We present the results of a comprehensive analytical and numerical study of ultrawide spectral broadening and compression of isolated extremely short visible, uv-vuv and middle infrared (MIR) pulses by high-order stimulated Raman scattering in hollow waveguides. Spectral and temporal characteristics of the output pulses and the mechanism of pulse compression using dispersion of the gas filling and output glass window are investigated without the slowly varying envelope approximation. Physical limitations due to phase mismatch, velocity walk off, and pump-pulse depletion as well as improvements through the use of pump-pulse sequences and dispersion control are studied. It is shown that phase-locked pulses as short as similar to2 fs in the visible and uv-vuv, and 6.5 fs in the MIR can be generated by coherent scattering in impulsively excited Raman media without the necessity of external phase control. Using pump-pulse sequences, shortest durations in the range of about 1 fs for visible and uv-vuv probe pulses are predicted.

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.

We present experimental results in which a second-order effect, namely two-photon ionization of atomic He induced by a superposition of harmonics, is observed. The harmonics are generated in a Xe gas-jet using a 790-nm 10-Hz femtosecond Ti:sapphire laser and are subsequently focused into a He gas-jet with a Kirkpatrick-Baez arrangement. The superposition is formed by using a thin In filter and it comprises the 7th to 13th harmonics. Solving the time-dependent Schrodinger equation for He in a polychromatic laser field, the He+ ion yield is calculated as a function of the total XUV intensity. Using the calculated yield and taking into account the focusing and transmission properties of the arrangement, the number of He+ ions produced per laser pulse is estimated and is found to be in reasonable agreement with its measured value. The total number of ions produced non-resonantly follows a nearly quadratic dependence on the harmonic intensity, thus establishing the feasibility of a second-order auto-correlation measurement of the superposition of harmonics, i.e., of a direct temporal characterization of attosecond pulse trains.

Recently the initial measurements of single attosecond pulses with laser-dressed single-photon XUV ionization of gas atoms were reported. Determination of the extreme-ultraviolet (XUV) pulse duration from the electron spectrum is based on a classical theory. Although classical models are known to give a qualitatively correct description of strong laser-atom interaction, the validity range for accurate determination of subfemtosecond pulses must be scrutinized by quantum mechanical analysis. We establish a theoretical framework for the accurate temporal characterization of attosecond XUV pulses by using a Fourier-Bessel expansion of the XUV electron spectrum under the strong field approximation and a semiclassical derivation, setting earlier results on a rigorous theoretical footing. Our analysis reveals an improved scheme that is by more than an order of magnitude more efficient than the one used so far and allows for direct experimental discrimination between single and multiple attosecond pulses. (C) 2003 Optical Society of America.

The first reported measurements of single attosecond pulses use laser dressed single-photon extreme ultraviolet (XUV) ionization of gas atoms. The determination of XUV pulse duration from the electron spectrum is based on a classical theory. Although classical models are known to give a qualitatively correct description of strong laser atom interaction, the validity must be scrutinized by a quantum-mechanical analysis. We establish a theoretical framework for the accurate temporal characterization of attosecond XUV pulses. Our analysis reveals an improved scheme that allows for direct experimental discrimination between single and multiple attosecond pulses.

We show that the complete characterization of arbitrarily short isolated attosecond x-ray pulses can be achieved by applying spectral shearing interferometry to photoelectron wave packets. These wave packets are coherently produced through the photoionization of atoms by two time-delayed replicas of the x-ray pulse, and are shifted in energy with respect to each other by simultaneously applying a strong laser field. The x-ray pulse is reconstructed with the algorithm developed for optical pulses, which requires no knowledge of ionization physics. Using a 800-nm shearing field, x-ray pulses shorter than similar to400 asec can be fully characterized.

The effect of the carrier-envelope phase of a few-cycle driving laser field on the generation and measurement of high-order harmonic attosecond pulses is investigated theoretically. We find that the position of the generated attosecond soft-x-ray pulse in the cutoff region is locked to the oscillation of the driving laser field, but not to the envelope of the laser pulse. This property ensures the success of the width measurement of an attosecond soft-x-ray pulse based on the cross correlation between the attosecond pulse and its driving laser pulse [M. Hentschel , Nature (London) 414, 509 (2001)]. However, there still exists a timing jitter of the order of tens of attoseconds between the attosecond pulse and its driving laser field. We also propose a method to detect the carrier-envelope phase of the driving laser field by measuring the spatial distribution of the photoelectrons induced by the attosecond soft-x-ray pulse and its driving laser pulse.

