Presentation on theme: "Rick Trebino, Pablo Gabolde, Pam Bowlan, and Selcuk Akturk"— Presentation transcript:
1Rick Trebino, Pablo Gabolde, Pam Bowlan, and Selcuk Akturk Measuring everything you’ve always wanted to know about an ultrashort laser pulse (but were afraid to ask)Rick Trebino, Pablo Gabolde, Pam Bowlan, and Selcuk AkturkFor the past decade and a half, my group has been developing techniques for measuring ultrashort laser pulses. And like nearly everyone else who has such pulses, we’ve concentrated on their behavior in time. But a technique that we recently developed has also proved to be able to measure a couple of spatio-temporal distortions. And because such capability hasn’t generally been available, most pulses we’ve measured are contaminated with them. This has gotten us interested in these distortions and has taken us on a journey that has led to the development of not one, but two, different techniques for measuring the complete spatio-temporal field of an ultrashort laser pulse.Georgia TechSchool of PhysicsAtlanta, GA 30332This work is funded by the NSF, Swamp Optics, and the Georgia Research Alliance.
2We desire the ultrashort laser pulse’s intensity and phase vs We desire the ultrashort laser pulse’s intensity and phase vs. time or frequency.Light has the time-domain spatio-temporal electric field:IntensityPhase(neglecting thenegative-frequencycomponent)Equivalently, vs. frequency:SpectrumSpectralPhaseKnowledge of the intensity and phase or the spectrum and spectral phase is sufficient to determine the pulse.
3Frequency-Resolved Optical Gating (FROG) FROG is simply a spectrally resolved autocorrelation.This version uses SHG autocorrelation.Pulse to be measuredBeamsplitterE(t–t)CameraSHGcrystalSpec-trometerE(t)Esig(t,t)= E(t)E(t-t)Variable delay, tFROG uniquely determines the pulse intensity and phase vs. time for nearly all pulses. Its algorithm is fast (20 pps) and reliable.
4SHG FROG traces for various pulses FrequencyIntensityTimeDelaySelf-phase-modulated pulseCubic-spectral-phase pulseDouble pulseSHG FROG traces are symmetrical, so it has an ambiguity in the direction of time, but it’s easily removed.
5The FROG algorithm even works well for very complex pulses “Measured” traceRetrieved traceReduced background in retrieved trace is due to noise reduction by algorithm.Pulse vs. wavelengthPulse vs. timeTBP = 94.3Grad student: Lina Xu
6FROG easily measures very complex pulses SHG FROG trace with 1% additive noiseFROG easily measures very complex pulsesOccasionally, a few initial guesses are necessary, but we’ve never found a pulse FROG couldn’t retrieve.Red = correct pulse; Blue = retrieved pulse
7FROG Measurements of a 4.5-fs Pulse! Baltuska,Pshenichnikov,and Weirsma,J. Quant. Electron.,35, 459 (1999).FROG is now even used to measure attosecond pulses.
8GRating-Eliminated No-nonsense Observation of Ultrafast Incident Laser Light E-fields (GRENOUILLE) FROG2 key innovations: A single optic that replaces the entire delay line,and a thick SHG crystal that replaces both the thin crystal and spectrometer.GRENOUILLEP. O’Shea, M. Kimmel, X. Gu, and R. Trebino, Opt. Lett
9The Fresnel biprismCrossing beams at a large angle maps delay onto transverse position.Input pulsePulse #1Pulse #2t = t(x)Here, pulse #1 arrivesearlier than pulse #2Here, the pulsesarrive simultaneouslylater than pulse #2xFresnel biprismEven better, this design is amazingly compact and easy to use, and it never misaligns!
