Few-femtosecond timing at fourth-generationX-ray light sourcesF. Tavella1,2*, N. Stojanovic1*, G. Geloni3 and M. Gensch4†*

Fourth-generation X-ray light sources are being developed todeliver laser-like X-ray pulses at intensities and/or repetitionrates that are beyond the reach of table-top devices. An impor-tant class of experiments at these new facilities comprisespump–probe experiments, which are designed to investigatechemical reactions and processes occurring on the molecularor even atomic level, and on the timescale of a few femto-seconds. Good progress has been made towards the generationof ultrashort X-ray pulses (for example, at FLASH1 or LCLS2),but experiments suffer from the intrinsic timing jitterbetween the X-ray pulses and external laser sources3. In thisLetter, we present a new approach that provides few-femto-second temporal resolution. Our method uses coherentterahertz radiation generated at the end of the X-ray undulatorby the same electron bunch that emits the X-ray pulse. It cantherefore be applied at any advanced light source workingwith ultrashort electron bunches and undulators.

Timing jitter at accelerator-based sources is primarily due tounavoidable energy fluctuations between the individual electronbunches, which leads to path-length differences in energy-dispersiveelements such as bunch compressors or dipole magnets in the accel-erator. As a result, the arrival time of the electron bunches at theX-ray undulator varies from shot to shot, leading to a timing jitterbetween the X-ray pulse and the radio frequency (RF) master oscil-lator4. For an optimized free-electron laser (FEL), the theoreticallower limit for this intrinsic timing jitter is believed to be severaltens of femtoseconds, so, even for an external laser perfectly syn-chronized to the RF master oscillator, the synchronizationbetween pump and probe pulse will still be an order of magnitudeworse than the pulse duration. The only possibility for overcomingthis severe problem is to accurately monitor the intrinsic jitterbetween the X-rays and the external sources and then later sortthe experimental data.

Here, we present a timing scheme for monitoring the arrival timejitter with a temporal resolution of only a few femtoseconds. In con-trast to earlier attempts, which aimed to monitor the arrival time ofthe electron bunches5,6 or used X-ray/optical cross-correlation tech-niques7,8, we make use of a cross-correlation between coherentterahertz radiation, generated parasitically at the same insertiondevice that emits the X-ray pulse, and the external laser system.Our technique has no effect on the X-ray pulse, it is independentof the X-ray photon energy, and can be used at any FEL or otherfourth-generation light source, including energy recovery linacs(ERLs)9,10. Of particular importance is the fact that, by using coher-ent radiation for the cross-correlation, the technique is largelyinsensitive to shot-to-shot variation in the longitudinal electronbunch profile, thereby circumventing the related fundamentallimits for electron bunch arrival-time monitors11. We take

advantage of the recent experimental finding that terahertz andX-ray pulses generated by the same electron bunch and transportedover several tens of metres into the experimental hall are intrinsi-cally synchronized to one another on the scale of a few femto-seconds12,13. As we show, phase-sensitive, single-shot cross-correlation between such terahertz pulses and near-infrared pumplaser pulses can therefore be used to clock an external laser to theX-rays on a similar timescale.

The terahertz pulses used in this work originate from abruptchanges in the longitudinal velocity of electrons as they exit theX-ray undulator and enter the beam dump. Because the longitudinallength of the electron bunches is only a few tens of micrometres9,10,the emitted terahertz radiation is coherent, phase-stable, intense,and can be described by a simple analytical model. As we discussbelow, the theoretically derived electric fields show good agreementwith experimental measurements, allowing us to conclude a generalapplicability of this method to fourth-generation X-ray light sources.

Relativistic electrons produce edge radiation when their longi-tudinal velocity is changed abruptly. This occurs as the electronspass an edge of an arbitrary magnetic device. To calculate theradiated electric field, we first consider the emission from a singleelectron in the space–frequency domain. In this description, theelectric field can be seen as originating from two virtual sources(X-ray undulator and beam dump) or, alternatively, as originatingfrom a single virtual source located at the centre of the straightsection14. Any virtual source plays the role of the waist of a laser-like beam, and we can predict its propagation using the principlesof Fourier optics. We describe the virtual source distribution atthe centre of the straight section with the approximate relation

Es(z = 0, r,v) = i4v(−e)

c2 Lrsinc

vr2

cL

( )

where r indicates the transverse observation point, v is thefrequency of the radiation, c is the speed of light in vacuum, (2e)is the electron charge, and L is the length of the straight section.

