Second-order autocorrelation of XUV FEL pulses via time resolved two-photon single ionization of

Second-order autocorrelation spectra of XUV free-electron laser pulses from the Spring-8 Compact SASE Source (SCSS) have been recorded by time and momentum resolved detection of two-photon single ionization of He at 20.45 eV using a split-mirror delay-stage in combination with highresolution recoil-ion momentum spectroscopy (COLTRIMS). From the autocorrelation trace we extract a coherence time of 8 ± 2 fs and a mean pulse duration of 28 ± 5 fs, much shorter than estimations based on electron bunch-length measurements. Simulations within the partial coherence model [Opt. Lett. 35, 3441 (2010)] are in agreement with experiment if a pulsefront tilt across the FEL beam diameter is taken into account that leads to a temporal shift of about 6 fs between both pulse replicas. ©2011 Optical Society of America OCIS codes: (030.1640) Coherence; (140.2600) Free-electron lasers (FELs); (340.7450) X-ray interferometry; (340.7480) X-rays, soft x-rays, extreme ultraviolet (EUV). 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Free electron lasers (FELs) deliver light pulses with unprecedented brilliance and ultra-short durations in the wavelength range from the extreme ultra-violet (XUV) to hard X-rays. They therefore open up unprecedented and entirely new possibilities for e.g. the visualization of ultra-fast dynamical processes in physical, chemical and biological systems on time scales of a few femtoseconds or even below. In order to quantify the actual time resolution and to #152650 $15.00 USD Received 11 Aug 2011; revised 14 Sep 2011; accepted 15 Sep 2011; published 19 Oct 2011 (C) 2011 OSA 24 October 2011 / Vol. 19, No. 22 / OPTICS EXPRESS 21699 ensure a meaningful interpretation of experimental results the precise knowledge of the temporal shape of the FEL pulses is of crucial importance, in particular if non-linear, i.e. multi-photon processes are involved because they sensitively depend on the evolution of the electric field strength and phase. For the prediction of multi-photon transitions in atoms, molecules or matter in general the pulse shape properties are often used as input parameters for theoretical calculations [1,2] and, thus, need to be known. In addition, to monitor the FEL source its

ensure a meaningful interpretation of experimental results the precise knowledge of the temporal shape of the FEL pulses is of crucial importance, in particular if non-linear, i.e. multi-photon processes are involved because they sensitively depend on the evolution of the electric field strength and phase.For the prediction of multi-photon transitions in atoms, molecules or matter in general the pulse shape properties are often used as input parameters for theoretical calculations [1,2] and, thus, need to be known.In addition, to monitor the FEL source itself it is important to obtain information about the pulse shapes, which crucially depend on the actual machine settings.The situation is hampered by the fact that all existing XUV and X-ray FELs, the SPring-8 Compact SASE Source (SCSS) [3], the Free-electron LASer at Hamburg (FLASH) [4], and the Linac Coherent Light Source (LCLS) [5], are operated in the so-called self-amplified-spontaneous-emission (SASE) mode, where lasing starts from the shot noise of individual electron bunches.This inherently leads to significant pulse-to-pulse variations with respect to intensity, temporal and spectral shape as well as coherence properties [6].Those are precisely predictable on the basis of the well-known statistical behaviour of the FEL if time-averaged properties of the radiation are known [7].However, the simultaneous determination of all essential FEL pulse parameters represents a non-trivial task that has, to the best of our knowledge, not yet been accomplished on a regular basis.
A common method to determine the duration of ultra-short laser pulses is intensity autocorrelation, where the pulse to be analyzed is split into two identical copies and both are directed onto a non-linear detector, whose response is monitored as a function of the adjustable delay-time between the two pulses [8].Whereas in the optical frequency domain semi-permeable beam splitters at hand to generate a pulse copy via intensity splitting, those are just under development [9] or simply missing at XUV wavelengths such that a geometrical or wave-front splitting must be applied.In either case both pulses are brought to an overlap in space and time at the detector while scanning the delay-time between the two pulses.From the obtained autocorrelation trace the intensity envelope of the pulse (FWHM) can be deduced, and, if structured or "spiky" and only partly coherent pulses are used, additional information like temporal coherence or other pulse properties can be extracted as will be discussed later.In the XUV-regime non-linear non-sequential single or multiple ionization of atoms or molecules may serve as a detector of n th -order, because the ionization yield Y ~In sensitively depends on the intensity (I) and the number n of absorbed photons.This approach in combination with geometrical (wave-front) pulse splitting devices was used to characterize attosecond pulse trains [10] and to determine the FEL pulse lengths at FLASH in several recent measurements.Second-order autocorrelation measurements via non-sequential (or direct) two-photon double ionization of He at photon energies of 51.8 eV [11] and 47.0 eV [12] revealed a pulse duration of ~30 fs and a temporal coherence length of ~7 fs.The observations were in agreement with numerical simulations assuming a sub-structure of individual FEL pulses separated by 12 fs [11].Using four-photon induced multiple ionization of N 2 at 38 eV as a 4th-order autocorrelator a pulse duration of 40 ± 10 fs with a coherence time of only 4 ± 1 fs was observed at FLASH in excellent agreement with simulation calculations based on the partial-coherence approach taking the molecular dynamics that is involved into account [13].Qualitatively very similar pulse parameters were extracted from terahertz-streaking measurements [14] and linear autocorrelation measurements at different wavelengths [15].