10Suppose white light with a large divergence angle impinges on an SHG crystal. The SH wavelength generated depends on the angle. And the angular width of the SH beam created varies inversely with the crystal thickness.The thick crystalVery thin crystal creates broad SH spectrum in all directions.Standard autocorrelators and FROGs use such crystals.Thin crystal creates narrower SH spectrum ina given direction and so can’t be usedfor autocorrelators or FROGs.ThinSHGcrystalVeryThinSHGcrystalThick crystal begins toseparate colors.ThickSHG crystalVery thick crystal acts likea spectrometer! Replace the crystal andspectrometer in FROG with a very thick crystal.Verythick crystal
11Testing GRENOUILLEGRENOUILLEFROGMeasuredRetrievedCompare a GRENOUILLE measurement of a pulse with a tried-and-true FROG measurement of the same pulse:Retrieved pulse in the time and frequency domains
12Testing GRENOUILLEGRENOUILLEFROGMeasuredRetrievedCompare a GRENOUILLE measurement of a complex pulse with a FROG measurement of the same pulse:Retrieved pulse in the time and frequency domains
13Spatio-temporal distortions Ordinarily, we assume that the electric-field separates into spatial and temporal factors (or their Fourier-domain equivalents):where the tilde and hat mean Fourier transforms with respect to t and x, y, z.
14Angular dispersion is an example of a spatio-temporal distortion. In the presence of angular dispersion, the mean off-axis k-vector component kx0 depends on frequency, w.PrismInput pulseAngularly dispersed output pulsexz
15Another spatio-temporal distortion is spatial chirp (spatial dispersion). Prism pairs and simple tilted windows cause spatial chirp.The mean beam position, x0, depends on frequency, w.Prism pairInput pulseSpatially chirped output pulseSpatially chirped output pulseInput pulseTilted window
16And yet another spatio-temporal distortion is pulse-front tilt. Gratings and prisms cause both spatial chirp and pulse-front tilt.The mean pulse time, t0, depends on position, x.GratingAngularly dispersed pulse with spatial chirp and pulse-front tiltInput pulsePrismAngularly dispersed pulse with spatial chirp and pulse-front tiltInput pulse
17Angular dispersion always causes pulse-front tilt! where g = dkx0 /dwInverse Fourier-transforming with respect to kx, ky, and kz yields:using the shift theoremInverse Fourier-transforming with respect to w-w0 yields:using the inverse shift theoremwhich is just pulse-front tilt!
18Spatially chirped input pulse The combination of spatial and temporal chirp also causes pulse-front tilt.Spatially chirped pulse with pulse-front tilt, but no angular dispersionDispersive mediumSpatially chirped input pulsevg(red) > vg(blue)The theorem we just proved assumed no spatial chirp, however. So it neglects another contribution to the pulse-front tilt.The total pulse-front tilt is the sum of that due to dispersion and that due to this effect.Xun Gu, Selcuk Akturk, and Erik Zeek
19General theory of spatio-temporal distortions To understand the lowest-order spatio-temporal distortions, assume a complex Gaussian with a cross term, and Fourier- transform to the various domains, recalling that complex Gaussians transform to complex Gaussians:Grad students: Xun Gu and Selcuk AkturkPulse-front tiltSpatial chirpdropping the x subscript on the kAngular dispersionTime vs. angle
20The imaginary parts of the pulse distortions: spatio-temporal phase distortions The imaginary part of Qxt yields: wave-front rotation.zxWave-propagation directionThe electric field vs. x and z.Red = + Black = -
21The imaginary parts of the pulse distortions: spatio-temporal phase distortions The imaginary part of Rxw is wave-front-tilt dispersion.zxw1Plots of the electric field vs. x and z for different colors.w2w3There are eight lowest-order spatio-temporal distortions, but only two independent ones.
22Coarse GDD tuning (change distance between prisms) The prism pulse compressor is notorious for introducing spatio-temporal distortions.Wavelength tuningWavelength tuningPrismPrismPrismPrismFine GDD tuningWavelength tuningWavelength tuningCoarse GDD tuning (change distance between prisms)Even slight misalignment causes all eight spatio-temporal distortions!
23The two-prism pulse compressor is better, but still a big problem. Coarse GDD tuningWavelength tuningRoof mirrorPeriscopePrismPrismFine GDD tuningWavelength tuning
24GRENOUILLE measures spatial chirp. Fresnel biprismSignal pulse frequencySHGcrystalSpatially chirped pulse-t0+t0DelayFrequency2w+dw2wdw+t0-t0Tilt in the otherwise symmetrical SHG FROG trace indicates spatial chirp!
