超短脉冲强度测量课件

The goal:measuring the intensity and phase vs.time(or frequency)The ways:The Spectrometer and Michelson InterferometerScanning AutocorrelationSingle-shot autocorrelationThe Autocorrelation and SpectrumThird-order AutocorrelationInterferometric AutocorrelationMeasuring Ultrashort Laser Pulses I:AutocorrelationE(t)E(tt)In order to measure an event in time,you need a shorter one.To study this event,you need a strobe light pulse thats shorter.But then,to measure the strobe light pulse,you need a detector whose response time is even shorter.And so onSo,now,how do you measure the shortest event?Photograph taken by Harold Edgerton,MITThe DilemmaUltrashort laser pulses are the shortest technological events ever created by humans.Its routine to generate pulses shorter than 10-13 seconds in duration,and researchers have generated pulses only a few fs(10-15 s)long.Such pulses have many applications in physics,chemistry,biology,and engineering.You can measure any eventas long as youve got a pulse thats shorter.So how do you measure the pulse itself?You must use the pulse to measure itself.But that isnt good enough.Its only as short as the pulse.Its not shorter.Techniques based on using the pulse to measure itself have not sufficed.To determine the temporal resolution of an experiment using it.To determine whether it can be made even shorter.To better understand the lasers that emit them and to verify models of ultrashort pulse generation.To better study media:the better we know the light in and light out,the better we know the medium we study with them.To use pulses of specific intensity and phase vs.time to control chemical reactions:“Coherent control.”To understand pulse-shaping efforts for telecommunications,etc.Because its there.Why measure an ultrashort laser pulse?As a molecule dissociates,its emission changes color(i.e.,the phase changes),revealing much about themolecular dynamics,not avail-able from the mere spectrum,or even the intensity vs.time.Excitation to excited stateEmissionGround stateExcited stateExptTheoryLinearLinear or nonlinearmediumMeasuring the intensity and phase of the pulses into and out of a medium tells us as much as possible about the linear and nonlinear effects in the medium.Studying Media by Measuring the Intensity and Phase of Light PulsesWith a linear medium,we learn the mediums absorption coefficient and refractive index vs.With a nonlinear-optical medium,we can learn about self-phase modulation,for example,for which the theory is much more complex.Indeed,theoretical models can be tested.Time(fs)IntensityPhaseNonlinearEaton,et al.,JQE 35,451(1999).Time(fs)IntensityPhaseA laser pulse has the time-domain electric field:EI(t)1/2 exp i0t i(t)IntensityPhase(t)=Re Equivalently,vs.frequency:exp -ij j(0)Spectral Phase(neglecting thenegative-frequencycomponent)E()=Re S()1/2We must measure an ultrashort laser pulsesintensity and phase vs.time or frequency.SpectrumKnowledge of the intensity and phase or the spectrum and spectral phaseis sufficient to determine the pulse.t d dtThe instantaneous frequency:Example:“Linear chirp”Phase,(t)timetimeFrequency,(t)timeWed like to be able to measure,not only linearly chirped pulses,but also pulses with arbitrarily complex phases and frequencies vs.time.The phase determines the pulses frequency(i.e.,color)vs.time.The spectrometer measures the spectrum,of course.Wavelength variesacross the camera,and the spectrum can be measured for a single pulse.Pulse Measurement in the Frequency Domain:The SpectrometerCollimating Mirror“Czerny-Turner”arrangementEntrance SlitCamera orLinear Detector ArrayFocusingMirrorGrating“Imaging spectrometers”allow many spectra to be measured simultaneously.Broad-bandpulsePulse Measurement in the Time Domain:DetectorsExamples:Photo-diodes,Photo-multipliersDetectors are devices that emit electrons in response to photons.Detectors have very slow rise and fall times:1 nanosecond.As far as were concerned,detectors have infinitely slow responses.They measure the time integral of the pulse intensity from to+:The detector output voltage is proportional to the pulse energy.By themselves,detectors tell us little about a pulse.Another symbolfor a detector:DetectorDetectorPulse Measurement in the Time Domain:Varying the pulse delaySince detectors are essentially infinitely slow,how do we make time-domain measurements on or using ultrashort laser pulses?Well delay a pulse in time.And how will we do that?By simply moving a mirror!Since light travels 300 m per ps,300 m of mirror displacement yields a delay of 2 ps.This is very convenient.Moving a mirror backward by a distance L yields a delay of:Do not forget the factor of 2!Light