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Observation of a Train of Attosecond Pulses from High Harmonic Generation

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Science  01 Jun 2001:
Vol. 292, Issue 5522, pp. 1689-1692
DOI: 10.1126/science.1059413

Abstract

In principle, the temporal beating of superposed high harmonics obtained by focusing a femtosecond laser pulse in a gas jet can produce a train of very short intensity spikes, depending on the relative phases of the harmonics. We present a method to measure such phases through two-photon, two-color photoionization. We found that the harmonics are locked in phase and form a train of 250-attosecond pulses in the time domain. Harmonic generation may be a promising source for attosecond time-resolved measurements.

The advent of subfemtosecond or attosecond (as) light pulses will open new fields of time-resolved studies with unprecedented resolution. Just as subpicosecond or femtosecond (fs) pulses have allowed the resolution of molecular movements, attosecond pulses may enable us to resolve electronic dynamics. Several groups around the world are researching the generation of subfemtosecond pulses. Large bandwidths are required to support such pulses. The spectrum of a 200-as unipolar pulse covers the optical spectrum from the near infrared to the extreme ultraviolet. There are two known kinds of sources with the potential to produce coherent radiation over such bandwidths: high harmonic generation (HHG) (1) and stimulated Raman scattering (2, 3). Both methods have, in theory, a tendency to produce a train of closely spaced pulses rather than a single pulse. Even such trains of attosecond pulses, applied to experiments, can open a new field of attosecond physics, allowing the study of processes of unprecedented speed. Moreover, methods of selecting only one pulse from the train have already been suggested (4). The present experimental study focuses on HHG and demonstrates that this process indeed results in a train of attosecond pulses.

If an intense femtosecond laser pulse is focused on an atomic gas jet, the nonlinear electronic response of the medium causes the generation of higher harmonics of the laser field. The harmonic spectrum consists of a series of narrow peaks separated by twice the frequency of the driving field, and it extends far into the extreme ultraviolet regime (1). For reasons of symmetry, only odd harmonics are emitted. Although high harmonics have been a familiar presence in many laser laboratories for more than 10 years, and although their generation is well understood experimentally and theoretically (5–7), some features of the generation process have remained inaccessible to direct experimental measurement. In particular, questions relating to the time profile of the harmonic emission are not easily resolved. Measurements of the harmonic pulse duration show that it is much shorter than that of the driving laser (8–10) and lasts for only a few femtoseconds. In addition to questions related to the pulse envelope of an individual harmonic, another measurement difficulty involves beating between various harmonics; this occurs on a subfemtosecond time scale, and no streak camera or autocorrelator developed for this wavelength range can reach such a high resolution.

Theoretical results for the temporal characteristics of the generation process are much more detailed, and they predict that the harmonics are locked in phase. If this is correct, a group of neighboring harmonics could beat together to form a very short intensity spike, provided they all add constructively at the same instant. Because of the constant frequency spacing of the harmonics, this would happen twice per optical cycle of the driving laser. The duration of the spike could be as short as T laser/2N (where N is the number of phase-locked harmonics) (11, 12). At a laser wavelength of 800 nm, and N = 5, the output pulse would then be in the attosecond regime.

Numerical calculations for the single-atom response indicate that the harmonics are not emitted exactly in phase, leading to the generation of not one but several spikes per optical half-cycle (13). In practice, propagation of the electromagnetic fields through the medium affects the spatial and temporal coherence properties of the harmonic radiation. The theoretical conclusion is that per half-cycle only one of the interference spikes survives the propagation, thus forming a train of attosecond pulses spaced by half the period of the fundamental (13–15).

A recent experiment (16) has confirmed that the harmonic radiation contains structure on an attosecond scale. However, that experiment was based on measuring the field autocorrelate, which is equivalent to measuring the power spectrum of the harmonics; therefore, no information could be obtained about the relative phases of the harmonic components. It is exactly those phases that determine whether the harmonic field exhibits strong amplitude modulation (i.e., forms an attosecond pulse train), rather than being a frequency-modulated wave of approximately constant amplitude.

