Space-time considerations in the phase locking of high harmonics

Bayesian optimal control of the ultrashort circularly polarized attosecond pulse generation by two-color polarization gating

We present ab initio simulations of optimal control of high-order-harmonic generation spectra that enable the synthesis of a circularly polarized 53-attosecond pulse in a single Helium atom response. The Bayesian optimization is used to achieve control of a two-color polarization gating laser waveform such that a series of harmonics in the plateau region are phase-matched, which can be used for attosecond pulse synthesis. To find the underlying mechanisms for generating these harmonics, we perform a wavelet analysis for the induced dipole moment in acceleration form, and compare the time-energy representation with the quantum paths extracted from the semiclassical calculation. We found that these coherent harmonics are excited along the short trajectories. The proposed method has the potential to migrate to laboratories for generation of isolated circularly polarized ultrashort attosecond pulses.

Transverse phase matching of high-order harmonic generation in single-layer graphene

The efficiency of high-harmonic generation (HHG) from a macroscopic sample is strongly linked to the proper phase matching of the contributions from the microscopic emitters. We develop a combined micro+macroscopic theoretical model that allows us to distinguish the relevance of high-order harmonic phase matching in single-layer graphene. For a Gaussian driving beam, our simulations show that the relevant HHG emission is spatially constrained to a phase-matched ring around the beam axis. This remarkable finding is a direct consequence of the non-perturbative behavior of HHG in graphene-whose harmonic efficiency scaling is similar to that already observed in gases- and bridges the gap between the microscopic and macroscopic HHG in single-layer graphene.

Extended ellipticity control for attosecond pulses by high harmonic generation

Attosecond (1  as=10^-18  s) pulses produced through high harmonic generation (HHG) are a basis for studies of electron dynamics during light-matter interaction on an electron's natural time scale. Extensively exploited HHG technology has, however, a few unsolved problems, where producing of circularly polarized or chiral attosecond pulses belongs to them. We have demonstrated experimentally a way to control the ellipticity of attosecond pulse trains produced via HHG in two-color, bi-circular laser fields. We show that the combination of a nonlinear medium position and the intensities of the two-color driving laser fields create an effective helicity-dependent filter. Based on this approach, we report generation of chiral spectra providing potential to produce attosecond pulses with polarization tuned from the rotating, but linear to highly elliptic, with ellipticity as much as ϵ=0.75. This new way to create a chiral-sensitive element offers a simple and practical knob to control polarization for a combined harmonics field in a smooth and predictable manner.

Attosecond pulse shaping around a Cooper minimum

High harmonic generation (HHG) is used to measure the spectral phase of the recombination dipole matrix element (RDM) in argon over a broad frequency range that includes the 3p Cooper minimum (CM). The measured RDM phase agrees well with predictions based on the scattering phases and amplitudes of the interfering s- and d-channel contributions to the complementary photoionization process. The reconstructed attosecond bursts that underlie the HHG process show that the derivative of the RDM spectral phase, the group delay, does not have a straightforward interpretation as an emission time, in contrast to the usual attochirp group delay. Instead, the rapid RDM phase variation caused by the CM reshapes the attosecond bursts.

Zeptosecond high harmonic keV x-ray waveforms driven by midinfrared laser pulses

We demonstrate theoretically that the temporal structure of high harmonic x-ray pulses generated with midinfrared lasers differs substantially from those generated with near-infrared pulses, especially at high photon energies. In particular, we show that, although the total width of the x-ray bursts spans femtosecond time scales, the pulse exhibits a zeptosecond structure due to the interference of high harmonic emission from multiple reencounters of the electron wave packet with the ion. Properly filtered and without any compensation of the chirp, regular subattosecond keV waveforms can be produced.

