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Near-field imaging of dipole emission modulated by an optical grating

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Abstract

Attosecond measurements have been achieved in technically demanding pump-probe experiments by photoelectron streaking with stable infrared lasers and extreme-ultraviolet (XUV) instruments. Here, we demonstrate an efficient single-image all-optical measurement of an isolated attosecond pulse for its complete temporal characterization. We create the attosecond pulse with a 0.1-mJ, few-cycle, infrared pump beam and modulate it with an obliquely incident same-frequency weak beam. By refocusing the XUV beams, we obtain a spectrally resolved XUV image, showing the spectral phase of the attosecond pulse. Near-field imaging allows us to measure our pulse in 150 shots. This efficiency will be important for attosecond pulses in the water-window region. For complex systems, multi-electron dynamics is encoded in the temporal structure of attosecond pulses.

© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

Corrections

17 December 2021: A typographical correction was made to the first sentence in the first paragraph on the fourth page.

1. INTRODUCTION

In visible and infrared optics, researchers have developed single shot, or single image, measurements for characterizing ultrashort pulses or ultrafast phenomena. Spectral phase interferometry for direct electric-field reconstruction (SPIDER) [1] is an example of a single image pulse duration measurement. However, for high harmonics or attosecond science, the commonly applied measurement methods of the reconstruction of attosecond beating by interference of two-photon transitions (RABBIT) [2] or streaking [3] require multiple time delays between the pulse (or phenomenon) to be measured and the pulse performing the measurement. Furthermore, both methods are based on photoelectron spectroscopy. Therefore, each time delay requires many shots to avoid space-charge limits. However, in spite of its limitations, RABBIT and streaking have led to well-characterized attosecond pulses [2,3] and have been used to study Auger decay in ions [4] or ultrafast shake-up during photoionization in atoms [5], the relative time delay of electrons ionized from different orbitals in atoms [6] or different bands in solids [7], and delays in resonant two-photon ionization [810].

As water-window (${300}\;{\rm eV} \lt {\rm h}\nu \lt {500}\;{\rm eV}$) attosecond pulses are generated and as the technology is extended to even shorter wavelengths [11], traditional photoelectron spectroscopy becomes increasingly demanding for both characterizing attosecond pulses and measuring ultrafast phenomena. Therefore, technology draws us to in situ methods of pulse measurement.

In situ measurement, different from two-source XUV spectral interferometers [1214], is ideally suited to strong fields, which is based on the perturbation by a weak field labeling the pulse without changing the underlying process. This perturbative method was introduced as a simplified approach to attosecond science in which generation and measurement take place simultaneously. Adding or subtracting a photon of a perturbing beam to the re-collision electron hardly changes a high-order process, yet it indelibly marks how the attosecond pulse is created on the emitted XUV photons. Such measurement is also employed to solids [15] by using photons instead of photoelectrons, providing greater efficiency without space-charge issues.

However, in situ methods seemed to have a fundamental weakness. If the three-step model of attosecond pulse generation [16] is interpreted as requiring that each step is independent, then the three-step model effectively states that the phase of the transition moment [17] (step 3) cannot be resolved by perturbing electron trajectories (step 2).

On the other hand, if the trajectory of an outgoing electron is sensitive to the spectral phase of the transition moment, then the trajectory of the re-collision electron must also be sensitive to the spectral phase of the transition moment. One is simply the reverse of the other. In other words, the three steps cannot be independent. (For further discussion, please see [18]).

In companion papers, we show (both theoretically and experimentally) that the time delay near the Cooper minimum in argon modifies the shape of an attosecond pulse and that this modified shape is accurately observed in shifted trajectories measured by in situ methods, that time delay due to multi-electron dynamics of the giant plasmon resonance in xenon is accurately measured, and that the Fano resonances in helium are encoded by shifted trajectories that determine the spectral phase of an attosecond pulse.

 figure: Fig. 1.

Fig. 1. Schematic diagram of the obliquely overlapped two laser beams with an angle $\theta$ and generated XUV beams. The strong beam propagates along the $z$-axis on the $z - y$ frame, and the weak beam travels along the $z^\prime$-axis on the $z^\prime - y^{\prime}$ frame. The electron trajectories for the XUV generation, dominated by the strong beam, are predominantly along the strong beam polarization, and the optical grating is $y$-coordinate dependent in this frame. The diffracted XUV beam has a frequency-shifted spectral phase $\varphi ({\omega _{\rm{XUV}}} + M{\omega _g})$ of the attosecond pulse, where $M$ is the grating diffraction order. The inset shows the grating modulation along the $y$-axis at different times. We image this time-dependent modulation to measure an isolated attosecond pulse.

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 figure: Fig. 2.

Fig. 2. Conceptual illustration of the single-image measurement of an attosecond pulse. A polarization-gated strong laser pulse generates an isolated attosecond pulse from xenon. A weak linearly polarized pulse perturbs the generation process with the moving grating. The different frequencies of the attosecond pulse are affected by the moving grating at different times. The modulated dipole emission creates a diffraction pattern on the toroidal mirror, which refocuses the dipole emission onto the XUV detector to recover the near-field image of the dipole. A physical grating spreads the frequencies of the dipole emission along the perpendicular direction of the optical grating to measure the frequency-dependent emission time of the attosecond pulse.

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Our purpose for this paper is to introduce an efficient, single-image form of perturbative, in situ, pulse measurement. In the following sections, we demonstrate near-field measurement of an isolated attosecond pulse, both experimentally and theoretically. This technique will be used in the companion paper to measure the spectral phase of the giant plasmon resonance of xenon [19]. With improved detection, a higher frequency driver, or a more powerful laser beam, our approach scales to a single-shot measurement of an attosecond pulse.

2. NON-STATIONARY OPTICAL GRATING IN ATTOSECOND PULSE GENERATION

Observing photons is preferred over photoelectrons because phase matching provides the limit of photons that is usually large, while photoelectrons, generated through a transition moment that is generally small in the XUV region, are constrained to a few quanta by space charge. Our single-image measurement of an attosecond pulse uses the control of high-harmonic generation by a weak laser field as the basis for measurement [2022]. The perturbation labels the electron trajectory associated with a given spectral component of an attosecond pulse, and this trajectory determines the attosecond pulse and strong-field dynamics. For maximum efficiency, we image the x-ray source on the detector (Fig. 2). This near-field measurement uses the many photons that we have very efficiently, placing single-shot pulse measurements within reach.

As described mathematically in Supplement 1, when two laser pulses overlap non-collinearly at an angle $\theta$, whether they have the same frequency or not, they induce a moving amplitude and phase gratings. This grating modulates the dipole emission and therefore, the XUV beams. A reader may worry that a grating created by same-frequency pulses is static when viewed along the bisecting angle between the strong and weak beams. However, one of our pulses is much weaker than the other. Therefore, it is appropriate to analyze its motion in the frame of the intense driving beam. In Fig. 1, the strong laser pulse propagates along $z$-axis with its wave front in $x - y$ frame. It is the principal coordinator for the dipole modulated by the weak field.

