Pulse Duration of Seeded Free-Electron Lasers

The pulse duration, and, more generally, the temporal intensity profile of free-electron laser (FEL) pulses, is of utmost importance for exploring the new perspectives offered by FELs; it is a nontrivial experimental parameter that needs to be characterized. We measured the pulse shape of an extreme ultraviolet externally seeded FEL operating in high-gain harmonic generation mode. Two different methods based on the cross-correlation of the FEL pulses with an external optical laser were used. The two methods, one capable of single-shot performance, may both be implemented as online diagnostics in FEL facilities. The measurements were carried out at the seeded FEL facility FERMI. The FEL temporal pulse characteristics were measured and studied in a range of FEL wavelengths and machine settings, and they were compared to the predictions of a theoretical model. The measurements allowed a direct observation of the pulse lengthening and splitting at saturation, in agreement with the proposed theory.

Popular Summary

Imaging matter at the molecular level requires more than a simple camera. By firing laser pulses at a sample of material and measuring how the light scatters and diffracts on a time scale that outruns radiation damage, researchers deduce the underlying physical structure of the sample. Capturing rapid changes as well requires a laser that is capable of generating pulses just a few millionths of a billionths of a second (a femtosecond) long. Free-electron lasers (FELs) deliver femtosecond pulses by accelerating a beam of electrons through a series of magnets, which in turn produces highly energetic photons that are then concentrated into a focused beam. Knowing the precise duration of the laser pulses is critical, but it is difficult to measure precisely. We characterized the shape of laser pulses generated at a novel FEL facility and confirmed that it routinely generates pulses lasting a few tens of femtoseconds.

The FERMI laser at Elettra-Sincrotrone Trieste in Italy is a novel class of FEL that is first seeded by an external conventional ultraviolet laser. Seeding the FEL enhances the longitudinal coherence of the pulses, which enhances stability, temporal coherence, and bandwidth. We measured, for the first time, the pulse duration of FERMI in a wide variety of conditions with two different setups based on the cross-correlation of the FEL pulse with an external optical laser. Our measurements are in mutual agreement and consistent with theoretical predictions.

Knowledge of a FEL’s pulse shape is essential to its scientific investigations. Our methods can provide an online diagnostic for not just FERMI but also FELs at other facilities, regardless of their mode of operation.

Figure 1

Layout of a HGHG FEL: UV seed and electrons are superimposed in a first modulator. The UV laser pulse imprints its temporal properties on the electron energy distribution; a dispersive section converts the energy modulation into a density modulation at the seed wavelength ${\lambda }_0$ and at its higher harmonics; the radiator, with resonance tuned to a specific harmonic $n$, amplifies this harmonic.

Figure 2

Pulse longitudinal profile [Eq. (9), with $n=10$] as a function of the normalized longitudinal coordinate $\zeta /{\sigma }_{\zeta }$ and of the modulation-dispersion product (left panel). Pulse longitudinal profiles (right panel) at selected ${\chi }_{10}$ positions. The dotted line (a) shows ${\chi }_{10}=0.8{\chi }_{10}^{\max }$, the solid line (b), ${\chi }_{10}={\chi }_{10}^{\max }$, and the dashed line (c), ${\chi }_n=1.2{\chi }_{10}^{\max }$.

Figure 3

Relative pulse length ${\sigma }_{\zeta }^{\mathrm{FEL}}(n,{\chi }_n)/{\sigma }_{\zeta }$, as a function of the harmonic conversion order $n$. Solid black line: ${\chi }_n={\chi }_n^{\max }$. Black dotted line: ${\chi }_n=0.5{\chi }_n^{\max }$. Black dashed line: ${\chi }_n=1.1{\chi }_n^{\max }$. Red dashed line: Solution in the limit ${\chi }_n\ll {\chi }_n^{\max }$, i.e., the function ${\sigma }_{\zeta }^{\mathrm{FEL}}/{\sigma }_{\zeta }=1/\sqrt{n}$. Blue dashed line: The function $7/(6n^{1/3})$.

Figure 4

Pulse length vs the function ${\chi }_n(\mathrm{\Delta }\gamma ,R_{56})$ for three different harmonics: $n=4$ (left panel), $n=8$ (center panel), and $n=13$ (right panel). Dashed line: The approximating function, Eq. (14).

Figure 5

Increase of the pulse duration associated with saturation effects at the end of the radiator. The behavior is independent of the harmonic order if the abscissa is scaled by the FEL gain length $L_g$. The vertical line indicates the condition of undulator length equal to the saturation length $L_u=z_{\mathrm{sat}}$ occurring after approximately 10 gain lengths in this example.

Figure 6

Layout of the FERMI beam transport section. The DiProI and LDM experimental stations share a common photon transport system that includes a beam-defining aperture (BDA), photon beam position monitors (BPM), a gas cell monitoring the FEL fluency (I0M), a gas attenuator (GA), a solid-state photon yield detector (PYD), an energy spectrometer, an autocorrelator, and plane steering mirrors [74, 75, 76]. On LDM and DiProI, the FEL beam is focused by a system of KB mirrors [77].

