Chapter4

IntegratedOpticWaveguide4.1DielectricSlabWaveguiden3n2n1dTrappingoflightrayinawaveguiden2<n1>n3q4.2MODESINTHESYMMETRIC-SLABWAVEGUIDEn2n2n1n1>n2Rangeofforboundwaves:PropagationfactorLongitudinalpropagationfactorForanaxialray,=90°andneff

=n1Foracriticalangleray=candTherangeofneff

isnow

Definethe

effectiveindexofrefraction:4.2.1ModeConditionn2n2n1n1>n2Thetwoboundaries(upperandlower)formacavity.Acavityisresonantwhentheroundtripphaseshiftis2m(wherem=1,2,3…).

=m2 (4.10)4.2.2TEandTMPolarizationTEpolarization(TransverseElectric)Thisisthesameasperpendicularpolarization(s).

Edn2n2n1zyzTMpolarization(TransverseMagnetic)Thisisthesameasparallelpolarization(p).

(4.11)whereweusedtherelationship4.2.3TEModeChartExampleConsideranAlGaAsLaserDiodeFortheTE0modethecalculationsyieldthetable:(1)(2)(3)(4)(5)(6)qnefftan(hd/2)hd2pn1cosqd/l80.43.550003.7570823.5650.6511.1553.1480.367843.5801.2611.7802.3640.753863.5912.1612.2751.5781.442883.5984.6532.7180.7893.445903.6003.14204.2.4HigherOrderModes(4.12)(4.13)qneffD(d/l)(d/l)280.43.5500.8360.8361.672823.5650.9981.3652.363843.5801.3292.0823.410863.5911.9913.4335.424883.5983.9807.42511.40903.600(d/l)000.3670.7531.4423.445(d/l)1TE0TE1TE2TE3TE4TE5d/lneffqExample:Letd=1.64m,=0.82m.Find,neff,andthenumberofallowedmodes.Fromthemodechart(nextslide):TEModeChartd/lneffqIngeneral,them-thmodecutsoff(nolongerpropagates)whend/lsatisfies:(4.14)ToinsureonlytheTE0modewillpropagate,makeThisproducesasingle-modewaveguide.(4.17)Inamultimodewaveguide:Lower-orderedraystravelwithlargeranglesthanhigher-orderedrays.

LowerHigherTE0,TM0TE1,TM1d/lqneff4.2.5TMModeChartDegeneratemodeSinglemodepropagationisobtainedbysatisfying(4.17)andpolarizingthelightasTEorTM.cos(hy)TE0TE1sin(hy)yye-a(y-d/2)e-a(y-d/2)d/2-d/24.2.6ModePatterncos(hy)TE2TE3sin(hy)yyd/2-d/2e-a(y-d/2)4.3ModesInTheAsymmetricWaveguidedn3n2n1zyExample:Let n1=2.29ZnS(zincsulfide) n2=1.5glass n3=1.0air

TE0TM0d/lneffq4.4CouplingToTheWaveguiden2n2n1dLightsource4.4.1 EdgeCouplingn2n2n110(4.21)Definethefractionalrefractiveindexchangeas:Assumethat

n1andn2arenearlyequal.ThenFinallyCladdingModesConsiderraysbeyondthecriticalangle,(<c)n2n2n1nb100%reflectionTheseraysmaybeguidedascladdingmodes.(Attheinnerboundarythereispartialreflection)4.4.2 PrismCouplinggapn1n2TE0fieldinthefilmpnpn3=airEpprismfieldPrism4.4.3 GratingCoupling4.5DispersionAndDistortionInTheSlabWaveguide4.5.1 WaveguideDispersionn1n2n1>n2AxialmodeL2n2cHigherordermodeL14.5.2 MultimodeDistortion(ModalDistortion)Axialmodetraveltime:Forthecriticalangleray,L1L2cThetotalpathofthecriticalanglerayisthen

Thetotaldelayis(4.27)Thetotalpulsespreadisgivenby4.6IntegratedOpticComponents4.6.1PassiveDevicesIntegratedOpticDirectionalCouplerSubstrateLP1P2P3P4Foranideal(lossless)couplertherelativeoutputpowersaregivenby: P2/P1=cos2(pL/2Lc)(4.30) P3/P1=sin2(pL/2Lc)(4.31)whereLciscalledthecouplinglength.AnysplittingratiobetweenthetwooutputportsispossiblebyappropriatechoiceoflengthL.Example:IftheactuallengthLofthecouplingregionisLc/2,computetheoutputcoupling.

P2/P1=cos2(p/4)=(0.707)2=0.5 P3/P1=sin2(p/4)=(0.707)2=0.550%ofthepowerexitsbothoftheoutputports.Since 10logP2/P1=10log0.5=-3dBthisisa3-dBegratedopticpowersplittersPin/2PinPin/24.6.2ActiveDevicesLightControlDevicesBeamSwitchesModulations

LightConversionDevicesLightSources(Transmitters)Photodetectors(Receivers)Theelectroopticswitch+V-AppliedEfieldduetoVPowerInoffonAsinthepassivecoupler,thepowerdistributionisgivenby: P2/P1=cos2(pL/2Lc) P3/P1=sin2(pL/2Lc)ListheinteractionlengthandLcisthecouplinglength.TheinteractionlengthLissetequaltothecouplinglengthLcP2/P1=cos2(/2)=0

P3/P1=sin2(/2)=1 Mach-ZehnderMo