Phase of the atomic polarization in high-order harmonic generation

Effects of driving laser jitter on the attosecond streaking measurement

Driving laser jitter is one of the main factors affecting the attosecond streaking measurement. The effect of carrier-envelope phase (CEP) jitter and the pulse energy jitter on the attosecond pulse characterization is studied in this paper. We have theoretically calculated and experimentally confirmed that CEP jitter could result in a symmetry trace in the streaking spectrogram, while the intensity jitter could result in a slight shift and broadening of the trace. Both of them can lead to an underestimate of the retrieved attosecond pulse duration.

Elliptical polarization favors long quantum orbits in high-order above-threshold ionization of noble gases

We demonstrate the significant role of long quantum orbits in strong-field atomic processes by investigating experimentally and theoretically the above-threshold ionization spectra of noble gases in intense elliptically polarized laser pulses. With increasing laser ellipticity, the yields of different energy regions of the measured electron spectrum in high-order above-threshold ionization drop at different rates. The experimental features can be reproduced by a theoretical simulation based on quantum-orbit theory, revealing that increasing ellipticity favors the contributions of the long quantum orbits in the high-order above-threshold ionization process.

Extreme ultraviolet interferometer using high-order harmonic generation from successive sources

We present a new interferometer technique whereby multiple extreme ultraviolet light pulses are generated at different positions within a single laser focus (i.e., from successive sources) with a highly controllable time delay. The interferometer technique is tested with two generating media to create two extreme ultraviolet light pulses with a time delay between them. The delay is found to be a consequence of the Gouy phase shift. Ultimately the apparatus is capable of accessing unprecedented time scales by allowing stable and repeatable delays as small as 100 zs.

Efficient generation of high beam-quality attosecond pulse with polarization-gating Bessel-Gauss beam from highly-ionized media

Single attosecond pulse generation with polarization gating Bessel-Gauss beam in relatively strongly-ionized media is investigated. The results show that Bessel-Gauss beam has the ability to suppress the spatial plasma dispersion effects caused by high density of free electrons, thus the laser field can maintain its spatial profile through highly-ionized medium. This indicates the use of Bessel-Gauss beam has advantages over Gaussian beam in high harmonic generation under high ionization conditions. In our scheme, significant improvement of spatiotemporal properties of harmonics is achieved and an isolated attosecond pulse with high beam quality is filtered out using polarization gating.

Invited review article: technology for attosecond science

We describe a complete technological system at Imperial College London for Attosecond Science studies. The system comprises a few-cycle, carrier envelope phase stabilized laser source which delivers sub 4 fs pulses to a vibration-isolated attosecond vacuum beamline. The beamline is used for the generation of isolated attosecond pulses in the extreme ultraviolet (XUV) at kilohertz repetition rates through laser-driven high harmonic generation in gas targets. The beamline incorporates: interferometers for producing pulse sequences for pump-probe studies; the facility to spectrally and spatially filter the harmonic radiation; an in-line spatially resolving XUV spectrometer; and a photoelectron spectroscopy chamber in which attosecond streaking is used to characterize the attosecond pulses. We discuss the technology and techniques behind the development of our complete system and summarize its performance. This versatile apparatus has enabled a number of new experimental investigations which we briefly describe.

Order-dependent structure of high harmonic wavefronts

The physics of high harmonics has led to the generation of attosecond pulses and to trains of attosecond pulses. Measurements that confirm the pulse duration are all performed in the far field. All pulse duration measurements tacitly assume that both the beam's wavefront and intensity profile are independent of frequency. However, if one or both are frequency dependent, then the retrieved pulse duration depends on the location where the measurement is made. We measure that each harmonic is very close to a Gaussian, but we also find that both the intensity profile and the beam wavefront depend significantly on the harmonic order. Thus, our findings mean that the pulse duration will depend on where the pulse is observed. Measurement of spectrally resolved wavefronts along with temporal characterization at one single point in the beam would enable complete space-time reconstruction of attosecond pulses. Future attosecond science experiments need not be restricted to spatially averaged observables. Our approach paves the way to recovery of the single molecule response to the strong field.

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.