Here we report on a 2nd-order autocorrelation measurement at the SPring-8 Compact SASE Source (SCSS) by recording single ionization of He induced by the absorption of two 20.45 eV photons.The comparison with simulations based on the so-called partial-coherence method [7] for the reconstruction of the statistically fluctuating FEL pulse shapes revealed a mean pulse duration that is much shorter than initial estimations extracted from independent electron bunch-lengths measurements.Excellent agreement with the experiment is achieved if FEL pulse distortions very similar to those that often occur for short-pulse high-power lasers in the near infrared are taken into account.A cold-target recoil-ion momentum spectrometer (COLTRIMS) [16] equipped with an onaxis back-reflection split-mirror setup for focusing and pulse-pair creation was installed at SCSS (Fig. 1).A mirror holding setup employed in the present measurement is the same as the one successfully used at FLASH [13,17].A new spherical multi-layer mirror (1 inch Mo/Si multilayer mirror, 60 cm focal length, ~10 µm focus diameter, made in LBNL, USA) is cut along the horizontal axis into two identical "half-mirrors".They are then mounted to this holding setup.While one half-mirror is mounted at a fixed position, the other one is movable along the FEL beam axis by means of a high precision piezo-stage.This way a time delay of up to ± 2 ps with a resolution of better than 1 fs is freely adjustable.The mirror has a reflectivity of ~40%, peaked around 20.45 eV with a FWHM of 2 eV such that higher-order harmonic radiation from the FEL is efficiently suppressed.The intensity of the incoming FEL-beam mm diameter) was equally distributed over both half-mirrors and the foci were merged inside a dilute and well-localized beam (less than 1 mm diameter) of He atoms in the centre of the COLTRIMS spectrometer.The spatial overlap of the two focal points was initially adjusted with ~100 µm precision by observing the optical interference pattern obtained with an external multimode diode laser that was aligned along the beamline.It also enabled a coarse adjustment of the time zero with a precision of ~50 fs.Further adjustment and fine tuning was performed with the FEL beam using a spatial imaging system for the created ions consisting of a defocusing electrostatic lens.By measuring the yield of He + -ions while scanning the position of one half-mirror with respect to the other in the plane tranverse to the beam direction the overlap of the foci was optimized and a diameter of ~10 µm for the foci was obtained.With pulse energies of about 10 µJ we reached peak intensities of I ~10 14 W/cm 2 .During the measurement the ions were projected by means of a homogeneous electric field (2 V/cm) onto a time-and position-sensitive detector (diameter 80 mm, position resolution 0.1 mm) and recorded as a function of the time delay.From the measured times-offlight and positions the ion momentum vectors were reconstructed.While sweeping the delay this information was recorded together with the number of created He + -ions during experiment.In order to obtain a quantitative interpretation of the result and to extract more information about the pulse structure we present in the following a simple model calculation for the autocorrelation trace after a brief discussion of the ionization mechanism.As illustrated in Fig. 2(a) the absorption of at least two photons is required at the present photon energy of 20.45 eV to overcome the ionization potential of He (24.58 eV).The first excited state in He that is accessible with a dipole allowed transition is at 20.98 eV (1s2pstate), clearly above the available FEL spectral range shown in Fig. 2(b).Thus, ionization may only proceed through non-sequential (direct) two-photon single ionization (TPSI), where an electron from the 1s 2 ground-state is promoted via a virtual intermediate state into the 1sεℓ continuum.The experimentally observed electron angular distribution as well as the intensity dependence of the ionization yield provides evidence for TPSI.In accordance with lowest order perturbation theory we obtained the expected quadratic intensity dependence for the creation of He + as shown in Fig. 3(a).For a cross-check in addition the yield of H 2 + from residual gas ionization is plotted that requires absorption of one photon only (H 2 ionization potential: 15.4 eV).The dominance of TPSI is further substantiated by inspection of the electron angular distribution which, for ionization of an s-electron, is expected to exhibit the characteristic structure of an outgoing electron-wave with angular momentum of either ℓ = 0 (isotropic emission) or ℓ = 2 (quadrupole like emission), or a superposition of both.In the experiment we measured the He + recoil-ion momentum along all three spatial dimensions and applied momentum conservation between ion and electron (P ion = -P el for |P el | >> |P ph | ≈0) to extract the electron angular distribution.The result is shown in Fig. 3(b).Clearly discernable is a lobe perpendicular to the polarization direction.This non-dipole contribution arises from the superposition of s-and d-wave emission and thus unambiguously identifies the creation of He + as a two-photon transition.Moreover, the observed angular distribution is well reproduced by the calculation with the full 6 + 1 dimensional time-dependent Schrödinger equation [18].The details of the calculations will be given elsewhere.We simulated the Fourier transform-limited Gaussian pulses with a width between 7 and 21 fs and found that the photoelectron angular distribution does not depend on the pulse width at this photon energy, indicating non-resonant two-photon ionization.
