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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 19, Iss. 3 — Jan. 31, 2011
  • pp: 1767–1776
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Attosecond dispersion control by extreme ultraviolet multilayer mirrors

Michael Hofstetter, Martin Schultze, Markus Fieß, Benjamin Dennhardt, Alexander Guggenmos, Justin Gagnon, Vladislav S. Yakovlev, Eleftherios Goulielmakis, Reinhard Kienberger, Eric M. Gullikson, Ferenc Krausz, and Ulf Kleineberg  »View Author Affiliations


Optics Express, Vol. 19, Issue 3, pp. 1767-1776 (2011)
http://dx.doi.org/10.1364/OE.19.001767


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Abstract

We report the first experimental demonstration of a-periodic multilayer mirrors controlling the frequency sweep (chirp) of isolated attosecond XUV pulses. The concept was proven with about 200-attosecond pulses in the photon energy range of 100-130 eV measured via photoelectron streaking in neon. The demonstrated attosecond dispersion control is engineerable in a wide range of XUV photon energies and bandwidths. The resultant tailor-made attosecond pulses with highly enhanced photon flux are expected to significantly advance attosecond metrology and spectroscopy and broaden their range of applications.

© 2011 OSA

1. Introduction

Attosecond (1 as = 10-18 s) light pulses at short wavelength from the extreme ultraviolet (XUV) to the soft X-ray regime have recently gained fundamental importance in studying electron motions in atoms, molecules or at surfaces [1

1. M. Drescher, M. Hentschel, R. Kienberger, G. Tempea, C. Spielmann, G. A. Reider, P. B. Corkum, and F. Krausz, “X-ray pulses approaching the attosecond frontier,” Science 291(5510), 1923–1927 (2001). [CrossRef] [PubMed]

5

5. 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(7307), 739–743 (2010). [CrossRef] [PubMed]

]. Here, fundamental ultrafast electron dynamics in excitation, transport and emission processes on time scales of a few tens of attoseconds can be observed. These ultrashort time-scales of electron motion are inevitably connected to atomic or mesoscopic spatial scales and nano-scaled microscopic resolution can be provided by the short wavelength nature of the soft X-ray pulses itself. The performance and applicability of attosecond spectroscopy critically depends on the flux, photon energy, bandwidth and dispersion control of attosecond pulses. Multilayer-coated XUV mirrors [6

6. A. Wonisch, U. Neuhäusler, N. M. Kabachnik, T. Uphues, M. Uiberacker, V. Yakovlev, F. Krausz, M. Drescher, U. Kleineberg, and U. Heinzmann, “Design, fabrication, and analysis of chirped multilayer mirrors for reflection of extreme-ultraviolet attosecond pulses,” Appl. Opt. 45(17), 4147–4156 (2006). [CrossRef] [PubMed]

8

8. M. Suman, G. Monaco, M.-G. Pelizzo, D. L. Windt, and P. Nicolosi, “Realization and characterization of an XUV multilayer coating for attosecond pulses,” Opt. Express 17(10), 7922–7932 (2009). [CrossRef] [PubMed]

] have served attosecond metrology from its very beginning [9

9. M. Hentschel, R. Kienberger, Ch. Spielmann, G. A. Reider, N. Milosevic, T. Brabec, P. Corkum, U. Heinzmann, M. Drescher, and F. Krausz, “Attosecond metrology,” Nature 414(6863), 509–513 (2001). [CrossRef] [PubMed]

], by focusing and isolating single attosecond pulses from coherent high-order harmonic radiation [10

10. I. P. Christov, M. M. Murnane, and H. C. Kapteyn, “High-Harmonic Generation of Attosecond Pulses in the “Single-Cycle” Regime,” Phys. Rev. Lett. 78(7), 1251–1254 (1997). [CrossRef]

13

13. E. Goulielmakis, M. Uiberacker, R. Kienberger, A. Baltuška, V. Yakovlev, A. Scrinzi, Th. Westerwalbesloh, U. Kleineberg, U. Heinzmann, M. Drescher, and F. Krausz, “Direct measurement of light waves,” Science 305(5688), 1267–1269 (2004). [CrossRef] [PubMed]

]. Chirped multilayer mirrors in the visible/infrared range, are inevitable components in generating few cycle laser pulses of a few femtosecond pulse-length only. Those are the necessary driving pulses for attosecond pulse generation [14

