Chapter 11Ultrafast MeasurementTechniques11.1Pump Probe Measurements11.1.1Non-Colinear Pump-Probe Measurement:Pump puiseTestdeviceChopperMode-locked Laser Beam spltterS(t)SlowdetectorProbe pulseFtLock-ln4AmnieTime delay between1fs<>0.15μmpumpandprobepulseS(t translation stageComputerscreenFigure 11.1: Non-colinear pump-probe setup with co-polarized pump-probebeams.Adapted from U. Keller.Figure 11.1 shows a non-colinear pump-probe measurement setup. To sup-press background light and low frequency noise of the probe beam the pump371
Chapter 11 Ultrafast Measurement Techniques 11.1 Pump Probe Measurements 11.1.1 Non-Colinear Pump-Probe Measurement: translation stage 1 fs 0.15 µm Beam splitter S(t) Slow detector Time delay between pump and probe pulse t Computer screen Pump pulse Probe pulse Lens Test device Chopper Lock-In Amplifier S(t) t Mode-locked Laser Figure 11.1: Non-colinear pump-probe setup with co-polarized pump-probe beams. Adapted from U. Keller. Figure 11.1 shows a non-colinear pump-probe measurement setup. To suppress background light and low frequency noise of the probe beam the pump 371
372CHAPTER 11.ULTRAFAST MEASUREMENT TECHNIQUESbeam is chopped. Typical chopper frequencies of regular mechanical chop-pers are fch = 100Hz- 2kHz: Mechanical choppers up to 20kHz have beenbuilt. With acousto-optic modulators or electro-optic modulators chopperfreuqencies up to several hundred MHz are possible.Lets denote Sin = So+&S as the probe pulse energy,where So is theaverage value and dsa low frequency noise of the pulse source and S(t)is the probe signal transmitted through thetest device.Then thedetectedsignal transmitted through the test device can be written as(11.1)S(t) = T(P(t))SindT(Pom(t))= ToSin +dpwhereTois the transmission without pumppulse, Po is the pumppulse energyand m(t) the chopper modulation function. It is obvious that if the noise ofthe probe laser ss is of low freuqency, then the signal can be shifted awayfrom this noise floor by chosing an appropriately large chopper frequency inm(t). Ideally, the chopper frequency is chosen large enough to enable shotnoise limited detection.Sometimes the test devices or samples have a rough surface and pumplight scattered from the surface might hit the detector.This can be partiallysuppressed by orthogonal pump and probe polarizationThis is a standard technique to understand relaxation dynamics in con-densed matter, such as carrier relaxation processes in semiconductors forexample.11.1.2ColinearPump-ProbeMeasurement:Sometimes pump and probe pulses have to be collinear, for example whenpump probemeasurements of waveguide devices have to be performed. Thenpump and probe pulse, which might both be at the same center wavelengthhave to be made separable. This can be achieved by using orthogonal pumpand probe polarization as shown in Figure 11.2 or by chopping pump andprobe at different frequencies and detecting at the difference frequency, seeFigure 11.3