Our experiment approaches the problem from a direction closely related to the theoretical work of Veniard et al. (17). We seek to determine the phase relation between the contributing harmonics by considering them in pairs. The periodic beat pattern of such a pair can be related to the phase of the infrared (IR) light from the driving laser according to how the combined fields ionize atoms. The intensities of the individual harmonics are too weak to cause nonlinear effects on the target atoms, and thus only cause ionization by single-photon processes, each harmonic producing photoelectrons according to Einstein's equation for the photoelectric effect. The IR field, however, can easily be made to induce additional multiphoton transitions in the continuum (18). Ionization with a harmonic photon can then be accompanied by absorption as well as emission of different numbers of IR photons. In the electron spectrum, this results in the appearance of sidebands (Fig. 1).

Figure 1

Photoelectron spectra of argon ionized by a superposition of odd harmonics from an IR laser (A). In (B and C) copropagating fundamental radiation was added, causing sidebands to appear between the harmonic peaks. Changing the time delay between IR and harmonics from –1.7 fs in (B) to –2.5 fs in (C) causes a strong amplitude change of the sidebands.

At low IR intensities, where the problem can be treated in second-order perturbation theory, each harmonic has only a single sideband on each side. These sideband peaks appear at energies corresponding to even multiples of the IR photon energy, and are thus located between the peaks caused by the harmonics themselves. Only the two nearest harmonics contribute to each sideband peak, each through two quantum paths (Fig. 2) that differ in the order in which the various photons are participating. According to Fermi's golden rule, the total transition probability from the initial ground state ψi, with energyE 0, to all final states ψf (where f represents the angular quantum numbers of the continuum electron) at the sideband energyEq = E 0 +qℏ︀ω is proportional to S = Σf|M f,q–1 (+)+ M f,q+1  (–)|2, withM f,q (±) = 〈ψf|D IR ±(Eq H)−1 D q ++ D q +(E ±1H)−1 D IR ±i〉. In these expressions, ℏ︀ is Planck's constant divided by 2π, ω is the IR field frequency, H is the atomic Hamiltonian, the dipole operators D + correspond to the energy-increasing part of the electromagnetic perturbation,Embedded Image(1)and their complex conjugates D to the energy-decreasing part (19). The IR field is present as D inM f,q+1 (−) , because of the emission of the IR photon, and it thus contributes a phase of the opposite sign with respect toM f,q−1 (+) . Explicitly writing the phases D ± = D 0exp(±iϕ), the interference terms in S becomeAf cos(2ϕIR + ϕq−1 − ϕq+1 + Δϕatomic f), whereAf = 2|M f,q−1  (+)||M f,q+1  (−)|. Delaying the IR field by a time τ with respect to the harmonic fields sets ϕIR = ωIRτ. By experimentally recording the magnitude of the sideband peak as a function of τ, and fitting a cosine to this, we determine ϕq–1 − ϕq+1. The appearance of Δϕatomic f is a consequence of the intrinsic complex phase of the matrix elements (20, 21), resulting from (EH)−1 being applied at an energy in the continuous atomic spectrum (22). This phase is small and can be obtained from established theory with high precision (Table 1).

Figure 2

The experimental setup. A beam of a titanium-sapphire laser (800 nm, 40 fs, 1 kHz) is split by a mask into an outer, annular part (3 mJ) and a small central part (30 μJ). Both parts are focused into an Ar jet, where the smaller focus of the annular part generates harmonics (XUV). The annular part is then blocked by a pinhole, and only the central part of the IR pulse and its harmonics propagates into a magnetic-bottle spectrometer. The light is refocused there by a spherical tungsten-coated mirror (focal length 35 mm) onto a second Ar jet, and the electrons resulting from photoionization in this jet are detected at the end of the time-of-flight (TOF) tube by microchannel plates (MCP). The harmonics and IR pulse can be delayed with respect to each other by using antireflection-coated glass plates (6 mm thick) cut from the same window. The inset shows the quantum paths contributing to the photoelectrons generated in the second argon jet by mixed-color two-photon ionization; ωlaser is the IR field frequency and ωq equalsqωlaser.

Table 1

The atomic phases Δϕatomic f and the relative strengths Af of each two-photon transition responsible for the sideband peaks. The numbers within the parentheses represent the values of the angular and magnetic quantum numbers of the initial 3p state and the final continuum state of the listed energy.

