Electron wave packet sampling with laser-generated extreme ultraviolet and terahertz fields

Electron wave packet sampling withlaser-generated extreme ultraviolet and

terahertz fields

Bernd Schutte, Ulrike Fruhling, Marek Wieland, Armin Azima, andMarkus Drescher*

Universitat Hamburg, Institut fur Experimentalphysik and Center for Free-Electron LaserScience (CFEL), Luruper Chaussee 149, 22761 Hamburg, Germany

*[email protected]

Abstract: We report on transferring the concept of light-field streakingwith intense terahertz fields from free-electron lasers to the laboratory scale.Utilizing a commercial laser system, synchronized 300 μm terahertz and13nm extreme ultraviolet pulses are generated by optical rectification andhigh harmonic generation, respectively. The terahertz fields are sufficientlystrong to support electron wave packet sampling with a few fs resolution.The capability of this approach is demonstrated by measuring the durationof electron pulses formed by direct photoemission from a neon gas target.

© 2011 Optical Society of America

OCIS codes: (020.2649) Strong field laser physics; (040.7480) X-rays, soft x-rays, extremeultraviolet (EUV); (190.2620) Harmonic generation and mixing; (320.2250) Femtosecond phe-nomena.

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#150024 - $15.00 USD Received 28 Jun 2011; revised 2 Aug 2011; accepted 4 Aug 2011; published 13 Sep 2011(C) 2011 OSA 26 September 2011 / Vol. 19, No. 20 / OPTICS EXPRESS 18833

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1. Introduction

In ultrafast optics, dynamic information is in most cases obtained from experiments applyingthe pump-probe technique, where the response of a system on two subsequent light pulses isstudied as a function of their relative timing. This approach requires scanning of a time delay;the evolution has therefore to be assembled from a set of experiments, taken consecutively atdifferent delay settings. For a linear system response, the time resolution is then given by aconvolution of the envelopes of both light fields. A different approach, which is able to samplethe evolution of a process in a single sweep, resembles the streak camera principle, where timeinformation imprinted in the temporal profile of an electron pulse is projected onto a spatialcoordinate by a rapidly varying electric field across deflection plates. In the realization of the’atomic streak camera’ this principle was modified by streaking photo-emitted electron wavepackets with the electric field of near infrared (NIR) light [1,2]. The temporal resolution in thiscase is not limited by the duration of the streaking light pulse envelope, but given by the rate ofchange of the oscillating electromagnetic field. With an oscillation period of 2.7femtosecond(fs) for 800nm light, events shorter than 100attoseconds have been resolved [3, 4].

The upper limit for the detectable wave packet duration within this concept is set by thelinear part of the field slope, corresponding to approximately a quarter of the field period, or 670attoseconds for a 800nm wavelength. However, many relevant electronic and nuclear processesin atoms and molecules evolve on a slower time scale. Inner shell relaxation by Auger decay isoften found in the few fs range [5,6]. Fragmentation following inner-shell relaxation occurs ona few fs to a few tens of fs scale [7]. Transfer of the concept of single-sweep light-field streakingto this temporal regime requires considerably slower oscillating, i.e. longer wavelength, fields.Correspondingly, the principle outlined above was utilized to realize a single-shot streak camerabased on a terahertz (THz) streaking field with a 300fs period and a usable time window ofabout 70fs [8], providing information on the duration of individual XUV pulses from the free-electron laser source FLASH. While for effective streaking THz pulse energies in the μJ rangeare mandatory, the synchronized extreme ultraviolet (XUV) pulses can be scaled down from


the several 100 μJ delivered by FELs to the nJ and pJ range, where laser-based XUV sourcesare available. This opens the opportunity to realize femtosecond electron wave packet samplingin the laboratory.

In this report, we introduce fully laser-based terahertz-field-driven streaking. Intense THzpulses generated by optical rectification in a nonlinear crystal are used to streak photoelectronsemitted from a gaseous target after irradiation with well synchronized, spectrally filtered XUVpulses from high-order harmonic generation (HHG). We demonstrate the applicability of thefemtosecond streaking concept by measuring the duration and linear chirp rate of electron wavepackets formed by direct photoemission from a neon target.