26GRENOUILLE measures pulse-front tilt. Fresnel biprismTilted pulse frontZero relative delay is off to side of the crystalSHGcrystalZero relative delay is in the crystal centerUntilted pulse frontAn off-center trace indicates the pulse front tilt!DelayFrequency
27GRENOUILLE accurately measures pulse-front tilt. Varying the incidence angle of the 4th prism in a pulse-compressor allows us to generate variable pulse-front tilt.Negative PFTZero PFTPositive PFT
28Focusing an ultrashort pulse can cause complex spatio-temporal distortions. In the presence of just some chromatic aberration, simulations predict that a tightly focused ultrashort pulse looks like this:Intensity vs. x & z (at various times)FocusWe’re now very good at measuring spatially smooth ultrashort pulses at the outputs of lasers. But nearly everyone focuses his ultrashort pulses, and it’s at the focus that we need to know its properties. Unfortunately, complex spatio-temporal distortions occur to focused ultrashort pulses.xzPropagation directionUlrike FuchsIncrement between images: 20 fs (6 mm).Measuring only I(t) at a focus is meaningless. We need I(x,y,z,t)!
29Also, researchers now often use shaped pulses as long as ~20 ps with complex intensities and phases. TimeSo we’ll need to be able measure, not only the intensity, but also the phase, that is, E(x,y,z,t), for even complex focused pulses.And we’ll also need great spectral resolution for such long pulses.And the device(s) should be simple and easy to use!
30We desire the ultrashort laser pulse’s intensity and phase vs We desire the ultrashort laser pulse’s intensity and phase vs. space and time or frequency.Light has the time-domain spatio-temporal electric field:IntensityPhase(neglecting thenegative-frequencycomponent)Equivalently, vs. frequency:SpectrumSpectralPhaseKnowledge of the intensity and phase or the spectrum and spectral phase is sufficient to determine the pulse.
31Strategy Measure a spatially uniform (unfocused) pulse in time first. GRENOUILLEThen use it to help measure the more difficult one with a separate measurement device.STRIPED FISHSEA TADPOLE
32Spectral Interferometry Measure the spectrum of the sum of a known and unknown pulse.Retrieve the unknown pulse E(w) from the cross term.~1/TTEunkErefErefFrequencyEunkSpectrometerCameraBeam splitterWith a known reference pulse, this technique is known as TADPOLE (Temporal Analysis by Dispersing a Pair Of Light E-fields).
33Retrieving the pulse in TADPOLE The “DC” termcontains onlyspectraThe “AC” termscontain phase informationInterference fringesin the spectrumFFTw0Frequency“Time”Filterout thesetwo peaksSpectrumFilter&ShiftThe spectral phase difference is the phase of the result.IFFTKeep this one.w0Frequency“Time”This retrieval algorithm is quick, direct, and reliable.It uniquely yields the pulse.Fittinghoff, et al., Opt. Lett. 21, 884 (1996).
34SI is very sensitive! 1 microjoule = 10-6 J 1 nanojoule = 10-9 J 1 picojoule = J1 femtojoule = J1 attojoule = JFROG’s sensitivity:TADPOLE ‘s sensitivity:1 zeptojoule = JTADPOLE has measured a pulse train with only 42 zeptojoules (42 x J) per pulse.
35Spectral Interferometry does not have the problems that plague SPIDER. Recently* it was shown that a variation on SI, called SPIDER, cannot accurately measure the chirp (or the pulse length).SPIDER’s cross-term cosine:Linear chirp (djunk/dw w) and wT are both linear in w and so look the same. Worse, wT dominates, so T must be calibrated—and maintained—to six digits!Desired quantity> 10wp< tp~ wp /100~ 100tpwp = pulse bandwidth; tp = pulse lengthThis is very different from standard SI’s cross-term cosine:The linear term of junk is just the delay, T, anyway!*J.R. Birge, R. Ell, and F.X. Kärtner, Opt. Lett., (13): p
36Examples of ideal SPIDER traces Even if the separation, T, were known precisely, SPIDER cannot measure pulses accurately.These two pulses are very different but have very similar SPIDER traces.Intensity (%)
37More ideal SPIDER traces Unless the pulses are vastly different, their SPIDER traces are about the same.Practical issues, like noise, make the traces even more indisting-uishable.Intensity (%)
38Spectral Interferometry: Experimental Issues The interferometer is difficult to work with.Mode-matching is important—or the fringes wash out.Phase stability is crucial—or the fringes wash out.UnknownSpectrometerBeams must be perfectly collinear—or the fringes wash out.To resolve the spectral fringes, SI requires at least five times the spectrometer resolution.
