Spectrotemporal Shaping of Seeded Free-Electron Laser Pulses

We demonstrate the ability to control and shape the spectrotemporal content of extreme-ultraviolet (XUV) pulses produced by a seeded free-electron laser (FEL). The control over the spectrotemporal properties of XUV light was achieved by precisely manipulating the linear frequency chirp of the seed laser. Our results agree with existing theory, which allows us to retrieve the temporal properties (amplitude and phase) of the FEL pulse from measurements of the spectra as a function of the FEL operating parameters. Furthermore, we show the first direct evidence of the full temporal coherence of FEL light and generate Fourier limited pulses by fine-tuning the FEL temporal phase. The possibility of tailoring the spectrotemporal content of intense short-wavelength pulses represents the first step towards efficient nonlinear optics in the XUV to x-ray spectral region and will enable precise manipulation of core-electron excitations using the methods of coherent quantum control.

Figure 1

The high-gain harmonic generation scheme. After interacting with the seed laser in the first undulator (modulator) and with the magnetic field of the dispersive section, the relativistic $e$ beam develops periodic density modulations (bunching) at harmonics of the seed wavelength. The microbunched $e$ beam is then injected into the second undulator (radiator), whose periodic magnetic field forces the electrons to emit coherent and powerful light pulses in the XUV or soft-x-ray region. The spectrotemporal properties of radiation are controlled by manipulating the seed laser electric field.

Figure 2

FEL pulse shaping through manipulations of the electron bunching envelope and FEL phase. (a) Theoretical bunching envelope [square modulus of $b_n(t)$, Eq. (1)], corresponding to the temporal FEL pulse shape, as a function of the dimensionless dispersive strength ($B$). Just before the bifurcation $B$ is optimized for maximum bunching, resulting in a single peak. Increasing $B$ leads to peak splitting due to electron overbunching in the central part. The envelope develops a multipeak structure as a result of electron rebunching when $B$ is increased even further. (c) The spectral map (FEL spectrum as a function of $B$) strongly depends on the FEL phase (b). For a significantly chirped FEL pulse there is a direct correspondence between the temporal and spectral domains (top). On the other hand, the spectral map of a Fourier limited pulse (with a flat phase) develops distinctive features with increasing $B$ due to interference between the individual peaks in the multipeak bunching structure (bottom). For the sake of visualization, the bunching and spectral maps are normalized in amplitude for each value of $B$.

Figure 3

FEL pulse spectra as a function of the dimensionless dispersive strength for three different conditions of the linear frequency chirp on the seed laser. (a) Significant positive chirp, (b) moderate positive chirp, and (c) slight negative chirp for chirp compensated FEL pulses. Insets are theoretical spectral maps reproduced using Eqs. (1) and (2) in the spectral domain. The wavelength shift (spectral map tilting) in (c) is due to the contribution of a linear-term coefficient $d\varphi (t)/dt$ from the $e$-beam energy profile. The experiment in (a) was done at $n=10$ using all of the six 2.4-m-long radiator sections, while for (b) and (c) $n=8$ and the number of active radiator sections was 4 and 5, respectively. In all cases, the $e$-beam energy, energy spread, current, bunch charge, and emittance were $\simeq 1.3\mathrm{GeV}$, $\simeq 150\mathrm{keV}$, $\simeq 600\mathrm{A}$, $\simeq 500\mathrm{pC}$, and $\simeq 1\mathrm{mm}\mathrm{mrad}$, respectively. For (a) and (b), the $e$-beam (positive) quadratic energy curvature was $\simeq 5\mathrm{MeV}/{\mathrm{ps}}^2$, while for (c) the value was $\simeq 12\mathrm{MeV}/{\mathrm{ps}}^2$. The data were acquired with a dedicated spectrometer [32, 33]. The maps in (a) and (b) consist of 10 accumulated single-shot spectra for each value of $B$, while data in (c) were taken by summing 3 multishot spectra (10 shots). The data within each spectral slice (for fixed $B$) are normalized in amplitude for better visualization.