2. Theory

The basic theory of electrons generated by photoionization of an XUV pulse in the presenceof an intense, linearly polarized light field can be adopted from attosecond metrology [9]. Ac-cording to the classical model, the momentum of the photoelectrons in the direction of theinteracting THz field is changed by

Δ�p(r, t) = e

∞∫

t

�ETHz(r, t′)dt ′ = e�ATHz(r, t), (1)

where t is the ionization time, e the electron charge, �ETHz the THz electric field strength and�ATHz the THz vector potential. Thus the momentum gain of the photoelectrons depends on theTHz vector potential at the ionization time. For electrons with a final drift velocity parallel tothe THz polarization, this translates into an energy shift of [2]

ΔW‖(t)≈√

2W0

meeATHz(t), (2)

with W0 being the electron kinetic energy without THz field and me being the the electron mass.We consider a linearly chirped Gaussian XUV pulse with an electric field given by

EXUV (t) = E0Xe−2ln2(t/τX )

2ei(ω0t+ct2), (3)

where E0X is the amplitude of the field, τX is the full width at half maximum (FWHM) pulse

duration of the intensity envelope, ω0 the frequency of the XUV field and c is the linear chirprate. The time t = 0 corresponds to the pulse peak.

When the XUV pulse duration is short compared to the THz oscillation period and the delaybetween the XUV and THz pulses is chosen such that the slope of ATHz is approximatelylinear, streaking will imprint an additional linear chirp to the electron wavepacket. The streakedphotoelectron spectrum maintains a Gaussian shape with a FWHM of

σX−streak =√

σ2X−0 + τ2

X (s2 ±4cs), (4)

where σX−0 corresponds to the measured width of the field-free spectrum and

s =∂ (ΔW‖)

∂ t≈√

2W0

meeETHz(t) (5)

is the streaking speed. The ± sign in Eq. (4) corresponds to the two different observation di-rections parallel and anti-parallel with respect to the THz polarization at a specific time. Bymeasuring the field-free spectrum and the streaked spectra in two opposite directions, the XUVpulse duration and its linear chirp rate are determined.


3. Experiment

For the generation of HHG and THz radiation, we use a Ti:sapphire laser that delivers 3mJpulses with a duration of 25fs at a repetition rate of 1kHz. High harmonics are generatedby focusing the laser into a tube which is continuously filled with neon gas to a pressure of110mbar. The harmonics are separated from the fundamental laser by a mirror with a centralaperture. Thus the less divergent harmonic radiation propagates through the aperture whilethe major fraction of the (NIR) light is recollimated and coupled out of the vacuum chamber.A zirconium filter is used to efficiently block the fundamental beam propagating through theaperture. The 59th harmonic order is selected by a molybdenum-silicon multilayer mirror andreflected into the experimental vacuum chamber.

The recollimated fundamental beam is used for the generation of THz radiation by opticalrectification [10] in a lithium niobate crystal. In order to prevent photorefractive damage, thecrystal is stoichiometrically doped with 1% of magnesium oxide. Efficient velocity matching ofthe NIR and THz pulses is achieved by tilting the pulse front of the NIR beam after diffractionoff a grating (2000lines/mm) [11, 12]. A λ/2 wave plate rotates the linear NIR polarizationby 90◦ to make it parallel to the optical axis of the lithium niobate crystal. The diffractedbeam is imaged into the crystal by a f = 75mm achromatic lens. After losses due to the HHGprocess, the optical setup and the diffraction grating, NIR pulses with an energy of 1.8mJ reachthe crystal. The divergent THz radiation is collimated by a teflon lens and coupled into theexperimental vacuum chamber. A periscope rotates the THz polarization by 90◦ to be in theplane of the electron detectors. Since both XUV and THz pulses are generated by the samelaser pulse, an inherent synchronization between them is ensured.

gas

multilayer mirror (f=500mm)

parabolic mirror (f=100mm)

left TOF

right TOF

THz

HHG

Fig. 1. Experimental setup. HHG (blue beam) and THz (red beam) pulses are collinearlyfocused into the interaction zone which consists of a neon gas jet. Two time-of-flight spec-trometers detect the kinetic energies of the generated photoelectrons.

The experimental setup of the streaking experiment is sketched in Fig. 1. An off-axisparabolic mirror with f = 100mm focuses the collimated THz beam to a FWHM size of1.0mm. Its pulse energy in the focal plane was measured with a calibrated pyroelectric de-tector as 1.7 μJ, Taking into account losses of the THz beam recollimation and focusing as well


as absorption in air, the overall NIR-to-THz conversion effciency is well above 1 · 10−3. TheHHG beam is focused by a concave molybdenum-silicon multilayer mirror with a focal lengthof 500mm. It passes through a central hole in the parabolic mirror such that it collinearly propa-gates with the THz radiation. The XUV diameter in the focal plane was measured to be 100 μm(FWHM). Neon is injected into the interaction zone with a gas nozzle. The photoelectrons gen-erated by the XUV pulse and streaked by the THz field are simultaneously detected with twotime-of-flight (TOF) spectrometers which are placed in opposite directions along both the XUVand the THz polarization axes.