372 CHAPTER 11. ULTRAFAST MEASUREMENT TECHNIQUES beam is chopped. Typical chopper frequencies of regular mechanical choppers are fch = 100Hz − 2kHz . Mechanical choppers up to 20kHz have been built. With acousto-optic modulators or electro-optic modulators chopper freuqencies up to several hundred MHz are possible. Lets denote Sin = S0 + δS as the probe pulse energy, where S0 is the average value and δs a low frequency noise of the pulse source and S(t) is the probe signal transmitted through the test device. Then the detected signal transmitted through the test device can be written as S(t) = T(P(t))Sin (11.1) = T0Sin + dT dP (P0m(t)) where T0 is the transmission without pump pulse, P0 is the pump pulse energy and m(t) the chopper modulation function. It is obvious that if the noise of the probe laser δS is of low freuqency, then the signal can be shifted away from this noise floor by chosing an appropriately large chopper frequency in m(t). Ideally, the chopper frequency is chosen large enough to enable shot noise limited detection. Sometimes the test devices or samples have a rough surface and pump light scattered from the surface might hit the detector. This can be partially suppressed by orthogonal pump and probe polarization This is a standard technique to understand relaxation dynamics in condensed matter, such as carrier relaxation processes in semiconductors for example. 11.1.2 Colinear Pump-Probe Measurement: Sometimes pump and probe pulses have to be collinear, for example when pump probe measurements of waveguide devices have to be performed. Then pump and probe pulse, which might both be at the same center wavelength have to be made separable. This can be achieved by using orthogonal pump and probe polarization as shown in Figure 11.2 or by chopping pump and probe at different frequencies and detecting at the difference frequency, see Figure 11.3
11.1.PUMPPROBEMEASUREMENTS373ProbepulseTestdevicePump puiseChopperLensPBSMode-Locked LaserPBSMZO入/2-plateOS(t)SlowdetectorLock-InAmplifierS(t)Figure 11.2: Colinear pump-probe with orthogonally polarized pump andprobe beams.Adapted from U. Keller.ProbepulseTestdevicePumppulseChopperfLensMLLS(t)SlowVtldetectorLock-InChopperf2Amplifieratff-f21S(t)Figure11.3:Colinearpump probewith choppingof pumpandprobe andlock-indetectionat thedifferencefrequency.Adapted from U. Keller
11.1. PUMP PROBE MEASUREMENTS 373 t Pump pulse Probe pulse Lens Test device S(t) Slow detector Chopper Lock-In Amplifier S(t) t PBS PBS λ/2-plate Mode-Locked Laser Figure 11.2: Colinear pump-probe with orthogonally polarized pump and probe beams. Adapted from U. Keller. MLL Pump pulse Probe pulse Lens Test device S(t) Slow detector S(t) t Chopper f1 Chopper f2 Lock-In Amplifier at f - f 1 2 Figure 11.3: Colinear pump probe with chopping of pump and probe and lock-in detection at the difference frequency. Adapted from U. Keller
374CHAPTER11.ULTRAFASTMEASUREMENTTECHNIQUES11.1.3Heterodyne Pump ProbeThe lock-in detection is greatly improved if the difference frequency at whichthe detection occurs can be chosen higher and the signal can be filtered muchbetter using a heterodyne receiver.This is shown in Figure 1l.4, whereAOM's are used to prepare a probe and reference pulse shiftet by 39 and 40MHz respectively. The pump beam is chopped at 1kHz. After the test devicetheprobeand referencepulseare overlayed with each other by delaying thereference pulse in a Michelson-Interferometer.The beat note at 1MHz isdownconverted to base band witha receiver.IotnnueePumppChopperMLLAOMT>>t+39 MhzAOM+40MHzReferenceProbeS(t)Slowdetector[1MHzReceiverLock-InAmplifierSftFigure 11.4:Colinear pump probe measurement with parallel polarizationand largedifferencefrequency.Adapted from U.Keller.If a AM or FM receiver is used and the interferometers generating thereference and probe pulse are interferometerically stable, both amplitude andphase nonlinearities can be detected with high signal to noise