14. V. Pervak, A. V. Tikhonravov, M. K. Trubetskov, S. Naumov, F. Krausz, and A. Apolonski, “1.5-octave chirped mirror for pulse compression down to sub-3 fs,” Appl. Phys. B 87(1), 5–12 (2007). [CrossRef]

]. In contrast to the development of chirped dielectric mirrors in the visible, the realization of chirped XUV multilayer mirrors requires new approaches in computational design, manufacturing and characterization, which have not been available and combined until now. So far, XUV dispersion control over multi-electron volt bandwidths could only be accomplished for photon energies below 100 eV [15

15. E. Gustafsson, T. Ruchon, M. Swoboda, T. Remetter, E. Pourtal, R. López-Martens, Ph. Balcou, and A. L’Huillier, “Broadband attosecond pulse shaping,” Opt. Lett. 32(11), 1353–1355 (2007). [CrossRef] [PubMed]

19

19. 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(6909), 803–807 (2002). [CrossRef] [PubMed]

]. Further, control of the spectral distribution and chirp of an attosecond extreme ultraviolet pulse have so far been realized by means of ultrathin metal filters (typical thickness ~100 nm) [15

15. E. Gustafsson, T. Ruchon, M. Swoboda, T. Remetter, E. Pourtal, R. López-Martens, Ph. Balcou, and A. L’Huillier, “Broadband attosecond pulse shaping,” Opt. Lett. 32(11), 1353–1355 (2007). [CrossRef] [PubMed]

17

17. 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(5798), 443–446 (2006). [CrossRef] [PubMed]

] and XUV multilayer mirrors [18

18. E. Goulielmakis, M. Schultze, M. Hofstetter, V. S. Yakovlev, J. Gagnon, M. Uiberacker, A. L. Aquila, E. M. Gullikson, D. T. Attwood, R. Kienberger, F. Krausz, and U. Kleineberg, “Single-cycle nonlinear optics,” Science 320(5883), 1614–1617 (2008). [CrossRef] [PubMed]

,19

19. 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(6909), 803–807 (2002). [CrossRef] [PubMed]

] with chirp control mainly relying on the metal filter components. Their applicability is limited due to strong XUV attenuation and the availability of only few materials, thus only specific spectral ranges, where the real part of the complex index of refraction provides sufficient (usually only negative) dispersion.

Specially designed non-periodic binary or ternary multilayer-coated XUV mirrors allow for a large degree of freedom in influencing the XUV pulse characteristics by reflection of those mirrors [20

20. Y. Ménesguen, S. de Rossi, E. Meltchakov, and F. Delmotte, “Aperiodic multilayer mirrors for efficient broadband reflection in the extreme ultraviolet,” Appl. Phys., A Mater. Sci. Process. 98(2), 305–309 (2010). [CrossRef]

,21

21. M. Hofstetter, M. Schultze, M. Fieß, A. Guggenmos, J. Gagnon, E. Magerl, E. Botschafter, R. Ernstorfer, R. Kienberger, E. M. Gullikson, F. Krausz, and U. Kleineberg, “First attosecond pulse control by multilayer mirrors above 100 eV photon energy,“ in Ultrafast Phenomena XVII, 11.17, M. Chergui, D. Jonas, E. Riedle, B. Schönlein, A. Taylor (Oxford University Press, New York, 2010).

]. So far, multilayer mirrors in attosecond physics applications were used as band-pass reflectors preserving the spectral phase of the attosecond pulse that is defined in the generation process and by the dispersion characteristics of all XUV optical elements passed by the pulse. In this work we demonstrate, how specially designed non-periodic multilayer XUV mirrors furnish attosecond technology with the ability to control the spectral phase in addition to spectral intensity of attosecond pulses, offering a great degree of freedom in influencing the XUV pulse characteristics, such as the pulse shape, duration, frequency sweep and central wavelength.

2. The Experiment

2.1 Concept

Within this paper, the group delay (GD) τ is defined as the negative derivative of the spectral phase ϕ(ω) with respect to angular frequency ω, τ = -dϕ/dω. Its derivative is the group delay dispersion GDD = dτ/dω, known to be the lowest order phase term that temporally broadens the pulse.