Macroscopic control of quantum paths in high order harmonics by a weak second harmonic field

The phase matching of quantum paths in high-order harmonic generation is investigated in a two-color laser field. Our results show that the phase-matching properties of the short and long trajectories can be modulated effectively by adding a weak second harmonic field. This scheme can not only achieve the quantum path selection, but more importantly it can achieve on-axis phase matching for both of the two trajectories simultaneously. A bright interference pattern induced by the simultaneously phase-matched two trajectories can be observed by placing a near-field on-axis filter, which has great potential for experimentally characterizing the full single-atom dipole moment.

Attosecond pulses with sophisticated spatio-spectral waveforms: spatio-spectral Airy and auto-focusing beams

We propose a scheme for producing attosecond pulses with sophisticated spatio-spectral waveforms. The profile of a seed attosecond pulse is modified and its central frequency is up-converted through interaction with an infrared pump pulse. The transverse profile of the infrared beam and a spatiotemporal shift between the seed and infrared pulses are used for manipulating the spatio-spectral waveform of the generated pulse beam. We present several examples of sophisticated isolated attosecond pulse beam generation, including spatio-spectral Airy beam that exhibits prismatic self-bending effect and a beam undergoing auto-focusing to a sub-micron spot without the need of a focusing lens or nonlinearity.

Analytic scaling analysis of high harmonic generation conversion efficiency

Closed form expressions for the high harmonic generation (HHG) conversion efficiency are obtained for the plateau and cutoff regions. The presented formulas eliminate most of the computational complexity related to HHG simulations, and enable a detailed scaling analysis of HHG efficiency as a function of drive laser parameters and material properties. Moreover, in the total absence of any fitting procedure, the results show excellent agreement with experimental data reported in the literature. Thus, this paper opens new pathways for the global optimization problem of extreme ultraviolet (EUV) sources based on HHG.

Few-cycle attosecond pulses with stabilized-carrier-envelope phase in the presence of a strong terahertz field

High-order harmonic generation in the presence of a strong terahertz field is investigated, and phase stabilization of the few-cycle laser pulses is extended to the extremely ultraviolet region. It is found that the strong terahertz field significantly breaks the symmetry between the consecutive half-cycle and greatly extends the harmonic cutoff, producing both odd and even harmonics which are covered with an extremely broad bandwidth and well locked in phase. These results can support the generation of few-cycle attosecond pulse trains with stabilized carrier-envelope phase from pulse to pulse, and also enables the generation of phase-stabilized pulse train with tunable wavelength.

Spectral phase distribution retrieval through coherent control of harmonic generation

The temporal intensity distribution of the third harmonic of a Ti:sapphire laser generated in Xe gas is fully reconstructed from its spectral phase and amplitude distributions. The spectral phases are retrieved by cross correlating the fundamental laser frequency field with that of the third harmonic, in a three laser versus one harmonic photon coupling scheme. The third harmonic spectral amplitude distribution is extracted from its field autocorrelation. The measured pulse duration is found to be in agreement with that expected from lowest order perturbation theory both for unstretched and chirped pulses.

High-contrast interference pattern of amplified spontaneous emission from dyes under transient grating excitation

We demonstrate a high-contrast interference fringe pattern formed by amplified spontaneous emission (ASE) in a noncollinear two-beam self-diffraction setup by use of dyes. In the presence of a transient grating a stable interference pattern is observed in ASE induced by one- and two-photon absorption. The fringe visibility varies from 0.2 to 0.65 with a temporal delay in the two beams. The variation of the angle between the two exciting beams at the temporal overlap shows an increase in the fringe visibility with an increase in the angle.

Second order autocorrelation of an XUV attosecond pulse train

Temporal widths of an attosecond (asec) XUV radiation pulse train, formed by the superposition of higher order harmonics, have been recently determined utilizing a 2nd order autocorrelation measurement. An assessment of the validity of the approach, for the broadband XUV radiation of asec pulses, is implemented through ab initio calculations modeling the spectral and temporal response of the two-XUV-photon He ionization detector employed. The measured width of the asec bursts is discussed in terms of the spectral phases of the individual harmonics, as well as in terms of the spatially modulated temporal width of the radiation, and is found in reasonable agreement with the expected duration.

