Femtosecond profiling of shaped x-ray pulses

In the 'spoiler' scheme, the beam emittance is accessed in a magnetic chicane, which is a dispersive section of the accelerator, and is analogous to a prism compressor used in ultrafast optics. In the chicane, as depicted in figure 1, high-energy electrons follow shorter trajectories than low energy electrons, which results in longitudinal compression of bunches that are initially linearly chirped in energy. Energy chirp is introduced or eliminated by appropriate phasing of the accelerating fields. In the middle of the chicane, the longitudinal, or temporal coordinate of the electron bunch phase-space is transformed into a transverse spatial coordinate x.

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At the LCLS, part of the SLAC National Accelerator Laboratory, femtosecond x-ray pulse pairs can be generated by inserting a thin metallic foil with two slots at this position. The regions of the bunch that pass through the openings in the 'double-V-slotted' foil propagate through the chicane with preserved emittance and are expected to lase normally in the FEL undulator. In contrast, Coulomb scattering of the electrons in the regions of the bunch that collide with the opaque parts of the foil causes an increase in the transverse emittance, leading to strong suppression of FEL gain. As a result, upon recompression and homogenization of the beam energy (to eliminate the residual energy chirp) the two unspoiled slices of the electron bunch generate a pair of collinear x-ray pulses with finite delay. In principle, for a double-slotted foil with slot separation Δx, the delay between the two unspoiled slices upon recompression can be estimated from [34]:

$$\begin{eqnarray}&&{\rm{\Delta }}t=\displaystyle \frac{{\rm{\Delta }}x}{\eta hCc},\end{eqnarray} \tag{ 1 }$$

where η is the momentum dispersion in the middle of the chicane, h is the degree of linear energy chirp introduced in the accelerator section prior to the magnetic chicane, C is the bunch compression factor, and c the speed of light in vacuum. Crucial beam parameters including bunch compression factor and initial chirp are difficult to calculate and are challenging to measure experimentally. Furthermore, it is not always accurate or desirable to assume that the bunch is initially linearly chirped. Even more important, due to shot-to-shot fluctuations it is not always clear that the 'unspoiled' parts of the bunch that pass through the slots in the foil will ultimately lead to amplified FEL emission, which is a highly nonlinear process.

As discussed in the introduction above, we used photoelectron streaking with single-cycle THz pulses as temporal diagnostic for the shaped x-ray pulses at LCLS since this method provides the capability for high-resolution consecutive, single-shot measurements. An overview of the THz streaking apparatus used for these measurements is shown schematically in figure 2. The x-ray pulses are focused onto a neon gas target and temporally and spatially overlapped with an intense linearly polarized THz pulse. The FEL pulse ionizes the gas target, producing a burst of photoelectrons with a temporal profile that replicates the profile of the incident photon pulse. The final kinetic energy of the electrons that compose the photoelectron burst is subsequently increased or decreased depending on their exact time of release into the THz field. The final kinetic energy, E_f, for an electron released at t₀ and observed parallel to the THz electric field, in atomic units, is given by [35]:

$$\begin{eqnarray}&&{E}_{f}({t}_{0})={E}_{i}-{p}_{i}A({t}_{0})+\displaystyle \frac{{A}^{2}({t}_{0})}{2}.\end{eqnarray} \tag{ 2 }$$

Here E_i and ${p}_{i}$ are the initial kinetic energy and momentum, respectively, of the electron, and A(t₀) is the THz vector potential at the instant of ionization. For a burst of photoelectrons emitted over a finite period of time, the photoelectron spectrum is broadened depending on the duration of emission and gradient of the streaking field. When the duration of the ionizing x-ray pulse is shorter than the half-cycle of the THz streaking field, the FEL pulse structure can be reconstructed from the measured photoelectron spectrum provided that the instantaneous THz vector potential is also known.

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X-rays delivered at LCLS were characterized at the atomic, molecular and optical end station. Two sets of experiments were performed using different methods of THz generation to optimize the dynamic range and measurement resolution. In the first set of experiments, single-cycle THz pulses were generated by rectification of near-IR laser pulses in lithium niobate (LN) by the tilted pulse-front method [36]. These pulses had a streaking field half-cycle of ∼660 fs, which gives an upper bound on the dynamic range of the measurement. While 660 fs is long enough to accommodate both the hundred-femtosecond timing jitter at LCLS [32, 37] and extended x-ray emission, the time resolution that can be achieved is limited to approximately 50 fs FWHM.