Spectroscopic measurements with increasingly higher time resolution are generally thought to require increasingly shorter laser pulses, as illustrated by the recent monitoring of the decay of core-excited krypton(1) using attosecond photon pulses(2),(3). However, an alternative approach to probing ultrafast dynamic processes might be provided by entanglement, which has improved the precision(4,5) of quantum optical measurements. Here we use this approach to observe the motion of a D-2(+) vibrational wave packet formed during the multiphoton ionization of D-2 over several femtoseconds with a precision of about 200 attoseconds and 0.05 angstroms, by exploiting the correlation between the electronic and nuclear wave packets formed during the ionization event. An intense infrared laser field drives the electron wave packet, and electron recollision(6-11) probes the nuclear motion. Our results show that laser pulse duration need not limit the time resolution of a spectroscopic measurement, provided the process studied involves the formation of correlated wave packets, one of which can be controlled; spatial resolution is likewise not limited to the focal spot size or laser wavelength.

Experience shows that the ability to make measurements in any new time regime opens new areas of science. Currently, experimental probes for the attosecond time regime (10(-18)-10(-15) s) are being established. The leading approach is the generation of attosecond optical pulses by ionizing atoms with intense laser pulses. This nonlinear process leads to the production of high harmonics during collisions between electrons and the ionized atoms. The underlying mechanism implies control of energetic electrons with attosecond precision. We propose that the electrons themselves can be exploited for ultrafast measurements. We use a 'molecular clock', based on a vibrational wave packet in H-2(+) to show that distinct bunches of electrons appear during electron-ion collisions with high current densities, and durations of about 1 femtosecond (10(-15) s). Furthermore, we use the molecular clock to study the dynamics of non-sequential double ionization.

A new technique for directly measuring the electric field of linearly polarized few-cycle laser pulses is proposed. Based on the solution of the time-dependent Schrodinger equation (TDSE) for an H atom in the combined field of infrared (IR) femtosecond (fs) and ultraviolet (UV) attosecond (as) laser pulses we show that, as a function of the time delay between two pulses, the difference (or equivalently, asymmetry) of photoelectron signals in opposite directions (along the polarization vector of laser pulses) reproduces very well the profile of the electric field (or vector potential) in the IR pulse. Such ionization asymmetry can be used for directly measuring the carrier-envelope phase difference (i.e., the relative phase of the carrier frequency with respect to the pulse envelope) of the IR fs laser pulse.

We investigate a simple scheme for autocorrelation measurement of an xuv pulse. It is based on double ionization of He. We have found that, in a certain photon energy range, the detection of doubly charged positive ions instead of energy-resolved photoelectrons is sufficient for autocorrelation, which greatly simplifies the detection system for practical use.

The combination of several high order harmonics can produce an attosecond pulse train, provided that the harmonics are locked in phase to each other. We present calculations that evaluate the degree of phase locking that is achieved in argon and neon gases interacting with an intense, 50 fs laser pulse, for a range of macroscopic conditions. We find that phase locking depends on both the temporal and the spatial phase behavior of the harmonics, as determined by the interplay between the intrinsic dipole phase and the phase matching in the nonlinear medium. We show that, as a consequence of this, it is not possible to compensate for a lack of phase locking by purely temporal phase manipulation.

Atomic stabilization is a highlight of superintense laser-atom physics. A wealth of information has been gathered on it; established physical concepts have been revised in the process; points of contention have been debated. Recent technological breakthroughs are opening exciting perspectives of experimental study. With this in mind, we present a comprehensive overview of the phenomenon.We discuss the two forms of atomic stabilization identified theoretically. The first one, 'quasistationary (adiabatic) stabilization' (QS), refers to the limiting case of plane-wave monochromatic radiation. QS characterizes the fact that ionization rates, as calculated from single-state Floquet theory, decrease with intensity (possibly in an oscillatory manner) at high values of the field. We present predictions for QS from various forms of Floquet theory: high frequency (that has led to its discovery and offers the best physical insight), complex scaling, Sturmian, radiative close coupling and R-matrix. These predictions all agree quantitatively, and high-accuracy numerical results have been obtained for hydrogen. Predictions from non-Floquet theories are also discussed. Thereafter, we analyse the physical origin of QS.The alternative form of stabilization, 'dynamic stabilization' (DS), is presented next. Ibis expresses the fact that the ionization probability at the end of a laser pulse of fixed shape and duration does not approach unity as the peak intensity is increased, but either starts decreasing with the intensity (possibly in an oscillatory manner), or flattens out at a value smaller than unity. We review the extensive research done on one-dimensional models, that has provided valuable insights into the phenomenon; twoand three-dimensional models are also considered. Full three-dimensional Coulomb calculations have encountered severe numerical handicaps in the past, and it is only recently that a comprehensive mapping of DS could be made for hydrogen. An adiabatic variation of the laser-pulse envelope keeps the system in the Floquet state associated with the initial state, that allows calculation of the ionization probability in terms of the corresponding rate. A nonadiabatic variation can excite other Floquet states, either discrete ('shake-up') or continuous ('shake-off'), with considerable consequences for DS. A unitary interpretation of these aspects of DS is presented in terms of 'multistate Floquet theory'. We then comment on the points of contention raised in connection with DS. Further, we review the extent to which the classical approach has been successful in describing DS.We next examine the concern that nonrelativistic (NR) predictions for stabilization may be inadequate in superintense fields, because relativistic corrections would invalidate them. It turns out that, although the relativistic corrections do limit stabilization, there is an ample 'window' of intensities for which the NR predictions remain valid.Finally, we discuss the experimental evidence in favour of stabilization. For lack of adequate lasers to study ground states of single-active-electron atoms, the experiments so far have been performed on low-lying Rydberg states. Two state-of-the-art experiments have determined ionization yields for pulses with adiabatic envelopes. Their results concur, are in agreement with the theoretical predictions and represent a clear-cut confirmation of DS.Our conclusion is that superintense field stabilization is firmly established, both theoretically and experimentally. Nevertheless, further research is desirable to solve interesting open problems, some of which we identify. Their research is made timely by the superintense high-frequency light sources that are being developed, such as VUV-FELs, or attosecond pulses from high-harmonic generation.