4. Results

The time-dependent THz vector potential is directly measured by acquiring streaked photoelec-tron spectra upon scanning the delay between the HHG and THz pulses. We exploit the fact thatthe electron drift velocity change is in good approximation proportional to the vector potentialof the THz field (Eq. (2)). Figure 2 depicts series of kinetic energy spectra for the streaked pho-toelectrons measured simultaneously with two TOF detectors. The time delay between HHGand THz pulses was varied in steps of 30fs, and each spectrum was averaged over 10000 shots.The scan reveals the single-cycle behavior of the THz pulse that is typically observed for thiskind of source. The measured energy shift at the right detector is just reversed with respect to theleft detector. From this measurement, the electric field is obtained by differentiation accordingto ETHz = ∂ATHz/∂ t which yields a maximal field strength of 14MV/m. For the calculation,the center of mass of each spectrum was determined, and the resulting curve was smoothedover five neighboring points. Albeit the obtained value is small compared to the electric fieldstrengths used in attosecond metrology, the electrons are accelerated for a longer time and thussimilar ponderomotive potentials and corresponding streaking amplitudes are achieved.

As can be seen in Fig. 3, the obtained temporal profile of the THz field is in good agreementwith measurements at this source utilizing an electro-optic sampling (EOS) [13] setup with a0.3mm thick ZnTe crystal. The two electric field transients in Fig. 3 have different amplituderatios in positive and negative directions and thus a slightly different carrier envelope phase(CEP). This can be explained by the influence of the Gouy phase [14] which describes the phasechange of the THz beam during propagation through the focus. A small displacement of theinteraction region of both measurements will therefore result in such a change of the CEP phase.In addition, the temporal profile of the THz pulse might have changed due to changing pumppulse parameters. As a result, ponderomotive streaking represents an alternative measurementtechnique for the temporal characterization of THz pulses. Unlike EOS, it does not suffer fromsaturation effects, bandwidth limitations and imperfections in a crystal and therefore yields amore accurate representation of the electric field strength. The THz spectrum is determinedfrom a Fourier transform of the electric field transient obtained by the streaking measurement.In accordance to the single-cycle behavior, the spectrum has a large width of 0.8THz, andthe average frequency is centered at 1.0THz. The shot-to-shot fluctuations of the THz fieldstrength measured by EOS were 3% at the first slope (at a time delay of 2.8ps). However, thefluctuations at the maximum vector potential (at a time delay of 3.1ps) are enhanced to 7%.Therefore, we restrict the determination of the XUV pulse duration to an analysis at a singledelay setting.

For characterizing the duration of electron wave packets formed by direct photoionization,field-free (Fig. 4(a), 4(b)) and streaked (Fig. 4(c), 4(d)) photoelectron spectra were taken withboth detectors at a time delay of 2.8ps where the slope of the vector potential has a maximum.The streaking speed (Eq. (5)) evaluated from Fig. 2 is 48meV/fs. The spectra show photo-electron peaks resulting from the 59th (at about 69eV) and the 61st harmonic (at about 72eV)shifted by the neon 2p binding energy. For an accurate determination of the field-free spectral


time delay (ps)

elec

tron

kine

tic e

nerg

y (e

V)

1 2 3 4 5 660

65

70

75

80

85

90intensity(arb.u.)

0 1

(a)

time delay (ps)

elec

tron

kine

tic e

nerg

y (e

V)

1 2 3 4 5 650

55

60

65

70

75

80(b)

Fig. 2. Series of neon 2p electron kinetic energy spectra obtained by a delay scan betweenthe ionizing XUV pulse and the THz streaking field (false-color representation) detected at(a) left and (b) right TOF. Each spectrum was normalized to a constant area.

widths, the peaks were fitted by individual Gaussian functions with a common fitted width pa-rameter, resulting in a FWHM of the 59th harmonic of 1.08eV for both TOFs. After switchingon the THz field, the streaked spectra clearly exhibit a broadening (Fig. 4(c), 4(d)). The widthof the 59th harmonic was now obtained by utilizing the spectral position, the amplitude andthe common width as fit parameters, while the spectral distances between the peaks and theiramplitude ratio obtained from the unstreaked spectra were kept constant. The correspondingwidths are 1.63eV and 1.75eV for the left and right TOF, respectively. According to Eq. (4),this results in a temporal width of 27fs (for more details of the calculation cf. [8]). However,this value slightly overestimates the actual HHG pulse duration. Since the focused THz beamexperiences a Gouy phase shift [14] with respect to the HHG pulse, signal is acquired fromslightly different phases along the interaction zone between HHG beam and the gas volume.For an evaluation of this effect, we have used EOS to measure temporal profiles at a distanceof one Rayleigh length (=10mm) before and after the focus. Both curves showed a temporalshift of 330fs. Taking into account the arctan behavior of the Gouy phase, this allowed us to


