Optical Sources.ppt

1,Chapter4OpticalSources,4.2LIGHT-EMITTINGDIODES(LEDs)4.2.1LEDStructures4.2.3QuantumEfficiencyandLEDPower4.2.4ModulationofLED4.3LASERDIODES4.3.1ModesandThresholdConditions4.3.2LaserDiodeRateEquations4.3.3ExternalQuantumEfficiency4.3.4ResonantFrequencies4.3.6Single-ModeLasers4.3.7ModulationofLaserDiodes4.4LIGHTSOURCELINEARITY,2,CharacteristicsofLEDs:Lowspeed(200-MHz;Typicallyhaveresponsetimeslessthan1-ns;Havingopticalbandwidthsof2-nmorless;Capableofcouplingseveraltensofmilliwattsofluminescentpower;Cancouplewithopticalfiberswithsmallcoresandsmallmode-fielddiameters.,4.3.1ModesandThresholdConditions,36,TheradiationinthelaserdiodeisgeneratedwithinaFabry-Perotresonatorcavity,asshowninFig.4-18.Thiscavityisapproximately250-500mmlong,5-15mmwide,and0.1-0.2mmthick.Thesedimensionsarecommonlyreferredtoasthelongitudinal,lateral,andtransversedimensionsofthecavity,respectively.,4.3.1ModesandThresholdConditions,37,IntheLDFabry-Perotresonator,apairofflat,partiallyreflectingmirrorsaredirectedtoenclosethecavity.Thelasercavitycanhavemanyresonantfrequencies.Thedevicewillemitlightatthoseresonantfrequenciesforwhichthegainissufficienttoovercomethelosses.,4.3.1ModesandThresholdConditions,38,Typicaldistributed-feedback(DFB)laserconfigurationisshowninFig.4-19.ThelasingactionisobtainedfromBraggreflectorsordistributed-feedbackcorrugations,whichareincorporatedintothemultilayerstructurealongthelengthofthediode.Theopticalradiationwithintheresonancecavityofalaserdiodesetsupapatternofelectricandmagneticfieldlinescalledthemodesofthecavity.Thesecanbeseparatedintotwoindependentsetsoftransverseelectric(TE)andtransversemagnetic(TM)modes.,4.3.1ModesandThresholdConditions,39,ThelongitudinalmodesarerelatedtothelengthLofthecavityanddeterminetheprincipalstructureofthefrequencyspectrumoftheemittedopticalradiation.SinceLismuchlargerthanthelasingwavelengthof1mm,manylongitudinalmodescanexist.Lateralmodeslieintheplaneofthepnjunction.Thesemodesdependonthesidewallpreparationandthewidthofthecavity,anddeterminetheshapeofthelateralprofileofthelaserbeam.,4.3.1ModesandThresholdConditions,40,Transversemodesareassociatedwiththeelectromagneticfieldandbeamprofileinthedirectionperpendiculartotheplaneofthepnjunction.Thesemodeslargelydeterminesuchlasercharacteristicsastheradiationpatternandthethresholdcurrentdensity.,4.3.1ModesandThresholdConditions,41,Todeterminethelasingconditionsandtheresonantfrequencies,weexpresstheEMwavepropagatinginthelongitudinaldirectionintermsoftheelectricfieldphasorE(z,t)=I(z).expj(wt-bk)(4-22)whereI(z)istheopticalfieldintensity,wistheopticalradianfrequency,andbisthepropagationconstant.,4.3.1ModesandThresholdConditions,42,Thestimulatedemissionrateintoagivenmodeisproportionaltotheintensityoftheradiationinthatmode.TheradiationintensityataphotonenergyhnvariesexponentiallywiththedistancezthatittraversesalongthelasingcavityaccordingtotherelationshipI(z)=I(0).expGg(hn)a(hn)z(4-23)wheregisthegaincoefficientintheFabry-Perotcavity,aistheeffectiveabsorptioncoefficientofthematerialintheopticalpath,andGistheoptical-fieldconfinementfactor-thefractionofopticalpowerintheactivelayer.,4.3.1ModesandThresholdConditions,43,Figure4-19.Structureofadistributed-feedback(DFB)laserdiode.,4.3.1ModesandThresholdConditions,44,Lasingoccurswhenthegainofguidedmodesexceedtheopticallossduringoneroundtripthroughthecavity.Duringtheroundtripz=2L,onlythefractionsR1andR2oftheopticalradiationarereflectedfromthelaserends.,4.3.1ModesandThresholdConditions,45,R1andR2aretheFresnelreflectioncoefficientsgivenbyR=(n1-n2)/(n1+n2)2(4-24)fortheopticalreflectionataninterfacebetweenmaterialshavingrefractiveindicesn1andn2.Fromthislasingcondition,Eq.