must travel the extra distance to the mirrorand back!Translation stageInput pulse E(t)E(tt)MirrorOutput pulseWe can also vary the delay using a mirror pair or corner cube.Mirror pairs involve tworeflections and displace the return beam in space:But out-of-plane tilt yieldsa nonparallel return beam.Corner cubes involve three reflections and also displace the return beam in space.Even better,they always yield a parallel return beam:“Hollow corner cubes”avoid propagation through glass.Translation stageInputpulseE(t)E(tt)MirrorsOutput pulseEdmundScientificMeasuring the interferogram is equivalent to measuring the spectrum.Pulse Measurement in the Time Domain:The Michelson Interferometer Pulse energy (boring)Field autocorrelation(maybe interesting,but)The FT of the field autocorrelation is just the spectrum!Beam-splitterInputpulseDelaySlow detectorMirrorMirrorE(t)E(tt)Okay,so how do we measure a pulse?V.Wong&I.A.Walmsley,Opt.Lett.19,287-289(1994)I.A.Walmsley&V.Wong,J.Opt.Soc.Am B,13,2453-2463(1996)Result:Using only time-independent,linear filters,complete characterization of a pulse is NOT possible with a slow detector.Translation:If you dont have a detector or modulator that is fast compared to the pulse width,you CANNOT measure the pulse intensity and phase.with only linear measurements,such as a detector,interferometer,or a spectrometer.We need a shorter event,and we dont have one.But we do have the pulse itself,which is a start.And we can devise methods for the pulse to gate itself using optical nonlinearities.Pulse Measurement in the Time Domain:The Intensity AutocorrelatorCrossing beams in an SHG crystal,varying the delay between them,and measuring the second-harmonic(SH)pulse energy vs.delay yields the Intensity Autocorrelation:The Intensity Autocorrelation:DelayBeam-splitterInputpulseAperture eliminates input pulsesand also any SH created by the individual input beams.Slow detectorMirrorE(t)E(tt)MirrorsSHGcrystalLensSingle-Shot AutocorrelationWhile this effect introduces a range of delays on any given pulse andcould cause a broadening of the trace in multi-shot measurements,it allows us to measure a pulse on a single laser shot if we use a largebeam and a large beam angle to achieve the desired range of delays.Single-Shot Autocorrelationc2Single-Shot AutocorrelationInput pulse(expanded in space to 1 cm)Beam-splitterSHGcrystalCameraE(t)E(tt)Cylindrical lens focuses the beam in the vertical direction(for high intensity),while the delay varies horizontally.No mirrormoves!Crossing the beams at a large angle,focusing with a cylindrical lens,and detecting vs.transverse position yields the autocorrelation for a single pulse.Lens images crystal onto camera and hence delayonto position at cameraThe beam must have constant intensityvs.horizontal position to avoid biases.ApertureSingle-Shot Autocorrelation of Longer PulsesIf a longer pulse is to be measured,a larger range of delays is required.A longer range can be achieved using a dispersive element,such as a prism or grating,which tilts the pulse fronts.Angular dispersion is undesired,however.Fortunately,if we need to use this trick,its because the pulse is long.As a result,its bandwidth is usually small,so angular dispersion is less of a problem(for pulses 10 ps).Practical Issues in AutocorrelationGroup-velocity mismatch must be negligible,or the measurementwill be distorted.Equivalently,the phase-matching bandwidth mustbe sufficient.So very thin crystals(1 J).When a shorter reference pulse is available:The Intensity Cross-CorrelationThe Intensity Cross-correlation:DelayUnknown pulseSlow detectorE(t)Eg(tt)SFGcrystalLensReference pulseIf a shorter reference pulse is available(it need not be known),then it can be used to measure the unknown pulse.In this case,we perform sum-frequency generation,and measure the energy vs.delay.If the reference pulse is much shorter than the unknown pulse,then the intensity cross-correlation fully determines the unknown pulse intensity.Pulse Measurement in the Time Domain:The Interferometric AutocorrelatorWhat if we use a collinear beam geometry,and allow the autocorrelatorsignal light to interfere with the SHG from each individual beam?Developed by J-C DielsUsualAutocor-relationtermNewtermsAlso called the“Fringe-Resolved Autocorrelation”FilterSlow detectorSHGcrystalLensBeam-splitterInputpulseDelayMirrorMirrorE(t)E(tt)Michelson InterferometerDiels and Rudolph,Ultrashort Laser Pulse Phenomena,Academic Press,1996.Interferometric Autocorrelation MathThe measured intensity vs.delay is:Multiplying this out:whereThe Interferometric Autocorrelation is thesum of four different quantities.Constant(uninteresting)Sum-of-intensities-weighted