Observation of Reverse Saturable Absorption of an X-ray Laser

A nonlinear absorber in which the excited state absorption is larger than the ground state can undergo a process called reverse saturable absorption. It is a well-known phenomenon in laser physics in the optical regime, but is more difficult to generate in the x-ray regime, where fast nonradiative core electron transitions typically dominate the population kinetics during light matter interactions. Here, we report the first observation of decreasing x-ray transmission in a solid target pumped by intense x-ray free electron laser pulses. The measurement has been made below the $K$-absorption edge of aluminum, and the x-ray intensity ranges are ${10}^{16}–{10}^{17}\mathrm{W}/{\mathrm{cm}}^2$. It has been confirmed by collisional radiative population kinetic calculations, underscoring the fast spectral modulation of the x-ray pulses and charge states relevant to the absorption and transmission of x-ray photons. The processes shown through detailed simulations are consistent with reverse saturable absorption, which would be the first observation of this phenomena in the x-ray regime. These light matter interactions provide a unique opportunity to investigate optical transport properties in the extreme state of matters, as well as affording the potential to regulate ultrafast x-ray free-electron laser pulses.

Figure 1

Measurement of x-ray transmission through an aluminum foil target. Each circle represents the data from a single shot. The red line is the known transmission value of cold Al from the CXRO database. The peak intensities of the highest pulse energies (pink circles) correspond to $\sim {10}^{17}\mathrm{W}/{\mathrm{cm}}^2$.

Figure 2

(a) Simulation of transmitted x-ray spectra through an aluminum sample at selected intensities (1, 3, 10, $30\times {10}^{16}\mathrm{W}/{\mathrm{cm}}^2$). The incident and final transmitted spectra are depicted in the red and blue curves. The sample is divided into 10 laminae, and the transmission after each lamina is shown in gray. Each curve is normalized to the highest spectral intensity of the incident spectrum. (b) Final transmission spectra, obtained by the blue divided by the red curves in (a), for $I=1–50\times {10}^{16}\mathrm{W}/{\mathrm{cm}}^2$. (c) Absorption coefficient of aluminum as a function of peak intensity. The circles represent the experimental data at 1485–1490 eV. The dashed line is the theoretical prediction from scfly. Note the intensity in (a) and (b) is at a single value without considering the intensity distribution of the XFEL focal spot. But in (c), the calculation includes the intensity distribution of the focal spot. Inset: Some simulation of transmitted SASE spectra. The incident spectra are corresponding to Gaussian profiles of 100 fs and 5 eV FWHM and a peak intensity of $\sim 1\times {10}^{17}\mathrm{W}/{\mathrm{cm}}^2$. In the main plot, the range of calculated absorption of 100 SASE pulse is shown as a green box.

Figure 3

(a) Temporal evolution of the spectral intensity (SI) of the resonant x-ray photons through each lamina. Lamina “0” above the dashed line represents the incident x-ray pulse. The SI is normalized to the peak value of each incident pulse. (b) For the case of $1\times {10}^{17}\mathrm{W}/{\mathrm{cm}}^2$, the top panel shows the SI through each lamina, and the second to fourth panels display the temporal evolution of the charge state (CS) III–V at each lamina. The first (1) and the last (10) laminas are plotted with thick solid lines.