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The experimental setup has been described in detail (9) and is shown in Fig. 2. At an intensity of ∼100 TW/cm2, many different odd harmonics are generated, but the tungsten mirror used to relay the beam into the electron spectrometer cuts off the spectrum beyond harmonic 19. The central part of the laser beam provides the IR light used to induce the sidebands, with adjustable phase (23). The spectrometer is observing an area with a radius of 125 μm, located 1.5 mm before the focus of the spherical mirror. This was done to avoid the 180° phase slip that occurs when a light beam goes through a focus, and to ensure that the relative phase of the IR light and harmonics stays constant over the observed volume. The IR peak intensity can be estimated as <1 TW/cm2, too weak to alter the photoelectron energies by ponderomotively shifting the ionization potential (9) (Fig. 1). This is also far below the threshold for multiphoton ionization of Ar by IR only.

The amplitudes of the first four sidebands, integrated over all corresponding energy channels, are plotted as a function of the time delay τ in Fig. 3. Each point is divided by the total signal at that delay to compensate for fluctuations in the harmonic intensity (which, because of the high order of the generation process, is an extremely sensitive function of laser intensity). The curves are oscillating in phase with a periodicity of 1.35 fs (i.e., half of the IR field period). The good modulation depth (a factor of about 2) shows that the relative phases do not fluctuate too much over the beam profile, between shots, or within the profile of a single pulse. The oscillation period is that expected for the sideband interference, which is half of that expected for interference between IR components in the two beam parts. (The gas pressure in the harmonics jet was deliberately kept low to avoid contamination of the harmonics by scattered IR light.)

Figure 3

Area of the first four sideband peaks (to higher energies from top to bottom) as a function of the time delay between the IR pulse and the harmonics. The first three curves oscillate in phase; the lowest one is shifted forward by 0.35 fs. The vertical lines are spaced by 1.35 fs, half the cycle time of the driving laser.

From the fitted pairwise phase differences, the phases of the involved harmonics (11 to 19) were found to be –2.6, –1.3, 0, 1.8, and 4.4 radians (24), respectively (arbitrarily assigning ϕ15 = 0). Together with the relative harmonic intensities [obtained from Fig. 1A, corrected for the different ionization cross sections (25)], they uniquely determine the temporal intensity profile of the total field (Fig. 4). This profile is thus found to be a sequence of 250-as peaks [full width at half maximum (FWHM)], spaced by 1.35 fs. Repeating this reconstruction several times with phases randomly modified according to the experimental standard error leads to similar results, with a standard deviation of 20 as in the FWHM pulse duration. The phase differences of the first four harmonics are close but not identical, so the resulting attosecond pulses will not be entirely bandwidth limited.

Figure 4

Temporal intensity profile of a sum of five harmonics, as reconstructed from measured phases and amplitudes. The FWHM of each peak is ∼250 as. The cosine function represents the IR probe field for zero delay. Note that this reconstruction recovers “typical” properties of pulses in the train by assuming all pulses are identical; in reality the pulse properties might have some variation around this “average.”

Provided the IR bandwidth is relatively small, our method in principle analyzes all individual frequency components within the harmonics bandwidth simultaneously and independently, with each part of the sideband peak responding to the two frequency components that contribute to it. The sideband peak profile will thus show modulation with τ if phase differences vary over the bandwidth. Such profile changes are not apparent in our data, hence the harmonics must be frequency- modulated (“chirped”) in a similar way. An identical chirp in all harmonics does not affect the intensity envelope of the attosecond pulses, only the phase of their carrier wave (which we cannot measure).

The experimental evidence presented here for the existence of attosecond pulses in the process of HHG confirms theoretical predictions that the natural phase with which groups of neighboring harmonics are generated is sufficient to cause such pulse trains. In addition, our technique of phase measurement is a general one, applicable to deep in the extreme ultraviolet, and scales without difficulty to larger groups of harmonics. A measurement scheme for the phases may enable their purposeful manipulation (e.g., through dispersion when propagating through a gas cell), even if the harmonics were initially generated with undesirable phases. With such techniques, it should ultimately become possible to properly phase all harmonics emerging from the generation jet, leading to pulses perhaps as short as 10 as. The generation of these pulses still must be investigated in more detail, and ways of control and selection must be developed, before attosecond pulses can be routinely used as light sources in experiments.

  • * To whom correspondence should be addressed. E-mail: muller{at}amolf.nl

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