The influence of plasma defocusing in high harmonic generation

We numerically investigate the influence of plasma defocusing in high harmonic generation (HHG) by solving the first-order wave equation in an ionized medium and defining an enhancement factor to quantitatively analyze the influence of plasma defocusing. While degrading the driver pulse intensity, plasma also has a strong impact on HHG phase-matching. Combined with the HHG wavelength scaling law, our results give an estimate of HHG efficiencies with different driver wavelengths and show a limited HHG efficiency in high density media.

Spectrally resolved maker fringes in high-order harmonic generation

We investigate macroscopic interference effects in high-order harmonic generation using a Ti:sapphire laser operating at a 100 kHz repetition rate. The structure and behavior of spectral and spatial interference fringes are explained and analytically described by transient phase matching of the long electron trajectory contribution. Time-frequency mapping due to the temporal chirp of the harmonic emission allows us to observe Maker fringes directly in the spectral domain.

Spatial coherence control of xuv supercontinuum generation by two-color laser field

We investigate the spatial characteristics of xuv supercontinuum generation in the two-color laser field consisting of a fundamental and a weak second harmonic field. By optimizing the synthesized two-color field, the spatial profile of the xuv supercontinuum varies from annular-like to Gaussian-like and then the spatial quality is improved effectively, which is beneficial for its potential applications. Moreover, our calculation shows that the spatial quality of the supercontinuum is stable when the intensity of the controlling field varies in the acceptable fluctuation.

Sawtooth grating-assisted phase-matching

We show that a sawtooth phase-modulation is the optimal profile for grating assisted phase matching (GAPM). Perfect (sharp) sawtooth modulation fully corrects the phase-mismatch, exhibiting conversion equal to conventional phase matching, while smoothened, approximate sawtooth structures are more efficient than sinusoidal or square GAPM modulations that were previously studied. As an example, we demonstrate numerically optically-induced sawtooth GAPM for high harmonic generation. Sawtooth GAPM is the most efficient method for increasing the conversion efficiency of high harmonic generation through quasi-phase-matching, with an ultimate efficiency that closely matches the ideal phase-matching case.

Role of autoionizing state in resonant high-order harmonic generation and attosecond pulse production

We suggest a high-order harmonic generation (HHG) model describing enhancement of the generation efficiency for the harmonic resonant with the transition between the ground and autoionizing state of the generating ion. The results of numerical and analytical calculations based on this model are in good quantitative agreement with the experiments showing HHG enhancement up to 2 orders of magnitude. Moreover, this model reproduces well the essential difference in HHG efficiency for different ions. We show that intense but relatively long attosecond pulses can be generated using the enhanced harmonics.

Spatiotemporal characterization of single-order high harmonic pulses from time-compensated toroidal-grating monochromator

Extreme ultraviolet (XUV) single-order high harmonic pulses with 10(6) photons/pulse were separated from multiple harmonic orders by a time-compensated toroidal-grating monochromator consisting of a pair of toroidal gratings. The first grating separates the harmonic order and the second one compensates for the pulse-front tilt. The center photon energies were tunable between 42 and 23 eV. The separated single harmonic pulses were spatially and temporally characterized as having a spot size of 58 +/- 3 microm at the focus, with a shortest pulse duration of 47 +/- 2 fs. The developed XUV light source is versatile for application to time- and space-resolved spectroscopy.

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.

Role of ionization in orientation dependence of molecular high-order harmonic generation

We investigate the orientation dependence of high-order harmonic generation (HHG) from O(2) and CO(2) molecules using the strong-field approximation (SFA). Our simulations reveal the important modulation of the ionization to the HHG orientation dependence, especially at larger orientation angles. By virtue of a simplified model arising from the SFA, we show that this modulation can be read from the harmonic order where the HHG spectra at different orientation angles intersect. These results give suggestions on probing the molecular structure and dynamics using HHG.

Harmonic generation beyond the Strong-Field Approximation: the physics behind the short-wave-infrared scaling laws

The physics of laser-mater interactions beyond the perturbative limit configures the field of extreme non-linear optics. Although most experiments have been done in the near infrared ( lambda <or= 1 microm), the situation is changing nowadays with the development of sources at longer wavelengths (<5 microm), opening new perspectives in the synthesis of shorter XUV attosecond pulses and higher frequencies. The theory of intense-field interactions is based either on the exact numerical integration of the time-dependent Schrödinger equation or in the development of models, mostly based on the strong-field approximation. Recent studies in the short-wave infrared show a divergence between the predictions of these models and the exact results. In this paper we will show that this discrepancy reveals the incompleteness of our present understanding of high-order harmonic generation. We discuss the physical grounds, provide a theoretical framework beyond the standard approximations and develop a compact approach that accounts for the correct scaling of the harmonic yield.