Therefore, in the second set of experiments, designed to measure shorter x-ray pulses and pulse structures below 50 fs, THz pulses were generated by rectification of IR laser pulses in the organic crystal DSTMS [38]. The resulting THz pulse has a frequency spectrum centred at ∼3 THz, compared to a spectrum centred at approximately 1 THz for pulses generated in LN. With higher frequency components, the THz streaking field is naturally steeper, providing higher time-resolution. However, the dynamic range of the measurement in this case is only ∼180 fs, which no longer accommodates the timing jitter at LCLS. To overcome this limitation, additional independent timing information is provided with ∼10 fs rms accuracy using the technique of spectral encoding [29, 31] as described in the methods section.

In the experiments, as shown in figure 2, THz pulses generated by either LN or DSTMS are overlapped with x-ray pulses with a photon energy of ∼1.0 keV and focused in a neon gas target where the 1 s core level is ionized. To establish temporal overlap, a series of single-shot photoelectron spectra is recorded as the set relative delay between standard, unshaped x-ray pulses and LN-THz pulses is scanned. The spectrogram shown in figure 3(a) is generated by averaging a series of sequential single-shot acquisitions. Here, the vector potential of the LN-THz pulse is clearly discernible, allowing the peak field strength to be accurately determined, which is crucial for calibration (see Methods). Next, the x-ray pulse was shaped by manipulating the electron bunch emittance in the magnetic chicane with the double-slotted spoiler. As shown schematically in figure 1, the spoiler has a V-shape so that the delay between x-ray pulse pairs can be tuned by varying the insertion depth of the foil. To verify control over the emitted pulse shape and delay between pulses, x-rays were observed as the foil was scanned.

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A characteristic measurement for one foil position is shown in figure 3, the streaked photoelectron spectrum is shown in figure 3(b), and the retrieved temporal profile is shown in figure 3(c). Here the observed delay between the x-ray pulses is ∼145 fs. Upon scanning the insertion depth, the maximum delay between the x-ray pulses was observed to be (215 ± 21) fs, while the minimum delay observed with this accelerator configuration was (65 ± 10) fs. As expected, the delay between the individual x-ray pulses in the double-pulse depends linearly on the insertion depth. The errors in the measured delays here and throughout the paper are determined from the numerical distribution of observed single-shot delays.

A crucial point, however, is that not all measurements revealed the double pulse structure in the streaked photoelectron spectrum. This indicates that the spoiler method is not guaranteed, highlighting the need for single-shot temporal diagnostics. The fraction of observed double-pulses was highest for the intermediate separation, while the double-pulse structure was less likely to be observed at the narrowest and furthest slot-separation. At the largest separation, when the double-pulse structure is not observed, it is believed that only one half of the x-ray pulse pair was produced. The production of only one half of the pulse pair may be due to inhomogeneity of the driving electron bunch in the far reaches of the leading and trailing edges of the electron bunch, which are the parts of the bunch that are unspoiled for this foil insertion depth in the magnetic chicane. In contrast, at the narrowest separation, where the delay is near the streaking measurement resolution, failure to observe the x-ray pulse pair is due to experimental limitation rather than a true absence of structure in the x-ray emission. This conclusion is supported by the second set of THz streaking measurements that were made with higher time-resolution.

Using DSTMS-generated THz pulses, with a rise time of ∼180 fs, time resolution of ∼20 fs FWHM was achieved. This value corresponds to the minimum separation between distinguishable peaks in an observed photoelectron spectrum and not the accuracy with which we can determine the separation between observed peaks. With this higher temporal resolution, LCLS was reconfigured to emit x-ray pulse pairs with smaller delay, which requires a higher compression factor in the compressor chicane. Under these conditions a spectrogram recorded at an intermediate slot-separation is shown in figure 4. By incorporating the independent arrival time information provided by the spectral timing tool, the averaged spectrogram can be constructed with an effective timing jitter of only 10 fs rms. As a result, the signal splits into two distinct curves around the zero-crossing of the THz streaking field, indicating the persistence of x-ray pulse pairs. Since the streaking effect is imprinted on both the positive and negative slope of the vector potential it should be possible to recover additional parameters such as the average chirp or spectral phase of individual pulses with our THz streaking technique [30]. Analysing the separation between the two THz vector potential curves in the averaged spectrogram at the field's zero-crossing gives a delay between the x-ray pulses of 56 fs. Complementary analysis of a single-shot measurement is plotted in figures 4(b) and (c), which yields a delay between the x-ray pulses of ∼54 fs, in agreement with the averaged measurement. In this set of experiments, the double-slotted spoiler and accelerator configuration were tuned to generate x-ray pulse pairs with a maximum measured time delay of (66 ± 4) fs and a minimum measured delay of (38 ± 6) fs.