374 CHAPTER 11. ULTRAFAST MEASUREMENT TECHNIQUES 11.1.3 Heterodyne Pump Probe The lock-in detection is greatly improved if the difference frequency at which the detection occurs can be chosen higher and the signal can be filtered much better using a heterodyne receiver. This is shown in Figure 11.4, where AOM’s are used to prepare a probe and reference pulse shiftet by 39 and 40 MHz respectively. The pump beam is chopped at 1kHz. After the test device the probe and reference pulse are overlayed with each other by delaying the reference pulse in a Michelson-Interferometer. The beat note at 1MHz is downconverted to base band with a receiver. Chopper t Pump pulse Probe pulse Test device S(t) Slow detector S(t) t Lock-In Amplifier AOM +39 Mhz AOM Probe +40 MHz Reference MLL T>>t Reference 1 MHz Receiver Figure 11.4: Colinear pump probe measurement with parallel polarization and large difference frequency. Adapted from U. Keller. If a AM or FM receiver is used and the interferometers generating the reference and probe pulse are interferometerically stable, both amplitude and phase nonlinearities can be detected with high signal to noise
11.1.PUMPPROBEMEASUREMENTS375TestdeviceProbepulsePumppulseReferChopperMLLLPZTAOMT>>t +39 MhzAOM+4oMHzReferenceProbeS(t)Slow.detector1 MHz HamRadioReciverAM or FMLock-InAmplifierS(t)Figure 11.5: Heterodyne pump probe using AM and FM receiver to detectamplitude and phase nonlinearities.Adapted from U.Keller
11.1. PUMP PROBE MEASUREMENTS 375 Chopper t Pump pulse Probe pulse Test device S(t) Slow detector S(t) t Lock-In Amplifier AOM +39 Mhz AOM Probe +40 MHz Reference MLL T>>t Reference 1 MHz Ham Radio Reciver AM or FM PZT Figure 11.5: Heterodyne pump probe using AM and FM receiver to detect amplitude and phase nonlinearities. Adapted from U. Keller
376CHAPTER11.ULTRAFASTMEASUREMENTTECHNIQUES11.2Electro-Optic Sampling:Electro-Optic Sampling was invented by Valdmanis and Mourou in the early1980's [8][5].Its is based on polarization rotation of a short laser pulsewhen propagating in a medium showing a linear electro-optic effect.Thepolarization rotation is due to an applied electric filed, i.e. the optical pulsesamples the instantaneous electric field, see Fig.11.6ExternalElectro-OpticSamplingSchemeProbebeam in(arriveatdelayed timesof t+n·△t)Excitation pulses(arrive attimet)ProbeBeamOutSwitchBiasElectro-OpticProbeCrystalSemiconductor SubstrateFigure11.6:Electro-optic sampling schemeaccording otJ.Whitaker.Univof Michigan, Ann Arbor.FigurebyMITOCW.In Fig.11.6 a electic transient is generated with a photo-conductiveswitch activated by a femtosecond laser pulse. A delayed pulse samples thetransient electronic pulse with an electro-optic probe as shown in Fig.11.7
376 CHAPTER 11. ULTRAFAST MEASUREMENT TECHNIQUES 11.2 Electro-Optic Sampling: Electro-Optic Sampling was invented by Valdmanis and Mourou in the early 1980’s [8][5]. Its is based on polarization rotation of a short laser pulse when propagating in a medium showing a linear electro-optic effect. The polarization rotation is due to an applied electric filed, i.e. the optical pulse samples the instantaneous electric field, see Fig.11.6 Figure 11.6: Electro-optic sampling scheme according ot J. Whitaker, Univ. of Michigan, Ann Arbor. In Fig. 11.6 a electic transient is generated with a photo-conductive switch activated by a femtosecond laser pulse. A delayed pulse samples the transient electronic pulse with an electro-optic probe as shown in Fig. 11.7. Switch Bias Semiconductor Substrate Electro-Optic Probe Crystal Probe Beam Out Excitation pulses (arrive at time t) Probe beam in (arrive at delayed times of t+n.∆t) External Electro-Optic Sampling Scheme Figure by MIT OCW
