Single $\mathrm{sub}\text{−}50\text{−}\text{attosecond}$ pulse generation from chirp-compensated harmonic radiation using material dispersion

A method for obtaining a single $\mathrm{sub}\text{−}50\text{−}\text{attosecond}$ pulse using harmonic radiation is proposed. For the generation of broad harmonic radiation during a single half-optical cycle, atoms are driven by a femtosecond laser pulse with intensity above the saturation intensity for optical field ionization and hence experience a large nonadiabatic increase of the laser electric field between optical cycles. Although the chirped structure of the harmonic radiation imposes a limit on the minimum achievable pulse duration, we demonstrate that its positive chirp can be compensated by the negative group delay dispersion of an appropriately selected x-ray filter material, used also for the spectral selection, resulting in a single attosecond pulse with a duration less than $50\mathrm{as}$.

Figure 1

(Color online) Spectrogram of the harmonic radiation from neon atoms exposed to $5\text{−}\mathrm{fs}$, $800\text{−}\mathrm{nm}$ pulse with peak intensity (at the medium) of (a) $4.7\times {10}^{15}\mathrm{W}∕{\mathrm{cm}}^2$ and (b) $7.0\times {10}^{14}\mathrm{W}∕{\mathrm{cm}}^2$. The dotted lines represent the short-trajectory component of the harmonic radiation obtained from the semiclassical calculation. The figures on the right side of the spectrogram show the harmonic spectra.

Figure 2

(Color online) Real and imaginary parts of the refractive index of a Sn filter. The spectral range of negative GDD is marked as a thick red line.

Figure 3

(Color online) (a) Chirp compensation of positively chirped harmonic radiation by a Sn x-ray filter. The spectral phase of the harmonic radiation with a positive linear chirp centered at $107{\omega }_0$, ${\tilde{\varphi }}_h\left(\omega \right)$, and the spectral phase shift induced by a $700\text{−}\mathrm{nm}$-thick Sn filter, $\mathrm{\Delta }{\tilde{\varphi }}_{\text{filter}}\left(\omega \right)$, are shown, respectively, by dotted and dashed lines. The spectral phase of the harmonic radiation after the Sn filter is shown as the solid line. (b) Spectral intensity of the harmonic radiation corresponding to Fig. 1a, transmitted through the Sn filter (solid line) and the transmittance of the Sn filter (dash-dotted line).

Figure 4

(Color online) Temporal profile of the chirp-compensated attosecond pulse in the $700\text{−}\mathrm{nm}$ Sn x-ray filter is shown along with the electric field of the $5\text{−}\mathrm{fs}$ driving laser pulse.