Temporal Structure of Attosecond Pulses from Intense Laser-Atom Interactions

We find that the high harmonics have a power-law spectrum $I_{\omega }\sim {\omega }^{-3.3\pm 0.25}$ in a wide frequency domain starting at the ionization potential $I_p$ and down to the plateau beginning. Our spectrotemporal analysis of the emitted radiation displays clear bowlike structures in the $(t,\omega )$ plane. These “bows” correspond to Corkum’s reencounters of the freed electron with the atom. We find that the bows are not filled and thus cannot be due to any bremsstrahlung. Rather, it is a resonant process that we call stimulated recombination (SR). It occurs when an electron with momentum $p$ reencounters the incompletely ionized atom, and interferes with itself still remaining in the ground state. The SR leads to a highly efficient resonant emission at $\hslash \omega =p^2/2m+I_p$ in the form of attosecond pulses. The SR relies on a low level of ionization and strongly benefits from the use of few-cycle laser pulses.

Figure 1

Spectral intensity (arbitrary units) of high harmonics for laser pulses with ponderomotive potentials $U_p=11$, 22, 44, and 93 eV.

Figure 2

Temporal profile of the radiation for the case $U_p=44\mathrm{e}\mathrm{V}$. (a) No filter applied: irregular pattern due to the lower harmonics. (b) Filter at 160 eV: a single ASP. (c) Filter at 130 eV: the ASP splits into two twins, and another ASP emerges $1/2$ laser period later. (d) Filter at 100 eV: separation between the first twins increases; the second ASP splits as well. The filter width applied here is 15 eV.

Figure 3

Spectral intensity (arbitrary units) vs time in TDSE simulations: (a) $U_p=44\mathrm{e}\mathrm{V}$; (b) $U_p=93\mathrm{e}\mathrm{V}$.

Figure 4

Solution of the returns Eq. (2): (a) roots $t^{\prime }$ for each $t$; (b) photon energy emitted at time $t$: $\hslash \omega (t)=1/2[A(t)-A(t^{\prime }){]}^2$. Compare Fig. 3.

Figure 5

Spectral intensity (a.u.) vs time of radiation emitted in electron collision with (a) fully ionized atom (no SR). (b) Incompletely ionized atom (SR appears promptly). Mean energy of the electron wave packet is 50 eV.