The characteristic time constants of the relaxation dynamics of core-excited atoms have hitherto been inferred from the linewidths of electronic transitions measured by continuous-wave extreme ultraviolet or X-ray spectroscopy. Here we demonstrate that a laser-based sampling system, consisting of a few-femtosecond visible light pulse and a synchronized sub-femtosecond soft X-ray pulse, allows us to trace these dynamics directly in the time domain with attosecond resolution. We have measured a lifetime of 7.9(-0.9)(+1.0) fs of M-shell vacancies of krypton in such a pump-probe experiment.

Single soft-x-ray pulses of similar to 90-electron volt (eV) photon energy are produced by high-order harmonic generation with 7-femtosecond (fs), 770-nanometer (1.6 eV) Laser pulses and are characterized by photoionizing krypton in the presence of the driver laser pulse. By detecting photoelectrons ejected perpendicularly to the Laser polarization, broadening of the photoelectron spectrum due to absorption and emission of Laser photons is suppressed, permitting the observation of a Laser-induced downshift of the energy spectrum with sub-laser-cycle resolution in a cross correlation measurement. We measure isolated x-ray pulses of 1.8 (+0.7/-1.2) fs in duration, which are shorter than the oscillation cycle of the driving Laser Light (2.6 fs). Our techniques for generation and measurement offer sub-femtosecond resolution over a wide range of x-ray wavelengths, paving the way to experimental attosecond science. Tracing atomic processes evolving faster than the exciting light field is within reach.

Photoelectrons excited by extreme ultraviolet or x-ray photons in the presence of a strong laser field generally suffer a spread of their energies due to the absorption and emission of laser photons. We demonstrate that if the emitted electron wave packet is temporally confined to a small fraction of the oscillation period of the interacting light wave, its energy spectrum can be upor down-shifted by many times the laser photon energy without substantial broadening. The light wave can accelerate or decelerate the electrons drift velocity, i.e., steer the electron wave packet like a classical particle. This capability strictly relies on a sub-femtosecond duration of the ionizing x-ray pulse and on its timing to the phase of the light wave with a similar accuracy, offering a simple and potentially single-shot diagnostic tool for attosecond pump-probe spectroscopy.

We report the generation and measurement of isolated soft-X-ray pulses (lambda(X) = 14 nm) with a duration of tau(X) = 650 150 attoseconds (as) by using few-cycle intense visible/near-infrared (lambda(0) = 750 nm) laser pulses. For the temporal characterization of the X-ray pulses, a cross-correlation technique relying on laser field assisted X-ray photoemission from krypton atoms was employed. The experimental results bear direct evidence of the X-ray pulse being synchronized to the field oscillations of the visible-light pulse with attosecond precision and of bound-free electronic transitions from the 4p state of krypton responding to 90-eV excitation on an attosecond time scale. As a first demonstration of attosecond metrology, the synchronized single sub-fs X-ray pulses were used for tracing the electric field oscillations in a visible-light wave with a resolution of better than 150 as.

A method is proposed for detailed determination of the temporal structure of XUV pulses. The method is especially suited for diagnostics on attosecond pulses and pulse trains that originate from temporal beating of various harmonics of an ultrashort laser pulse. A recent experiment already showed the feasibility of this method when applied to long attosecond pulse trains, where it measured the average pulse characteristics. Here we argue that the same method is also suitable for determining differences between the individual attosecond pulses in a short train, or the properties of a single attosecond pulse.

