Dynamical diffraction of ultrashort X-ray free-electron laser pulses

Abstract

Calculations are presented for the femtosecond time‐evolution of intensities of beams diffracted by perfect Bragg crystals illuminated with radiation expected from X‐ray free‐electron lasers (XFELs) operating through the self‐amplified spontaneous emission (SASE) process. After examining the case of transient diffraction of an electromagnetic delta‐function impulse through flat, single‐ and double‐crystal monochromators, the propagation of a 280 fs‐duration SASE XFEL pulse of 8 keV photons through the same optics is discussed. The alteration of the sub‐femtosecond spiky microbunched temporal structure of the XFEL pulse after it passes through the system is shown for both low‐order (broad bandwidth) and high‐order (narrow bandwidth) crystal reflections. Finally, the shot‐to‐shot statistical fluctuations of the integrated diffracted intensity is simulated. Implications of these results for XFEL applications are addressed.

Single shot speckle and coherence analysis of the hard X-ray free electron laser LCLS

“…12 (b). An additional source of broadening also comes from the transient response of the crystal, which is expected to be about 5 fs [38]. A convolution of these effects leads to the final pulse duration of 31 fs that lies within uncertainty of our experimental result.…”

Short X-ray pulses in a Laue-case crystal

“…An observer at a ®xed position behind the crystal will see the intensity in a time interval that is easily calculated from (17), recalling that z H is restricted to the interval [0, 2T ], Át 2T sin 2 Âa c cos  Y 23 a result already found by Shastri et al (2001a). However, their treatment did not involve the refractive effects in Laue geometry.…”

“…In this paper, the time-dependence of X-ray diffraction is considered by describing the input radiation as an integral over plane waves, then the results of the dynamical theory are used for steady-state plane waves, and ®nally the time-dependent output radiation is obtained by Fourier backtransform, thereby following the approach of Shastri et al (2001a). Time-dependent fundamental equations such as the time-dependent Takagi±Taupin equations (Chukovski & Fo È rster, 1995) are not used.…”

Reflection of attosecond x-ray free electron laser pulses

“…Previous work on the time-dependent diffraction of x-ray pulses from semi-infinite Si crystals has shown that the (111) reflection has a transient response that decays within a few femtoseconds for a photon energy of 8 keV. It was also found that this decay is slower for higher order reflections [10][11]. Such a diffractive optic is based on the volumetric (and thereby slow) response of the material and may be not suitable for pulses that are shorter than a femtosecond.…”

“…We found that the materials continue to emit energy after the pulse has ended, as shown in Figure 2 for the case of silicon. Whereas Bragg reflections take a few femtoseconds or longer to decay [10][11], we found the impulse response time for normal surface reflections away from the Bragg peaks andfor noncrystalline materials to be shorter than 0.3 fs, see Figure 3. The impulse response time is substantially shorter (less than 0.3 as for o 1 .…”