When we consider an infinitesimal propagation distance, $dz$ or $dz^{\prime}$, for the strong and weak beams with angular frequencies of ${\omega _d}$ and ${\omega _p}$, respectively, during $dt$ at $z = {0}$, where the XUV is generated, the wave front of the weak beam has a phase shift with respect to that of the strong beam by ${\delta _g}(t,y) = {\omega _g}(t - {t_y})$, where ${t_y} = (y/c){\tan}{\theta _g}$, implying a non-stationary grating on a $z - y$ frame. Here, ${\omega _g} = {\omega _d} + {\omega _p}{\cos}\theta$ is the angular frequency of the optical grating, $c$ is the speed of light, and ${\theta _g} = {{\tan}^{- 1}}({\omega _p}{\sin}\theta /{\omega _g})$ is the propagation angle of the optical grating. In this frame, the wave front of the optical grating moves in time along a line of $y = z{\tan}{\theta _g}$, as shown in Fig. 1. The recollision electron motion and the wave front of the zero-order XUV beam are mainly determined by the strong laser beam. The wave fronts of higher-order diffracted XUV beams are, however, modified by the optical grating according to the momentum conservation of photons as described by the violet arrows in Fig. 1.

 figure: Fig. 3.

Fig. 3. Measured XUV continuum spectra without/with the weak laser pulse in (a) and (b), respectively. The numerically simulated XUV continuum spectra without/with the weak laser pulse in (c) and (d), respectively, by considering parameters in the experiment.

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We determine the emission time of each XUV frequency by measuring the position of grating modulation (i.e., the grating phase) at that frequency, as illustrated in the three insets of the xenon jet in Fig. 2. Details of the experimental apparatus and the time-dependent dipole perturbed with a non-collinear beam and numerical simulations of the spectrally resolved near-field dipole for characterizing an attosecond pulse are described in Supplement 1.

3. EXPERIMENTS AND RESULTS

To experimentally demonstrate our single-image near-field measurement of an isolated attosecond pulse, we first generate an attosecond pulse from xenon using a carrier-envelope phase (CEP) stabilized few-cycle laser pulse and detect the pulse by a near-field imaging XUV spectrometer, as illustrated in Fig. 2 [23,24].

Figure 3(a), measured by the apparatus in Fig. 2, shows the spectrally resolved near-field dipole emission of an attosecond pulse generated by polarization gating [25]. The peak intensity of the linearly polarized part of the $\lambda = {1.8}\;\unicode{x00B5}{\rm m}$ pulse is $I = {4} \times {{10}^{13}}\;{\rm W}/{{\rm cm}^2}$, which is strong enough to drive xenon for a broadband XUV spectrum up to 50 eV, as shown in Fig. 3(a). For this measurement, we adjust the slit of our XUV spectrometer for a resolving power of 70.5 in the energy domain. We confirm that the XUV source has a uniform size of 100 µm from 22 eV to 30 eV, corresponding to the laser beam size. Higher energy photons near the cut-off have a smaller size because the laser intensity to generate these frequencies is only sufficiently strong over a smaller cross-section of the driving beam. We use it as a background image for the better quality of analysis to obtain the grating position in frequency.

Figure 3(c) shows the result obtained by solving the time-dependent Schrödinger equation (TDSE) with parameters chosen to match the measured near-field dipole spectrum in Fig. 3(a). Experimental details are described in Section 4 of Supplement 1.

In Fig. 3(b) we add a weak pulse at an angle of 33 mrad and an intensity of ${4} \times {{10}^{11}}\;{\rm W}/{{\rm cm}^2}$ to perturb the dipole emission, creating a grating with the period of 54 µm. The grating modulation on the dipole emission is clearly pronounced when Fig. 3(b) is compared with Fig. 3(a) (the same color scale is used). Numerical simulation using the same parameters [Fig. 3(d)] agrees with the measured near-field dipole spectrum in Fig. 3(b).

The subtracted XUV spectral image, plotted in Fig. 4(a), with Figs. 3(a) and 3(b) shows that each frequency of the attosecond pulse is created with a different grating position ${y_g}$ (thereby, a different emission time) marked by a magenta solid line, implying the intrinsic atto-chirp [26]. We obtain ${y_g}$ of each photon energy by fitting the grating modulation using ${\sin}({2}\pi /{\lambda _g}(y - {y_g}))$, where ${\lambda _g} = {\lambda _p}/{\sin}\theta$ and ${\lambda _p}$ is the wavelength of the weak laser field. The grating phase ${\phi _g}$ is hence $({2}\pi /{\lambda _g}){y_g}$.

 figure: Fig. 4.

Fig. 4. (a) Subtracted XUV spectral image with Figs. 3(a) and 3(b). The optical grating induced by the weak laser field is clearly revealed on the near-field dipole emission with 1.5-cycle modulation. The spectrally resolved grating position is marked by a magenta line at the middle of the grating modulation for each frequency. (b) The measured spectral intensity (blue solid line) and emission time (red solid line) of the isolated attosecond pulse. The magenta shade indicates the statistical error of the emission time after taking 70 measurements with 150 shots accumulated for each image. The green dashed line is the dispersion curve of the isolated attosecond pulse calculated by the strong-field approximation (SFA) model [16]. The green shade implied the dispersion curves for the range of peak intensity within ${\pm}\;{5}\%$.

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For this measurement, we have chosen parameters such that xenon has a smooth recombination cross-section over the measured XUV spectrum, as confirmed by density functional theory in Supplement 1. (A reader is referred to a higher intensity measurement in xenon where the giant plasmon resonance is resolved [19]).

The recombination time of the re-colliding electron is the emission time of the corresponding XUV frequency. This mapping allows us to link recollision and emission times (i.e., ${\phi _g}(\omega) = \Delta \varphi (\omega))$, as explained by equation (S15) of Supplement 1. Here, $\Delta \varphi (\omega) = \varphi (\omega + {\omega _g}) - \varphi (\omega)$ represents the differential of the spectral phase $\varphi (\omega)$ of the attosecond pulse. Due to the non-stationary optical grating, the first diffractive order has a spectral phase of $\varphi (\omega + {\omega _g})$, which is the spectral phase of the attosecond pulse with a frequency shift by ${\omega _g}$. Thus, the emission time ${\tau _e}(\omega)$ of the attosecond pulse is found by ${\tau _e}(\omega) = \Delta \varphi (\omega)/\Delta \omega = {\phi _g}(\omega)/{\omega _g}$ of the equation (S18) in Supplement 1, as shown in Fig. 4(b) with a red solid line as well as the spectral intensity obtained from Fig. 3(a). The red shade indicates the standard deviation of the measured emission time by repeating the measurement for statistical analysis (70 images with 150 shots per image).

 figure: Fig. 5.

Fig. 5. Complete temporal characterization of an isolated attosecond pulse obtained by taking Fourier transform of the measured spectral amplitude and phase. The shaded areas are the standard deviations of the temporal intensity (blue) and phase (red) from the statistical analysis. Dotted lines are the intensity and phase achieved by a TDSE calculation using the strong driving laser pulse only. The inset shows the measured attosecond pulse on a logarithm scale to confirm it as a single isolated attosecond pulse.