377ELECTRO-OPTICSAMPLING:11.2.Electro-Optic ProbeFused SilicaProbeBeamSupportLiTaO,Electro-OpticCrystalFigure 11.7: LiTaO3-Electro-Otpic Probe according to J.Whitaker, Univ.Michigan.FigurebyMIT OCW.Fig.11.8 shows an overal versionofan electro-optic sampling systemaccording to J. Whitaker, Univ. of Michigan [6]Electro-OpticSamplingSystemSchematicTo Lock-In AmplifierEyepieceDetectorsAnalyzerIlluminationFiberDichroicLaser02Beam SplitterLensPolarizerDelayTriggerBeamBiasProbetipCircuitFigure 11.8: Electro-Otpic Sampling System according to J. Whitaker, Univ.Michigan.Figure by MIT OCW
11.2. ELECTRO-OPTIC SAMPLING: 377 Figure 11.7: LiTaO3−Electro-Otpic Probe according to J. Whitaker, Univ. Michigan. Fig. 11.8 shows an overal version of an electro-optic sampling system according to J. Whitaker, Univ. of Michigan [6] Figure 11.8: Electro-Otpic Sampling System according to J. Whitaker, Univ. Michigan. Electro-Optic Sampling System Schematic Delay Lens Polarizer Trigger Beam Fiber Detectors To Lock-In Amplifier Analyzer Bias Circuit Probe tip Dichroic Beam Splitter Illumination Eyepiece Laser LiTaO3 Electro-Optic Crystal Electro-Optic Probe Probe Beam Fused Silica Support Figure by MIT OCW. Figure by MIT OCW
378CHAPTER11.ULTRAFASTMEASUREMENTTECHNIQUES11.3THz Spectroscopy and ImagingPhoto-conductive switches activated by sub-100 fs pulses or optical rectifica-tion with sub-1o0 fs pulsesleads tothe generation of THz electro-magneticimpulses, that can be received with similar photo-conductive receivers or byelectro-optic sampling [8][9]. This technique was pioneered by Ch. Fattingerand D. Grischkowsky [7].Delay50-100 fsFemtosecond LaserTi:sapphire orCr:LiSAFTHz TransmitterTHzDetectorSampleCurrentLaserPulseDielectrics, Tissue,IC-Packaging etc.LT-GaAsSubstrateFigure 11.9: THz Time Domain Spectroscopy according to[8]FigurebyMITOCW
378 CHAPTER 11. ULTRAFAST MEASUREMENT TECHNIQUES 11.3 THz Spectroscopy and Imaging Photo-conductive switches activated by sub-100 fs pulses or optical rectification with sub-100 fs pulses leads to the generation of THz electro-magnetic impulses, that can be received with similar photo-conductive receivers or by electro-optic sampling [8][9]. This technique was pioneered by Ch. Fattinger and D. Grischkowsky [7]. Figure 11.9: THz Time Domain Spectroscopy according to [8] Femtosecond Laser Ti:sapphire or Cr:LiSAF 50-100 fs Delay THz Transmitter V Sample Dielectrics, Tissue, IC-Packaging etc. Laser Pulse LT-GaAs Substrate Current THz Detector Figure by MIT OCW
11.3.THZSPECTROSCOPYANDIMAGING379GalnAs/GaAs/AlAsDelay12fsE2Ti:sapphireEiOscillatorOpticalRectificationQWin GaAsTHz -OPOsFIR-Probe:THz -OPAs15fs~5-15μm15fs~60THzQuantum-CascadeLaser6 fs>100 THzFigure 11.10: THz Time Domain Spectroscopy using optical rectification inGaAs [9].Figure by MIT OCW.Figure 11.11: Terahertz waveforms modified by passage through (a) a 10mmblock of stycast and (b) a chinese fortune cookie. The dashed lines show theshape of the input waveform multiplied by 0.5 in (a) and by 0.1 in 9b).In *a(the transmitted plse exhibits a strong"chirp"due to frequency-dependentindex, while in (b),pulse broadening indicates preferential absorption of highfrequencies [8]Figure 11.11 shows typical generated THz waveforms and distortions dueto propagation through materials