Multi-quantum-path interference in high harmonic generation driven by a chirped laser pulse

We theoretically investigate the quantum-path interference during the high harmonic generation in argon and observe the multi-quantum- path-interference (MQPI) effect related to the chirp of driving laser pulse. We successfully identify the interference originated from four significantly contributing quantum paths in the interaction of "isolated" atom with the driving laser field. Moreover, the MQPI effect is further demonstrated beyond the single atom response by spatial filtering which is used for angle-selective detection of transmitted light when three-dimensional propagation is considered. It implies that the role of high-order electron returning trajectories during high harmonic generation can be observed in the experiment.

Ionization effects on spectral signatures of quantum-path interference in high-harmonic generation

The interference between the emission originating from the short and long electron quantum paths is intrinsic to the high harmonic generation process. We investigate the universal properties of these quantum-path interferences in various generation media and discuss how ionization effects influence the observed interference structures. Our comparison of quantum-path interferences observed in xenon, argon, and neon demonstrates that our experimental tools are generally applicable and should also allow investigating more complex systems such as molecules or clusters.

Spectral signature of short attosecond pulse trains

We report experimental measurements of high-order harmonic spectra generated in Ar using a carrier-envelope-offset (CEO) stabilized 12 fs, 800 nm laser field and a fraction (less than 10%) of its second harmonic. Additional spectral peaks are observed between the harmonic peaks, which are due to interferences between multiple pulses in the train. The position of these peaks varies with the CEO and their number is directly related to the number of pulses in the train. An analytical model, as well as numerical simulations, support our interpretation.

Asymmetric molecular gating for supercontinuous high harmonic generation in the plateau

Molecular wave packets provide an alternative route to steer the high harmonic generation (HHG). Here we present a new method for isolated attosecond pulse generation from high harmonics in the plateau with asymmetric molecules. It is shown that the photoionization depends on the molecular structure. Through steering the ionization, HHG is controlled with the asymmetric molecule and supercontinuous high harmonics are produced in the plateau, from which an isolated 95-attosecond pulse is generated. In contrast to the cutoff which declines sharply, the plateau shows almost a constant intensity, indicating a higher yield. Moreover, the plateau covers a very broad bandwidth, thus is preferable to produce an isolated attosecond pulse with a rather short duration.

Quantum path interferences in high-order harmonic generation

We have investigated the intensity dependence of high-order harmonic generation in argon when the two shortest quantum paths contribute to the harmonic emission. For the first time to our knowledge, experimental conditions were found to clearly observe interference between these two quantum paths that are in excellent agreement with theoretical predictions. This result is a first step towards the direct experimental characterization of the full single-atom dipole moment and demonstrates an unprecedented accuracy of quantum path control on an attosecond time scale.

Simulated laser-pulse evolution for high-order harmonic generation in a semi-infinite gas cell

We numerically simulate the propagation of high-intensity laser pulses in helium to investigate the role of nonlinear effects in gas-cell high-harmonics experiments. An aperture located before the focusing lens is also included in the simulation. Numerical results for the radial fluence profile as a function of axial position, as well as for the spectral shift and ionization levels, agree with experimental observations. The simulations confirm that a significant Kerr effect is not required to generate the observed double focus in the fluence. The beam simulation also permits an investigation of high-harmonic phase matching. Most of the harmonic energy is seen to come from the forward portion of the laser pulse, whereas the latter portion gives rise to the incidental double laser focusing. Good phase matching for the harmonics arises in large measure from a balance between the linear phase delay of the neutral atoms and the Gouy shift, which is elongated and nearly linearized when the aperture is partially closed on the beam.