39SEA TADPOLE x Spatially Encoded Arrangement (SEA) CameraxCylindrical lensSpatially Encoded Arrangement (SEA)SEA TADPOLE uses spatial, instead of spectral, fringes.lReference pulseFibersGratingUnknown pulseGrad student: Pam BowlanSpherical lensSEA TADPOLE has all the advantages of TADPOLE—and none of the problems. And it has some unexpected nice surprises!
40Why is SEA TADPOLE a better design? Fibers maintain alignment.Our retrieval algorithm is single shot, so phase stability isn’t essential.Single mode fibers assure mode-matching.Collinearity is not only unnecessary; it’s not allowed.And the crossing angle is irrelevant; it’s okay if it varies.And any and all distortions due to the fibers cancel out!
41We retrieve the pulse using spatial fringes, not spectral fringes, with near-zero delay. The beams cross, so the relative delay, T, varies with position, x.1D Fourier Transform from x to kThe delay is ~ zero, so this uses the full available spectral resolution!
44SEA TADPOLE measurements SEA TADPOLE has enough spectral resolution to measure a 14-ps double pulse.
45An even more complex pulse… An etalon inside a Michelson interferometer yields a double train of pulses, and SEA TADPOLE can measure it, too.
46SEA TADPOLE achieves spectral super-resolution! Blocking the reference beam yields an independent measurement of the spectrum using the same spectrometer.For comparison we obtained independent spectra of the unknown pulse using the same device by blocking the reference arm beam. The fast features in the unknown spectrum that we retrieved from the SEA TADPOLE trace are not washed out as they are in the independent spectrum.The improvement in spectral resolution will not be this great for all pulses. Because double Pulses have zero crossings in their fields, which is what is being resolved here, the contrast or depth of the features in the spectrum is not harmed by the smearing due to the spectral response function. Because the field will always be a wider (or fatter) function than the spectrum, there is still a smaller improvement in resolution when there are no zero crossings in the field.The SEA TADPOLE cross term is essentially the unknown-pulse complex electric field. This goes negative and so may not broaden under convolution with the spectrometer point-spread function.
47SEA TADPOLE spectral super-resolution When the unknown pulse is much more complicated than the reference pulse, the interference term becomes:Sine waves are eigenfunctions of the convolution operator.
48Scanning SEA TADPOLE: E(x,y,z,t) By scanning the input end of the unknown-pulse fiber, we can measure E(w) at different positions yielding E(x,y,z,ω).So we can measure focusing pulses!
49E(x,y,z,t) for a theoretically perfectly focused pulse. E(x,z,t)SimulationIn all of our experiments and simulations, the beams had spot sizes of 3 mm and bandwidths of 25 nm and lenses with diameters of 24.5 mm.Pulse FrontsColor is the instantaneous frequency vs. x and t.Uniform color indicates a lack of phase distortions.
50Measuring E(x,y,z,t) for a focused pulse. Aspheric PMMA lens with chromatic (but no spherical) aberration and GDD.f = 50 mm NA = 0.03Measurement810 nmSimulation790 nm
51Spherical and chromatic aberration Singlet BK-7 plano-convex lens with spherical and chromatic aberration and GDD.f = 50 mm NA = 0.03MeasurementSimulation810 nm790 nm
52A ZnSe lens with chromatic aberration Singlet ZnSe lens with massive chromatic aberration (GDD was canceled).Measurement804 nmSimulation796 nm
53SEA TADPOLE measurements of a pulse focusing 796 nm804 nmA ZnSe lens with lots of chromatic aberration.Lens GDD was canceled out in this measurement, to better show the effect of chromatic aberration.
54Distortions are more pronounced for a tighter focus. ExperimentSinglet BK-7 plano-convex lens with a shorter focal length.f = 25 mm NA = 0.06814 nmSimulation787 nm
55SEA TADPOLE measurements of a pulse focusing 787 nm814 nmA BK-7 lens with some chromatic and spherical aberration and GDD.f = 25 mm.
