Decreasing ultrafast x-ray pulse durations with saturable absorption and resonant transitions

Saturable absorption is a nonlinear effect where a material's ability to absorb light is frustrated due to a high influx of photons and the creation of electron vacancies. Experimentally induced saturable absorption in copper revealed a reduction in the temporal duration of transmitted x-ray laser pulses, but a detailed account of changes in opacity and emergence of resonances is still missing. In this computational work, we employ nonlocal thermodynamic equilibrium plasma simulations to study the interaction of femtosecond x rays and copper. Following the onset of frustrated absorption, we find that a $K\text{–}M$ resonant transition occurring at highly charged states turns copper opaque again. The changes in absorption generate a transient transparent window responsible for the shortened transmission signal. We also propose using fluorescence induced by the incident beam as an alternative source to achieve shorter x-ray pulses. Intense femtosecond x rays are valuable to probe the structure and dynamics of biological samples or to reach extreme states of matter. Shortened pulses could be relevant for emerging imaging techniques.

Figure 1

Schematic representation of a 1D simulation that follows the effects of an incident Gaussian pulse $I_0\left(t\right)$ in the material and monitors transmission $I_{\mathrm{T}}\left(t\right)$ and fluorescence $I_{\mathrm{F}}\left(t\right)$ intensities. Electron and ion temperatures, radiation landscape, and electronic state are sampled at nine different nodes. The transmission and fluorescence spectra were taken from the back node along the forward direction over a $2\pi$ solid angle.

Figure 2

Calculated intensity at the (a) front and (b) back of the copper slab irradiated with a $3.5\times {10}^5\mathrm{J}$/${\mathrm{cm}}^2$ pulse. We did not consider a specific detector distance and neglected intensity decays following the inverse square law. $K{\alpha }_1=8012$ eV, $K{\alpha }_2=7992$ eV, and $K{\beta }_1=8868$ eV. (c) Incident, transmitted (9000 eV), and fluorescent (8006 eV) pulse durations with increasing fluence. Error bars represent a $95\%$ confidence bound of the best fit's width.

Figure 3

(a) Average ion charge at the end of the pulse and (b) maximum $K$-shell population created in the material. The incident photon energy is not large enough to create a second core hole state. We attribute the nonzero $1s^0$ state population to electron-ion collisional ionization. If the rate of this process is faster than the relaxation time of photoionization, a single core hole state can become doubly ionized.

Figure 4

(a) Radiation dynamics for a $3.5\times {10}^5$ J/${\mathrm{cm}}^2$ incident beam revealed transmission occurred early in the radiation exposure and extinguished before the peak of the incident pulse at 30 fs. (b) Transmission profiles shifted earlier in time with increasing fluence and (c) emission at 8006 eV became wider with increasing fluence. (d) Summary of peak intensity times. The small variations in the order of subfemtoseconds are due to a combination of the dynamic time step and finite temporal resolution of the simulations.

Figure 5

(a)–(c) Opacity averaged over all zones showing displacement of the $K$-edge and resonant $K\text{–}M$ transition for three incident fluences. The vertical dashed line indicates the XFEL pulse photon energy. Horizontal lines in (b) are cuts through the absorption shown in the three panels to the right. (d)–(f) Opacities at $3.5\times {10}^5$ J/${\mathrm{cm}}^2$ averaged over all zones at three instances during the simulation. The 10 fs snapshot shows opacities for a cold sample, the 27 fs shows a dip in the opacity at 9 keV, and the 33 fs snapshot shows an increased opacity at 9 keV.

Figure 6

(a) Transmission and (b) fluorescence durations for an incident beam of varying photon energy and 7 fs FWHM. At 9 keV, fluorescence is prolonged by the resonant $K\text{–}M$ transition. The resonance does not extend to 9.1 keV, causing the fluorescence signal to become temporally shorter. See the Supplemental Material [21] for full spectra comparison.