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1、X.Wu,M.J.Li,H.M.YanDept.ofOpt.Engr.,ZJU2011Class2Class2ChromaticdispersioneffectDispersioncompensatingtechniquesOptimizationofresidualdispersionoritsmap3SpectrumbroadeningDifferenceingroupvelocityWavelengthGroupvelocity1 11 10 0OriginalsignalTimeTransmitteroutputTimeReceiverinput1 11 11 1Regenerated
2、signalWavelengthOpticalspectrumPulsebroadening(Waveformdistortion)OpticalfiberTransmitteroutReceivedwaveformLowopticalpowerHighpowerintensityFrequencychirpRefractiveindexchangeWaveformdistortionduetochromaticdispersionOpticalfiberSpectrumbroadening40Gb/sopticalsignalTransmissionfiberPositivedispersi
3、on(Negativedispersion)+Negativedispersion(Positivedispersion)LongerwavelengthSlow(Fast)ShorterwavelengthFast(Slow)LongerwavelengthFast(Slow)ShorterwavelengthSlow(Fast)AfterfibertransmissionTransmitteroutput25psAfterdispersioncomp.Fiber#1DCDCFiber#2DistancekmR.D.ps/nmPost-comp.+-0Fiber#1DCDCFiber#2Di
4、stancekmR.D.ps/nmPre-comp.-+0Fiber#1DCDCFiber#2DCDistancekmR.D.ps/nmPost-&Pre-comp.-+0Needtoconsiderthevariationoftoleranceduetocharacteristicsoftransmitter,fibernon-lineareffectsanddispersionmap.Evenifresidualdispersionvaluesaresame,thereceivedwaveformsaredifferent,affectedbytheseparameters.Paramet
5、ersaffectingtothetoleranceSignalbitrateChannelcountsandspacingDistanceornumberofspansFibertypeFiberinputpowerPre-chirpingoftransmitter-Modulationschemeoftransmitter-DCFallocation/valueDistancekmDispersionps/nmDispersiontoleranceofreceiver-+-Dispersionps/nm+0PenaltydBLongerwavelengthShorterwavelength
6、CenterwavelengthAllowablepenaltyLight in an optical fiberslowly varying componentpolarizationcarrierTransverse field profile defined by modeThe nonlinear Schrdinger equation (NLSE)Fiber transmission - The Nonlinear Schrdinger EquationLaunched signal:C.R.Menyuk,IEEEJ.QuantumElectron.25,12,2674-2682,D
7、ecember1,1989.L. F. Mollenauer et al., in Opt. Fiber Telecommunications iVA, (Academic, San Diego, Calif., 1997).Fiber transmission NLSE general definitionsAttenuationDispersionNonlinearitya a - Loss coefficient km-1b b - dispersion coefficient ps2/kmg = 2g = 2p p n2/(l l Aeff) - nonlinear coefficie
8、nt W-1km-1t = told z/vgto remove propagation delay- is the optical power WFiber transmission Renormalizing the lossesDefine:zLoss normalized NLSEFor simplicity of physical insight we may assume G(z) = 1Chromatic dispersion or group velocity dispersion (GVD)“Positive” or “negative” dispersion depends
9、 on the definitionD 0 b b 0 “anomalous” dispersionD 0 “normal” dispersionps/nm/kmb b ps2/kmLinear propagation of pulsesNegligible nonlinearity low power (|a|2 is small)Trivial solution in the Fourier domainQuadratic phase term in frequency: power spectrum is unchangedImportant example The Gaussian p
10、ulseTime domainFrequency domainFTIFTexp(ib b W W2z/2)Where:is the pulse-widthis the chirp parameteris the dispersion lengthtimetimew wL|a|2The chirp of a pulseinstantaneous frequencyAmplitudev.s.timeFrequencyv.s.timetimeIf b b 0Transmission fiber b b 0Amplifier module Time is a parameter. There is a
11、 closed-form solutionPropagation of pulses: zero dispersion caseZero dispersion: Self phase modulationtimeThe pulse acquires a chirp, but its amplitude profile does not change. Bandwidth increases. Generation of new frequenciesThe pulse leading edge shifts to the red and the trailing to the blueThe
12、pulse acquires a chirpw w(t,z)Nonlinear lengthLength over which the nonlinear phase shift is 1 radianP: peak power of the pulsenonlinear length, characteristic length of the nonlinear evolutionDispersion + nonlinearity: The split-step methodD DzD DzD Dznonlinearity onlydispersion onlydispersion + no
13、nlinearityG. P. Agrawal, Nonlinear Fiber Optics, Third Edition, (Academic, New York, 2001). NonlinearityBalancing dispersion and nonlinearity a simplified exampleNonlinearity: leading edge shifted to the red, trailing to the blueb b 0 : the blue part of the pulse travels faster than the red part lea
14、ding to pulse compression and inversion of chirpPossible to achieve average compensation between nonlinear compression and the dispersive broadening Stable pulse propagationDispersionb b 0Transmission fiber b b 0Amplifier moduletime0.01480.01520.01560.0160.016400.040.080.121/Bandwidth2 frequency dis
15、persionEvolution along the dispersion mapNonlinear dynamics of a single pulseIf linear and nonlinear chirp compensate exactly after one dispersion map period constant bandwidth. If linear and nonlinear chirp do not compensate exactly bandwidth oscillations over a scale larger than the amplifier spac
16、ingLarge gap between linear and nonlinear chirp Pulse destroys Dispersing pulses010203040506070809010011.522.5SpansBandwidthSingle channel bandwidth evolution complete simulation l l1 1l l2 2l lMMS o u r c e sR e c e i v e r sRx1 1Rx2 2RxMMDCMDCMDCMDCMBand-pass filtersProperties of nonlinear transmi
17、ssion: response to inline filteringPre-compensation v.s. post-compensationPre-compensation v.s. post-compensationPre-compPost-comp.Homework: see if you can simulate a real-world casePre-comp10Gbit/s750kmregenerator-freeWDMfieldtrialupgradinganoperated2.5Gbit/sbasedsystemwithoutchangingtheinstalledinfrastructure.OFC99SanDiegoEhrhardt,A.;Gladisch,A.;Hanik,N.;Technologiezentrum,DeutscheTelekom,Berlin
