Scaling of Wave-Packet Dynamics in an Intense Midinfrared Field

A theoretical investigation is presented that examines the wavelength scaling from near-visible ($0.8\mu \mathrm{m}$) to midinfrared ($2\mu \mathrm{m}$) of the photoelectron distribution and high harmonics generated by a “single” atom in an intense electromagnetic field. The calculations use a numerical solution of the time-dependent Schrödinger equation (TDSE) in argon and the strong-field approximation in helium. The scaling of electron energies (${\lambda }^2$), harmonic cutoff (${\lambda }^2$), and attochirp (${\lambda }^{-1}$) agree with classical mechanics, but it is found that, surprisingly, the harmonic yield follows a ${\lambda }^{-(5–6)}$ scaling at constant intensity. In addition, the TDSE results reveal an unexpected contribution from higher-order returns of the rescattering electron wave packet.

Figure 1

(a) TDSE angle-integrated electron spectra for argon exposed to a flat-top 8-cycle pulse with intensity $0.16\mathrm{PW}/{\mathrm{cm}}^2$ and wavelengths of 2 (solid line) and $0.8\mu \mathrm{m}$ (dashed line). (b) Harmonic spectra for the same conditions.

Figure 2

The wavelength dependence of the integrated HHG yield at constant intensity for TDSE (●) and SFA (+). The TDSE results for argon at $0.16\mathrm{PW}/{\mathrm{cm}}^2$ are integrated from 20–50 eV. SFA results for helium at $0.445\mathrm{PW}/{\mathrm{cm}}^2$ are integrated from 40–80 eV. The dashed and solid lines show a ${\lambda }^{-5}$ and ${\lambda }^{-6}$ dependence, respectively.

Figure 3

TDSE time history of the HHG emission energy for argon excited by (a) 2 and (b) $0.8\mu \mathrm{m}$ driving laser with intensity $0.16\mathrm{PW}/{\mathrm{cm}}^2$. The solid black lines are the purely classical prediction for return energy. The numeric label corresponds to the ${\tau }_n$ trajectory. The top trace shows the electric field of the input pulse.

Figure 4

Representative pulse trains for driving wavelengths of (a) 0.8 and (b) $2\mu \mathrm{m}$ using the optimum bandwidths of 24.8 and 37.2 eV, respectively. (c) TDSE chirp (●) of the ${\tau }_1$ trajectory in argon as a function of wavelength for an intensity of $0.16\mathrm{PW}/{\mathrm{cm}}^2$. Solid line is the classical ${\lambda }^{-1}$ prediction.