This relation is derived from equation (30) in ref. 14, which isvalid in the case w¼ 2pL/g2l≪ 1. Here, L¼ 12 m is thelength of a straight section between the exit of the X-ray undulatorand the bending magnet, g is the Lorentz factor, and l¼ 120 mm(ZnTe cutoff ), which gives w¼ 0.49. Although such a value isnot much smaller than unity, it should be considered as an upperlimit to the value of w for l¼ 120 mm. In fact, the time-domainfield includes Fourier components with wavelengths longer thanthat limiting value.

Once the single-electron emission in the space–frequencydomain has been calculated, the time-domain field radiated by the

1HASYLAB/DESY, Notkestrasse 85, 22607 Hamburg, Germany, 2Helmholtz-Institut Jena, Helmholtzweg 4, 07743 Jena, Germany, 3European XFEL GmbH,Albert-Einstein-Ring 19, 22603 Hamburg, Germany, 4Helmholtz-Zentrum Berlin, Albert-Einstein-Strasse. 15, 12489 Berlin, Germany; †Present address:Helmholtz-Zentrum Dresden-Rossendorf, Bautzner Landstrasse 400, 01328 Dresden, Germany. *e-mail: franz.tavella@desy.de; nikola.stojanovic@desy.de;m.gensch@hzdr.de

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entire electron bunch, which is imaged onto a ZnTe crystal (seeSupplementary Information), can be calculated by convolving theinverse Fourier transform of the single-electron virtual source distri-bution in the centre of the straight section with the temporal profileof the electron bunch. In the calculations, we consider a 580 MeVelectron-beam energy and standard electron-beam parameters forFLASH1. We neglect waveguide effects, but we account for a sharpcutoff at wavelengths shorter than 120 mm to accommodate theresponse function of the ZnTe crystal15.

The total temporal and transverse distribution of edge radiationis therefore given by

ETHz(r, t) = (−e)2vcrpcr2

∫1

−1

dt sincvcr2

cL− vct

( )f (t − t)

[

−∫1

−1

dt sinc −vcr2

cL− vct

( )f (t − t)

]

where vc is the cutoff frequency associated with the ZnTe crystaland f(t) is the longitudinal electron bunch density distribution func-tion, and the nonlinear bunch compression has been modelled as inref. 1. Figure 1 shows the temporal and transverse distribution ofedge radiation ETHz(r, t) on the ZnTe crystal calculated accordingto our simple description. To further model the experimentalresults, as seen by the temporal decoding setup, we integrateETHz(r,t) along the radial coordinate. The integration goes fromzero up to r¼ 25 mm to account for the real beam size that isprobed by the spot of the optical laser in the ZnTe crystal. Weplot the resulting averaged field distribution E(t) together with ameasurement in Fig. 2a. The calculation allows this field to be inter-preted as the combination of two separate sources of coherentterahertz radiation. The sources are the exit ‘edge’ of the X-rayinsertion device and the entrance ‘edge’ of the final bendingmagnet of the accelerator that deflects the electrons into the dump.

It is important to note that when the electron bunch duration iswell below the temporal width of the single electron field (first zerocrossings are at+300 fs), the electric field of the generated coherentterahertz pulse ETHz(r, t) becomes largely independent of the elec-tron bunch width and profile because it is a convolution in timebetween the single-particle field and the electron bunch profile.To illustrate this, Fig. 2b shows the small changes of the temporaldistribution of the electric field following variation of the electronbunch duration. The calculation assumes the electron bunchprofile for the short bunch mode of operation of FLASH1 and a dur-ation of 30 fs full-width at half-maximum (FWHM) expected at thiselectron beam energy16. Typical variations of the electron bunchduration are on the order of +5–15% (r.m.s.), depending on themachine performance17. The resulting change of the peak position

defines the uncertainty of our method. Note that the distancebetween the two electric field peaks is linearly dependent on elec-tron bunch duration. As we outline in the SupplementaryInformation, this distance can be used to determine the electronbunch duration for each individual shot and to correct the timingmeasurement to achieve an accuracy of a few femtoseconds, evenfor much more unstable machine conditions.

