Nonlinear polarization and ionization in O2: metastable electronic state model.

We present a computational model for the nonlinear response of molecular oxygen exposed to strong mid-wavelength and long-wavelength infrared optical fields. Based on a non-Hermitian approach utilizing metastable electronic states, the nonlinear polarization and strong-field ionization are described as intimately connected properties. Good agreement with the measured nonlinear index and ionization rates is shown, and parameterized response functions are provided to facilitate applications in large-scale simulations of infrared optical pulses interacting with gaseous media.

Bright circularly polarized soft X-ray high harmonics for X-ray magnetic circular dichroism.

We demonstrate, to our knowledge, the first bright circularly polarized high-harmonic beams in the soft X-ray region of the electromagnetic spectrum, and use them to implement X-ray magnetic circular dichroism measurements in a tabletop-scale setup. Using counterrotating circularly polarized laser fields at 1.3 and 0.79 µm, we generate circularly polarized harmonics with photon energies exceeding 160 eV. The harmonic spectra emerge as a sequence of closely spaced pairs of left and right circularly polarized peaks, with energies determined by conservation of energy and spin angular momentum. We explain the single-atom and macroscopic physics by identifying the dominant electron quantum trajectories and optimal phase-matching conditions. The first advanced phase-matched propagation simulations for circularly polarized harmonics reveal the influence of the finite phase-matching temporal window on the spectrum, as well as the unique polarization-shaped attosecond pulse train. Finally, we use, to our knowledge, the first tabletop X-ray magnetic circular dichroism measurements at the N4,5 absorption edges of Gd to validate the high degree of circularity, brightness, and stability of this light source. These results demonstrate the feasibility of manipulating the polarization, spectrum, and temporal shape of high harmonics in the soft X-ray region by manipulating the driving laser waveform.

Generation of bright isolated attosecond soft X-ray pulses driven by multicycle midinfrared lasers.

High harmonic generation driven by femtosecond lasers makes it possible to capture the fastest dynamics in molecules and materials. However, to date the shortest subfemtosecond (attosecond, 10(-18) s) pulses have been produced only in the extreme UV region of the spectrum below 100 eV, which limits the range of materials and molecular systems that can be explored. Here we experimentally demonstrate a remarkable convergence of physics: when midinfrared lasers are used to drive high harmonic generation, the conditions for optimal bright, soft X-ray generation naturally coincide with the generation of isolated attosecond pulses. The temporal window over which phase matching occurs shrinks rapidly with increasing driving laser wavelength, to the extent that bright isolated attosecond pulses are the norm for 2-µm driving lasers. Harnessing this realization, we experimentally demonstrate the generation of isolated soft X-ray attosecond pulses at photon energies up to 180 eV for the first time, to our knowledge, with a transform limit of 35 attoseconds (as), and a predicted linear chirp of 300 as. Most surprisingly, advanced theory shows that in contrast with as pulse generation in the extreme UV, long-duration, 10-cycle, driving laser pulses are required to generate isolated soft X-ray bursts efficiently, to mitigate group velocity walk-off between the laser and the X-ray fields that otherwise limit the conversion efficiency. Our work demonstrates a clear and straightforward approach for robustly generating bright isolated attosecond pulses of electromagnetic radiation throughout the soft X-ray region of the spectrum.

Mollow sidebands in high order harmonic spectra of molecules.

Novel feature of high order harmonic generation process for molecules is presented for several molecules at their equilibrium geometries. The high order harmonic spectra reveal additional sidebands for each odd harmonic, which are a consequence of the resonant coupling of two valence orbitals, a mechanism analogous to Mollow triplets known from quantum optics. Strong modification of the high order harmonic generation process is illustrated with time frequency analysis in which there appear additional minima dependent on the Rabi frequency for the corresponding transition. The orbital coupling further leads to the modification of the electron dynamics which is presented using total electron density difference maps.

Multielectron contributions in elliptically polarized high-order harmonic emission from nitrogen molecules.

We have studied the polarization and ellipticity of high-order harmonics from nitrogen molecules using the time-dependent density functional theory. The results of our numerical calculations are in excellent agreement with the data of recent experiments. The theoretical analysis of our results reveals that at least three contributions, namely those from the HOMO, the HOMO-1, and the HOMO-2 orbitals, contribute to the observed high harmonic spectra. Furthermore, we confirm that a proper account of the distribution of the alignment in the molecular ensemble is necessary to obtain agreement with the experimental data.

Time delays in two-photon ionization.