Figure 1
Fig. 1 Operational principle of XUV chirped multilayers: Calculated square of the electric field amplitude of the standing wave formed in the multilayer structure upon reflection in the 94–133 eV photon energy range, normalized to that of the incident wave. Following the energy dependent maxima of the standing field, it is obvious that the penetration depth is wavelength dependent. Thus the mirrors introduce positive (a) and negative (b) chirp, resulting in an increasing and decreasing group delay for increasing photon energy respectively as the energy-dependent penetration depth signifies as depicted by the coloured arrows. The multilayer structure assumed here resembles the experimentally realized a-periodic multilayer mirrors as displayed in Fig. 2 (a/d) and (c/f).
displays a computational example for group-delay dispersion (GDD) management by non-periodic multilayer coatings optimized to introduce positive (left panel) or negative (right panel) GDD to an initially unchirped XUV pulse (higher order dispersion control like third order dispersion TOD by non-periodic multilayer is also feasible, although not demonstrated here). The square of the electric field amplitude of the standing wave resulting from the superposition of the incident and reflected radiation depicted by the false-colour plots reveals a penetration depth varying nearly linearly with photon energy in the centre of the high-reflectivity (HR) range of the multilayer Bragg peak (≈ 100-130 eV). The penetration depth increasing and decreasing with photon energy imposes a positive and negative chirp, respectively, on an originally bandwidth-limited attosecond pulse reflected by the mirror. Thus, introducing positive GDD results in a positive chirp of an initially unchirped pulse and vice versa.

2.2 Design

To prove the validity of the concept for precision chirp control of attosecond XUV pulses, we have developed a set of three multilayer mirrors exhibiting distinctly different GDD but similar reflectivity characteristics. Optimized for an incident angle of 45° they exhibit high reflectivity within the range of 100-130 eV with comparable full widths at half maximum energy bandwidth: ΔE = 11-13 eV FWHM and peaking at different central energies within the range of 107-122 eV.

The multilayer designs have been calculated and optimized by a Fresnel equation thin film code coupled to a needle optimization algorithm [22

22. A. V. Tikhonravov, M. K. Trubetskov, and G. W. DeBell, “Optical coating design approaches based on the needle optimization technique,” Appl. Opt. 46(5), 704–710 (2007). [CrossRef] [PubMed]

]. The mirrors have been designed such, that the GDD is almost maximum and mostly linear within the final attosecond pulse spectrum. Small shifts of the mirror spectrum due to the thin metal filter or the shape of the high harmonic cut-off spectrum have been estimated and taken into account in the design. The calculated designs have been optimized for additional suppressed reflectivity contributions in the near vicinity of the main Bragg peak and have been tested for stability against small layer thickness deviations. X-ray optical constants in the XUV are based on the tabulated data of Henke and Gullikson [23

23. B. L. Henke, E. M. Gullikson, and J. C. Davis, “X-ray interactions: photoabsorption, scattering, transmission, and reflection at E=50-30000 eV, Z=1-92,” At. Data Nucl. Data Tables 54(2), 181–342 (1993). [CrossRef]

]. The final multilayer coating designs are displayed in the lower panels (d-f) of Fig. 2
Fig. 2 Characteristics of XUV chirped multilayer coatings designed and manufactured for the experiments: Set of XUV multilayers with positive (a), near zero (b) and negative (c) group delay dispersion. The diagrams compare the measured (solid black) with the designed (dotted green) reflectivity curves. The calculated group delays (derivative of the spectral phase with respect to angular frequency) are also displayed (dashed red curve). The transmittivity of a 150-nm palladium foil is additionally qualitatively plotted in panel (b), depicted by the blue dash-dotted line. The lower panels (d), (e) and (f) show the corresponding mirror-designs of the appropriate mirrors above. Each colour represents one material as explained by the legend in 2(e).
. While the designs of the positively- and the negatively-chirped mirrors contain around 30 layers Mo/B4C the almost unchirped mirror is a 17 layer Mo/Si/B4C stack. The mirrors have been deposited by means of Dual Ion Beam Deposition (DIBD) on flat high-polished glass substrates. Interface losses and compound formation have been included in the calculation and could be compensated within the coating procedure.

