VOLUME 80, NUMBER 6 P H Y S I C A L R E V I E W L E T T E R S 9 FEBRUARY 1998

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Measurement of the Spatiotemporal Evolution of High-Order Harmonic RadiationUsing Chirped Laser Pulse Spectroscopy

J. W. G. Tisch,1 D. D. Meyerhofer,2 T. Ditmire,1,* N. Hay,1 M. B. Mason,1 and M. H. R. Hutchinson11Blackett Laboratory, Imperial College of Science Technology and Medicine, London SW7 2BZ, United King

2Laboratory for Laser Energetics, University of Rochester, 250 East River Road, Rochester, New York 14623(Received 20 June 1997)

We report the first spatially resolved measurements of the time dependence of high-order harmonicradiation. We have measured the time evolution of the harmonic distribution at the exit of the gas jetfor the 13th harmonicsl ­ 60 nmd generated in a low-density xenon jet by a 780 nm, 1 ps chirpedlaser pulse in the1013 1014 W cm22 range. We show that the harmonic source can become annularwith a radius that increases in time during the laser pulse owing primarily to ionization depletion ofthe neutral medium. Under certain focusing conditions, we demonstrate that this can lead to significantharmonic pulse shortening. [S0031-9007(97)05277-0]

PACS numbers: 42.65.Ky, 06.60.Jn, 32.80.Rm, 42.65.Re

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High-order harmonic generation (HHG) [1] providesunique source of high brightness, coherent radiationthe extreme ultraviolet (XUV) region of the spectrumand is thus of considerable interest from an applicatioviewpoint. The properties of the harmonic radiation aalso an important probe of both the high-intensity laseatom interaction and the physics of the phase-matchprocess.

The time dependence of high harmonic radiatiois perhaps the least well characterized aspect ofprocess, largely due to the difficulties in making timeresolved measurements at high harmonic wavelengs,5 100 nmd. Streak cameras have been used to timresolve relatively low-order harmonics that were geerated with laser pulses of 50–150 ps duration [2,3but they have insufficient resolution to time resolvharmonics pulses much shorter than 1 ps. Only a feexperiments have been conducted to time resolve hharmonics with femtosecond resolution, all of thembased on pump-probe type schemes [4–6]. In thoexperiments, the harmonic radiation was refocused inthe pump-probe interaction region, so the pulse duratimeasurements were spatially integrated. In this Letwe report the first spatially resolved measurements of tsubpicosecond time evolution of high harmonic radiatio

In our experiment, the harmonic radiation is time resolved using a novel technique which we call chirpepulse spectroscopy. Using a chirped laser pulse,record the spectrum of the harmonics using a convetional time-integrating XUV detector. The time resolution comes from the linear frequency chirp on the laspulse, which means that the instantaneous laser frequeis a linear function of time,v1std ­ v0 1 bt, whereb

is the chirp parameter. Under conditions where additiontime-dependent frequency shifts of the harmonic radiati(e.g., due to ionization [7] or the theoretically predicteintensity-dependent atomic dipole phase [8]) are smcompared to the harmonic bandwidth, the instantaneo

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harmonic frequency is simplyqv1std, whereq is the har-monic order. Hence, the harmonic is also linearly chirpallowing a linear transformation of the frequency or wavlength axis of the harmonic spectrum into time.

A linearly chirped laser pulse can be produced readin a chirped pulse amplification (CPA) laser systeby changing the separation of the compressor gratirelative to the optimum-compression position [9]. If thcompressed pulse duration ist1 (assumed to be atransform-limited Gaussian pulse with a bandwidthDv1)and the chirped pulse duration istc ¿ t1, the chirp pa-rameter is given byb ø 2ystct1d ­ Dv1ytc. The tem-poral dispersion at the harmonic wavelength is thus givby dtydljl1yq ­ qtcyDl1 (to first order inbtyv0), andthe temporal resolution istres ­ qtcDlspecyDl1, whereDl1 ­ 2pcDv1yv

20 is the laser bandwidth andDlspec

is the spectral resolution. Note that this estimate of ttemporal resolution is valid providedtres is greater thanthe transform limit associated with the spectral resolutioas is the case in this experiment.