Amplitude and phase control of attosecond light pulses

We report the generation, compression, and delivery on target of ultrashort extreme-ultraviolet light pulses using external amplitude and phase control. Broadband harmonic radiation is first generated by focusing an infrared laser with a carefully chosen intensity into a gas cell containing argon atoms. The emitted light then goes through a hard aperture and a thin aluminum filter that selects a 30-eV bandwidth around a 30-eV photon energy and synchronizes all of the components, thereby enabling the formation of a train of almost Fourier-transform-limited single-cycle 170 attosecond pulses. Our experiment demonstrates a practical method for synthesizing and controlling attosecond waveforms.

Optimization of attosecond pulse generation

The generation of attosecond pulses by superposition of high harmonics relies on their synchronization in the emission. Our experiments in the low-order, plateau, and cutoff regions of the spectrum reveal different regimes in the electron dynamics determining the synchronization quality. The shortest pulses are obtained by combining a spectral filtering of harmonics from the end of the plateau and the cutoff, and a far-field spatial filtering that selects a single electron quantum path contribution to the emission. This method applies to isolated pulses as well as pulse trains.

Attosecond Synchronization of High-Harmonic Soft X-rays

Subfemtosecond light pulses can be obtained by superposing several high harmonics of an intense laser pulse. Provided that the harmonics are emitted simultaneously, increasing their number should result in shorter pulses. However, we found that the high harmonics were not synchronized on an attosecond time scale, thus setting a lower limit to the achievable x-ray pulse duration. We showed that the synchronization could be improved considerably by controlling the underlying ultrafast electron dynamics, to provide pulses of 130 attoseconds in duration. We discuss the possibility of achieving even shorter pulses, which would allow us to track fast electron processes in matter.

Attosecond angle-resolved photoelectron spectroscopy

We report experiments on the characterization of a train of attosecond pulses obtained by high-harmonic generation, using mixed-color (XUV+IR) atomic two-photon ionization and electron detection on a velocity map imaging detector. We demonstrate that the relative phase of the harmonics is encoded both in the photoelectron yield and the angular distribution as a function of XUV-IR time delay, thus making the technique suitable for the detection of single attosecond pulses. The timing of the attosecond pulse with respect to the field oscillation of the driving laser critically depends on the target gas used to generate the harmonics.

Direct observation of attosecond light bunching

Temporal probing of a number of fundamental dynamical processes requires intense pulses at femtosecond or even attosecond (1 as = 10(-18) s) timescales. A frequency 'comb' of extreme-ultraviolet odd harmonics can easily be generated in the interaction of subpicosecond laser pulses with rare gases: if the spectral components within this comb possess an appropriate phase relationship to one another, their Fourier synthesis results in an attosecond pulse train. Laser pulses spanning many optical cycles have been used for the production of such light bunching, but in the limit of few-cycle pulses the same process produces isolated attosecond bursts. If these bursts are intense enough to induce a nonlinear process in a target system, they can be used for subfemtosecond pump-probe studies of ultrafast processes. To date, all methods for the quantitative investigation of attosecond light localization and ultrafast dynamics rely on modelling of the cross-correlation process between the extreme-ultraviolet pulses and the fundamental laser field used in their generation. Here we report the direct determination of the temporal characteristics of pulses in the subfemtosecond regime, by measuring the second-order autocorrelation trace of a train of attosecond pulses. The method exhibits distinct capabilities for the characterization and utilization of attosecond pulses for a host of applications in attoscience.

Measurement of the subcycle timing of attosecond XUV bursts in high-harmonic generation

The absolute timing of the high-harmonic attosecond pulse train with respect to the generating IR pump cycle has been measured for the first time. The attosecond pulses occur 190+/-20 as after each pump field maxima (twice per optical cycle), in agreement with the "short" quantum path of the quasiclassical model of harmonic generation.