(4-23)becomesI(2L)=I(0)R1R2.exp2LGg(hn)a(hn)(4-25),4.3.1ModesandThresholdConditions,46,Atthelasingthreshold,asteady-stateoscillationtakesplace,andthemagnitudeandphaseofthereturnedwavemustbeequaltothoseoftheoriginalwave:I(2L)=I(0)andexp-j2bL=1(4-26)Equ.(4-26)givesinformationconcerningtheresonantfrequenciesoftheFabry-Perotcavity.,4.3.1ModesandThresholdConditions,47,Theconditiontojustreachthelasingthresholdisthepointatwhichtheopticalgainisequaltothetotallossatinthecavity.FromEq.(4-26),thisconditionisGgth=at=a+(1/2L).ln(1/R1R2)=a+aend(4-28)whereaendisthemirrorlossinthelasingcavity.,4.3.1ModesandThresholdConditions,48,Forlasingtooccur,wemusthavethegainggth.Thismeansthatthepumpingsourcethatmaintainsthepopulationinversionmustbesufficientlystrongtosupportorexceedalltheenergy-consumingmechanismswithinthelasingcavity.Example4-7:ForGaAs,R1=R2=0.32foruncoatedfacets(i.e.,32%oftheradiationisreflectedatafacet)anda=10cm-1.ThisyieldsGgth=33cm-1foralaserdiodeoflengthL=500mm.,4.3.1ModesandThresholdConditions,49,TherelationshipbetweenopticaloutputpoweranddiodedrivecurrentispresentedinFig.4-20.Atlowdiodecurrents,onlyspontaneousradiationisemitted.BoththespectralrangeandthelateralbeamwidthofthisemissionarebroadlikethatofanLED.Adramaticandsharplydefinedincreaseinthepoweroutputoccursatthelasingthreshold.Asthistransitionpointisapproached,thespectralrangeandthebeamwidthbothnarrowwithincreasingdrivecurrent.,4.3.1ModesandThresholdConditions,50,Thefinalspectralwidthof1nmandthefullynarrowedlateralbeamwidthofnominally5-10arereachedjustpastthethresholdpoint.ThethresholdcurrentIthisdefinedbyextrapolationofthelasingregionoftheL-Icurve,asshowninFig.4-20.Athighpoweroutputs,theslopeofthecurvedecreasesbecauseofjunctionheating.,4.3.1ModesandThresholdConditions,51,Forlaserstructuresthathavestrongcarrierconfinement,thethresholdcurrentdensityforstimulatedemissionJthcantoagoodapproximationberelatedtothelasing-thresholdopticalgainbygth=bJth(4-29)wherebisaconstantthatdependsonthespecificdeviceconstruction.,4.3.1ModesandThresholdConditions,52,Figure4-20.Relationshipbetweenopticaloutputpowerandlaserdiodedrivecurrent.Belowthelasingthreshold,theopticaloutputisaspontaneousLED-typeemission.,4.3.1ModesandThresholdConditions,53,Forapnjunctionwithacarrier-confinementregionofdepthd:TherateequationgovernsthenumberofphotonsFisgivenbydF/dt=CnF+RspF/tph(4-30)=stimulatedemission+spontaneousemission+photonloss.Therateequationgovernsthenumberofelectronsnisgivenbydn/dt=J/qd-n/tsp-CnF(4-31)=injection+spontaneousemission+stimulatedemission.,4.3.2LaserDiodeRateEquations,54,Here,Cisacoefficientdescribingthestrengthoftheopticalabsorptionandemissioninteractions;Rspistherateofspontaneousemissionintothelasingmode,tphisthephotonlifetime,tspisthespontaneous-recombinationlifetime,andJistheinjection-currentdensity.,4.3.2LaserDiodeRateEquations,55,Externaldifferentialquantumefficiencyhextisdefinedasthenumberofphotonsemittedperradiativeelectron-holepairrecombinationabovethreshold:hext=hi(gtha)/gth(4-37)Here,gthisthefixedgaincoefficientandhiistheinternalquantumefficiency.,4.3.3ExternalQuantumEfficiency,56,Experimentally,hextisgivenby(4-38)whereEgistheband-gapenergyinelectronvolts,dPistheincrementalchangeintheemittedopticalpowerforanincrementalchangedIinthedrivecurrent,andlistheemissionwavelength.ForstandardLDs,externaldifferentialquantumefficienciesof15-20%perfacetaretypical.High-qualitydeviceshavedifferentialquantumefficienciesof30-40%.,4.3.3ExternalQuantumEfficiency,57,TheconditioninEq.(4-27)holdswhen2bL=2pm(4-39)wheremisaninteger.Usingb=2pn/lforthepropagationconstantfromEq.(2-46),wehavem=L/(l/2n)=(2Ln/c)n(4-40)wherec=nl.Thecavityresonateswhenanintegernumberofhalf-wavelengthsspanstheregionbetweenthemirrors.,4.3.4ResonantFrequencies,58,TherelationshipbetweengainandfrequencycanbeassumedtohavetheGaussianformg(l)=g(0)exp-(l-lo)2/2s2(4-41)whereloisthewavelengthatthecenterofthespectrum,sisthespectralwidthofthegain,andthemaximumgaing(0)isproportionaltothepopulationinversion.,4.3.4ResonantFrequencies,59,4.3.4ResonantFrequencies,Figure4-21.Typicalspectrumfromagain-guidedGaAlAs/GaAslaserdiode.,60,Tofindthefrequencyspacing,considersuccessivemodesoffrequenciesnm-1andnm.FromEq.(4-40),wehavem-1=(2Ln/c)nm-1andm=(2Ln/c)nm(4-43)Subtractingthesetwoequationsyields(2Ln/c)(nm-nm-1)=(2Ln/c)(Dn)=1(4-44)fromwhichwehavethefrequencyandwavelengthspacingsDn=c/2LnandDl=l2/2Ln.(4-46)GivenEqs.(4-41)and(4-46),theoutputspectrumofamultimodelaserfollowstheplotgiveninFig.4-21.,4.3.4ResonantFrequencies,61,Example4-8:AGaAslaseroperatingat850-nmhasa500-mmlengthandarefractiveindexn=3.7.Whatarethefrequencyandwavelengthspacings?If,atthehalf-powerpoint,l-lo=2nm,whatisthespectralwidthsofthegain?Solution:FromEq.(4-45)wehaveDn=81-GHz,andfromEq.(4-46)wefindthatDl=0.2nm.UsingEq.(4-41)withg(l)=0.5g(0)yieldss=1.70nm.,4.3.4ResonantFrequencies,62,Threetypesoflaserconfigurationsusingfrequency-selectivereflector(thecorrugatedphasegrating)areshowninFig.4-28.Thecouplingbetweenthecounter-propagatingtravelingwavesisatamaximumforwavelengthsclosetotheBraggwavelengthlB:lB=2neL/k,(4-47)whereListheperiodofthecorrugations,neistheeffectiverefractiveindexofthemode,andkistheorderofthegrating.,4.3.6Single-ModeLasers,63,InaDFBlaser(Figs.4-28a&4-29),thelongitudinalmodesarespacedsymmetricallyaroundlBatwavelengths(4-48)wheremisthemodeorderandLeistheeffectivegratinglength.,4.3.6Single-ModeLasers,64,FortheDBRlaser,thegratingsarelocatedattheendsofthenormalactivelayertoreplacethecleavedendmirrorsusedintheFabry-Perotopticalresonator(Fig.4-28b).TheDRlaserconsistsofactiveandpassivedistributedreflectors(Fig.4-28c).ThestructureimprovesthelasingpropertiesofconventionalDFBandDBRlasers,andhasahighefficiencyandhighoutputcapability.,4.3.6Single-ModeLasers,65,4.3.6Single-ModeLasers,Figure4-28.Threetypesoflaserstructuresusingbuilt-infrequency-selectiveresonatorgratings:(a)Distributed-feedback(DFB)laser,(b)Distributed-Bragg-reflector(DBR)laser,(c)Distributed-reflector(DR)laser.,66,4.3.6Single-ModeLasers,Figure4-29.Outputspectrumsymmetricallydistributedaroundinanidealizeddistributed-feedback(DFB)laserdiode.,67,ModulationofLDscanberealizedby:DirectModulationvaryingthelaserdrivecurrentwiththeinformationstreamtoproduceavaryingopticaloutputpower.ExternalModulationneededforhigh-speedsystems(2.5Gb