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For plotting the emission time in Fig. 4(b), we adjust the offset to synchronize the emission time at 25.4 eV for all measurements. The emission time near the cut-off shows a larger deviation than that of the low energy due to the small amplitude of the XUV spectrum. For comparison, we also plot the emission time (green dashed line) from semi-classical electron trajectories calculated using the experimental parameters. The measured emission time agrees with the calculated value for the short trajectories, which dominate for a long-wavelength driver [27,28]. For this experiment, we achieve a temporal resolution of 46 as at 25 eV to measure the emission time.

Figure 5 presents the reconstructed isolated attosecond pulse, showing a positive chirp with a duration of ${320}\;{\pm}\;{20}$ as. The transform-limited duration is 160 as. The pulse from the TDSE simulation [Fig. 3(c)] is overlaid by dashed lines in Fig. 5 and agrees with the measured temporal intensity and phase of the attosecond pulse. The shaded areas in blue and red of Fig. 5 represent statistical errors for the temporal intensity and phase, respectively. Neighboring pulses at ${\pm}\;{3}\;{\rm fs}$ contain 0.2% of the pulse energy, shown in the inset of Fig. 5.

4. CONCLUSION AND FUTURE REMARKS

Measuring a pulse by imprinting its information onto photons (called in situ) is much more efficient than onto electrons (RABBIT or streaking), yet it contains almost the same information [29]. In this paper, we have used a perturbing field with the same frequency but a different incident angle of the fundamental laser, and we have confirmed its utility for attosecond pulse measurement experimentally and theoretically. While second harmonic was previously employed as the perturbing field for better time-domain sensitivity of the optical grating [21], using only the fundamental frequency is simpler to implement the optical grating with the same sensitivity by increasing $\theta$. Since a single frequency is sufficient and changing delay is unnecessary, it can be further simplified by impressing the perturbation onto the fundamental beam as a weak phase modulation (written by a spatial light modulator or a physical grating) and then re-imaging the beam onto the nonlinear medium where the measurement is made. In the long run, a grating imprinted on the fundamental beam will allow almost every attosecond pulse from not only gases but also solids to be individually measured. Our method will also be applied to measure attosecond pulses growing through the XUV generation medium.

The all-optical method using photons rather than electrons allows us to utilize the many available photons for measurement. We have further enhanced measurement efficiency by employing an x-ray imaging system to refocus the diffracted XUV beams. This approach follows earlier work applying the near-field method to femtosecond autocorrelation [30]. Near-field measurement has made us extend attosecond measurement to the single image regime. We record our image in 300 ms (150 shots) using a 100-μJ 1.8-µm laser. This is the first single image technology developed for attosecond science. Projecting our results to 800 nm where the single atom response is stronger [31], we predict single-shot measurements of attosecond pulses are available using few-cycle mJ-level lasers.

The technology for measuring ultrafast pulses is similar to that for ultrafast dynamics. This has been true for ultrafast science in general, including for RABBIT [2] and streaking [3], as discussed in the introduction. It is also true for perturbative in situ measurement, as we discuss in companion papers [19,32]. In these papers, phenomenon measurement is integrated with pulse measurement, but it needs not to be. The integration allows us to use only one medium, but an intermediate focus that enhances the photon efficiency further in our XUV imaging system can be utilized for x-ray absorption spectroscopy [33] with a fully characterized attosecond pulse.

Finally, while very closely related, in situ and ex situ (RABBIT and streaking) measurements are sensitive to different things. They behave differently for some multichannel processes like molecular rearrangement [34] or plasmonic resonance [35]. In situ measurements observe the system and its dynamics in the presence of the strong laser field [21,22], while ex situ measurements can (but not always) use low intensity laser beams [2,3]. This allows in situ methods to observe multi-electron dynamics occurring during the strong-field driven recollision process [36]. In a forthcoming paper, we extend the measurement described above to show how recolliding electrons are affected by recollision-induced plasmonic excitation of xenon in experiment [19].

Funding

Air Force Office of Scientific Research (FA9550-16-1-0109); Natural Sciences and Engineering Research Council of Canada; Canada Research Chairs; Canada Foundation for Innovation.

Acknowledgment

We are grateful for the technical assistance of Yu-Hsuan Wang and discussions with Dr. David Villeneuve.

Disclosures

The authors declare no conflicts of interest.

Data availability

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

Supplemental document

See Supplement 1 for supporting content.

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References

  • View by:

  1. C. Iaconis and I. A. Walmsley, “Spectral phase interferometry for direct electric-field reconstruction of ultrashort optical pulses,” Opt. Lett. 23, 792–794 (1998).
    [Crossref]
  2. P. M. Paul, E. S. Toma, P. Breger, G. Mullot, F. Augé, P. H. Balcou, H. G. Muller, and P. Agostini, “Observation of a train of attosecond pulses from high harmonic generation,” Science 292, 1689–1692 (2001).
    [Crossref]
  3. R. Kienberger, E. Goulielmakis, M. Uiberacker, A. Baltuska, V. Yakovlev, F. Bammer, A. Scrinzi, Th. Westerwalbesloh, U. Kleineberg, U. Heinzmann, M. Drescher, and F. Krausz, “Atomic transient recorder,” Nature 427, 817–821 (2004).
    [Crossref]
  4. M. Drescher, M. Hentschel, R. Kienberger, M. Uiberacker, V. Yakovlev, A. Scrinzi, Th. Westerwalbesloh, U. Kleineberg, U. Heinzmann, and F. Krausz, “Time-resolved atomic inner-shell spectroscopy,” Nature 419, 803–807 (2002).
    [Crossref]
  5. M. Uiberacker, Th. Uphues, M. Schultze, A. J. Verhoef, V. Yakovlev, M. F. Kling, J. Rauschenberger, N. M. Kabachnik, H. Schröder, M. Lezius, K. L. Kompa, H.-G. Muller, M. J. J. Vrakking, S. Hendel, U. Kleineberg, U. Heinzmann, M. Drescher, and F. Krausz, “Attosecond real-time observation of electron tunneling in atoms,” Nature 446, 627–632 (2007).
    [Crossref]
  6. M. Schultze, M. Fiess, N. Karpowicz, J. Gagnon, M. Korbman, M. Hofstetter, S. Neppl, A. L. Cavalieri, Y. Komninos, T. Mercouris, C. A. Nicolaides, R. Pazourek, S. Nagele, J. Feist, J. Burgdörfer, A. M. Azzeer, R. Ernstorfer, R. Kienberger, U. Kleineberg, E. Goulielmakis, F. Krausz, and V. S. Yakovlev, “Delay in Photoemission,” Science 328, 1658–1662 (2010).
    [Crossref]
  7. A. L. Cavalieri, N. Müller, Th. Uphues, V. S. Yakovlev, A. Baltuška, B. Horvath, B. Schmidt, L. Blümel, R. Holzwarth, S. Hendel, M. Drescher, U. Kleineberg, P. M. Echenique, R. Kienberger, F. Krausz, and U. Heinzmann, “Attosecond spectroscopy in condensed matter,” Nature 449, 1029–1032 (2007).
    [Crossref]
  8. M. Swoboda, T. Fordell, K. Klünder, J. M. Dahlström, M. Miranda, C. Buth, K. J. Schafer, J. Mauritsson, A. L’Huillier, and M. Gisselbrecht, “Phase measurement of resonant two-photon ionization in helium,” Phys. Rev. Lett. 104, 103003 (2010).
    [Crossref]
  9. S. Gilbertson, M. Chini, X. Feng, S. Khan, Y. Wu, and Z. Chang, “Monitoring and controlling the electron dynamics in helium with isolated attosecond pulses,” Phys. Rev. Lett. 105, 263003 (2010).
    [Crossref]
  10. K. T. Kim, D. H. Ko, J. Park, N. N. Choi, C. M. Kim, K. L. Ishikawa, J. Lee, and C. H. Nam, “Amplitude and phase reconstruction of electron wave packets for probing ultrafast photoionization dynamics,” Phys. Rev. Lett. 108, 093001 (2012).
    [Crossref]
  11. C. Hernández-García, J. A. Pérez-Hernández, T. Popmintchev, M. M. Murnane, H. C. Kapteyn, A. Jaron-Becker, A. Becker, and L. Plaja, “Zeptosecond high harmonic keV X-ray waveforms driven by midinfrared laser pulses,” Phys. Rev. Lett. 111, 033002 (2013).
    [Crossref]
  12. C. Corsi, A. Pirri, E. Sali, A. Tortora, and M. Bellini, “Direct interferometric measurement of the atomic dipole phase in high-order harmonic generation,” Phys. Rev. Lett. 97, 023901 (2006).
    [Crossref]
  13. J. Lu, E. F. Cunningham, Y. S. You, D. A. Reis, and S. Ghimire, “Interferometry of dipole phase in high harmonics from solids,” Nat. Photonics 13, 96–100 (2019).
    [Crossref]
  14. D. Azoury, O. Kneller, S. Rozen, B. D. Bruner, A. Clergerie, Y. Mairesse, B. Fabre, B. Pons, N. Dudovich, and M. Krüger, “Electronic wavefunctions probed by all-optical attosecond interferometry,” Nat. Photonics 13, 54–59 (2019).
    [Crossref]
  15. G. Vampa, T. J. Hammond, N. Thiré, B. E. Schmidt, F. Légaré, C. R. McDonald, T. Brabec, and P. B. Corkum, “Linking high harmonics from gases and solids,” Nature 522, 462–464 (2015).
    [Crossref]
  16. P. B. Corkum, “Plasma perspective on strong field multiphoton ionization,” Phys. Rev. Lett. 71, 1994–1997 (1993).
    [Crossref]
  17. M. Spanner, J. B. Bertrand, and D. M. Villeneuve, “In situ attosecond pulse characterization techniques to measure the electromagnetic phase,” Phys. Rev. A 94, 023825 (2016).
    [Crossref]
  18. P. Salières, B. Carré, L. Le Déroff, F. Grasbon, G. G. Paulus, H. Walther, R. Kopold, W. Becker, D. B. Milošević, A. Sanpera, and M. Lewenstein, “Feynman’s path-integral approach for intense-laser-atom interactions,” Science 292, 902–905 (2001).
    [Crossref]
  19. G. G. Brown, D. H. Ko, C. Zhang, and P. B. Corkum, “Characterizing multielectron dynamics during recollision,” arXiv:2010.06165v1 (2020).
  20. N. Dudovich, O. Smirnova, J. Levesque, Y. Mairesse, M. Y. Ivanov, D. M. Villeneuve, and P. B. Corkum, “Measuring and controlling the birth of attoseconod XUV pulses,” Nat. Phys. 2, 781–786 (2006).
    [Crossref]
  21. K. T. Kim, C. Zhang, A. D. Shiner, S. E. Kirkwood, E. Frumker, G. Gariepy, A. Naumov, D. M. Villeneuve, and P. B. Corkum, “Manipulation of quantum paths for space-time characterization of attosecond pulses,” Nat. Phys. 9, 159–163 (2013).
    [Crossref]
  22. J. B. Bertrand, H. J. Wörner, H.-C. Bandulet, É. Bisson, M. Spanner, J.-C. Kieffer, D. M. Villeneuve, and P. B. Corkum, “Ultrahigh-order wave mixing in noncollinear high harmonic generation,” Phys. Rev. Lett. 106, 023001 (2011).
    [Crossref]
  23. S. Roy, D. Parks, K. A. Seu, R. Su, J. J. Turner, W. Chao, E. H. Anderson, S. Cabrini, and S. D. Kevan, “Lensless X-ray imaging in reflection geometry,” Nat. Photonics 5, 243–245 (2011).
    [Crossref]
  24. Z. Chang, A. Rundquist, H. Wang, M. M. Murnane, and H. C. Kapteyn, “Generation of coherent soft X rays at 2.7 nm using high harmonics,” Phys. Rev. Lett. 79, 2967–2970 (1997).
    [Crossref]
  25. G. Sansone, E. Benedetti, F. Calegari, C. Vozzi, L. Avaldi, R. Flammini, L. Poletto, P. Villoresi, C. Altucci, R. Velotta, S. Stagira, S. De Silvestri, and M. Nisoli, “Isolated single-cycle attosecond pulses,” Science 314, 443–446 (2006).
    [Crossref]
  26. K. T. Kim, K. S. Kang, M. N. Park, T. Imran, G. Umesh, and C. H. Nam, “Self-compression of attosecond high-order harmonic pulses,” Phys. Rev. Lett. 99, 223904 (2007).
    [Crossref]
  27. E. Constant, D. Garzella, P. Breger, E. Mével, Ch. Dorrer, C. Le Blanc, F. Salin, and P. Agostini, “Optimizing high harmonic generation in absorbing gases: model and experiment,” Phys. Rev. Lett. 82, 1668–1671 (1999).
    [Crossref]
  28. A. D. Shiner, C. Trallero-Herrero, N. Kajumba, B. E. Schmidt, J. B. Bertrand, K. T. Kim, H.-C. Bandulet, D. Comtois, J.-C. Kieffer, D. M. Rayner, P. B. Corkum, F. Légaré, and D. M. Villeneuve, “High harmonic cutoff energy scaling and laser intensity measurement with a 1.8 µm laser source,” J. Mod. Opt. 60, 1458–1465 (2013).
    [Crossref]
  29. Z. Yang, W. Cao, X. Chen, J. Zhang, Y. Mo, H. Xu, K. Mi, Q. Zhang, P. Lan, and P. Lu, “All-optical frequency-resolved optical gating for isolated attosecond pulse reconstruction,” Opt. Lett. 45, 567–570 (2020).
    [Crossref]
  30. T. J. Hammond, A. Korobenko, A. Y. Naumov, D. M. Villeneuve, P. B. Corkum, and D. H. Ko, “Near-field imaging for single-shot waveform measurements,” J. Phys. B 51, 065603 (2018).
    [Crossref]
  31. A. D. Shiner, C. Trallero-Herrero, N. Kajumba, H.-C. Bandulet, D. Comtois, F. Légaré, M. Giguère, J.-C. Kieffer, P. B. Corkum, and D. M. Villeneuve, “Wavelength scaling of high harmonic generation efficiency,” Phys. Rev. Lett. 103, 073902 (2009).
    [Crossref]
  32. G. G. Brown, D. H. Ko, C. Zhang, and P. B. Corkum, “Attosecond measurement via high-order harmonic generation in low-frequency fields,” Phys. Rev. A (to be published).
  33. E. Goulielmakis, Z.-H. Loh, A. Wirth, R. Santra, N. Rohringer, V. S. Yakovlev, S. Zherebtsov, T. Pfeifer, A. M. Azzeer, M. F. Kling, S. R. Leone, and F. Krausz, “Real-time observation of valence electron motion,” Nature 466, 739–743 (2010).
    [Crossref]
  34. S. Baker, J. S. Robinson, C. A. Haworth, H. Teng, R. A. Smith, C. C. Chirilă, M. Lein, J. W. G. Tisch, and J. P. Marangos, “Probing proton dynamics in molecules on an attosecond time scale,” Science 312, 424–427 (2006).
    [Crossref]
  35. R. A. Ganeev, L. B. Elouga Bom, J. Abdul-Hadi, M. C. H. Wong, J. P. Brichta, V. R. Bhardwaj, and T. Ozaki, “Higher-order harmonic generation from fullerene by means of the plasma harmonic method,” Phys. Rev. Lett. 102, 013903 (2009).
    [Crossref]
  36. S. Pabst and R. Santra, “Strong-field many-body physics and the giant enhancement in the high-harmonic spectrum of xenon,” Phys. Rev. Lett. 111, 233005 (2013).
    [Crossref]

