An analytical approach to high harmonic generation

Abstract

With the recently introduced concept of dominant interaction Hamiltonians, we construct numerically as well as analytically the spectrum of high harmonics (HH) generated in electron-ion scattering under an intense laser field. This is achieved by switching the interaction along classical electron trajectories between the integrable cases of the dipole coupled laser field or the ionic potential, depending on which potential is stronger. As a side effect, the intrinsically chaotic character of the dynamics is mapped onto the potential switching sequence while the trajectories become regular. As a consequence, only a few per cent of the trajectories needed in full semiclassical calculations are sufficient to construct the HH spectrum.

Quantum and semiclassical phase-space dynamics of a wave packet in strong fields using initial-value representations

“…These oscillations, together with spatial localization, are responsible for the HHG plateau. They have been identified and discussed in previous publications employing the TDSE [62] and the HK propagator [6,7,33], for an initial wave packet far from the core. They have also been studied in a different context, namely the adiabatic approximation [63] and Bohmian trajectories [58,64].…”

“…Furthermore, the numerical effort in IVRs does not scale exponentially with the degrees of freedom involved (for discussions related to the CCS and HK methods applied to multidimensional systems, see [3][4][5], respectively). This efficiency may be increased by employing several strategies, such as dominant Hamiltonians in specific phase-space regions [6,7] or quantum-state reprojection [8,9]. For that reason, IVRs have been successfully used in the modeling of the short-time dynamics of quantum systems with many degrees of freedom, such as polyatomic molecules and small clusters.…”

“…Since the 1990s, there has been considerable debate about whether one may model tunneling employing semiclassical IVRs such as the HK propagator, and if so, to what extent (see [37][38][39][40][41]). To circumvent this problem, in [6,7,33] the initial electronic wave packet has been placed far away from the core. Unfortunately, these initial conditions leave out many strong-field problems, for which tunneling is expected to be the dominant ionization mechanism.…”

Coherent buildup of high-order harmonic radiation: The classical perspective

“…By z = 0.37 mm, the wavepacket is thus nearly centered over the ion, with the electron velocities distributed about zero. When part of the wavepacket arrives to the core with a low kinetic energy like this, it has a high probability of becoming trapped there [37], and indeed a trapped part of the wavepacket is clearly observed in the subsequent snapshot of the distribution function at τ 0 (lower right panel of Fig. 3).…”

High-order harmonic generation with twisted electrons

“…This process can be viewed as a laser-assisted collision [11]. Guided by work with standard Gaussian electrons [12,13], we will be able to provide an analytical approximation allowing us to understand this non-linear process and its basic features with their parameter dependence.…”