w“interferogram”of E(t)w(oscillates at w in delay)Intensity autocorrelationInterferogram of the second harmonic;equivalent to the spectrum of the SH w(oscillates at 2w in delay)The interferometric autocorrelation simply combines several measuresof the pulse into one(admittedly complex)trace.Conveniently,however,they occur with different oscillation frequencies:0,w,and 2w.Interferometric Autocorrelation and StabilizationInterferometric Autocorrelation Traces for a Flat-phase Gaussian pulse:PulselengthFortunately,its not always necessary to resolve the fringes.With stabilizationWithout stabilizationTo resolve the w and 2w fringes,which are spaced by only l and l/2,we must actively stabilize the apparatus to cancel out vibrations,which perturb the delay by many l.C.Rulliere,Femtosecond Laser Pulses,Springer,1998.Interferometric Autocorrelation:ExamplesThe extent of the fringes(at w and 2w)indicates the approximate width ofthe interferogram,which is the coherence time.If its the same as the w width of the the low-frequency component,which is the intensity w autocorrelation,then the pulse is near-Fourier-transform limited.w Unchirped pulse(short)Coherencetime PulselengthChirped pulse(long)Coherencetime PulselengthThe interferometric autocorrelation nicely reveals the approximate pulselength and coherence time,and,in particular,their relative values.Solid black lines have been added.They trace the intensity autocorrelation component(for reference).C.Rulliere,Femtosecond Laser Pulses,Springer,1998.Does the interferometric autocorrelation yield the pulse intensity and phase?No.The claim has been made that the Interferometric Autocorrelation,combined with the pulse interferogram(i.e.,the spectrum),could do so Naganuma,IEEE J.Quant.Electron.25,1225-1233(1989).But the required iterative algorithm rarely converges.The fact is that the interferometric autocorrelation yields little more information than the autocorrelation and spectrum.We shouldnt expect it to yield the full pulse intensity and phase.Indeed,very different pulses have very similar interferometric autocorrelations.Pulses with Very Similar Interferometric AutocorrelationsPulse#1IntensityPhasetFWHM=24fsPulse#2IntensityPhasetFWHM=21fsWithout trying to find ambiguities,we can just try Pulses#1 and#2:Despite the very different pulses,these IA traces are nearly identical!Chung and Weiner,IEEE JSTQE,2001.Interferometric Autocorrelations for Pulses#1 and#2Difference:#1 and#2Pulses with Very Similar Interferometric AutocorrelationsChung and Weiner,IEEE JSTQE,2001.Its even harder to distinguish the traces when the pulses are shorter,and there are fewer fringes.Consider Pulses#1 and#2,but 1/5 as long:Interferometric Autocorrelations for Shorter Pulses#1 and#2#1 and#2Pulse#1IntensityPhasetFWHM=4.8fs-20 -10 0 10 20Pulse#2IntensityPhasetFWHM=4.2fs-20 -10 0 10 20In practice,it would be virtually impossible to distinguish these traces also.Difference:More Pulses with Similar Interferometric AutocorrelationsChung and Weiner,IEEE JSTQE,2001.Without trying to find ambiguities,we can try Pulses#3 and#4:IntensityPhasetFWHM=37fsPulse#3IntensityPhasetFWHM=28fsPulse#4Interferometric Autocorrelations for Pulses#3 and#4Difference:#3 and#4Despite very different pulse lengths,these pulses have nearly identical IAs.More Pulses with Similar Interferometric AutocorrelationsShortening Pulses#3 and#4 also yields very similar IA traces:Interferometric Autocorrelations for Shorter Pulses#3 and#4Chung and Weiner,IEEE JSTQE,2001.Difference:Shortenedpulse(1/5as long)#3 and#4It is inappropriate to derive a pulse length from the IA.IntensityPhasetFWHM=7.4fsPulse#3-40 -20 0 20 40IntensityPhasetFWHM=5.6fsPulse#4-40 -20 0 20 40Interferometric Autocorrelation:Practical Details and ConclusionsA good check on the interferometric autocorrelation is that it should be symmetrical,and the peak-to-background ratio should be 8.This device is difficult to align;there are five very sensitive degrees offreedom in aligning two collinear pulses.Dispersion in each arm must be the same,so it is necessary to insert a compensator plate in one arm.The typical ultrashort pulse is still many wavelengths long.So many fringes must typically be measured:data sets are large,and scans are slow.It is difficult to distinguish between different pulse shapes and,especially,different phases from interferometric autocorrelations.Like the intensity autocorrelation,it must be curve-fit to an assumedpulse shape and so should only be used for rough estimates.Questions:1.Please briefly introduce the characteristics of intensity autocorrelation(second-order),third-order autocorrelation,Interferometric Autocorrelations.