In order to calculate the autocorrelation trace we use the recently published partial coherence method (PCM, for details see [7]) to generate statistically fluctuating, partially coherent individual FEL pulses from the measured average frequency spectrum and the average pulse duration.Briefly, in the PCM the FEL spectral electric field of each individual pulse (i) is described as ( ) ( ) exp(i ( ) given by the frequency spectrum ( ) I ω (see Fig. is constructed by multiplying this initial field ( ) i E t with a Gaussian (or any other) temporal filter function ( ) F t that corresponds to the average (measured) FEL pulse duration.Due to the random choice of the initial spectral phases ( ) i φ ω , the obtained temporal fields ( ) f i E t will be different for each choice, i.e. for each individual pulse.The quality of the reconstructed spectral phase function can be confirmed e.g. by comparing the simulated average frequency spectrum ( ) I ω (solid line in Fig. 2(b)) with the measured one.
With the PCM we generate shot-by-shot temporal electric fields and calculate the 2nd-order autocorrelation function: To simulate the experiment we evaluate the autocorrelation function for a large number of individually generated pulse shapes and consider in the following the average of I(∆t) over many pulses.In addition the resulting autocorrelation function is smoothed over one period of the VUV wave (∆t = 0.2 fs) to account for the fact that the two beams reflected from the split mirror merge at the target under an angle of ~10 mrad.For the given focus diameter of ~10 µm this small deviation from an ideally co-linear overlap leads to an effective time-resolution that is comparable or slightly larger than one wave-period.The experimental autocorrelation trace, i.e. the yield of He + -ions as a function of the pulse-to-pulse delay time, is shown in Fig. 4. Here, several thousand complete delay scans are summed in order to collect a statistically significant number of ions at the given low target density (number of created ions per laser shot < 1).In addition, the result of a PCM simulation is plotted (thin line in Fig. 4) assuming a Gaussian shaped FEL pulse with an envelope of 28.3 fs FWHM.For a direct comparison with the experiment a constant background is added.Moreover, the y-axis is scaled because the theoretically expected peak-to-background ratio of three, which is a general property or 2nd-order intensity autocorrelation, is considerably higher than the experimentally measured ratio of ~1.6 only.This discrepancy can be explained by either a non-perfect spatial overlap of the two pulses in the focus or a limited transversal coherence of the incoming FEL beam, or a mixture of both.From experiments at FLASH it is known that the beam is transversally coherent over a distance of a few millimeters or less, depending on the wavelength and the setting of the machine [19][20][21].Assuming similar conditions for the SCSS we cannot expect to achieve maximum contrast in the autocorrelation spectrum as the diameter of the incoming beam is ~10 mm.We would like to note that our split-mirror setup can be used to quantitatively measure the transversal coherence properties of the FEL and corresponding pulse diagnostics measurements are planned for the future.
The autocorrelation trace exhibits a broad maximum of ~40 fs FWHM superimposed with a narrow peak (~10 fs FWHM) at zero delay-time in agreement with our recent measurement at FLASH [16], where four-photon induced multiple ionization of N 2 at 38 eV was studied (4th order autocorrelation).As follows from FEL theory and the PCM as well as directly observed in spectral domain measurements, each individual FEL pulse comprises several subpulses (or modes) (see e.g [6,14,19]).The number of modes, their intensities and the overall temporal structure is fluctuating statistically from pulse to pulse.Each sub-pulse is intrinsically coherent giving rise to a sharp spike in the autocorrelation spectrum at zero delay (Fig. 4), whose width is a measure of the sub-pulse duration or the coherence time.The underlying broader contribution can be attributed to the temporal width of the pulse-envelope averaged over many fluctuating FEL pulses.From the data we extract a coherence time of 8.5 fs and an average pulse duration of 28.3 fs FWHM, much shorter than the 100-150 fs expected from electron bunch length measurements [22].
