High Harmonic Generation Via Continuum Wave-Packet Interference

High-order harmonic generation (HHG) is investigated theoretically in the over-the-barrier ionization regime revealing the strong signature of interference between two separately ionized and separately propagating free wave packets of a single electron. The interference leads to the emission of coherent light at a photon energy corresponding to the kinetic-energy difference of the two recolliding electron quantum paths, thus complementary to the well-known classical three-step picture of HHG. As will be shown by time-frequency analysis of the emitted radiation, the process entirely dominates the coherent HHG emission after the atomic ground state has been depleted by a strong field. Moreover, it can be isolated from the continuum–bound harmonics via phase matching.

Figure 1

Electron-atom collision and analysis of the dipole-acceleration response. Windowed Fourier transforms on a logarithmic scale are shown for four cases: (a) monochromatic electron wave packet (47.8 a.u. kinetic energy) colliding with a partially ionized atom, (b) same as (a) but for a fully ionized atom, (c) a bichromatic electron wave packet (47.8 a.u., 33.1 a.u. kinetic energies) colliding with a fully ionized atom, and (d) same as (c) but for a partially ionized atom. In (c) and (d) the signature of CC electron interference is observed at the difference kinetic energy of 14.7 a.u.

Figure 2

Time-frequency analysis of HHG showing the signature of CC wave-packet interference. (a) Driver pulse used in the simulation (solid line) and the reliable part of the ground-state population (dashed line) calculated via 13. (b) Windowed Fourier transform of the HHG emission on a logarithmic scale. Dashed (black) lines: classically calculated kinetic energies of electrons returning to the ion. Solid (red) line: difference between the two black dashed curves.

Figure 3

CC HHG by using an analytical approach based on the SFA for the same field as in Fig. 2a. Panel (a) is the windowed Fourier transform of the acceleration on a logarithmic scale within a chosen time window in excellent agreement with the TDSE results of Fig. 2. Panel (b) shows single-atom spectral photon yield per solid angle per shot of the same time window as in (a).