2020 (1)

2019 (2)

J. Lu, E. F. Cunningham, Y. S. You, D. A. Reis, and S. Ghimire, “Interferometry of dipole phase in high harmonics from solids,” Nat. Photonics 13, 96–100 (2019).
[Crossref]

D. Azoury, O. Kneller, S. Rozen, B. D. Bruner, A. Clergerie, Y. Mairesse, B. Fabre, B. Pons, N. Dudovich, and M. Krüger, “Electronic wavefunctions probed by all-optical attosecond interferometry,” Nat. Photonics 13, 54–59 (2019).
[Crossref]

2018 (1)

T. J. Hammond, A. Korobenko, A. Y. Naumov, D. M. Villeneuve, P. B. Corkum, and D. H. Ko, “Near-field imaging for single-shot waveform measurements,” J. Phys. B 51, 065603 (2018).
[Crossref]

2016 (1)

M. Spanner, J. B. Bertrand, and D. M. Villeneuve, “In situ attosecond pulse characterization techniques to measure the electromagnetic phase,” Phys. Rev. A 94, 023825 (2016).
[Crossref]

2015 (1)

G. Vampa, T. J. Hammond, N. Thiré, B. E. Schmidt, F. Légaré, C. R. McDonald, T. Brabec, and P. B. Corkum, “Linking high harmonics from gases and solids,” Nature 522, 462–464 (2015).
[Crossref]

2013 (4)

C. Hernández-García, J. A. Pérez-Hernández, T. Popmintchev, M. M. Murnane, H. C. Kapteyn, A. Jaron-Becker, A. Becker, and L. Plaja, “Zeptosecond high harmonic keV X-ray waveforms driven by midinfrared laser pulses,” Phys. Rev. Lett. 111, 033002 (2013).
[Crossref]

K. T. Kim, C. Zhang, A. D. Shiner, S. E. Kirkwood, E. Frumker, G. Gariepy, A. Naumov, D. M. Villeneuve, and P. B. Corkum, “Manipulation of quantum paths for space-time characterization of attosecond pulses,” Nat. Phys. 9, 159–163 (2013).
[Crossref]

A. D. Shiner, C. Trallero-Herrero, N. Kajumba, B. E. Schmidt, J. B. Bertrand, K. T. Kim, H.-C. Bandulet, D. Comtois, J.-C. Kieffer, D. M. Rayner, P. B. Corkum, F. Légaré, and D. M. Villeneuve, “High harmonic cutoff energy scaling and laser intensity measurement with a 1.8 µm laser source,” J. Mod. Opt. 60, 1458–1465 (2013).
[Crossref]

S. Pabst and R. Santra, “Strong-field many-body physics and the giant enhancement in the high-harmonic spectrum of xenon,” Phys. Rev. Lett. 111, 233005 (2013).
[Crossref]

2012 (1)

K. T. Kim, D. H. Ko, J. Park, N. N. Choi, C. M. Kim, K. L. Ishikawa, J. Lee, and C. H. Nam, “Amplitude and phase reconstruction of electron wave packets for probing ultrafast photoionization dynamics,” Phys. Rev. Lett. 108, 093001 (2012).
[Crossref]

2011 (2)

J. B. Bertrand, H. J. Wörner, H.-C. Bandulet, É. Bisson, M. Spanner, J.-C. Kieffer, D. M. Villeneuve, and P. B. Corkum, “Ultrahigh-order wave mixing in noncollinear high harmonic generation,” Phys. Rev. Lett. 106, 023001 (2011).
[Crossref]

S. Roy, D. Parks, K. A. Seu, R. Su, J. J. Turner, W. Chao, E. H. Anderson, S. Cabrini, and S. D. Kevan, “Lensless X-ray imaging in reflection geometry,” Nat. Photonics 5, 243–245 (2011).
[Crossref]

2010 (4)

E. Goulielmakis, Z.-H. Loh, A. Wirth, R. Santra, N. Rohringer, V. S. Yakovlev, S. Zherebtsov, T. Pfeifer, A. M. Azzeer, M. F. Kling, S. R. Leone, and F. Krausz, “Real-time observation of valence electron motion,” Nature 466, 739–743 (2010).
[Crossref]

M. Schultze, M. Fiess, N. Karpowicz, J. Gagnon, M. Korbman, M. Hofstetter, S. Neppl, A. L. Cavalieri, Y. Komninos, T. Mercouris, C. A. Nicolaides, R. Pazourek, S. Nagele, J. Feist, J. Burgdörfer, A. M. Azzeer, R. Ernstorfer, R. Kienberger, U. Kleineberg, E. Goulielmakis, F. Krausz, and V. S. Yakovlev, “Delay in Photoemission,” Science 328, 1658–1662 (2010).
[Crossref]

M. Swoboda, T. Fordell, K. Klünder, J. M. Dahlström, M. Miranda, C. Buth, K. J. Schafer, J. Mauritsson, A. L’Huillier, and M. Gisselbrecht, “Phase measurement of resonant two-photon ionization in helium,” Phys. Rev. Lett. 104, 103003 (2010).
[Crossref]

S. Gilbertson, M. Chini, X. Feng, S. Khan, Y. Wu, and Z. Chang, “Monitoring and controlling the electron dynamics in helium with isolated attosecond pulses,” Phys. Rev. Lett. 105, 263003 (2010).
[Crossref]

2009 (2)

R. A. Ganeev, L. B. Elouga Bom, J. Abdul-Hadi, M. C. H. Wong, J. P. Brichta, V. R. Bhardwaj, and T. Ozaki, “Higher-order harmonic generation from fullerene by means of the plasma harmonic method,” Phys. Rev. Lett. 102, 013903 (2009).
[Crossref]

A. D. Shiner, C. Trallero-Herrero, N. Kajumba, H.-C. Bandulet, D. Comtois, F. Légaré, M. Giguère, J.-C. Kieffer, P. B. Corkum, and D. M. Villeneuve, “Wavelength scaling of high harmonic generation efficiency,” Phys. Rev. Lett. 103, 073902 (2009).
[Crossref]