We present results of ab initio numerical simulations of time delays in two-photon ionization of the helium atom using the attosecond streaking technique. The temporal shifts in the streaking traces consist of two contributions, namely, a time delay acquired during the absorption of the two photons from the extreme-ultraviolet field and a time delay accumulated by the photoelectron after photoabsorption. In the case of a nonresonant transition, the absorption of the two photons is found to occur without time delay. In contrast, for a resonant transition a substantial absorption time delay is found, which scales linearly with the duration of the ionizing pulse. The latter can be related to the phase acquired during the transition of the electron from the initial ground state to the continuum and the influence of the streaking field on the resonant structure of the atom.

Visualizing electron rearrangement in space and time during the transition from a molecule to atoms.

Imaging and controlling reactions in molecules and materials at the level of electrons is a grand challenge in science, relevant to our understanding of charge transfer processes in chemistry, physics, and biology, as well as material dynamics. Direct access to the dynamic electron density as electrons are shared or transferred between atoms in a chemical bond would greatly improve our understanding of molecular bonding and structure. Using reaction microscope techniques, we show that we can capture how the entire valence shell electron density in a molecule rearranges, from molecular-like to atomic-like, as a bond breaks. An intense ultrashort laser pulse is used to ionize a bromine molecule at different times during dissociation, and we measure the total ionization signal and the angular distribution of the ionization yield. Using this technique, we can observe density changes over a surprisingly long time and distance, allowing us to see that the electrons do not localize onto the individual Br atoms until the fragments are far apart (∼5.5 Å), in a region where the potential energy curves for the dissociation are nearly degenerate. Our observations agree well with calculations of the strong-field ionization rates of the bromine molecule.

Tomographic reconstruction of circularly polarized high-harmonic fields: 3D attosecond metrology.

Bright, circularly polarized, extreme ultraviolet (EUV) and soft x-ray high-harmonic beams can now be produced using counter-rotating circularly polarized driving laser fields. Although the resulting circularly polarized harmonics consist of relatively simple pairs of peaks in the spectral domain, in the time domain, the field is predicted to emerge as a complex series of rotating linearly polarized bursts, varying rapidly in amplitude, frequency, and polarization. We extend attosecond metrology techniques to circularly polarized light by simultaneously irradiating a copper surface with circularly polarized high-harmonic and linearly polarized infrared laser fields. The resulting temporal modulation of the photoelectron spectra carries essential phase information about the EUV field. Utilizing the polarization selectivity of the solid surface and by rotating the circularly polarized EUV field in space, we fully retrieve the amplitude and phase of the circularly polarized harmonics, allowing us to reconstruct one of the most complex coherent light fields produced to date.

Ultraviolet surprise: Efficient soft x-ray high-harmonic generation in multiply ionized plasmas.

High-harmonic generation is a universal response of matter to strong femtosecond laser fields, coherently upconverting light to much shorter wavelengths. Optimizing the conversion of laser light into soft x-rays typically demands a trade-off between two competing factors. Because of reduced quantum diffusion of the radiating electron wave function, the emission from each species is highest when a short-wavelength ultraviolet driving laser is used. However, phase matching--the constructive addition of x-ray waves from a large number of atoms--favors longer-wavelength mid-infrared lasers. We identified a regime of high-harmonic generation driven by 40-cycle ultraviolet lasers in waveguides that can generate bright beams in the soft x-ray region of the spectrum, up to photon energies of 280 electron volts. Surprisingly, the high ultraviolet refractive indices of both neutral atoms and ions enabled effective phase matching, even in a multiply ionized plasma. We observed harmonics with very narrow linewidths, while calculations show that the x-rays emerge as nearly time-bandwidth-limited pulse trains of ~100 attoseconds.

Bright coherent ultrahigh harmonics in the keV x-ray regime from mid-infrared femtosecond lasers.

High-harmonic generation (HHG) traditionally combines ~100 near-infrared laser photons to generate bright, phase-matched, extreme ultraviolet beams when the emission from many atoms adds constructively. Here, we show that by guiding a mid-infrared femtosecond laser in a high-pressure gas, ultrahigh harmonics can be generated, up to orders greater than 5000, that emerge as a bright supercontinuum that spans the entire electromagnetic spectrum from the ultraviolet to more than 1.6 kilo-electron volts, allowing, in principle, the generation of pulses as short as 2.5 attoseconds. The multiatmosphere gas pressures required for bright, phase-matched emission also support laser beam self-confinement, further enhancing the x-ray yield. Finally, the x-ray beam exhibits high spatial coherence, even though at high gas density the recolliding electrons responsible for HHG encounter other atoms during the emission process.