Figure 2(a)2(c) shows the calculated reflectivity and group delay of the three multilayer mirrors versus photon energy, compared with the reflectivity measured by X-ray reflectometry using synchrotron radiation [24

24. E. M. Gullikson, J. H. Underwood, P. Batson, and V. Nikitin, “A soft x-ray/EUV reflectometer based on a laser produced plasma source,” J. XRay Sci. Technol. 3(4), 283–299 (1992). [PubMed]

]. The measured and computed XUV reflectivities are in excellent agreement, revealing maximum peak reflectivities between 4 and 10 percent. Notable deviations in the peak shape appear only in Fig. 2(c) near 120 eV, possibly due to minor uncertainties in the deposition layer thicknesses. In our proof-of-concept experiments, radiation at photon energies below 100 eV is suppressed by a 150 nm thick Palladium (Pd) filter (its transmittivity is shown in Fig. 2(b) by the blue dash-dotted line). The throughput of this high-pass filter combination could be enhanced by fine-tuning the filter thickness and the mirrors’ high-reflectivity band. Since isolated attosecond pulses can be extracted by spectral filtering from the cut-off part of the generated HH spectrum [9

9. M. Hentschel, R. Kienberger, Ch. Spielmann, G. A. Reider, N. Milosevic, T. Brabec, P. Corkum, U. Heinzmann, M. Drescher, and F. Krausz, “Attosecond metrology,” Nature 414(6863), 509–513 (2001). [CrossRef] [PubMed]

], the high energy extend of the spectrum has to coincide with the high reflectivity range of the mirror. Reflectivity above this energy window thus does not affect the attosecond pulse generation. The three mirrors are designed to introduce substantial positive GDD, negligible GDD, and substantial negative GDD, with computed values of 19.5x103 as 2, −0.5x103 as 2, and −14x103 as 2, respectively.

2.3 Streaking spectrograms and analyses

In contrast to the reflectivity, there is no standard frequency-domain technique available for measuring GDD in the extreme ultraviolet spectral range. Aquila et. al. have characterized the GDD of a multilayer mirror by measuring the photoelectron yield from its surface [25

25. A. Aquila, F. Salmassi, and E. Gullikson, “Metrologies for the phase characterization of attosecond extreme ultraviolet optics,” Opt. Lett. 33(5), 455–457 (2008). [CrossRef] [PubMed]

]. Here we have resorted to attosecond metrology for measuring the attosecond pulse dispersion directly and assessing the mirrors’ capability of controlling the chirp of isolated attosecond XUV pulses [12

12. F. Krausz and M. Ivanov, “Attosecond physics,” Rev. Mod. Phys. 81(1), 163–234 (2009). [CrossRef]

,15

15. E. Gustafsson, T. Ruchon, M. Swoboda, T. Remetter, E. Pourtal, R. López-Martens, Ph. Balcou, and A. L’Huillier, “Broadband attosecond pulse shaping,” Opt. Lett. 32(11), 1353–1355 (2007). [CrossRef] [PubMed]

,26

26. M. Kitzler, N. Milosevic, A. Scrinzi, F. Krausz, and T. Brabec, “Quantum theory of attosecond XUV pulse measurement by laser dressed photoionization,” Phys. Rev. Lett. 88(17), 173904 (2002). [CrossRef] [PubMed]

].

Unlike in the well known collinear setup [27

27. R. Kienberger, M. Hentschel, M. Uiberacker, Ch. Spielmann, M. Kitzler, A. Scrinzi, M. Wieland, Th. Westerwalbesloh, U. Kleineberg, U. Heinzmann, M. Drescher, and F. Krausz, “Steering attosecond electron wave packets with light,” Science 297(5584), 1144–1148 (2002). [CrossRef] [PubMed]

,28

28. M. Schultze, E. Goulielmakis, M. Uiberacker, M. Hofstetter, J. Kim, D. Kim, F. Krausz, and U. Kleineberg, “Powerful 170-attosecond XUV pulses generated with few-cycle laser pulses and broadband multilayer optics,” N. J. Phys. 9(7), 243 (2007). [CrossRef]

], where a concentric double mirror is used to introduce a delay between the inner (lower divergent) XUV beam and the outer (higher divergent) laser beam, in our setup the laser and XUV beam are completely spatially separated in two paths of an interferometric setup before recollimation [29

29. M. Fieß, M. Schultze, E. Goulielmakis, B. Dennhardt, J. Gagnon, M. Hofstetter, R. Kienberger, and F. Krausz, “Versatile apparatus for attosecond metrology and spectroscopy,” Rev. Sci. Instrum. 81, 1 (2010). [CrossRef]

]. Thus focusing of the XUV radiation (by means of a grazing incidence parabola) and time delay introduction between the XUV and the laser pulse (by means of a delay stage in the optical beam path) is decoupled from the plane XUV multilayer mirror. This technique allows for an easy and rapid exchange and alignment of the 45 deg XUV mirrors, which is inevitable for future XUV phase sensitive attosecond experiments.