Figure 7

Two-color (FEL at 25.78 nm, IR at 784 nm) photoelectron spectra of atomic He acquired at time delay $\mathrm{\Delta }t=0$ for IR intensities: (a) about $3.2\times {10}^{12}\mathrm{W}/{\mathrm{cm}}^2$ (used for the pulse duration on FEL-1) and (b) about $4.3\times {10}^{13}\mathrm{W}/{\mathrm{cm}}^2$ (maximum intensity available).

Figure 8

Cross-correlation curves derived from He sidebands as a function of the delay between the FEL and IR pulses. (a) FEL-1 pulses, IR intensity of about $3.2\times 10^{12}\mathrm{W}/{\mathrm{cm}}^2$. (b) FEL-2.1 pulses, IR intensity of about $1.4\times 10^{13}\mathrm{W}/{\mathrm{cm}}^2$.

Figure 9

(a) Autocorrelation signal (dotted black line) of the noncollinear optical parametric amplifier (NOPA) probe, pumped by the FERMI IR laser (784 nm, 100 fs, $200\mu \mathrm{J}$). Reconstructed temporal pulse shape from dispersion modeling (blue line) and Gaussian fit of pulse shape (red line). (b) Spectrum of the NOPA signal centered at 630 nm. (c) Schematic of the experimental setup.

Figure 10

(a) Single-shot cross-correlation curve from a ${\mathrm{Si}}_3{\mathrm{N}}_4$ target (grey): ${\tau }_{\mathrm{seed}}=157.5\mathrm{fs}$, FEL wavelength 26.17 nm; fits calculated with the cross-correlation simple model (yellow line) and the full-scale cross-correlation function (red line). (b) Solid black line: Retrieved single-shot pulse structure $I_{\mathrm{FEL}}(t)$. Solid red line: FEL gating function. The single-shot pulse duration is ${\tau }_{\mathrm{FEL}}=74.9\mathrm{fs}$. (c) Series of $N=100$ single-shot cross-correlation curves (smoothed) normalized between a transmission (T) of 1 and 0; ${\tau }_{\mathrm{seed}}=112.5\mathrm{fs}$. The spatial position of the transient edge depends on the relative arrival time between the probe laser and the FEL pulse. Measured average pulse duration ${\tau }_{\mathrm{FEL}}=(51.2\pm 2.0)\mathrm{fs}$; average time-of-arrival jitter is 2.2 fs (rms).

Figure 11

Summary of measurements. Blue squares show method A; green triangles show method B. These measurements are associated with data in Table 1 corresponding to the normal “optimized” configuration ($\mathrm{mode}=\mathbf{n}$). Red dashed line: The function $1/\sqrt{n}$. Blue dotted line: Optimized peak bunching factor, scaling as about $7/(6n^{1/3})$. The red points, obtained with an excess of seed power or dispersion, causing an evident broadening in the spectrum ($\mathrm{mode}=\mathrm{s}$ in Table 1), are instead characterized by a systematic larger duration.

Figure 12

(a) Cross-correlation curve at a wavelength ${\lambda }_{\mathrm{FEL}}=42.96\mathrm{nm}$ (6th harmonics) for the source FEL-1 measured with method A. (b) Wavelength dispersion of the pulse (average over 200 shots) as measured with the beam-line spectrometer PRESTO. Temporal and wavelength profiles were fitted with two Gaussian peaks (solid black lines).

Figure 13

Measured FEL pulse duration and bandwidth of 200 consecutive shots at fixed machine conditions. Blue dots are the measured data, the dashed black line shows the theoretical curve for FEL pulses with a perfect FT-limited Gaussian profile, and the solid red line is the bandwidth as a function of the duration of an ideal Gaussian pulse with chirp $\alpha \sim 4\times {10}^{26}\mathrm{rad}/{\mathrm{s}}^2$ (corresponding to a group delay dispersion of about $540{\mathrm{fs}}^2$). All FEL pulse durations are measured with the single-shot cross-correlation. The red stars represent the grouped average of the data points.

Figure 14

Pulse temporal profile as a function of the $R_{56}$ parameter. Left panel: Single-shot cross-correlation retrieved FEL temporal pulse profile. Right panel: Temporal separation of the split pulses at $R_{56}>40\mu \mathrm{m}$ (blue diamonds); separation calculated from Eq. (9) under the assumption that ${\chi }_n={\chi }_n^{\max }$ is obtained at $R_{56}=40\mu \mathrm{m}$ (black dashed line); pulse separation estimated from the spectral traces in Fig. 15 (green diamonds).

Figure 15

Spectrum of the radiation at the corresponding values of dispersion as shown in Fig. 14. Each image is the result of an average over five single-shot acquisitions; the spectral features are relatively stable in time.