2007 (3)

K. T. Kim, K. S. Kang, M. N. Park, T. Imran, G. Umesh, and C. H. Nam, “Self-compression of attosecond high-order harmonic pulses,” Phys. Rev. Lett. 99, 223904 (2007).
[Crossref]

A. L. Cavalieri, N. Müller, Th. Uphues, V. S. Yakovlev, A. Baltuška, B. Horvath, B. Schmidt, L. Blümel, R. Holzwarth, S. Hendel, M. Drescher, U. Kleineberg, P. M. Echenique, R. Kienberger, F. Krausz, and U. Heinzmann, “Attosecond spectroscopy in condensed matter,” Nature 449, 1029–1032 (2007).
[Crossref]

M. Uiberacker, Th. Uphues, M. Schultze, A. J. Verhoef, V. Yakovlev, M. F. Kling, J. Rauschenberger, N. M. Kabachnik, H. Schröder, M. Lezius, K. L. Kompa, H.-G. Muller, M. J. J. Vrakking, S. Hendel, U. Kleineberg, U. Heinzmann, M. Drescher, and F. Krausz, “Attosecond real-time observation of electron tunneling in atoms,” Nature 446, 627–632 (2007).
[Crossref]

2006 (4)

C. Corsi, A. Pirri, E. Sali, A. Tortora, and M. Bellini, “Direct interferometric measurement of the atomic dipole phase in high-order harmonic generation,” Phys. Rev. Lett. 97, 023901 (2006).
[Crossref]

S. Baker, J. S. Robinson, C. A. Haworth, H. Teng, R. A. Smith, C. C. Chirilă, M. Lein, J. W. G. Tisch, and J. P. Marangos, “Probing proton dynamics in molecules on an attosecond time scale,” Science 312, 424–427 (2006).
[Crossref]

N. Dudovich, O. Smirnova, J. Levesque, Y. Mairesse, M. Y. Ivanov, D. M. Villeneuve, and P. B. Corkum, “Measuring and controlling the birth of attoseconod XUV pulses,” Nat. Phys. 2, 781–786 (2006).
[Crossref]

G. Sansone, E. Benedetti, F. Calegari, C. Vozzi, L. Avaldi, R. Flammini, L. Poletto, P. Villoresi, C. Altucci, R. Velotta, S. Stagira, S. De Silvestri, and M. Nisoli, “Isolated single-cycle attosecond pulses,” Science 314, 443–446 (2006).
[Crossref]

2004 (1)

R. Kienberger, E. Goulielmakis, M. Uiberacker, A. Baltuska, V. Yakovlev, F. Bammer, A. Scrinzi, Th. Westerwalbesloh, U. Kleineberg, U. Heinzmann, M. Drescher, and F. Krausz, “Atomic transient recorder,” Nature 427, 817–821 (2004).
[Crossref]

2002 (1)

M. Drescher, M. Hentschel, R. Kienberger, M. Uiberacker, V. Yakovlev, A. Scrinzi, Th. Westerwalbesloh, U. Kleineberg, U. Heinzmann, and F. Krausz, “Time-resolved atomic inner-shell spectroscopy,” Nature 419, 803–807 (2002).
[Crossref]

2001 (2)

P. M. Paul, E. S. Toma, P. Breger, G. Mullot, F. Augé, P. H. Balcou, H. G. Muller, and P. Agostini, “Observation of a train of attosecond pulses from high harmonic generation,” Science 292, 1689–1692 (2001).
[Crossref]

P. Salières, B. Carré, L. Le Déroff, F. Grasbon, G. G. Paulus, H. Walther, R. Kopold, W. Becker, D. B. Milošević, A. Sanpera, and M. Lewenstein, “Feynman’s path-integral approach for intense-laser-atom interactions,” Science 292, 902–905 (2001).
[Crossref]

1999 (1)

E. Constant, D. Garzella, P. Breger, E. Mével, Ch. Dorrer, C. Le Blanc, F. Salin, and P. Agostini, “Optimizing high harmonic generation in absorbing gases: model and experiment,” Phys. Rev. Lett. 82, 1668–1671 (1999).
[Crossref]

1998 (1)

1997 (1)

Z. Chang, A. Rundquist, H. Wang, M. M. Murnane, and H. C. Kapteyn, “Generation of coherent soft X rays at 2.7 nm using high harmonics,” Phys. Rev. Lett. 79, 2967–2970 (1997).
[Crossref]

1993 (1)

P. B. Corkum, “Plasma perspective on strong field multiphoton ionization,” Phys. Rev. Lett. 71, 1994–1997 (1993).
[Crossref]

Abdul-Hadi, J.

R. A. Ganeev, L. B. Elouga Bom, J. Abdul-Hadi, M. C. H. Wong, J. P. Brichta, V. R. Bhardwaj, and T. Ozaki, “Higher-order harmonic generation from fullerene by means of the plasma harmonic method,” Phys. Rev. Lett. 102, 013903 (2009).
[Crossref]

Agostini, P.

P. M. Paul, E. S. Toma, P. Breger, G. Mullot, F. Augé, P. H. Balcou, H. G. Muller, and P. Agostini, “Observation of a train of attosecond pulses from high harmonic generation,” Science 292, 1689–1692 (2001).
[Crossref]

E. Constant, D. Garzella, P. Breger, E. Mével, Ch. Dorrer, C. Le Blanc, F. Salin, and P. Agostini, “Optimizing high harmonic generation in absorbing gases: model and experiment,” Phys. Rev. Lett. 82, 1668–1671 (1999).
[Crossref]

Altucci, C.

G. Sansone, E. Benedetti, F. Calegari, C. Vozzi, L. Avaldi, R. Flammini, L. Poletto, P. Villoresi, C. Altucci, R. Velotta, S. Stagira, S. De Silvestri, and M. Nisoli, “Isolated single-cycle attosecond pulses,” Science 314, 443–446 (2006).
[Crossref]

Anderson, E. H.

S. Roy, D. Parks, K. A. Seu, R. Su, J. J. Turner, W. Chao, E. H. Anderson, S. Cabrini, and S. D. Kevan, “Lensless X-ray imaging in reflection geometry,” Nat. Photonics 5, 243–245 (2011).
[Crossref]

Augé, F.

P. M. Paul, E. S. Toma, P. Breger, G. Mullot, F. Augé, P. H. Balcou, H. G. Muller, and P. Agostini, “Observation of a train of attosecond pulses from high harmonic generation,” Science 292, 1689–1692 (2001).
[Crossref]

Avaldi, L.

G. Sansone, E. Benedetti, F. Calegari, C. Vozzi, L. Avaldi, R. Flammini, L. Poletto, P. Villoresi, C. Altucci, R. Velotta, S. Stagira, S. De Silvestri, and M. Nisoli, “Isolated single-cycle attosecond pulses,” Science 314, 443–446 (2006).
[Crossref]

Azoury, D.

