Role of the Intramolecular Phase in High-Harmonic Generation

Abstract

We study numerically the generation of high-order harmonics by two-center molecules for arbitrary angles between the molecular axis and the laser polarization axis. For fixed angle, the harmonic spectrum exhibits a minimum at a frequency which is independent of the laser parameters. The amplitude of each harmonic is strongly angle dependent, and a pronounced minimum is found at the same angle where a sudden jump in the harmonic phase occurs. By calculating the spatial dependence of the harmonic amplitudes and phases, we are able to explain these effects in terms of interfering contributions from various regions within the molecule. DOI: 10.1103/PhysRevLett.88.183903 PACS numbers: 42.65.Ky, 33.80.Rv The interaction of strong laser pulses with atoms or molecules leads to the generation of high-order harmonics [1][2][3][4]. This process is one of the most studied aspects of strong-field physics because it serves as a source of coherent radiation at high frequencies. Nevertheless, most of the experimental and theoretical work has been devoted to atoms, and, in contrast, high-harmonic generation by molecules still leaves open many questions.The production of high harmonics in atoms is well explained by a recollision mechanism [5]: The strong electric field ionizes the atom or molecule and thus creates a free electron. The electron is then accelerated by the oscillating field and may be driven back to the core if the laser pulse is linearly polarized. A high-energy photon is emitted if the recollision with the core leads to recombination. Other than radiation, recollisions can also result in elastic backscattering [6] or double ionization [5]. In the case of atoms, a maximum kinetic energy of 3.17U p for the returning electron is predicted, leading to a cutoff at a photon energy of I p 1 3.17U p . Here, U p E 2 0 ͑͞4v 2 ͒ is the ponderomotive potential in the laser field of amplitude E 0 and frequency v, and I p is the ionization potential. By its simplicity, the recollision picture is extremely useful for purposes of interpretation and will be utilized to explain our results below.Previous theoretical work on two-center molecules has pointed towards interesting effects which are specific to molecules: Early work has demonstrated the importance of charge-resonance effects [7]. Further, an electron can be emitted at one center and recombine at the other center, giving rise to new cutoff laws [8,9]. Also, it was demonstrated that non -Born-Oppenheimer dynamics becomes relevant in the case of oriented isotopically asymmetric molecules [10]. Particularly related to the present work are earlier model calculations which showed that the harmonic yield depends on the orientation of the molecule with respect to the electric field [8,11]. Reference [8] concentrated mainly on internuclear separations above the equilibrium distance. For molecules at their equilibrium distance, Refs. [8,11] compared only between parallel and perpendicular alignment of the molecules relative to the field. Furthermore, the orientation dependence...

Linked attosecond phase interferometry for molecular frame measurements

“…An amplitude minimum in the vicinity of q=21 and θ = 0 • , accompanied by a rapid local phase variation with increasing q, is observed experimentally. The position of this minimum (q=21) is consistent with the two-center interference model [28]; a similar feature around q=23 was also observed in the recombination dipole of aligned CO 2 measured by the RABBIT technique [7], Br 2 and CO 2 having the same ordering of valence molecular orbitals.…”

High-Harmonic Spectroscopy: From Femtosecond to Attosecond Molecular Dynamics

“…This property arises from the de-Broglie wavelength of the recolliding electron which amounts to ~1-2 Å under typical conditions. Since the returning electron wave diffracts in the electrostatic molecular potential before it recombines, the high-harmonic spectrum reveals structural signatures such as twocenter interference [12] and features of electronic structure. [13][14][15][16] In addition, a high-harmonic spectrum also encodes dynamical information.…”

Theory of Nonlinear Propagation of High Harmonics Generated in a Gaseous Medium

“…Following the twocenter interference model by Lein et al [68], Kanai et al [69] observed the constructive and destructive interference occurred for selected harmonics subject to a Bragg condition for the returning electron. Since then one can deduce the internuclear distances in the molecule by using the harmonic order where constructive or destructive interference occurs.…”

“…Earlier attempts to extract structure information from HHG spectra were based on the two-center interference model [68] and the strong-field approximation (SFA) [85,86].…”