/s)tominimizeundesirablenonlineareffectssuchachirping.,4.3.7ModulationofLaserDiodes,68,LimitationonLDsModulationRate:Thespontaneouslifetimetspisafunctionofthesemiconductorbandstructureandthecarrierconcentration.Thestimulatedcarrierlifetimetstdependsontheopticaldensityinthelasingcavityandisontheorderof10ps.Thephotonlifetimetphistheaveragetimethatthephotonresidesinthelasingcavitybeforebeinglosteitherbyabsorptionorbyemissionthroughthefacets.,4.3.7ModulationofLaserDiodes,69,Ifthelaseriscompletelyturnedoffaftereachpulse,thespontaneouscarrierlifetimewilllimitthemodulationrate.AttheonsetsofacurrentpulseIp,aperiodoftimetdgivenbytd=tlnIp/Ip+(IB-Ith)(4-50)isneededtoachievethepopulationinversiontoproduceagaintoovercometheopticallossesinthelasingcavity.,4.3.7ModulationofLaserDiodes,70,InEq.(4-50)theparameterIBisthebiascurrentandtistheaveragecarrierlifetimeinthecombinationregionwhenthetotalcurrentI=Ip+IBisclosetoIth.Thedelaytimecanbeeliminatedbydc-biasingthediodeatthelasingthresholdcurrent.Pulsemodulationiscarriedoutbymodulatingthelaserintheoperatingregionabovethreshold.Inthisregion,thecarrierlifetimeisshortenedtothestimulatedemissionlifetime,sothathighmodulationratesarepossible.,4.3.7ModulationofLaserDiodes,71,Whenusingadirectlymodulatedlaserdiodeforhigh-speedtransmissionsystems,themodulationfrequencycanbenolargerthanthefrequencyoftherelaxationoscillationsofthelaserfield.Therelaxationoscillationdependsonboththespontaneouslifetimeandthephotonlifetime.Foralineardependenceoftheopticalgainoncarrierdensity,therelaxationoscillationoccursapproximatelyatf=(1/2p).1/(tsptph)1/2.I/Ith-11/2(4-51),4.3.7ModulationofLaserDiodes,72,Sincetspis1nsandtphis2psfora300-mm-longlaser,thenwhentheinjectioncurrentIisabouttwicethethresholdcurrentIth,themaximummodulationfrequencyisafewGHz.Exampleofalaserhavingrelaxation-oscillationpeakat3-GHzisshowninFig.4-30.,4.3.7ModulationofLaserDiodes,73,4.3.7ModulationofLaserDiodes,Figure4-30.Exampleoftherelaxation-oscillationofalaserdiode.,74,InFig.4-35,theelectricanalogsignals(t)isusedtomodulatedirectlyanopticalsourceaboutabiaspointIB.Withnosignalinput,theopticalpoweroutputisPt.Whenthesignals(t)isapplied,theopticaloutputpowerP(t)isP(t)=Pt1+ms(t)(4-53)Here,misthemodulationindexdefinedasm=DI/IB(4-54)whereIB=IBforLEDsandIB=IBIthforlaserdiodes.TheparameterDIisthevariationincurrentaboutthebiaspoint.,4.4LIGHTSOURCELINEARITY,75,Topreventdistortionsintheoutputsignal,themodulationmustbeconfinedtothelinearregionoftheL-Icurve.IfDIIB(i.e.,m100%),thelowerportionofthesignalgetscutoffandseveredistortionwillresult.Typicalmvaluesforanalogapplicationsrangefrom0.25to0.50.,4.4LIGHTSOURCELINEARITY,76,4.4LIGHTSOURCELINEARITY,Figure4-35.BiaspointandAMrangeforLEDsandlaserdiodes.,77,Ifthesignalinputtoanonlineardeviceisasimplecosinewavex(t)=Acoswt,theoutputwillbey(t)=Ao+A1coswt+A2cos2wt+A3cos3wt(4-55)Theoutputsignalconsistsofacomponentattheinputfrequencywplusspuriouscomponentsatzerofrequency,atthe2ndharmonicfrequency2w,atthe3rdharmonicfrequency3w,andsoon.Theaboveeffectisknownasharmonicdistortion.Theamountofnth-orderdistortionisgivenbynth-orderharmonicdistortion=20log(An/A1)(4-56),4.4LIGHTSOURCELINEARITY,78,Todetermineintermodulationdistortion(IMD),themodulatingsignalofanonlineardeviceistakentobex(t)=A1coswt+A2cos2wt.Theoutputsignalwillbeoftheformy(t)=Sm,nBmn.cos(m