Spectrotemporal control of soft x-ray laser pulses

We exploit echo-enabled harmonic generation (EEHG) to produce fully coherent free-electron laser (FEL) pulses at soft-x-ray wavelengths and shape their spectrotemporal content. In an EEHG FEL, the longitudinal phase space of the relativistic electron beam that amplifies light is precisely tailored using two external seed lasers and two magnetic chicanes. We show that the spectrotemporal properties of the emitted radiation can be controlled by tuning the bandwidth, linear frequency chirp, and intensity of one of the seed lasers. The experimental data are supported by analytical and numerical models. Our results open a pathway toward coherent control of quantum processes at short wavelengths in the fields of applied physics, chemistry and biology, where manipulating the radiation spectrum is essential. The ability to precisely control the spectrotemporal content of intense, short-wavelength FEL pulses and the low sensitivity of the radiation to electron-beam imperfections make the technique an ideal candidate for use in chirped-pulse amplification schemes.

Figure 1

The components of the EEHG scheme: first modulator (M1), first (strong) dispersive section (DS1), second modulator (M2), and second (weaker) dispersive section (DS2); see text for details. The nanobunched electron beam exiting DS2 is injected into the radiator (R), whose periodic magnetic field forces the electrons to emit coherent and powerful EUV or soft-x-ray pulses.

Figure 2

Normalized single shot EEHG spectra at the 36th harmonic in the $n=-1$ tune for (a) short and (b) long second seed pulses. (c) Relative FEL bandwidth as a function of the second seed GDD: red crosses are experimental data (error bars show RMS fluctuations), while the dashed black and solid blue lines show the relative bandwidths obtained from Eq. (2) and Eq. (4), respectively (see text for details). The inset shows the central wavelength stability as a function of the second seed GDD. The data in c) were acquired in the $n=-2$ tune.

Figure 3

FEL spectrum vs seed modulation amplitude $A_2$ for a GDD of (a) $-4100{\mathrm{fs}}^2$, (b) $0{\mathrm{fs}}^2$, and (c) $+2000{\mathrm{fs}}^2$. The spectral maps were obtained by averaging the FEL spectrum at harmonic 37 over 50 shots and normalizing the result for each value of $A_2$. Insets show calculated spectral maps reproduced using Eq. (2). In all cases, $A_1\simeq 4$, $B_1=11.4$, while $B_2$ was adjusted to maximize bunching. The experimental spectral maps at short wavelengths in (b) and (c) are less intense probably due to the FEL gain (not taken into account in the calculations), as well as due to a possible small mismatch between the optimum and actual EEHG parameters. The relative variation of the FEL intensity with $A_2$ for all cases is shown in (d).

Figure 4

Normalized square modulus (blue solid line, corresponding to the FEL pulse envelope) and phase (red dashed line, corresponding to the FEL phase) of the bunching factor in the time domain $b(t)$, obtained from the Fourier transform of the (calculated) bunching spectra indicated along the dashed lines in the insets of Fig. 3 for (a) $\mathrm{GDD}=-4100{\mathrm{fs}}^2$, (b) $\mathrm{GDD}=0{\mathrm{fs}}^2$, and (c) $\mathrm{GDD}=2000{\mathrm{fs}}^2$.