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1、COMPUTATIONALMETHODSFORTHEANALYSISANDDESIGNOFPHOTONICBANDGAPSTRUCTURESMinQiuKTHDivisionofElectromagneticTheoryDepartmentofSignals,SensorsandSystemsRoyalInstituteofTechnologyStockholm2000AkademiskavhandlingsommedtillståndavKungligaTekniskaHögskolanframläggestilloffentliggra
2、nskningföravläggandeavtekniskdoktorsexameniteoretiskelektroteknik,onsdagenden22november2000,kl.10.15,iKollegiesalen,Administrationsbyggnaden,KTH,Valhallavägen79,Stockholm.Avhandlingenkommerattförsvaraspåengelska.ISBN91-7170-640-2Copyright©MinQiu,2000Stockholm2000KTHHögskol
3、etryckerietAbstractInthepresentthesis,computationalmethodsfortheanalysisanddesignofphotonicbandgapstructureareconsidered.Manynumericalmethodshavebeenusedtostudysuchstructures.Amongthem,theplanewaveexpansionmethodisveryoftenused.Usingthismethod,weshowthatinclusionsofellipti
4、cairholescanbeusedeffectivelytoobtainalargercompletebandgapfortwo-dimensional(2D)photoniccrystals.Anoptimaldesignofa2Dphotoniccrystalisalsoconsideredinthethesisusingacombinationoftheplanewaveexpansionmethodandtheconjugategradientmethod.Wefindthatamaximumcomplete2Dbandgapca
5、nbeobtainedbyconnectingdielectricrodswithveinsforaphotoniccrystalwithasquarelatticeofairholesinGaAs.Forsomeproblems,suchasdefectmodes,theplanewaveexpansionmethodisextremelytime-consuming.Itseemsthatthefinite-differencetime-domain(FDTD)methodispromising,sincethecomputationa
6、ltimeisproportionaltothenumberofthediscretizationpointsinthecomputationdomain(i.e.,itisoforderN).AFDTDschemeinanonorthogonalcoordinatesystemispresentedinthethesistocalculatethebandstructureofa2Dphotoniccrystalconsistingofaskewlattice.Thealgorithmcaneasilybeusedforanycompli
7、catedinclusionconfiguration,whichcanhaveboththedielectricandmetallicconstituents.TheFDTDmethodisalsoappliedtocalculatetheoff-planebandstructuresof2Dphotoniccrystalsinthepresentthesis.Wealsoproposeanumericalmethodforcomputingdefectmodesin2Dcrystals(withdielectricormetallici
8、nclusions).ComparedtotheFDTDtransmissionspectramethod,ourmethodreducesthecomputationtimea