We used a 160 fs Ti:sapphire CPA laser capableproducing pulses with energy up to 60 mJ at a 10repetition rate [10]. The FWHM bandwidth of the pulsewas Dl1 ­ 65 Å centered at a wavelength ofl1 ­780 nm. To obtain a positivesb . 0d or negativesb ,

0d chirped pulse we, respectively, decreased or increathe separation of the compressor gratings while ensurthat the beam alignment and pulse spectrum remaiunchanged. The chirped pulse FWHM duration wasto tc ø 1 ps sb ø 61.25 3 1025 s22d by changing thecompressor grating separation while monitoring the puduration using a single-shot autocorrelator.

The linearly polarized laser pulse was focusedan fy17 lens into a pulsed gas jet. Beam profilinindicated a confocal parameterb ø 2 mm and focal spotdiameter2w0 ø 50 mm. The harmonics were detectewith a microchannel plate detector producing a twdimensional single-shot image with wavelength dispers

© 1998 The American Physical Society

VOLUME 80, NUMBER 6 P H Y S I C A L R E V I E W L E T T E R S 9 FEBRUARY 1998

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in one direction and spatial resolution in the orthogondirection. We observed the 13th harmonic spectrumthe second diffraction order of a 2400 linesymm gratingsDlspec ø 0.5 Åd, giving tres ø 100 fs.

To minimize the effects of ionization blueshifting[7], the Xe density in the gas jet was,5 3 1016 cm23.The amount of ionization induced blueshifting waestimated by generating the 13th harmonic with th160 fs compressed pulse for intensities in the ran1013 1014 W cm22. A maximum shift of ,0.1 Å wasobserved. For the chirped pulse, a shift of this sizwould produce a temporal shift of,10 fs. The blueshiftwill actually be lower for the chirped pulse due to itslonger duration, and hence its effects here are negligibThe intensity-dependent atomic dipole phase can aeffect the linearity of the harmonic chirp. A worst-casestimate based on the theoretical results of Lewenstet al. [8] indicates that for the 1 ps laser pulse, thresulting nonlinear harmonic chirp does not significantaffect the linearity of this technique.

Figure 1 shows two spatially and temporally resolveimages of the 13th harmonic emission for negative (lehalf of figure) and positive (right half) laser chirp. Thejet was positioned 5 mm before the laser best focand 20 cms¿bd from the entrance slit of a 1-m imag-ing spectrometer. The peak intensity in the Xe jet wa1.3 3 1014 W cm22 for both cases, an intensity at whichsignificant ionization occurs. The vertical axis is the hamonic divergence, while the horizontal axis is the pulswavelength or time. The temporal peak of the laser pul(vertical dotted line) is taken to be the center of thspectrum of the 13th harmonic generated with the 160compressed pulse under conditions where ionizationduced blueshifting was completely negligible (any spetral broadening due to the predicted intensity-dependedipole phase should be symmetric about the spectrum cter for the case where ionization is negligible). The cre

FIG. 1. Spatiotemporal images of the 13th harmonic sourdistribution for negative and positive chirped laser pulses atpeak intensity of1.3 3 1014 W cm22. The dotted vertical linecorresponds to the temporal peak of the laser pulsest ­ 0d,while the dotted horizontal line is the laser axissr ­ 0d.

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cent shapes reveal that at early time (largest wavelenshift from the center) the harmonic emission is initiallpeaked on axis and then becomes annular with a radwhich increases with time during the rising edge of thlaser pulse. This picture is confirmed by the fact ththe crescent reverses direction when the sign of the ch(and hence the time arrow) is reversed. The observspatiotemporal distribution is the same as the harmonear-field (or source) distribution that has been predicfrom modeling of harmonic emission in the presenceionization [11,12]. The observation of the predicted neafield distribution in the far field suggests that the harmonemission at the exit of the gas jet is already in its far fiel

This picture of the harmonic emission is confirmeby an investigation of the spatiotemporal harmonic dtribution as a function of laser intensity. Figures 2(a)2(d) show time- and space-resolved images of the 1harmonic source for four different peak intensities, 5.7.3, 9.6, and13 3 1013 W cm22. The images in the toprow are the experimental data (forb . 0), each one av-eraged over,100 laser shots, while those in the bottom row are simulations of the harmonic emission at texit of the gas target at the same peak intensity. Tsimulated spectra were calculated from a simple moof the harmonic generation that includes ionizationthe nonlinear medium. In the plane-wave limit, witb ¿ L, where L (ø1 mm for the gas jet) is the inter-action length, the harmonic intensity can be writtenIq ~ N2