D. Azoury, O. Kneller, S. Rozen, B. D. Bruner, A. Clergerie, Y. Mairesse, B. Fabre, B. Pons, N. Dudovich, and M. Krüger, “Electronic wavefunctions probed by all-optical attosecond interferometry,” Nat. Photonics 13, 54–59 (2019).
[Crossref]

Azzeer, A. M.

M. Schultze, M. Fiess, N. Karpowicz, J. Gagnon, M. Korbman, M. Hofstetter, S. Neppl, A. L. Cavalieri, Y. Komninos, T. Mercouris, C. A. Nicolaides, R. Pazourek, S. Nagele, J. Feist, J. Burgdörfer, A. M. Azzeer, R. Ernstorfer, R. Kienberger, U. Kleineberg, E. Goulielmakis, F. Krausz, and V. S. Yakovlev, “Delay in Photoemission,” Science 328, 1658–1662 (2010).
[Crossref]

E. Goulielmakis, Z.-H. Loh, A. Wirth, R. Santra, N. Rohringer, V. S. Yakovlev, S. Zherebtsov, T. Pfeifer, A. M. Azzeer, M. F. Kling, S. R. Leone, and F. Krausz, “Real-time observation of valence electron motion,” Nature 466, 739–743 (2010).
[Crossref]

Baker, S.

S. Baker, J. S. Robinson, C. A. Haworth, H. Teng, R. A. Smith, C. C. Chirilă, M. Lein, J. W. G. Tisch, and J. P. Marangos, “Probing proton dynamics in molecules on an attosecond time scale,” Science 312, 424–427 (2006).
[Crossref]

Balcou, P. H.

P. M. Paul, E. S. Toma, P. Breger, G. Mullot, F. Augé, P. H. Balcou, H. G. Muller, and P. Agostini, “Observation of a train of attosecond pulses from high harmonic generation,” Science 292, 1689–1692 (2001).
[Crossref]

Baltuska, A.

R. Kienberger, E. Goulielmakis, M. Uiberacker, A. Baltuska, V. Yakovlev, F. Bammer, A. Scrinzi, Th. Westerwalbesloh, U. Kleineberg, U. Heinzmann, M. Drescher, and F. Krausz, “Atomic transient recorder,” Nature 427, 817–821 (2004).
[Crossref]

Baltuška, A.

A. L. Cavalieri, N. Müller, Th. Uphues, V. S. Yakovlev, A. Baltuška, B. Horvath, B. Schmidt, L. Blümel, R. Holzwarth, S. Hendel, M. Drescher, U. Kleineberg, P. M. Echenique, R. Kienberger, F. Krausz, and U. Heinzmann, “Attosecond spectroscopy in condensed matter,” Nature 449, 1029–1032 (2007).
[Crossref]

Bammer, F.

R. Kienberger, E. Goulielmakis, M. Uiberacker, A. Baltuska, V. Yakovlev, F. Bammer, A. Scrinzi, Th. Westerwalbesloh, U. Kleineberg, U. Heinzmann, M. Drescher, and F. Krausz, “Atomic transient recorder,” Nature 427, 817–821 (2004).
[Crossref]

Bandulet, H.-C.

A. D. Shiner, C. Trallero-Herrero, N. Kajumba, B. E. Schmidt, J. B. Bertrand, K. T. Kim, H.-C. Bandulet, D. Comtois, J.-C. Kieffer, D. M. Rayner, P. B. Corkum, F. Légaré, and D. M. Villeneuve, “High harmonic cutoff energy scaling and laser intensity measurement with a 1.8 µm laser source,” J. Mod. Opt. 60, 1458–1465 (2013).
[Crossref]

J. B. Bertrand, H. J. Wörner, H.-C. Bandulet, É. Bisson, M. Spanner, J.-C. Kieffer, D. M. Villeneuve, and P. B. Corkum, “Ultrahigh-order wave mixing in noncollinear high harmonic generation,” Phys. Rev. Lett. 106, 023001 (2011).
[Crossref]

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K. T. Kim, D. H. Ko, J. Park, N. N. Choi, C. M. Kim, K. L. Ishikawa, J. Lee, and C. H. Nam, “Amplitude and phase reconstruction of electron wave packets for probing ultrafast photoionization dynamics,” Phys. Rev. Lett. 108, 093001 (2012).
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K. T. Kim, K. S. Kang, M. N. Park, T. Imran, G. Umesh, and C. H. Nam, “Self-compression of attosecond high-order harmonic pulses,” Phys. Rev. Lett. 99, 223904 (2007).
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R. Kienberger, E. Goulielmakis, M. Uiberacker, A. Baltuska, V. Yakovlev, F. Bammer, A. Scrinzi, Th. Westerwalbesloh, U. Kleineberg, U. Heinzmann, M. Drescher, and F. Krausz, “Atomic transient recorder,” Nature 427, 817–821 (2004).
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M. Drescher, M. Hentschel, R. Kienberger, M. Uiberacker, V. Yakovlev, A. Scrinzi, Th. Westerwalbesloh, U. Kleineberg, U. Heinzmann, and F. Krausz, “Time-resolved atomic inner-shell spectroscopy,” Nature 419, 803–807 (2002).
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M. Uiberacker, Th. Uphues, M. Schultze, A. J. Verhoef, V. Yakovlev, M. F. Kling, J. Rauschenberger, N. M. Kabachnik, H. Schröder, M. Lezius, K. L. Kompa, H.-G. Muller, M. J. J. Vrakking, S. Hendel, U. Kleineberg, U. Heinzmann, M. Drescher, and F. Krausz, “Attosecond real-time observation of electron tunneling in atoms,” Nature 446, 627–632 (2007).
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K. T. Kim, D. H. Ko, J. Park, N. N. Choi, C. M. Kim, K. L. Ishikawa, J. Lee, and C. H. Nam, “Amplitude and phase reconstruction of electron wave packets for probing ultrafast photoionization dynamics,” Phys. Rev. Lett. 108, 093001 (2012).
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M. Schultze, M. Fiess, N. Karpowicz, J. Gagnon, M. Korbman, M. Hofstetter, S. Neppl, A. L. Cavalieri, Y. Komninos, T. Mercouris, C. A. Nicolaides, R. Pazourek, S. Nagele, J. Feist, J. Burgdörfer, A. M. Azzeer, R. Ernstorfer, R. Kienberger, U. Kleineberg, E. Goulielmakis, F. Krausz, and V. S. Yakovlev, “Delay in Photoemission,” Science 328, 1658–1662 (2010).
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M. Uiberacker, Th. Uphues, M. Schultze, A. J. Verhoef, V. Yakovlev, M. F. Kling, J. Rauschenberger, N. M. Kabachnik, H. Schröder, M. Lezius, K. L. Kompa, H.-G. Muller, M. J. J. Vrakking, S. Hendel, U. Kleineberg, U. Heinzmann, M. Drescher, and F. Krausz, “Attosecond real-time observation of electron tunneling in atoms,” Nature 446, 627–632 (2007).
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K. T. Kim, D. H. Ko, J. Park, N. N. Choi, C. M. Kim, K. L. Ishikawa, J. Lee, and C. H. Nam, “Amplitude and phase reconstruction of electron wave packets for probing ultrafast photoionization dynamics,” Phys. Rev. Lett. 108, 093001 (2012).
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M. Spanner, J. B. Bertrand, and D. M. Villeneuve, “In situ attosecond pulse characterization techniques to measure the electromagnetic phase,” Phys. Rev. A 94, 023825 (2016).
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J. B. Bertrand, H. J. Wörner, H.-C. Bandulet, É. Bisson, M. Spanner, J.-C. Kieffer, D. M. Villeneuve, and P. B. Corkum, “Ultrahigh-order wave mixing in noncollinear high harmonic generation,” Phys. Rev. Lett. 106, 023001 (2011).
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M. Drescher, M. Hentschel, R. Kienberger, M. Uiberacker, V. Yakovlev, A. Scrinzi, Th. Westerwalbesloh, U. Kleineberg, U. Heinzmann, and F. Krausz, “Time-resolved atomic inner-shell spectroscopy,” Nature 419, 803–807 (2002).
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G. G. Brown, D. H. Ko, C. Zhang, and P. B. Corkum, “Characterizing multielectron dynamics during recollision,” arXiv:2010.06165v1 (2020).