Fig. 3. Comparison of the electric field transients obtained by electro-optic sampling andby the THz streaking method.

estimate the temporal shift within the 0.75mm long interaction zone as 16fs. The measuredtemporal width represents a convolution of the XUV pulse duration and the temporal broad-ening due to averaging over a range Gouy phases. Deconvolution yields a corrected value forthe XUV pulse duration of τX = (22+4

−6) fs. The ratio in pulse durations between harmonic andfundamental beam is larger than what is typically observed at lower harmonic orders [15, 16].In contrast to these lower harmonics, however, the order of nonlinearity is close to one for the59th harmonic [17]. Therefore, the measured pulse duration is in good agreement with the ex-pectation. The different widths of the streaked spectra are due to a small linear chirp of theharmonic beam with a value of c =−(2±2)meV/fs. Here the negative sign for a non-chirpedfundamental pulse is attributed to the atomic dipole phase and is consistent with earlier ob-servations [18]. When a negative chirp is applied to the driving laser, this is transferred to the59th harmonic (Fig. 4(e), 4(f)). For a fundamental pulse with a duration of 35fs, the resultingXUV pulse duration after accounting for the Gouy phase-induced broadening is τX = (31+4

−5) fs.The spectra detected with the two TOFs have clearly different widths from which an increasednegative linear chirp rate of c =−(4±2)meV/fs is determined.

The temporal resolution of a light-field-driven streak camera is typically defined as the condi-tion where the XUV bandwidth is equal to the broadening induced by the streaking field. Whenwe optimize the laser parameters for a maximum output of THz energy, a streaking speed of0.1 eV/fs is achieved which corresponds to a temporal resolution of 10fs for a field-free spectralwidth of 1eV. With the tilted-pulse-front setup the THz energies can further be scaled by usingpump pulses with higher energies. In this way it is possible to achieve a time resolution of afew fs.

For a complete reconstruction of the temporal profile including higher orders of chirp, an ap-propriate reconstruction algorithm known as FROG-CRAB is now widely used [19, 20]. How-ever, the transfer of this technique from NIR streaking to THz streaking is problematic dueto several reasons. Although it has been shown that FROG-CRAB is robust against laser shotnoise [21], one has to realize that the significance of field fluctuations is dramatically enhancedin the case considered here. While for NIR streaking the maximum energy shift is similar tothe photoelectron spectral widths [2], the maximum energy shift for THz streaking is an orderof magnitude higher than the corresponding spectral widths. As an example, the fluctuationsat the maximum vector potential in Fig. 2 are approximated by 0.07 · 13eV= 0.91eV which


Fig. 4. Photoelectron spectra measured at the left detector (a) and at the right detector (b)without THz field. The main peak corresponds to the 59th harmonic shifted by the neon2p binding energy, while the peak on the right side results from the 61st harmonic. Whenswitching on the THz field, the spectra at the left (c) and right (d) detector show a broad-ening. (e),(f) Introducing a negative chirp to the fundamental laser leads to an increasednegative linear chirp of the harmonic pulse. The streaking speed in (c),(d) was 46meV/fsand in (e),(f) it was 48meV/fs.

leads to a significant broadening of the measured spectra. In addition, the improvement of theFROG-CRAB algorithm due to the redundant information from several NIR oscillation cyclesmentioned in [21] is not given for the single-cycle THz pulse considered here. Therefore, welimit the reconstruction of the pulse duration and the linear chirp to one time delay, where thefluctuations are the lowest and the energy shift is small. Here the field fluctuations are carefullyaccounted for by an increased uncertainty of the streaking speed. An improvement of the THzsource is expected to reduce the influence of the fluctuations on the measured streaking trace.This can explicitly be achieved by higher THz frequencies and thus shorter oscillation periods.


Such an improvement may possibly allow for an application of the FROG-CRAB algorithm inthe future.

5. Conclusion

In conclusion, a completely laser-based terahertz-field-driven streak camera for measuring theduration of femtosecond electron wave packets was presented. We have demonstrated its appli-cability for sampling the temporal profile of electron wave packets formed from ultrashort XUVpulses by direct photoemission. The results represent a novel way of determining the durationand linear chirp of high-order harmonic pulses. A single-shot capability for characterizing XUVpulses in the nJ range is predicted.

Acknowledgments

We gratefully acknowledge financial support from the Deutsche Forschungsgemeinschaft(Graduiertenkolleg 1355), the Landesexzellenzinitiative Hamburg and the Joachim HerzStiftung.


Electron wave packet sampling with laser-generated extreme ultraviolet and terahertz fields

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