Destructive interference during high harmonic generation in mixed gases

We report on the first experimental evidence of the destructive and constructive interference of high harmonics generated in a mixed gas of He and Ne, which facilitates the coherent control of high harmonic generation. Theoretically, we develop an analytical model of high harmonic generation in mixed gases and succeed in reproducing the experimental results and deriving the optimization conditions for the process. The observed interference modulation is attributed to the difference between the phases of the intrinsically chirped harmonic pulses from He and Ne, which leads to a novel method for broadband measurement of the harmonic phases and for observing the underlying attosecond electron dynamics.

Probe of high-order harmonic generation in a hollow waveguide geometry using counterpropagating light

We use counterpropagating light to directly observe the coherent buildup of high harmonic generation in a hollow waveguide geometry. We measure, for the first time, coherence lengths for high photon energies that cannot be phase matched using conventional approaches. We also probe the transition through phase matching, the ionization level at which different harmonic orders are generated, and the change in the coherence length as the driving laser is depleted. These results directly prescribe the optimal structures or pulse trains required for implementing quasiphase matching.

Monitoring molecular dynamics using coherent electrons from high harmonic generation

We report a previously undescribed spectroscopic probe that makes use of electrons rescattered during the process of high-order harmonic generation. We excite coherent vibrations in SF(6) using impulsive stimulated Raman scattering with a short laser pulse. A second, more intense laser pulse generates high-order harmonics of the fundamental laser, at wavelengths of approximately 20-50 nm. The high-order harmonic yield is observed to oscillate, at frequencies corresponding to all of the Raman-active modes of SF(6), with an asymmetric mode most visible. The data also show evidence of relaxation dynamics after impulsive excitation of the molecule. Theoretical modeling indicates that the high harmonic yield should be modulated by both Raman and infrared-active vibrational modes. Our results indicate that high harmonic generation is a very sensitive probe of vibrational dynamics and may yield more information simultaneously than conventional ultrafast spectroscopic techniques. Because the de Broglie wavelength of the recolliding electron is on the order of interatomic distances, i.e., approximately 1.5 A, small changes in the shape of the molecule lead to large changes in the high harmonic yield. This work therefore demonstrates a previously undescribed spectroscopic technique for probing ultrafast internal dynamics in molecules and, in particular, on the chemically important ground-state potential surface.

Direct interferometric measurement of the atomic dipole phase in high-order harmonic generation

We report the first direct measurements of the atomic dipole phase in the process of high-order harmonic generation. Differently from previously reported studies based on frequency chirp measurements, we use extreme ultraviolet interferometry as the most natural and direct way to measure phase shifts. Our approach has the important advantage of allowing us to investigate the effects associated to both the main quantum paths involved in the emission of a particular harmonic, thus offering a particularly clear and simple picture of the underlying electronic dynamics.

Reconstruction of attosecond pulse trains using an adiabatic phase expansion

We propose a new method to reconstruct the electric field of attosecond pulse trains. The phase of the high-order harmonic emission electric field is Taylor expanded around the maximum of the laser pulse envelope in the time domain and around the central harmonic in the frequency domain. Experimental measurements allow us to determine the coefficients of this expansion and to characterize the radiation with attosecond accuracy over a femtosecond time scale. The method gives access to pulse-to-pulse variations along the train, including the timing, the chirp, and the attosecond carrier envelope phase.

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.

Gouy phase shift for few-cycle laser pulses

We measured for the first time the influence of the Gouy effect on focused few-cycle laser pulses. The carrier-envelope phase is shown to undergo a smooth variation over a few Rayleigh distances. This result is of critical importance for any application of ultrashort laser pulses, including high-harmonic and attosecond pulse generation, as well as phase-dependent effects.

Observation of carrier-envelope phase phenomena in the multi-optical-cycle regime

So far the role of the carrier-envelope phase of a light pulse has been clearly experimentally evidenced only in the sub-6-fs temporal regime. Here we show, both experimentally and theoretically, the influence of the carrier-envelope phase of a multi-optical-cycle light pulse on high-order harmonic generation. For the first time, we demonstrate that the short and long electron quantum paths contributing to harmonic generation are influenced in a different way by the pulse carrier-envelope phase.

