftheelectricandmagneticfieldsatsymmetric/anti-symmetricboundariesSymmetric/Anti-SymmetricandB63Symmetric/Anti-SymmetricandBlochboundaryconditionsSettingthecorrectboundaryconditionswhenbeamsareused?2009LumericalSolutions,Inc.Symmetric/Anti-SymmetricandB64Symmetric/Anti-SymmetricandBlochboundaryconditionsSymmetry/Anti-Symmetrycanevenbeusedforperiodicstructures:Openthefilefarfield4.fsp?2009LumericalSolutions,Inc.Symmetric/Anti-SymmetricandB65Symmetric/Anti-SymmetricandBlochboundaryconditionsSymmetry/Anti-Symmetrycanevenbeusedforperiodicstructures

:ImagethenearfieldwiththeGUIat1.3microns

:Imagethefarfield

:Imagethenearfieldwithscripting????x=getdata(“transmission”,”x”);y=getdata(“transmission”,”y”);E2=pinch(getelectric(“transmission”),4,50);image(x,y,E2);

?2009LumericalSolutions,Inc.Symmetric/Anti-SymmetricandB66Symmetric/Anti-SymmetricandBlochboundaryconditionsSymmetry/Anti-Symmetrycanevenbeusedfor

periodicstructures

:Wecangetthesameresultsasinfarfield3.fspbutthe simulationrunsfaster

:Farfieldprojectionscanstillbedone

:Thedataisautomatically“unfolded”soweseethefullimageActualsimulationGUIandscriptresults?2009LumericalSolutions,Inc.Symmetric/Anti-SymmetricandB67Symmetric/Anti-SymmetricandBlochboundaryconditionsPeriodicboundariescanbeusedforperiodicstructureswhenthesourceisatnormalincidenceBlochboundariescanbeusedfor::structureswhenthesourceisnotatnormalincidenceBandstructurecalculations(photoniccrystals)Blochboundariesconditionsensurethat:E(x+a)=exp(ika)*E(x)??aisthesimulationspankistheBlochvector:PeriodicboundariesarejustaspecialcaseofBlochboundaries(k=0)!WhenusingBlochboundariesfornon-normalplanewaves,youmustcheckthefollowingSymmetric/Anti-SymmetricandB68Symmetric/Anti-SymmetricandBlochboundaryconditionsConsiderthedifferencebetweencorrectandincorrectksettingsforaplanewaveinfreespace

Correct Incorrect

?2009LumericalSolutions,Inc.Symmetric/Anti-SymmetricandB69Symmetric/Anti-SymmetricandBlochboundaryconditionsWhenthesettingsarecorrect,wecanstudyperiodicstructureilluminatedbyplanewavesatanglesusingtheBlochBCs:Wecancalculatefarfieldprojections?Assumeperiodicitythesameaswithperiodicboundaryconditions:Wecancalculategratingorderefficiencies,thesameaswithperiodicboundaryconditions:WemustbecautiousaboutthePMLperformancewhentheangleofincidenceissteep?Sometimes,weneedtoincreasethenumberoflayersofPMLtogetaccurateresultsSymmetric/Anti-SymmetricandB70?2009LumericalSolutions,Inc.DispersiveMaterialsTOPICSDispersivematerialsinFDTDmethodMaterialmodelsinFDTDSolutions?2009LumericalSolutions,In71ED)()()(wwwtdtttEtEttD)()()()()(?2009LumericalSolutions,Inc.DispersiveMaterialsThefieldsinFDTDarereal:exceptionforBlochboundaries(withintension)FDTDisatimedomaintechnique.Therelations0tAFouriertransformthoeremED72DispersiveMaterialsFDTDSolutionssupportsthefollowingmodels::::::::::DielectricSampledMaterialPEC(PerfectElectricalConductor)(n,k)DielectricConductivePlasmaDebyeLorentzKerrnonlinearPDLC(Plasma–Debye–Lorentz–Conductive)

?Backwardscompatibilitymodeonly:Sellmeier

?2009LumericalSolutions,Inc.DispersiveMaterials:Dielectri73constnr)(w?2009LumericalSolutions,Inc.DispersiveMaterialsDielectricMaterialThereisnodependenceonfrequency!Restriction:n>=12constnr74?2009LumericalSolutions,Inc.DispersiveMaterialsSampledMaterialThereisexperimental(ortheoretical,oruser’s

own)datafor(n,k)asafunctionofwavelength:Frombuilt-inmaterialdatabase:FromyourowndataFDTDSolutionsautomaticallyfitsthedataoverthewavelengthrangeofyoursources:Multi-coefficientmodel:Youchoose?Thenumberofcoefficients?Thefittolerance:Morecoefficientstakesmoretimeandmemory?2009LumericalSolutions,In75ExampleGaAs,12coefficientsMulti-coefficientmodelGaAs,200-800nmExampleGaAs,12coefficient76Auto-fittingofmaterialsFittingyour(proprietary)data:Example,representativedataofcolorfiltersRedfilter?2009LumericalSolutions,Inc.Auto-fittingofmaterialsFit77Auto-fittingofmaterialsFittingyour(proprietary)data:Example,representativedataofcolorfiltersBluefilter?2009LumericalSolutions,Inc.Auto-fittingofmaterialsFit78Auto-fittingofmaterialsMetalsarenotnecessarilysimpleplasmamaterialsChromium?2009LumericalSolutions,Inc.Auto-fittingofmaterialsMet79SometipsformaterialfittingChecktheimaginarydatatoavoid“fake”gainFixedfittingwavelengthrangefordifferentsim.?2009LumericalSolutions,Inc.Sometipsformaterialfitting80Auto-fittingofmaterialsBuiltinmaterialdatawithauto-fitting?2009LumericalSolutions,Inc.Auto-fittingofmaterialsBui81?2009LumericalSolutions,Inc.WorkinginsimulationsSimpletests:FDTDvstheoryfora50nmthickspanofSi:AnalyticresultforRandTcanbeeasilycalculatedTheyellowareaissimulated?2009LumericalSolutions,In82?2009LumericalSolutions,Inc.WorkinginsimulationsSimpletests:FDTDvstheoryfora50nmthickspanofSi:multi-coefficientauto-fittoSi?2009LumericalSolutions,In83?2009LumericalSolutions,Inc.WorkinginsimulationsSimpletests:FDTDvstheoryfora50nmthickspanofSi:Calculatethetheoreticalcurvefromthefit:Averagedifference=0.001:Maxdifference=0.008?2009LumericalSolutions,In84

WorkinginsimulationsSimpletests:FDTDvstheoryfora50nmthickspanofSi::::CalculatethetheoreticalcurvefromtheoriginalmaterialdataAveragedifference=0.0023Maxdifference=0.031Resultscomefromonesimulation

?2009LumericalSolutions,Inc. Workinginsimulations:Calcul85

WorkinginsimulationsCompareLorentzmodelwith