Spatiotemporal shaping of attosecond X-rays with time-dependent orbital angular momentum

Abstract

Attosecond X-ray pulses are indispensable for exploring ultrafast phenomena in matter on Angstrom and attosecond scales. Here we propose a new method to realize spatiotemporal shaping of attosecond X-rays through temporal control of the orbital angular momentum mode content using an X-ray free-electron laser. The method exploits transverse-mode-dependent frequency pulling in a deliberately detuned second stage, together with slippage between the seed and the amplified radiation. Three-dimensional simulations show a double-spike waveform in which the two spikes carry different dominant topological charges. The spike separation is tunable and can reach several hundred attoseconds. This provides a source-level route to spatiotemporally structured attosecond X-rays with controllable temporal structure and topological mode content.

Figures (4)

• Figure 1: Schematic of the generation of attosecond X-ray pulse pairs with different dominant topological charges. Temporal power of the FEL pulse at (a) the end of the first stage, (b) the entrance of the second stage and (c) the end of the second stage. The electron-beam head is on the left-hand side of each panel.
• Figure 2: Simulation results under various detuning conditions. (a) and (b) show results for pure mode seed pulses. (a) Pulse energy at the exit of the first undulator segment for different transverse modes. (b) Undulator length required for the pulse energy to increase by a factor of $e$. (c)–(f) show results for mixed mode seed pulses. (c) Power profile at the position where the pulse energy has increased by a factor of $e$. (d) Energy gain of different modes as a function of reduced detuning. (e) Temporal power profile at the exit of the twelfth undulator segment for $\hat{C}=4.2$. (f) Temporal power profile for $m=0$ and $m=2$ mode at the exit of the seventh undulator segment for $\hat{C}=2.0$.
• Figure 3: (a) Temporal power at the end of the second stage for 200 simulation runs. Thin lines show individual single-shot realizations, and thick lines show the ensemble-averaged power for the $m=0$ (red) and $m=1$ (blue) components. (b) Scatterplot of $E_{m=1}$ versus $E_{m=0}$ for the head (blue) and tail (red) spikes, where the pulse energies are evaluated within the FWHM window of each spike. (c) Scatterplot of $t_{m=1}$ versus $t_{m=0}$ for the head (blue) and tail (red) spikes, where the arrival time is defined as the intensity-weighted temporal centroid within the same window.
• Figure 4: (a) Temporal power of the second-stage radiation as a function of the reduced detuning parameter $\hat{C}$ for a representative single-run simulation. The blue and red lines trace the tail and head spikes, respectively. (b) Temporal separation between the two spikes as a function of $\hat{C}$. The solid line shows a representative single-run result, while the points indicate the statistical spread obtained from 20 shot-noise simulation runs at each value of $\hat{C}$. (c),(d) Single-run power of the $m=0$ (red) and $m=1$ (blue) components sampled at the positions of the head spike (c) and the tail spike (d), respectively. In panels (b)–(d), only values of $\hat{C}$ for which two distinct spikes can be clearly resolved are shown.