Ponderomotive shearing for spectral interferometry of extreme-ultraviolet pulses

We propose a novel method for completely characterizing ultrashort pulses at extreme-ultraviolet (XUV) wavelengths by adapting the technique of spectral phase interferometry for direct electric-field reconstruction to this spectral region. Two-electron wave packets are coherently produced by photoionizing atoms with two time-delayed replicas of the XUV pulse. For one of the XUV pulses, photoionization occurs in the presence of a strong infrared pulse that ponderomotively shifts the binding energy, thereby providing the spectral shear needed for reconstruction of the spectral phase of the XUV pulse.

Effects of carrier-envelope phase differences of few-optical-cycle light pulses in single-shot high-order-harmonic spectra

For the first time single-shot harmonic spectra generated by few-optical-cycle pulses have been measured. Clear carrier-envelope phase effects have been observed in the cutoff harmonic spectral structure. Results have been interpreted in terms of the nonadiabatic single-atom response of the nonlinear medium excited by few-optical-cycle pulses.

Frequency-resolved optical gating of femtosecond pulses in the extreme ultraviolet

Femtosecond extreme ultraviolet (XUV) pulses were fully characterized for the first time by using a newly developed cross-correlation frequency-resolved optical gating (FROG) technique in the XUV region. This method utilizes laser-assisted two-photon ionization as a nonlinear optical process. Near-infrared pulses characterized by FROG were used as a reference. The amplitude and phase of XUV pulses with a pulse duration of 10 fs were found to be in good agreement with a model analysis, taking into account phase modulation by ionization, self-phase modulation, and the atomic dipole phase.

Global optimization of high harmonic generation

We investigate the relevance of the absorption limit concept in the optimization of high harmonic generation. Thanks to the first direct observation of the coherence length of the process from high-contrast Maker fringes, we unravel experimental conditions for which the harmonic dipole response is enhanced when phase matching is realized within the absorption limit, leading to record conversion efficiencies in argon. Moreover, we show that harmonic generation in guided or freely propagating geometries are equivalent in the loose focusing regime. This analysis is generalized to other advanced phase-matching schemes, thereby predicting the possibility to boost the conversion efficiencies using light noble gases.

Time-frequency characterization of femtosecond extreme ultraviolet pulses

We present energy-resolved cross-correlation measurements of an extreme ultraviolet (XUV) pulse, generated as the fifth harmonic (15.5 eV) of an intense 80 fs laser pulse centered at 400 nm. Spectrally resolving the cross-correlation signal allows us to characterize the time-dependent frequency of the XUV pulse. We find that the fifth harmonic has a small negative chirp in excess of that predicted by perturbation theory. In addition, by manipulating the chirp of the driving laser we can induce and measure a positive or a negative chirp on the XUV pulse.

Measurement of the intensity-dependent atomic dipole phase of a high harmonic by frequency-resolved optical gating

The temporal profile and phase of the fifth harmonic of a Ti:sapphire laser were fully characterized by two-photon ionization frequency-resolved optical gating technique for the first time. The fifth harmonic was found to have negative chirp and the pulse compression was demonstrated. The negative chirp is well explained by using a zero-range potential model. This technique is scalable to extreme ultraviolet (XUV) and soft x-ray regions by using currently available light sources, making it possible to measure the pulse duration and phase of vacuum ultraviolet, XUV, and soft x-ray pulses.

Attosecond time-scale intra-atomic phase matching of high harmonic generation

Using a model of high-harmonic generation that couples a fully quantum calculation with a semiclassical electron trajectory picture, we show that a new type of phase matching is possible when an atom is driven by an optimal optical waveform. For an optimized laser pulse shape, strong constructive interference is obtained in the frequency domain between emissions from different electron trajectories, thereby selectively enhancing a particular harmonic order. This work demonstrates that coherent control in the strong-field regime is possible by adjusting the peaks of a laser field on an attosecond time scale.

Spectral features and modeling of high-order harmonics generated by sub-10-fs pulses

Harmonic radiation generated in a neon gas jet by sub-10-fs laser pulses was investigated both experimentally and theoretically. The spectral profile of the harmonics with respect to the order, their intensity and relative spectral shifts were measured as a function of the position of the gas jet. The results point out spectral features typical of the quasi-single-cycle excitation regime. A nonadiabatic three-dimensional numerical model was developed, which provides harmonic spectra in remarkable agreement with the experiments.