P. Salières

Study of the Spatial and Temporal Coherence of High-Order Harmonics

We apply the theory of high-order harmonic generation by low-frequency laser fields in the strong field approximation to the study of the spatial and temporal coherence properties of the harmonics. We discuss the role of dynamically induced phases of the atomic polarization in determining the optimal phase matching conditions and angular distributions of harmonics. We demonstrate that the phase matching and the spatial coherence can be controlled by changing the focusing parameters of the fundamental laser beam. Then we present a detailed study of the temporal and spectral properties of harmonics. We discuss how the focusing conditions influence the individual harmonic spectra and time profiles, and how the intensity dependence of the dynamically induced phase leads to a chirp of the harmonic frequency. This phase modulation can be used to control the temporal and spectral properties of the harmonic radiation. Temporally, the harmonic chirped pulse can be recompressed to very small durations. Spectrally, chirping of the fundamental beam may be employed to compensate for the dynamically induced chirp and to control the individual harmonic spectrum. Finally, we discuss the short pulse effects, in particular nonadiabatic phenomena and the possibility of generating attosecond pulses. Comment: Latex file with 37 pages, 25 postscript figures. to appear in Advances in Atomic, Molecular and Optical Physics

Self-probing of molecules with high harmonic generation

This tutorial presents the most important aspects of the molecular self-probing paradigm, which views the process of high harmonic generation as a molecule being probed by one of its own electrons. Since the properties of the electron wavepacket acting as a probe allow a combination of attosecond and Angstrom resolutions in measurements, this idea bears great potential for the observation, and possibly control, of ultrafast quantum dynamics in molecules at the electronic level. Theoretical as well as experimental methods and concepts at the basis of self-probing measurements are introduced. Many of these are discussed as the example of molecular orbital tomography.

Imaging orbitals with attosecond and Ångström resolutions: toward attochemistry?

The recently developed attosecond light sources make the investigation of ultrafast processes in matter possible with unprecedented time resolution. It has been proposed that the very mechanism underlying the attosecond emission allows the imaging of valence orbitals with Ångström space resolution. This controversial idea together with the possibility of combining attosecond and Ångström resolutions in the same measurements has become a hot topic in strong-field science. Indeed, this could provide a new way to image the evolution of the molecular electron cloud during, e.g. a chemical reaction in real time. Here we review both experimental and theoretical challenges raised by the implementation of these prospects. In particular, we show how the valence orbital structure is encoded in the spectral phase of the recombination dipole moment calculated for Coulomb scattering states, which allows a tomographic reconstruction of the orbital using first-order corrections to the plane-wave approach. The possibility of disentangling multi-channel contributions to the attosecond emission is discussed as well as the necessary compromise between the temporal and spatial resolutions.

Attosecond emission from chromium plasma

We present the first measurement of the attosecond emission generated from underdense plasma produced on a solid target. We generate high-order harmonics of a femtosecond Ti:sapphire laser focused in a weakly ionized underdense chromium plasma. Using the Reconstruction of Attosecond Beating by Interference of Two-photon Transitions (RABITT) technique, we show that the 11th to the 19th harmonic orders form in the time domain an attosecond pulse train with each pulse having 300 as duration, which is only 1.05 times the theoretical Fourier transform limit. Measurements reveal a very low positive group delay dispersion of 4200 as2. Beside its fundamental interest, high-order harmonic generation in plasma plumes could thus provide an intense source of attosecond pulses for applications.

Phase distortions of attosecond pulses produced by resonance-enhanced high harmonic generation

Resonant enhancement of high harmonic generation can be obtained in plasmas containing ions with strong radiative transitions resonant with harmonic orders. The mechanism for this enhancement is still debated. We perform the first temporal characterization of the attosecond emission from a tin plasma under near-resonant conditions for two different resonance detunings. We show that the resonance considerably changes the relative phase of neighboring harmonics. For very small detunings, their phase locking may even be lost, evidencing strong phase distortions in the emission process and a modified attosecond structure. These features are well reproduced by our simulations, allowing their interpretation in terms of the phase of the recombination dipole moment.

