title: High-harmonic generation and parametric amplification in the soft X-rays from extended electron trajectories.
abstract: We report, for the first time, the generation of high-order harmonics in a spectral range between 200 eV and 1 keV with an unusual spectral property: only every 4(th) (4i + 1, i∈ℵ) harmonic line appears, whereas the usual high-harmonic spectra consist of every odd (2i + 1) harmonic. We attribute this unique property to the quantum path interference of two extended electron trajectories that experience multiple re-scattering. In the well-established theory, electrons emitted via tunnel ionisation are accelerated by a laser field, return to the ion and recombine. The acceleration typically lasts for less than one optical cycle, and the electrons radiate in the extreme ultraviolet range at recombination. In contrast, for extended trajectories, electrons are accelerated over two or more optical cycles. Here, we demonstrate that two sets of trajectories dominate and provide substantial contributions to the generated soft X-ray radiation because they fulfil the resonance condition for X-ray parametric amplification.
authors.affiliation: 1] Institute of Optics and Quantum Electronics, Abbe Center of Photonics, Friedrich Schiller University, Max Wien Platz 1, 07743 Jena, Germany [2] Insitute of Atomic and Subatomic Physics, Vienna University of Technology, Stadionallee 2, 1020 Vienna, Austria.
authors.forename: J
authors.initials: J
authors.lastname: Seres
authors.affiliation: 1] Institute of Optics and Quantum Electronics, Abbe Center of Photonics, Friedrich Schiller University, Max Wien Platz 1, 07743 Jena, Germany [2] Insitute of Atomic and Subatomic Physics, Vienna University of Technology, Stadionallee 2, 1020 Vienna, Austria [3] Helmholtz Institute Jena, Fröbelstieg 3, 07743 Jena, Germany.
authors.forename: E
authors.initials: E
authors.lastname: Seres
authors.affiliation: 1] Institute of Optics and Quantum Electronics, Abbe Center of Photonics, Friedrich Schiller University, Max Wien Platz 1, 07743 Jena, Germany [2] Helmholtz Institute Jena, Fröbelstieg 3, 07743 Jena, Germany.
authors.forename: B
authors.initials: B
authors.lastname: Landgraf
authors.affiliation: 1] Helmholtz Institute Jena, Fröbelstieg 3, 07743 Jena, Germany [2] GSI Helmholtz Centre for Heavy Ion Research, Planckstrasse 1, 64291 Darmstadt, Germany.
authors.forename: B
authors.initials: B
authors.lastname: Ecker
authors.affiliation: 1] Helmholtz Institute Jena, Fröbelstieg 3, 07743 Jena, Germany [2] GSI Helmholtz Centre for Heavy Ion Research, Planckstrasse 1, 64291 Darmstadt, Germany.
authors.forename: B
authors.initials: B
authors.lastname: Aurand
authors.affiliation: 1] Helmholtz Institute Jena, Fröbelstieg 3, 07743 Jena, Germany [2] GSI Helmholtz Centre for Heavy Ion Research, Planckstrasse 1, 64291 Darmstadt, Germany.
authors.forename: T
authors.initials: T
authors.lastname: Kuehl
authors.affiliation: 1] Institute of Optics and Quantum Electronics, Abbe Center of Photonics, Friedrich Schiller University, Max Wien Platz 1, 07743 Jena, Germany [2] Helmholtz Institute Jena, Fröbelstieg 3, 07743 Jena, Germany.
authors.forename: C
authors.initials: C
authors.lastname: Spielmann