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It should be noted that the minimum delay observed with the DSTMS-generated THz was not limited by the measurement resolution. This is evidenced by the fact that the modulation depth between the two pulses at the minimum observed delay of 38 fs is greater than 50% of the peak maximum. Nor was the minimum observed delay limited by the accelerator. Rather, a configuration of the machine that would have resulted in a narrower separation was not explored in this work. Nevertheless, it can be expected that x-ray pulse pairs with shorter delay can be generated and that with the current THz diagnostic, these pulse pairs can be distinguished to a minimum separation of ∼20 fs. As in the case for LN-based THz diagnostic, this limit is determined using the product of the field-free photoelectron bandwidth and the THz streaking strength.

The results of all pulse shaping and characterization measurements are summarized in figure 5. As previously mentioned, the delay between the x-ray pulses varies linearly with the separation between the slots in the spoiler. For comparison, the delay between the pulses can also be calculated. This requires simulating the linear accelerator configuration to obtain values for the momentum dispersion, chirp and compression factor, which are then substituted in equation (1). The calculation is overlaid on the experimental data points in figure 5. There is excellent agreement between the measured and calculated values, indicating that the machine parameters are relatively well known for this simple double-slotted spoiler case.

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THz streaking spectroscopy was used to verify paired x-ray pulse production at LCLS using the double-slotted spoiler. We employed two different THz sources, optical rectification from LiNbO₃ and from the organic nonlinear crystal DSTMS. Because of the longer streaking ramp of 600 fs, the LN source is best suited to measure longer x-ray pulse separations and provides absolute time-of arrival information with respect to the optical pump laser. In contrast the much shorter THz pulses from the DSTMS source provide temporal resolution of 20 fs or better but require additional jitter correction with a spectral encoding time tool.

In the future, single-cycle THz streaking could be used to optimize and diagnose the pair pulse production facilitating x-ray pump/x-ray probe experiments. While this is a basic demonstration of the concept of x-ray pulse shaping by electron beam manipulation, these advances may lead to more sophisticated, spectrally and temporally tailored pulse shapes for targeted experimental applications. Electron bunch manipulation, in combination with other new technologies, may even lead to intense isolated attosecond x-ray pulse generation with photon energy that can be freely tuned into the hard x-ray regime. Further into the future, reliable control over the electron beam momentum phase space would allow for emission of chirped x-ray pulses that could then be recompressed with dispersive x-ray optics [39]. This method has recently been demonstrated in the EUV regime [40], indicating that the methods of chirped pulse amplification that have been crucial to the development of high-power ultrafast laser science and technology may be extended to the hard x-ray regime.

The key to these and other future developments in machine and experimental applications will be the ability to temporally characterize the emitted FEL x-ray pulse. Here, using THz waveforms for streaking spectroscopy, a measurement resolution of ∼20 fs FWHM has been achieved. By using stronger THz fields, or shorter streaking wavelengths in the mid-IR and IR, the resolution can be improved to accommodate sub-femtosecond x-ray pulses or pulses with substructure on the attosecond time scale.

Portions of this research were carried out at the Linac Coherent Light Source (LCLS) at the SLAC National Accelerator Laboratory. Use of the Linac Coherent Light Source (LCLS), SLAC National Accelerator Laboratory, is supported by the US Department of Energy, Office of Science, Office of Basic Energy Sciences under Contract No. DE-AC02-76SF00515. DCU contribution was made possible under Science Foundation Ireland IvP Grant No. 12/IA/1742 and the EU EMJD 'EXTATIC' under framework partnership agreement FPA-2012-0033. M I acknowledges funding from the Volkswagen foundation within the Peter Paul Ewald-Fellowship. WH, RK and WS acknowledge funding from the Bavaria California Technology Center (BaCaTeC). MMes acknowledges support by NSF award 1231306. KZ and GD acknowledge support from US NSF grant PHY-1004778 and US DOE grant DE-FG02-04ER15614. SL acknowledge support from NRF-2014M3C1A8048818, NRF- 2014M1A7A1A01030128, NRF-2016K1A3A7A09005386. CB and GD are supported by the U.S. Department of Energy, Office of Basic Energy Sciences, Division of Chemical Sciences, Geosciences, and Biosciences under contract DE-AC02-06CH11357.T.M. and M.M. acknowledge support by the Deutsche Forschungsgemeinschaft (DFG) under Grant No. SFB925/A1.ARM acknowledges fundingby BMBF-05K16GU2.

The authors would like to thank Steve Edstrom for expert laser support and Nick Hartmann for help with the spectral encoding time-tool.

ALC and MCH conceived the experiment. CB, Ch B, JB, HBALC, RC, JTC, LFD, YD, GD, IG, WH, MCH, MI, RK, SL, ARM, TM, MM, MMes, SS, WS and KZ performed the experiment. YD implemented the double-slotted spoiler. RC devised spectral encoding time-tool. IG, HB, ALC, SL and TM performed the data analysis. IG, CB, ALC, JTC, LFD, MCH and MM contributed significantly in the preparation of the manuscript.