The experimental data presented in this Letter were taken duringcommissioning shifts of FLASH with an electron beam energy of580 MeV. The terahertz pulses were coupled at the X-ray beamlinedirectly after the last bending magnet and were transported into theexperimental hall by the dedicated terahertz beamline12. The cross-correlation between the actual electric field of the terahertz pulseand the optical pulse was performed in the terahertz photon diag-nostic station. We measured the cross-correlation between theelectric field in the terahertz pulse and the optical laser pulseusing a variation of the electro-optic sampling technique18,19.With this technique, we achieved a time resolution of only a fewfemtoseconds, although the actual duration of the terahertz pulseswas much longer. The terahertz electric field induces the Pockels,

r (m

m)

Time (ps)−2 −1.5 −1 −0.5 0 0.5 1 1.5 2

50

40

30

20

10

0

−1

−0.5

0

0.5

1ETHz(r, t)

Figure 1 | Calculated radial and temporal distribution of the terahertz edge

radiation pulse generated from the X-ray undulator and the electron beam

dump for a 580 MeV electron beam energy. ETHz(r, t) has been

subsequently processed, as explained in the text, to obtain the calculated

edge radiation curve.

Time (ps)−2 −1.5 −1 −0.5 0 0.5 1 1.5 2

−1

−0.5

0

0.5

1El

ectr

ic fi

eld

(nor

mal

ized

)

Time (ps)

Bunc

h du

ratio

n (f

s)

Time (ps)

26

28

30

32

34

36t1s

24b

a−0.5 0 0.5 1 1.5 2

Curr

ent

−0.4

−0.2

0

0.2

−0.15 −0.1 −0.05 0 0.05 0.1 0.15 0.2

tb = 30 fs

t2s

Figure 2 | Electric field of the edge radiation pulse. a, Comparison between

measured (red line) and calculated (black line) edge radiation seen by the

temporal decoding setup. Inset: femotsecond-mode electron bunch

distribution, with 30 fs FWHM temporal width of the peak. b, Calculated

temporal distribution of the terahertz edge radiation generated by different

electron bunch durations. Full white lines mark peak positions in time for

30 fs bunch length; dotted white lines mark peak positions for varying bunch

lengths. Deviation of the position of the electric field peak t1s for the X-ray

undulator edge contribution and t2s for the bending magnet contribution.

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or electro-optic, effect, in a ZnTe crystal, which transforms the tera-hertz electric field into a time-varying birefringence, imprinting theterahertz pulse shape onto a co-propagating optical probe pulse as apolarization modulation (Fig. 3; see Supplementary Informationfor details).

Figure 4a shows 300 consecutive single-shot measurements ofthe electric field of the terahertz edge radiation collected over aperiod of 60 s. Each horizontal line in the image is a false-colourrepresentation of the electric field, analogous to the lineout shownin Fig. 2a. Evaluation of the shot-to-shot time deviation is carriedout by a fit on the first negative peak of the electric field. Thefitting function used is a higher-order polynomial fit. As mentionedearlier, these terahertz pulses have been shown to be synchronizedto the corresponding X-ray pulses by better than 5 fs (r.m.s.)13

and are therefore an excellent marker for the arrival time of theX-ray pulses. Evaluating the position of the electric field peak foreach lineout, we retrieve the relative timing jitter of the terahertzpulses and therefore that of the X-ray pulses, with respect to theexternal laser. This is shown on the right-hand side of Fig. 4a.

Figure 4b shows three consecutive electric field lineouts, which areenlarged in Fig. 4c.

Although the FWHM of the peaks is of the order of 250 fs, we areable to determine their relative positions by fitting the curve with anaccuracy better than 1 fs. The overall accuracy that can be achievedwith our method is estimated to values in the sub-10 fs regime (seeMethods for details).

