3D FDTD simulation of photonic crystal

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1、ThreeDimensionalFinite-DierenceTime-Domain-SimulationsofPhotonicCrystalsVonderFakult•atfur•MathematikundPhysikderUniversit•atStuttgartzurErlangungderWurde•einesDoktorsderNaturwissenschaften(Dr.rer.nat.)genehmigteAbhandlungvonChristianHermannausMullheim•Hauptberichter:Prof.Dr.O.HessMitbericht

2、er:Prof.Dr.H.HerrmannTagdermundlic•henPrufung:•18.Juni2004TheoretischeQuantenelektronikInstitutfur•TechnischePhysik,DLRPfaenwaldring38-40D-70569Stuttgart2004AcknowledgementsFirstofallIwanttothankProf.Dr.OrtwinHessforhissupportandthepossibilitytoworkinhisgroup.Manythanksalsoforprovidingmewith

3、excellentfacilitiesandinfrastructure.IalsowouldliketothankProf.Dr.HansHerrmannandProf.Dr.TilmanPfauforagreeingtobeanexaminer.ManythanksgototheresearchgroupsinStuttgartandGuildford:Dr.StefanScholzforintroducingmeintotheeldandlayingthefoundationoftheFDTD-codes.AchimHamm,AndreasKlaedtkeandChr

4、istianSimmendingerfortheirpatiencewhilesolvingmycomputerproblems,inparticularAndreasKlaedtkeforimple-mentingthePML-boundaries.Dr.EdeltraudGehrig,Dr.DietmarPreisserandKlausB•ohringerformanyhelpfuldiscussions.HeikoPittner,HuiBian,KosmasTsakmakidisandDurgaAryalforbearingmysupervisions....andal

5、lofthemfortheexcellentworkingatmosphere.SpecialthanksIwouldliketoexpresstoCecileJamoisfromMax-Planck-InstituteHalleforanexcellentcooperationandmanyinspiringsuggestionsanddiscussions.Thankstomyparentsformakingitpossibleformetoachievemyaims.And,lastbutnotleast,manythankstomyfamily,JoschuaandMo

6、nika,forallyourloveandsupport.34Contents1Summary72IntroductionandOverview113PrinciplesofPhotonicCrystals153.1ElectromagnetismofPeriodicDielectrics..................153.1.1Maxwell'sEquations.........................153.1.2Bloch'sTheorem...........................173.1.3TheConceptofBrillouin-Zo

7、neandBandstructure.........193.1.4TheBandgap.............................213.1.5Symmetries..............................223.1.6DensityofStates...........................243.2One-DimensionalPhotonicCrystals:TheBraggMirror..........253.3Two-Dim