0 Ip1 fsinsDkLy2dysDkLy2dg2, where we have used

an effective power law formulation for the harmonic polarization, as described in Ref. [1]. Here,N0sr , td is theneutral density which can become depleted in a spaand time-dependent manner owing to ionization,I1sr , tdis the laser intensity (we assume a Gaussian laser pin space and time),p (­9 [13]) is the effective orderof the process,Dksr , td ­ spqyl1d fnesr, tdyncritg is thephase mismatch due to dispersion from free electrons cated by ionization,ne is the electron density, andncrit ­1.8 3 1021 cm23 is the critical density atl1 ­ 780 nm.Ionization is treated using tunneling ionization ratesAmmosovet al. for Xe [14].

The evolution of the images with increasing intensity is accurately reproduced in the simulations. Thmodel indicates that ionization depletion of the neutrmedium is primarily responsible for the termination othe harmonic generation and the resulting crescent fmation [for the low density jet we used, the electrophase mismatch is relatively small; e.g., the electron desity arising from 50% ionization of the neutral mediumleads to a reduction in the harmonic intensity by ona factor fsinsDkLy2dysDkLy2dg2 ø 0.95]. For the low-est intensity in Fig. 2, ionization levels are quite low(,10% depletion of the neutrals on axis at the peakthe laser pulse) so the harmonic distribution in spaand time is essentially the laser distribution raisedthe pth power. For the higher intensities, significandepletion occurs during the laser pulse which modifi

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VOLUME 80, NUMBER 6 P H Y S I C A L R E V I E W L E T T E R S 9 FEBRUARY 1998

tionsty the

FIG. 2. Intensity evolution of the 13th harmonic source distribution. The experimental data are shown in the top row, simulain the bottom row. The model does not include propagation of the harmonic from the gas jet to the detector, so for claridivergence in the simulations has been matched to the experimental data.

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the harmonic distribution. The depleted region in the jexpands radially in time, confining the harmonic emissioto an annulus limited on the outside by the nonlineintensity dependence of the harmonic polarization. Thcrescent shape observed in the spatiotemporal imagethus the time dependence of a slice through this annuemitting region, as selected by the entrance slit of thspectrometer.

By radially integrating the harmonic signal in our 2Dimages at each time step we obtain the time dependeof the total harmonic yield. Figure 3 shows the resulfor images 3(a)–3(d) in the top row of Fig. 2. Asthe intensity increases, the peak of the harmonic pumoves earlier in time relative to the laser pulse aionization occurs progressively earlier during the risin

FIG. 3. Radially integrated 13th harmonic pulses for a rangof laser intensities [calculated from the experimentally mesured images Figs. 2(a)–2(d)].

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edge of the laser pulse. The slower falling edgesthe harmonic pulses are due to harmonic generatcontinuing in the wings of the focal distribution aftethe center becomes depleted. At the lowest intensityFig. 2, where ionization effects are small, the harmonFWHM pulse duration istq ­ 250 fs 6 25%. This isconsistent with the expectedtcyp

p pulse width in thelow intensity regime. The harmonic pulse durations weapproximately the same forb , 0. The data in Fig. 2also show that the harmonic pulse duration decreawith increasing intensity owing to ionization terminatinthe emission. The observed pulse shortening (ab10% for the highest intensity) is limited by the spatiaintegration that is normally inherent in harmonic pulswidth measurements.

Without this spatial integration, the pulse shorteninarising from ionization can be much more significant,is demonstrated in Fig. 4. Here horizontal line-outs froFig. 2(d) (top row) at three different radial positions havbeen taken to obtain the time dependence of the harmoemission at those positions. The pulse duration of temission on axis is,120 fs, about a factor of 2 shorterthan the spatially integrated duration for this shot, aapproximately 8 times shorter than the laser pulse.