High-Order Harmonic Generation

Thanks to the invention of the laser in 1960, intensities never reached before became available allowing the observation of a number of new phenomena. Among them, the discovery in 1961 of optical harmonic generation by Franken et al. 1marked the birth of nonlinear optics, one of the richest field in optics that has found applications in nearly all areas of science. By generating the second harmonic of a Ruby laser in a quartz crystal, they demonstrated that atoms could absorb simultaneously two optical photons and emit a photon of doubled energy. This opened wide perspectives for the extension of coherent light sources to shorter wavelengths. Indeed, harmonic orders from 3 to 11 could be generated in the following years, but the quickly decreasing conversion efficiency with the order prevented the observation of higher orders. The intuitive explanation is that in this perturbative (weak-field) regime, the probability of absorbing simultaneously n photons decreases quickly when n increases, so that the extension of the process to shorter wavelengths seemed hopeless.

Spectrally resolved multi-channel contributions to the harmonic emission in N 2

When generated in molecules, high-order harmonics can be emitted through different ionization channels. The coherent and ultrafast electron dynamics occurring in the ion during the generation process is directly imprinted in the harmonic signal, i.e. in its amplitude and spectral phase. In aligned N2 molecules, we find evidence for a fast variation of this phase as a function of the harmonic order when varying the driving laser intensity. Basing our analysis on a three-step model, we find that this phase variation is a signature of transitions from a single- to a multi-channel regime. In particular, we show that significant nuclear dynamics may occur in the ionization channels on the attosecond timescale, affecting both the amplitude and the phase of the harmonic signal.

Polarization-resolved pump-probe spectroscopy with high harmonics

High harmonic generation in gases can be used as a probe of the electronic structure of the emitting medium, with attosecond temporal resolution and angstrom spatial resolution. The prospect of measuring molecular dynamics by pump-probe spectroscopy with such precision is attracting a lot of interest. An important issue in pump-probe spectroscopy lies in the ability to detect small signals: the detected signal can be easily dominated by the contributions from non-excited molecules or from a carrier gas. In this paper, we demonstrate that polarization-resolved pump-probe spectroscopy can be used to overcome this issue. We study high harmonic generation from rotationally excited molecules. We show that by measuring the harmonic field that is generated orthogonally to the driving laser field, the contrast in the detection of alignment revivals in nitrogen can be increased by a factor 4. We use this configuration to measure alignment revivals in an argon-nitrogen mixture, in which the total harmonic signal is dominated by the contributions from argon.

Spatial fingerprint of quantum path interferences in high order harmonic generation

We have spatially and spectrally resolved the high order harmonic emission from an argon gas target. Under proper phase matching conditions we were able to observe for the first time the spatial fine structure originating from the interference of the two shortest quantum paths in the harmonic beam. The structure can be explained by the intensity-dependent harmonic phase of the contributions from the two paths. The spatially and spectrally resolved measurements are consistent with previous spatially integrated results. Our measurement method represents a new tool to clearly distinguish between different interference effects and to potentially observe higher order trajectories in the future with improved detection sensitivity. Here, we demonstrate additional experimental evidence that the observed interference pattern is only due to quantum-path interferences and cannot be explained by a phase modulation effect. Our experimental results are fully supported by simulations using the strong field approximation and including propagation.

Generation of ultrashort coherent XUV pulses by harmonic conversion of intense laser pulses in gases: towards attosecond pulses

The generation of high-order harmonics of intense laser pulses focused in gases is an intriguing and spectacular process: nonlinear orders as high as 300 have been reported recently. In addition to its fundamental interest, this radiation presents unique properties of coherence and ultrashort pulse duration that makes it a useful XUV source. The measurement of such short durations has required us to develop new characterization techniques in the XUV range, that have evidenced harmonic pulses as short as a few femtoseconds. This property opens the way to studying ultrafast dynamics in atomic and molecular spectroscopy, solid-state and plasma physics. Moreover, the possibility of generating yet shorter pulses, so-called attosecond pulses, is under investigation.