We have solved the time-dependent Schrodinger equation describing the simultaneous interaction of the He 1s2s S-1 state with two laser-generated pulses of trapezoidal or Gaussian shape, of duration 86 fs and of frequencies omega(1) = 1.453 au and omega(2) = 1.781 au. The system is excited to the energy region of two strongly correlated doubly excited states, chosen for this study according to specific criteria. It is demonstrated quantitatively that, provided one focuses on the dynamics occurring within the attosecond timescale, the corresponding orbital configurations, 2s2p and 2p3d P-1(o), exist as nonstationary states, with occupation probabilities that are oscillating as the states decay exponentially into the 1sepsilonp continuum, during and after the laser-atom interaction. It follows that it is feasible to probe by attosecond pulses the motion of configurations of electrons as they correlate via the total Hamiltonian. For the particular system studied here, the probe pulses could register the oscillating doubly excited configurations by de-exciting to the He 1s3d D-1 state, which emits at 6680 Angstrom.

An electron generated by x-ray photoionization can be deflected by a strong laser field. Its energy and angular distribution depends on the phase of the laser field at the time of ionization. This phase dependence can be used to measure the duration and chirp of single sub100-attosecond x-ray pulses.

The phases of the circularly polarized harmonics with alternating helicity generated by a bichromatic laser field whose two components are circularly polarized in the same plane but rotate in opposite directions an investigated. Only one trajectory contributes to harmonic generation in the plateau region. The dependence of the harmonic phase on the laser field intensity is weak (with the slope similar to 0.2 U-p /omega). Adjacent harmonics having the same helicity are relatively closely phase locked. As a result, a train of three attosecond pulses per optical cycle of the driving field is generated, each having a width of 80 as. Depending upon whether the two helicity components can be separated the polarization of the pulses is close to circular or close to linear with three different orientations per optical cycle.

A numerical simulation of attosecond harmonic pulse generation in a three-dimensional field-ionizing gas is presented. Calculated harmonic efficiencies quantitatively reproduce experimental findings. This allows a quantitative characterization of attosecond pulse generation revealing information currently not accessible by experiment. The rapid phase variation and spatiotemporal distortions of harmonics are smaller than anticipated, allowing focusing of 30-nm, 750-as pulses to intensities in excess of 10(13) W/cm(2). Feasibility of such pulses brings novel applications such as extreme ultraviolet nonlinear optics and attosecond pump probe spectroscopy within reach.

The generation of ultrashort pulses is a key to exploring the dynamic behaviour of matter on ever-shorter timescales. Recent developments have pushed the duration of laser pulses close to its natural limit-the wave cycle, which lasts somewhat longer than one femtosecond (1 fs = 10(-15) s) in the visible spectral range. Time-resolved measurements with these pulses are able to trace dynamics of molecular structure, but fail to capture electronic processes occurring on an attosecond (1 as = 10(-18) s) timescale. Here we trace electronic dynamics with a time resolution of less than or equal to 150 as by using a subfemtosecond soft-X-ray pulse and a few-cycle visible light pulse. Our measurement indicates an attosecond response of the atomic system, a soft-X-ray pulse duration of 650 +/- 150 as and an attosecond synchronism of the soft-X-ray pulse with the light field. The demonstrated experimental tools and techniques open the door to attosecond spectroscopy of bound electrons.

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-held regime is possible by adjusting the peaks or a laser field on an attosecond time scale.

Generation and propagation of high-order harmonics by intense, ultrashort laser pulses in static gas cells and gas-filled hollow waveguides are numerically investigated. The calculations are performed utilizing a self-consistent solution of the time-dependent Schrodinger and wave equations. It is shown that, when the 30-fs laser pulse is focused into a gas cell the emission spectrum consists of discrete and well-resolved harmonics. These high-order harmonics can be used for generation of a train of subfemtosecond pulses. When the 5-fs laser pulse propagates along a gas-filled hollow waveguide the emission spectrum exhibits a quasicontinous structure that permits the generation of a single subfemtosecond pulse. The effects of laser intensity and position of the interacting medium relative to the laser focus on the emission spectrum and pulse profile are investigated. The differences between results obtained by our model and by the model that uses the strong-field approximation for single-atom calculations are discussed.

Using a coherent nonlinear optical technique, slipping of the carrier through the envelope of 6-fs light wave packets emitted from a mode-locked-oscillator/pulse-compressor system has been measured, permitting the generation of intense, few-cycle light with precisely reproducible electric and magnetic fields. These pulses open the way to controlling the evolution of strong-field interactions on the time scale of the light oscillation cycle and are indispensable to reproducible attosecond x-ray pulse generation.