Zeptosecond High Harmonic keV X-Ray Waveforms Driven by Midinfrared Laser Pulses

We demonstrate theoretically that the temporal structure of high harmonic x-ray pulses generated with midinfrared lasers differs substantially from those generated with near-infrared pulses, especially at high photon energies. In particular, we show that, although the total width of the x-ray bursts spans femtosecond time scales, the pulse exhibits a zeptosecond structure due to the interference of high harmonic emission from multiple reencounters of the electron wave packet with the ion. Properly filtered and without any compensation of the chirp, regular subattosecond keV waveforms can be produced.

Figure 1

(a) Envelope of the x-ray bursts (dark blue line) and group delay (light blue line) obtained using a $3.9\mu \mathrm{m}$ wavelength laser. The HHG spectrum is shown in the inset, whereas in the panels below the spectral content of each burst is shown. (b) Schematic of the driving field and an example of the interfering trajectories contributing to the fs burst at 71 fs. (c) Time-frequency analysis (logarithmic scale). The dotted lines represent classical calculations of the electronic rescattering energies of trajectories with different rescattering orders.

Figure 2

(a) Detailed structure of an x-ray burst from the tailing edge of the keV pulse train shown in Fig. 1. The spectrum of the selected burst is shown in (b) for Al filters of 0.1 and $0.5\mu \mathrm{m}$ thickness. Plots (c) and (d) show a magnification of the temporal structure for the two Al filters, respectively, whereas (e) corresponds to the x-ray field obtained by selecting only the highest frequency contributions to the spectra.

Figure 3

(a) Predictions for the width of each keV beat in the waveform ($T/2$) as a function of the laser wavelength. (b) Envelope of the x-ray bursts obtained from a 1.5-cycle mid-IR pulse with wavelength $\lambda =9\mu \mathrm{m}$. Left insets: electric field of the driving pulse and high harmonic spectrum. Right inset: spectral content of the second fs burst. Panels (c)–(e) detail the fine temporal structure of the second fs burst: (solid pink line) absolute value of the electric field, and (dashed blue line) field envelope.