FDTD-Solutions-介绍

IntroductoryTraining版权所有，请勿外传FDTDSolutions©2009LumericalSolutions,Inc.OutlineIntroductionOverviewofFDTDmethodInstallFDTDSolutionsFeaturesofFDTDSolutionsFDTDSolutionsworkflowSimpleexamplesReviewandtips2©2009LumericalSolutions,Inc.GoalsUnderstandthetypesofproblemsthatrequireFDTDSolutionsLearnthefundamentalsoftheFDTDmethodLearnthebasicfeaturesofFDTDSolutionsGainexperienceusingFDTDSolutions3©2009LumericalSolutions,Inc.OverviewofFDTDmethodTOPICSMaxwellequationsYeecellTimedomaintechniqueFouriertransformSourcesandMonitorsComputationalrequirements2Dvs.3DAdvantagesoftheFDTDmethod4NameDifferentialformIntegralformGauss’lawGauss'lawformagnetism(absenceofmagneticmonopoles):Faraday’slawofinduction:Ampère’slaw(withMaxwell'sextension):©2009LumericalSolutions,Inc.Maxwell’sEquationsDescribethebehaviorofboththeelectricandmagneticfields,aswellastheirinteractionswithmatter.5SymbolMeaningSIUnitofMeasureelectricfieldvoltpermetermagneticfieldalsocalledtheauxiliaryfieldamperepermeterelectricdisplacementfieldalsocalledtheelectricfluxdensitycoulombpersquaremetermagneticfluxdensityalsocalledthemagneticinductionalsocalledthemagneticfieldtesla,orequivalently,weberpersquaremeterfreeelectricchargedensity,notincludingdipolechargesboundinamaterialcoulombpercubicmeterfreecurrentdensity,notincludingpolarizationormagnetizationcurrentsboundinamaterialamperepersquaremeter©2009LumericalSolutions,Inc.Maxwell’sEquations6©2009LumericalSolutions,Inc.WaveOptics–FreespaceplanewaveInvacuum,withoutcharges(=0)orcurrents(J=0)Maxwell’sequationshaveasimplesolutionintermsoftravelingsinusoidalplanewavesTheelectricandmagneticfielddirectionsareorthogonaltooneanotherandthedirectionoftravelkTheE,Hfieldsareinphase,travelingatthespeedcH7©2009LumericalSolutions,Inc.WaveOptics-SimpleMaterialsInlinearmaterials,theDandBfieldsarerelatedtoEandHby:DEB0Hwhere:εistheelectricalpermittivityofthematerial,andμ0isthepermeabilityoffreespaceAtopticalrange,veryoftenthematerial’sdispersion(εisafunctionofwavelength)isverystrong!FDTDSolutionsdoesnotallowformagneticmaterials8012132©2009LumericalSolutions,Inc.EHEH…2ndorderaccurateintime:error~Dt2HowtheFDTDmethodworks(n1)Dt2ThebasicFDTDtime-steppingrelation:EHH9©2009LumericalSolutions,Inc.MaxwellEquationsonameshYeecellEandHarediscreteinspace10©2009LumericalSolutions,Inc.XEzHxEyHyEx(x,y,z)HzKaneYee(1966).NumericalsolutionofinitialboundaryvalueproblemsinvolvingMaxwell'sequationsinisotropicmedia.AntennasandPropagation,IEEETransactionson14:302–307.TheYeecellSpatiallystaggerthevectorcomponentsoftheE-fieldandH-fieldaboutrectangularunitcellsofaCartesiancomputationalgrid.ZYeecellY2ndorderaccurateinspace11©2009LumericalSolutions,Inc.2Dvs.3DFDTDsimulationscanberunin2Dor3D2D:StructureisinfiniteinzdirectionZXY3DZYX12©2009LumericalSolutions,Inc.UsingFDTDSolutionsDefinethephysicalstructures:Thiswillbeusedtocreate(permittivity)foreachcellwithinthecomputationaldomain.:Typically,thematerialiseitherfree-space(air),dielectricordispersive(metal,semi-conductor,…)DefineasimulationregionandBCs:Thisisthephysicalregionoverwhichthesimulationwillbeperformed.Defineasourceoflight:AlightbeamoradipolesourceDefinemonitorstorecorddataforanalysisAnalysisandpost-processing©2009LumericalSolutions,Inc.FDTDisatimedomaintechnique!Timedomainmethod:E(t)andH(t)Mostuserswanttoknowthefieldasafunctionofwavelength,E(l),orequivalentlyfrequency,E(w),稳态场Thesteadystate,continuouswave(CW)fieldE(w)iscalculatedfromE(t)（瞬态场）byFouriertransformduringthesimulation.TSimiwt0SeesectiononUnitsandNormalizationofReferenceManualformoredetails:注：如果使用所谓“渐变的”稳态场激励，就丧失了时域算法的优势14©2009LumericalSolutions,Inc.AdvantagesoftheFDTDmethodAdvantagesFewinherentapproximations=accurateAverygeneraltechniquethatcandealwithmanytypesofproblemsArbitrarilycomplexgeometriesOnesimulationgivesbroadbandresults154.4m©2009LumericalSolutions,Inc.dropl~1.55mExample,ringresonatorthroughn=2.91516©2009LumericalSolutions,Inc.Example:waveguideringresonatortimel1FourierTransforml217©2009LumericalSolutions,Inc.Example:waveguideringresonatorthroughdrop18©2009LumericalSolutions,Inc.FDTDSolutionsFeaturesandWorkflowStartingFDTDSolutionsBasicprogramlayoutStructuresSimulationregionSourcesMonitorsAnalysisScriptcommands19©2009LumericalSolutions,Inc.Features–Generallayout20©2009LumericalSolutions,Inc.Structures21©2009LumericalSolutions,Inc.Simulation22©2009LumericalSolutions,Inc.Sources23©2009LumericalSolutions,Inc.SourcesFDTDSolutionshasavarietyofsourcesavailable:BasicSourcesDipole*GaussianbeamPlanewaveModeAdvancedsourcesTotalfield/scatteredfieldLargeNAsourceASAPUser-definedPolarizationsLinear/circular/elliptic/otherPartial/non-polarized**Coherentandincoherent***24©2009LumericalSolutions,Inc.DipoleTMTE25©2009LumericalSolutions,Inc.Gaussianandplane26AngledplanewavesUseBlochboundaryconditions(Lumerical&MIT)27©2009LumericalSolutions,Inc.AngledplanewavesShouldnotuseperiodicboundaryconditionsT