An aspect of the data in Fig. 3 that is still not fullyunderstood is the large temporal offset between the pof the positively chirped laser pulse and the peak of tharmonic pulses,200 fsd at the lowest intensitys5.3 3

1013 W cm22d. This shift was not observed forb , 0 atthe same intensity. A similar difference between positiand negative chirp was observed by Zhouet al. [15].They suggested that the negative chirp might partiastabilize the atom against ionization (compared to tpositive chirp case), thus permitting the atom to survi

VOLUME 80, NUMBER 6 P H Y S I C A L R E V I E W L E T T E R S 9 FEBRUARY 1998

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FIG. 4. Measured angular dependence of the 13th harmopulse duration [corresponding to Fig. 2(d)] at a peak intensiof 1.3 3 1014 W cm22. The curves have been offset verticallyfor clarity.

to the peak of the pulse, whereas for the positive chirionization occurs on the rising edge. This explanatiodoes not appear to be applicable in our case, since this no evidence for ionization terminating the emissioin the low intensity positive chirp case, as this woulmanifest itself through the formation of a crescent ithe 2D image, which is not observed in Fig. 2(a). Ware currently investigating other explanations, suchresonances effects, or residual atomic dipole phase effe

We have examined the effect of changing the positioof the gas jet relative to the laser focus. When thjet was moved to the other side of the focus (i.e., j,2b after focus), we found that, although the radiallintegrated harmonic pulse durations for a given intensiwere similar to the jet-before-focus case, we could nlonger resolve the annular structure of the harmonsource profile. Since ionization depletion effects shoube unchanged by a symmetric shift of the jet about thbest focus position, this observation means that whthe jet was positioned after the focus, the harmonsource distribution was not preserved in propagatingthe detector, suggesting that the harmonic radiation win its quasinear field as it left the jet. This asymmetryconsistent with the atomic dipole phase being a decreasfunction of intensity, as theoretically predicted [8]. Theradial variation of the laser intensity means that this dipophase would tend to flatten the harmonic phase front whthe jet was after the focus, while increasing the phasfront curvature when the jet was positioned before thfocus. We plan to discuss this further in a forthcominarticle.

In conclusion, we have time-resolved harmonic radition with a resolution of,100 fs using linearly chirped

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laser pulses. By positioning the gas jet significantly before the laser focus, we found that we could measure tharmonic distribution at the exit of the nonlinear mediumand thus record, for the first time, the time evolution othe harmonic source distribution. Our results show thathe source can become annular with a radius that icreases in time during the laser pulse due to ionizatiodepletion of the neutral medium. We have also demonstrated that the harmonic pulse duration at a particulangle in the far field can be substantially shorter than thspatially integrated pulse duration. Obviously, harmonipulse shortening in this way can be applied to shorter laspulses. Our modeling indicates that for a 20 fs pulse,3 3 1014 W cm22 in Xe the 13th harmonic pulse dura-tion on axis would be,3 fs. The fact that the harmonicdistribution at the exit of the jet can be preserved in propagating to the detector if the jet is positioned significantlybefore the focus implies that a small aperture on axis somdistance from the laser focus would select this ultrashoharmonic pulse.

We acknowledge financial support of the U.K. EPSRCD. D. M. acknowledges travel support from NATO Con-tract No. CRG 930274 and additional support from thU.S. NSF.

*Present address: L-440 7000 East Avenue, LawrencLivermore National Laboratory, Livermore, CA 94550.

[1] A. L’Huillier et al., in Atoms in Intense Laser Fields,edited by M. Gavrila (Academic Press, Boston, 1992)pp. 139–202.

[2] M. E. Faldon et al., J. Opt. Soc. Am. B 9, 2094(1992).

[3] T. Starczewskiet al., J. Phys. B27, 3291 (1994).[4] Y. Kobayashiet al., Opt. Lett.21, 417 (1996).[5] T. E. Gloveret al., Phys. Rev. Lett.76, 2468 (1996).[6] A. Bouhal et al., J. Opt. Soc. Am. B14, 950 (1997).[7] W. M. Wood et al., Phys. Rev. Lett.67, 3523 (1991).[8] See, e.g., M. Lewensteinet al., Phys. Rev. A52, 4747

(1995), and references therein.[9] E. B. Treacy, IEEE J. Quantum Electron.QE5, 454

(1969).[10] D. J. Fraser and M. H. R. Hutchinson, J. Mod. Opt.43,

1055 (1996).[11] J. E. Muffettet al., J. Phys. B27, 5693 (1994).[12] T. Ditmire et al., J. Opt. Soc. Am. B13, 406 (1996).[13] The effective order has not been measured for 1 p

780 nm pulses in Xe.p ­ 9 gives the best agreementwith the experimental data, but the results of the modeare fairly insensitive to the exact value ofp in the range,5 10.

[14] M. V. Ammosov et al., Sov. Phys. JETP64, 1191(1986).

[15] J. Zhouet al., Phys. Rev. Lett.76, 752 (1996).

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