Even though reasonable agreement is obtained, the experimental autocorrelation spectrum (Fig. 4) exhibits a noticeable asymmetry with respect to time zero that is significantly outside statistical uncertainties and not explainable with the above discussed model calculation.As obvious from the autocorrelation function (Eq.( 1)) such behaviour can only be explained if the shapes of the two pulse replicas differ explicitly.Since we geometrically cut the incoming beam (10 mm diameter) by the split mirror along the horizontal axis into an upper and a lower part this observation directly implies that the FEL pulse shape changes along the vertical beam cross-section.This is a well-known phenomenon for short-pulse lasers in the optical or infrared regimes where the most important and common spatial pulse distortions are the socalled "chirp", where the frequency spectrum varies across the beam, and pulse-front tilt.While the former is expected to be of minor importance for the non bandwidth-limited FEL pulses, a tilt of the pulse-front cannot be excluded.Without discussing possible scenarios that might result in a spatial tilt of the pulse-front in the generation process of FEL light-pulses we implemented an assumed pulse-front tilt in the PCM calculations via a simple model and investigated its influence on corresponding autocorrelation trace.To illustrate our considerations it is helpful to imagine the transversally extended FEL pulse as a moving radiation disk with ~10 mm diameter and a length of only a few 10 µm along the beam direction, corresponding to a pulse length of about 30 fs.A tilt of the pulse-front is equivalent to a tilt of the moving disk meaning that the FEL pulse hits the mirror at different times depending on the vertical position.Consequently, geometrically cutting the beam along the vertical direction introduces a mean time delay (2τ) between both reflected beams even for zero displacement of the half-mirrors (nominal setting for zero delay).This is modelled by simply introducing effective envelope offsets ± τ into the temporal amplitude function ( ) F t τ ± for the upper and lower pulse, respectively, and thus constructing two timedependent electric fields ( / ) ( ) ( ) ( ) for each single shot that overlap in the focus.Note that both pulses exhibit identical (averaged) spectral shapes and statistical fluctuations (same spectral amplitude function  choice of ( / ) ( ) ( ) for each individual pulse before the Fourier transform, taking care of the fact that both parts of the pulse emerge from the same source and, thus, should share the essential part of their temporal coherence properties.Finally the obtained electric fields for the two beams are then used to calculate the autocorrelation spectrum as described before and the envelope offset time between both pulses τ serves as a fit parameter that quantifies the tilt.The crucial point here is that since the FEL radiation is not fully coherent the offset of the envelope by τ ± leads to different temporal shapes of the upper and lower pulses which give rise to the observed asymmetry in the simulated autocorrelation trace.As shown in Fig. 4 (thick line), we find the result of such a simulation to be in excellent agreement with the experimental data for an envelope offset time of τ = 2.9 fs and an average FEL pulse duration of 28.3 fs (FWHM).Conversion of the envelope offset time into a pulsefront tilt angle leads to a value of ~0.02 degrees for a beam diameter of 10 mm, or, in other words, the upper edge of the disk shaped FEL pulse precedes the lower edge (or vice versa) by a distance of about 3.5 µm.After focusing of the whole beam this seemingly small effect, however, result in a significant broadening of the pulse width by 2τ ~5.8 fs and thus contributes about 20% to the total pulse duration.
In summary, using single ionization of He induced by direct two-photon absorption as detector for 2nd-order autocorrelation we extract information about the temporal coherence (8.5 fs), the average pulse length (28.3 fs FWHM) as well as the pulse-front tilt (0.02 degrees) of FEL pulses at SCSS.Our results have important consequences for any time-dependent measurement at FELs since the here identified pulse-front distortion may occur at any VUV and X-ray SASE FEL and, moreover, might be expected to depend on the actual setting of the machine.We would like to note that the presented autocorrelation scheme, which is based on geometrical (wave-front) pulse splitting, can be easily extended to the horizontal or any other direction by rotating the spit-mirror assembly around the beam axis as well as to simultaneous diagnostics of transverse spatial coherence by using appropriate beam masks.

Fig. 2 .
Fig. 2. (a) Schematic illustration of the TPSI process.The dashed line depicts a virtual intermediate state.For details see text.(b) Measured average frequency spectrum (red squares).Solid line: result of partial coherence method.

Fig. 3 .
Fig. 3. (a) Intensity dependent yields of He + (two-photon transition) and H2 + (one-photon reaction, residual gas contribution) at 20.45 eV photon energy.The maximum intensity is in the order of ~10 14 W/cm 2 .(b) Electron angular distribution for single ionization of He.Polarization is horizontal.Solid line: TDSE calculation.

Fig. 4 .
Fig. 4. Experimental 2nd-order autocorrelation spectrum.Plotted is the yield of He + ions as a function of the pump-probe delay time measured with 20.45 eV photons at an intensity of about 10 14 W/cm 2 .Thin solid line: PCM result for identical pulse replica normalized to the same maximum value as the experiment.Thick solid line: PCM result including pulse-front tilt (see text).