56Focusing a pulse with spatial chirp and pulse- front tilt. ExperimentAspheric PMMA lens.f = 50 mm NA = 0.03812 nmI used the -1 order of a reflective grating (400g/mm) to create the angular dispersion, so I think that the results make sense but please let me know if you do not agree. The focusing lens was the ashpere that we used in the Optics Express paper( NA = 0.03 in this case).Simulation790 nm
57Array of spectrally-resolved holograms Single-shot measurement of E(x,y,z,t). Multiple holograms on a single camera frame: STRIPED FISHArray of spectrally-resolved hologramsSpatially andTemporallyResolvedIntensity andPhaseEvaluationDevice:FullInformation from aSingleHologramGrad student: Pablo Gabolde
58Holography Spatially uniform, monochromatic reference beam CameraSpatially uniform, monochromatic reference beamUnknown beamObjectMeasure the integrated intensity I(x,y) of the sum of known and unknown monochromatic beams.Extract the unknown monochromatic field E(x,y) from the cross term.
59Frequency-Synthesis Holography for complete spatio-temporal pulse measurement Performing holography with a monochromatic beam yields the full spatial intensity and phase at the beam’s frequency (w0):Performing holography using a well-characterized ultrashort pulse and measuring a series of holograms, one for each frequency component, yields the full pulse in the space-frequency domain.E(x,y,t) then acts as the initial condition in Maxwell’s equations, yielding the full spatio-temporal pulse field: E(x,y,z,t). This approach is called “Fourier-Synthesis Holography.”
61The 2D diffraction grating creates many replicas of the input beams. Glass substrateChrome patternUnknownReference50 μmUsing the 2D grating in reflection at Brewster’s angle removes the strong zero-order reflected spot.
62The band-pass filter spectrally resolves the digital holograms
63STRIPED FISH Retrieval algorithm Complex imageIntensityand phasevs. (x,y,λ)
65Measurements of the spectral phase Group delayGroup-delay dispersion
66Reconstruction procedure Takeda et al, JOSA B 72, (1982).IFFTFFT2-D Fourier transform of H(x,y)Intensity of the entire pulse (spatial reference)2-D digital hologram H(x,y)Reconstructed intensity I(x,y) at λ = 830 nmCCD cameraReconstructed phase φ(x,y) at λ = 830 nmλ = 782 nmλ = 806 nmλ = 830 nmSpatially-chirped input pulse
67Results for a pulse with spatial chirp Contours indicate beam profileReconstructed intensity for a few wavelengthsxyλ = 782 nm λ = 806 nm λ = 830 nmReconstructed phase at the same wavelengthsλ = 782 nm λ = 806 nm λ = 830 nm(wrapped phase plots)
68The spatial fringes depend on the spectral phase! Zero delayWith GD(b)(a)
69A pulse with temporal chirp, spatial chirp, and pulse-front tilt. Suppressing the y-dependence, we can plot such a pulse:x [mm]t [fs]803 nm777 nmy = 4.5 mrad797 nm775 nmy = 11.3 mradwhere the pulse-front tilt angle is:Pablo Gabolde made this nice picture.
70Complete electric field reconstruction Pulse with horizontal spatial chirp
71Complete 3D profile of a pulse with temporal chirp, spatial chirp, and pulse-front tilt 797 nm775 nmDotted white lines: contour plot of the intensity at a given time.
72The Space-Time-Bandwidth Product How complex a pulse can STRIPED FISH measure?xytAfter numerical reconstruction, we obtain data “cubes” E(x,y,t) that are~ [200 by 100 pixels] by 50 holograms.Space-BandwidthProduct (SBP)Time-BandwidthProduct (TBP)Space-Time-BandwidthProduct (STBP)=STRIPED FISH can measure pulses with STBP ~ 106 ~ the number of camera pixels.SEA TADPOLE can do even better (depends on the details)!
73Single-prism pulse compressor is spatio-temporal-distortion-free! Corner cubePrismWavelength tuningGDD tuningRoof mirrorPeriscope
75The total dispersion is always zero. The dispersion depends on the direction through the prism.
76A zoo of techniques!GRENOUILLE easily measures E(t) (and spatial chirp and pulse-front tilt).SEA TADPOLE measures E(x,y,z,t) of focused and complex pulses (multi-shot).STRIPED FISH measures E(x,y,z,t) of a complex (unfo-cused) pulse on a single shot.
77To learn more, visit our web sites… You can have a copy of this talk if you like. Just let me know!And if you read only one ultrashort-pulse-measurement book this year, make it this one!