11.3. THZ SPECTROSCOPY AND IMAGING 379 Figure 11.10: THz Time Domain Spectroscopy using optical rectification in GaAs [9]. Figure 11.11: Terahertz waveforms modified by passage through (a) a 10mm block of stycast and (b) a chinese fortune cookie. The dashed lines show the shape of the input waveform multiplied by 0.5 in (a) and by 0.1 in 9b). In *a( the transmitted plse exhibits a strong "chirp" due to frequency-dependent index, while in (b), pulse broadening indicates preferential absorption of high frequencies [8]. Figure 11.11 shows typical generated THz waveforms and distortions due to propagation through materials. 12 fs Ti:sapphire Oscillator Delay E2 E1 QW THz -OPOs THz -OPAs Quantum-Cascade Laser GaInAs/GaAs/AlAs Optical Rectification in GaAs FIR - Probe: 15 fs ~ 5-15 µm 15 fs ~ 60 THz 6 fs > 100 THz Figure by MIT OCW
380CHAPTER 11.ULTRAFASTMEASUREMENT TECHNIQUES11.4Four-Wave MixingA more advanced ultrafast spectroscopy technique than pump-probe is four-wave mixing (FWM). It enables to investigate not only energy relaxationprocesses, as is the case in pump-probe measurements, but also dephasingprocesses in homogenous as well as inhomogenously broadened materials.The typical set-upis shown in Fig.11.12t231.12Pulse 2Samplek1k3Pulse 3k2Pulse1kg+(k2-k)DetectorFigure 11.12: Typical Four-Wave-Mixing (FWM) beam geometryLets assume these pulses interact resonantely with a two-level systemmodelled by the Bloch Equations derived in chapter 2 (2.1592.162). p(+)(2,t),102E(+)(z,t) = (11.2)Poatcoot2p(+)(z,t) = -2NM*d(z,t)(11.3)IME(+)w,d(z,t) = -(,- jweg)d +(11.4)T22jhw-wo1(M*E(-)d - ME(+)d'011.5)i(z,t)T+丽The two-level system, located at z = 0, will be in the ground state, i.e.d(t = 0) = 0 and w(t = 0) = -1, before arrival of the first pulses. Thatis, no polarization is yet present. Lets assume the pulse interacting with thetwo-level system are weak and we can apply perturbation theory. Then thearrival of the first pulse with the complex fieldE(+(±,t) = E(+) (t)e(cegt-ik,2)(11.6)
380 CHAPTER 11. ULTRAFAST MEASUREMENT TECHNIQUES 11.4 Four-Wave Mixing A more advanced ultrafast spectroscopy technique than pump-probe is fourwave mixing (FWM). It enables to investigate not only energy relaxation processes, as is the case in pump-probe measurements, but also dephasing processes in homogenous as well as inhomogenously broadened materials. The typical set-up is shown in Fig. 11.12 t 23 12 t Sample Pulse 1 Pulse 3 Pulse 2 k1 k2 k3 k1 k2 k3+( ) - Detector Figure 11.12: Typical Four-Wave-Mixing (FWM) beam geometry. Lets assume these pulses interact resonantely with a two-level system modelled by the Bloch Equations derived in chapter 2 (2.1592.162). µ ∆ − 1 c2 0 ∂2 ∂t2 ¶ E (+)(z, t) = µ0 ∂2 ∂t2P (+)(z, t), (11.2) P (+)(z, t) = −2NM ∗ d(z, t) (11.3) ˙d(z, t) = −( 1 T2 − jωeg)d + 1 2j~ M E (+)w, (11.4) w˙(z, t) = −w − w0 T1 + 1 j~ (M ∗ E (−) d − M E (+)d∗ (11.5) ) The two-level system, located at z = 0, will be in the ground state, i.e. d(t = 0) = 0 and w(t = 0) = −1, before arrival of the first pulses. That is, no polarization is yet present. Lets assume the pulse interacting with the two-level system are weak and we can apply perturbation theory. Then the arrival of the first pulse with the complex field E (+)(x, t) = E (+) 0 δ(t)ej(ωegt−j k1x) (11.6)