To summarize, the online X-ray pulse arrival time monitor pre-sented in this Letter solves the main obstacle that is impeding ultra-fast science on the few-femtosecond timescale at currentlyoperational FELs. Its working principle, based on phase-sensitivecross-correlation between coherent terahertz pulses and femto-second optical laser pulses, can be applied at essentially every undu-lator in fourth-generation facilities. The technique, presented herefor the short bunch mode at FLASH, works with every availableultrashort electron bunch form (see, for example, the calculationspresented in the Supplementary Information for the Gaussian elec-tron bunch form recently available at FLASH). The accuracy of ourmethod is, in general, commensurate with the mean value of the

THz beam

Pump/probe Laser

ZnTe crystalStretcher β-Barium boratecrystal

Spatial cross-correlator

LINAC X-rayundulator Electron-

beam dump

X-ray beam

Master clock

Injector laser

Electron gun

I-CC

D

Figure 3 | Principle layout of the FLASH facility and the single-shot cross-correlation setup.

−500 Jitter (fs)a

b

c

500 0

−1

1

0

0.5

−0.5

Shot

num

ber

150

100

50

−2,000 −1,000 0 1,000TIme (fs)

2,000 −50−100Time (fs)

Time (fs)El

ectr

ic fi

eld

(a.u

.)El

ectr

ic fi

eld

(a.u

.)

−150

−0.8

1

0.5

−0.5

−1

0

−0.85

−0.9

−0.95

−1

1,000−1,000 0 2,000

200

250

300

Figure 4 | Single-shot electric field profiles. a, Series of electric field profiles measured over 1 min, and respective jitter evaluation (side panel). b, Electric

field profiles for three consecutive shots. c, Enlarged view of lower peaks of b.

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electron bunch duration and in the specific case of the short bunchmodus at FLASH is �7 fs (r.m.s.).

Our findings represent a breakthrough, because the provision offew-femtosecond timing expands the scientific applicability of exist-ing and future facilities to the fastest fundamental processes, includ-ing exchange interaction between spins, atomic Auger decay, ordephasing processes of coherent excitations in complex materials.

MethodsExperimental setup. We mapped the terahertz electric field onto an intensifiedcharge-coupled device (CCD) as a modulation of the second harmonic signalintensity (Fig. 3; see Supplementary Information). The temporal decoding andFourier filtering technique allowed us to retrieve the shape and position of terahertzelectric field peaks with respect to the external laser for each shot. We used afrequency bandpass to filter the frequency components of the edge radiation fromthe spectrum of the raw data, which did not affect the accuracy of our measurements.This bandpass filter had a lower limit of 0.1 THz and an upper limit of 2.5 THz. Thelower limit is given by the cutoff frequency of the bending magnet vacuum chamber,and the upper limit is set by the frequency filter function of the ZnTe crystal used inour measurement setup15.

Accuracy of the timing technique. The overall accuracy of the timing schemeoriginates from two contributions. The first is the dependence of the electric fieldform on electron bunch duration, which gives an uncertainty of 5 fs (r.m.s.) underthe worst beam conditions (15% r.m.s. jitter of bunch duration17). The second is thejitter between the X-ray pulse and the corresponding terahertz pulse, which has beenexperimentally determined to be 5 fs (r.m.s.)13. This gives a value of

p(52þ 52) ≈

7 fs (r.m.s.). Note that these values neglect potential drifts in the path length of theoptical laser, which limit the sub-10 fs accuracy of our present setup to timescales ofa few hours (see Supplementary Information for more details).

Received 8 June 2010; accepted 6 December 2010;published online 30 January 2011; corrected online13 February 2011

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AcknowledgementsThe authors acknowledge technical support from B. Polzin and fruitful discussion withB. Faatz, E. Saldin, E. Schneidmiller and M.V. Yurkov (Deutsches Elektronen Synchrotron).We are deeply indebted to A.L. Cavalieri (Max Planck Research Group for StructuralDynamics) and A. Azima (University of Hamburg) for sharing insights. This workwas supported by the German Ministry of Education and Research (BMBF;grant no. 05K10CHC).

Author contributionsM.G., N.S. and F.T. contributed equally to the work. G.G. performed calculation of theterahertz electric fields.

Additional informationThe authors declare no competing financial interests. Supplementary informationaccompanies this paper at www.nature.com/naturephotonics. Reprints and permissioninformation is available online at http://npg.nature.com/reprintsandpermissions/.Correspondence and requests for materials should be addressed to F.T., N.S. and M.G.

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