G. G. Brown, D. H. Ko, C. Zhang, and P. B. Corkum, “Attosecond measurement via high-order harmonic generation in low-frequency fields,” Phys. Rev. A (to be published).

Zhang, J.

Zhang, Q.

Zherebtsov, S.

E. Goulielmakis, Z.-H. Loh, A. Wirth, R. Santra, N. Rohringer, V. S. Yakovlev, S. Zherebtsov, T. Pfeifer, A. M. Azzeer, M. F. Kling, S. R. Leone, and F. Krausz, “Real-time observation of valence electron motion,” Nature 466, 739–743 (2010).
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A. D. Shiner, C. Trallero-Herrero, N. Kajumba, B. E. Schmidt, J. B. Bertrand, K. T. Kim, H.-C. Bandulet, D. Comtois, J.-C. Kieffer, D. M. Rayner, P. B. Corkum, F. Légaré, and D. M. Villeneuve, “High harmonic cutoff energy scaling and laser intensity measurement with a 1.8 µm laser source,” J. Mod. Opt. 60, 1458–1465 (2013).
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J. Phys. B (1)

T. J. Hammond, A. Korobenko, A. Y. Naumov, D. M. Villeneuve, P. B. Corkum, and D. H. Ko, “Near-field imaging for single-shot waveform measurements,” J. Phys. B 51, 065603 (2018).
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Nat. Photonics (3)

S. Roy, D. Parks, K. A. Seu, R. Su, J. J. Turner, W. Chao, E. H. Anderson, S. Cabrini, and S. D. Kevan, “Lensless X-ray imaging in reflection geometry,” Nat. Photonics 5, 243–245 (2011).
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Nature (6)

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G. Vampa, T. J. Hammond, N. Thiré, B. E. Schmidt, F. Légaré, C. R. McDonald, T. Brabec, and P. B. Corkum, “Linking high harmonics from gases and solids,” Nature 522, 462–464 (2015).
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M. Drescher, M. Hentschel, R. Kienberger, M. Uiberacker, V. Yakovlev, A. Scrinzi, Th. Westerwalbesloh, U. Kleineberg, U. Heinzmann, and F. Krausz, “Time-resolved atomic inner-shell spectroscopy,” Nature 419, 803–807 (2002).
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M. Uiberacker, Th. Uphues, M. Schultze, A. J. Verhoef, V. Yakovlev, M. F. Kling, J. Rauschenberger, N. M. Kabachnik, H. Schröder, M. Lezius, K. L. Kompa, H.-G. Muller, M. J. J. Vrakking, S. Hendel, U. Kleineberg, U. Heinzmann, M. Drescher, and F. Krausz, “Attosecond real-time observation of electron tunneling in atoms,” Nature 446, 627–632 (2007).
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Opt. Lett. (2)

Phys. Rev. A (1)

M. Spanner, J. B. Bertrand, and D. M. Villeneuve, “In situ attosecond pulse characterization techniques to measure the electromagnetic phase,” Phys. Rev. A 94, 023825 (2016).
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S. Gilbertson, M. Chini, X. Feng, S. Khan, Y. Wu, and Z. Chang, “Monitoring and controlling the electron dynamics in helium with isolated attosecond pulses,” Phys. Rev. Lett. 105, 263003 (2010).
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Supplementary Material (1)

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Supplement 1       Supplemental Document

Data availability

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

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Figures (5)

Fig. 1.
Fig. 1. Schematic diagram of the obliquely overlapped two laser beams with an angle $\theta$ and generated XUV beams. The strong beam propagates along the $z$ -axis on the $z - y$ frame, and the weak beam travels along the $z^\prime$ -axis on the $z^\prime - y^{\prime}$ frame. The electron trajectories for the XUV generation, dominated by the strong beam, are predominantly along the strong beam polarization, and the optical grating is $y$ -coordinate dependent in this frame. The diffracted XUV beam has a frequency-shifted spectral phase $\varphi ({\omega _{\rm{XUV}}} + M{\omega _g})$ of the attosecond pulse, where $M$ is the grating diffraction order. The inset shows the grating modulation along the $y$ -axis at different times. We image this time-dependent modulation to measure an isolated attosecond pulse.
Fig. 2.
Fig. 2. Conceptual illustration of the single-image measurement of an attosecond pulse. A polarization-gated strong laser pulse generates an isolated attosecond pulse from xenon. A weak linearly polarized pulse perturbs the generation process with the moving grating. The different frequencies of the attosecond pulse are affected by the moving grating at different times. The modulated dipole emission creates a diffraction pattern on the toroidal mirror, which refocuses the dipole emission onto the XUV detector to recover the near-field image of the dipole. A physical grating spreads the frequencies of the dipole emission along the perpendicular direction of the optical grating to measure the frequency-dependent emission time of the attosecond pulse.
Fig. 3.
Fig. 3. Measured XUV continuum spectra without/with the weak laser pulse in (a) and (b), respectively. The numerically simulated XUV continuum spectra without/with the weak laser pulse in (c) and (d), respectively, by considering parameters in the experiment.
Fig. 4.
Fig. 4. (a) Subtracted XUV spectral image with Figs. 3(a) and 3(b). The optical grating induced by the weak laser field is clearly revealed on the near-field dipole emission with 1.5-cycle modulation. The spectrally resolved grating position is marked by a magenta line at the middle of the grating modulation for each frequency. (b) The measured spectral intensity (blue solid line) and emission time (red solid line) of the isolated attosecond pulse. The magenta shade indicates the statistical error of the emission time after taking 70 measurements with 150 shots accumulated for each image. The green dashed line is the dispersion curve of the isolated attosecond pulse calculated by the strong-field approximation (SFA) model [16]. The green shade implied the dispersion curves for the range of peak intensity within ${\pm}\;{5}\%$ .
Fig. 5.
Fig. 5. Complete temporal characterization of an isolated attosecond pulse obtained by taking Fourier transform of the measured spectral amplitude and phase. The shaded areas are the standard deviations of the temporal intensity (blue) and phase (red) from the statistical analysis. Dotted lines are the intensity and phase achieved by a TDSE calculation using the strong driving laser pulse only. The inset shows the measured attosecond pulse on a logarithm scale to confirm it as a single isolated attosecond pulse.

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