FiberOpticNetworkDesignX.Wu,M.J.Li,H.M.YanDept.ofOpt.Engr.,ZJU2011Class3Outline

FWM:definition&originFWMinfiber,effectonWDMHowtoreduceit&simulationSolutionsPolarizationallocationUnequalchannelspacingDispersionmanagementDefinition:Nonlineareffectthatoccursinnonlinearopticalmaterialssuchasphotonicswitch,opticalfibercable,etc.Thisinteractionbetweenwavesleadstointeractionbetweenchannelsgeneratesoneormorenewchannels(orharmonics).Forinstance,whenthreewavesatfrequenciesfi,fj,andfktraverseafibertheygenerateanothersignallocatedatTheeffectsofFWMFour-WaveMixing(FWM)FiberExample:Theinputistwosignalslocatedat

1and

2traverseafiberoflength(L)andtheoutputisfourdifferentsignalslocatedat1,

2,21-2,and22-1.Ingeneralthenumberofnewlygeneratedsignalsisgivenby

WherePi,Pj,PkaretheinputpowerofthechannelsDisthedegeneracyfactor3and6fortwo-toneand6forthree-toneproductWhereAeffistheeffectivecross-sectionalareaandLeffistheeffectivelengthofthefibergivenby

Thepowerofofnewlygeneratedsignalsisgivenby

Andisgivenby

Thenonlinearsusceptibility1111TheefficiencyηisgivenbyWherefmn=fm-fn,(m,n=1,2,3)

ThefollowingfiguredemonestratestheeffectofFWMwhenFoursignalswithequallypower3mwtraversesafiberwiththefollowingspecifications

Description ValuesAttenuationfactor()0.2dB/kmEffectivefibercross-sectionalarea(Aeff)6.4x10-11m2Thirdordernonlinearsusceptibility(1111)6x10-15cm3/ergChromaticdispersion(Dc)1ps/nm.kmDispersionslope()

.07ps/km.nm2Refractive-index(n)1.48LengthL75kmWavelength()1550nmTheOriginalinputsignalsThenewlygeneratedsignalsandtheircorrespondingpowerindBmThenewlygeneratedsignalsandtheircorrespondingpowerindBmafterfiltration

TheoriginalandthenewlygeneratedsignalsafterfiltrationaswellastheircorrespondingpowerindBm

OriginofFWMEffectonWDMsystemsSolutionsPolarizationAllocationUnequalChannelSpacingDispersionManagement

OriginofFWM[1]ThirdordernonlinearityEnergyConservationMomentumConservation—phasematchingOriginofFWM—PhaseMatching[2]

EffectsonWDMSystems[2]WhenChannelspacingandfiberdispersionaresmallenoughPhaseMatchConditionsTheefficiencycurveversusthechannelseparationin(GHz)&dispersionslopesEffectsonWDMSystems[3]NonlinearCrosstalkequallyspacing,producttermsfallatchannelfrequencyCoherentinterferenceEffectsonWDMSystems[4]BitpatternPowerDepletionEffectsonWDMSystems—SolutionsPolarizationAllocationUnequalspacingDispersionmanagementPolarizationAllocation[5]PolarizationAllocation[5]PolarizationAllocation[5]AddpolarizationfilteratthereceiverendUnequalChannelSpacing[6]UnequalChannelSpacing[6]Dispersion-Management[4]Nodispersion-zeropointTotalaccumulateddispersionnearzero

DispersionManagement[7]Dispersionmapfordispersion-compensatingfiber(DCF)SmallcoreareaNewTypeofFibersLargeeffectiveareafiberNonzerodispersionshiftedfiber(NZ-DSF)Large-effective-areafiber(red)suppressedfour-wavemixingcrosstalkto-22.5dB,comparedto-19.0dBforNZ-DSFfiber(blue).

References[1]G.Agrawal“NonlinearFiberOptics”,3rdedition[2]GAgrawal“Fiber-OpticsCommunicationSystems”3rdedition[3]NoriSibata,RalfBraunandRobertWaarts,IEEEJ.QuantumElectron.QE23,1205,1987[4]IvanKaminowandThomasKoch,OFTIIIA[5]C.Mahon,L.Olofsson,E.Bodtker,G.Jacobsen,IEEEPhoton.Tech.Lett.8,575,1996[6]F.Forghieri,R.Tkach,A.Chroplyvy,J.LightwaveTech,13,8891995[7]R.Tkach,R.Derosierandet.al,IEEEPhoton.Tech.Lett.7,1369,1995NoiseContributionsinOpticalSystemsanddetection

I.ThermalNoise:

kisBoltzmannconstant,TistheabsolutetemperatureinKelven,BisthereceiverelectricalbandwidthandRistheloadresistancevalue.II.ShotNoise

Whereqistheelectroniccharge,IisthemeanopticallygeneratedcurrentandIdisthephotodetectordarkcurrentIII.RelativeIntensityNoise(RIN):

TheOpticalSignal-to-NoiseRatio(OSNR)isgivenbyWhereisgivenby

ThenoiseduetoFWMphenomenonisgivenby[Reference]

Thebiterrorrate(Pe)versusthequalityfactorQ

Now,thequestion:howtoincludetheeffectofFWMinthefibermetricsBasedonthesystemdesigntarget,whichismainlytheBER,Q(orOSNR)canbeevaluatedfromtheBERcurve.Thenoiseinthe