We have implemented attosecond streaking by liberating photoelectrons from the 2p sub-shell of an ensemble of neon atoms with sub-300-attosecond XUV pulses filtered by the combination of a Pd foil and one of the band-pass multilayer mirrors described above. The energy distribution of the ejected electrons has been streaked by the controlled linearly polarized electric field of near-single-cycle near-infrared (NIR) laser pulses [11

11. R. Kienberger, E. Goulielmakis, M. Uiberacker, A. Baltuška, V. Yakovlev, F. Bammer, A. Scrinzi, Th. Westerwalbesloh, U. Kleineberg, U. Heinzmann, M. Drescher, and F. Krausz, “Atomic transient recorder,” Nature 427(6977), 817–821 (2004). [CrossRef] [PubMed]

,18

18. E. Goulielmakis, M. Schultze, M. Hofstetter, V. S. Yakovlev, J. Gagnon, M. Uiberacker, A. L. Aquila, E. M. Gullikson, D. T. Attwood, R. Kienberger, F. Krausz, and U. Kleineberg, “Single-cycle nonlinear optics,” Science 320(5883), 1614–1617 (2008). [CrossRef] [PubMed]

,26

26. M. Kitzler, N. Milosevic, A. Scrinzi, F. Krausz, and T. Brabec, “Quantum theory of attosecond XUV pulse measurement by laser dressed photoionization,” Phys. Rev. Lett. 88(17), 173904 (2002). [CrossRef] [PubMed]

]. The streaked spectra for electrons collected in a narrow cone aligned with the laser polarization were recorded as a function of the delay between the ionizing XUV pulse and the streaking NIR field.

To access the temporal intensity profile of the synthesized attosecond pulses and their frequency sweep we performed a frequency-resolved optical gating (FROG) analysis [30

30. R. Trebino, K. W. DeLong, D. N. Fittinghoff, J. N. Sweetser, M. A. Krumbügel, B. A. Richman, and D. J. Kane, “Measuring ultrashort laser pulses in the time-frequency domain using frequency-resolved optical gating,” Rev. Sci. Instrum. 68(9), 3277 (1997). [CrossRef]

,31

31. A download link of the program can be found at http://www.attoworld.de/Home/ourResearch/Downloads/index.html

] of the acquired streaking spectrograms. This method gives not only access to a full characterization of the laser vector potential, it allows us as well to characterize the spectral intensity distribution and the group delay variation [32

32. Y. Mairesse, A. de Bohan, L. J. Frasinski, H. Merdji, L. C. Dinu, P. Monchicourt, P. Breger, M. Kovačev, R. Taïeb, B. Carré, H. G. Muller, P. Agostini, and P. Salières, “Attosecond synchronization of high-harmonic soft x-rays,” Science 302(5650), 1540–1543 (2003). [CrossRef] [PubMed]

,33

33. J. Gagnon, E. Goulielmakis, and V. S. Yakovlev, “The accurate FROG characterization of attosecond pulses from streaking measurements,” Appl. Phys. B 92(1), 25–32 (2008). [CrossRef]

] of the final attosecond XUV pulse reflected from the mirrors after passing the filter, allowing for a direct comparison of its GDD with the design values of the mirrors’ GDD. The resultant streaking spectrograms recorded with the three mirrors of Fig. 2(a)2(c) are displayed in Fig. 3(a)
Fig. 3 Measured and retrieved attosecond electron streaking spectrograms, upper and lower row, respectively. Panels (a)-(c) and (d)-(f) display spectrograms recorded with attosecond pulses reflected off the mirrors described in Fig. 2(a)2(c), respectively. The energy shift in the recorded spectra is proportional to the vector potential AL(t) of the streaking laser field at the instant of photoemission, hence the dependence of this energy shift on the delay between the attosecond XUV pulse and the NIR laser field reflects the temporal evolution of the NIR laser field’s vector potential, AL(t). Narrowing and broadening in the streaked electron spectra at the zero crossings is displayed by enhanced and diminished electron count rates, respectively. The small insets show the energy calibrated raw data before subtraction of the background.
3(c) along with their corresponding FROG retrievals in Fig. 3(d)3(f), respectively. The streaked energy spectra of electrons ejected from the 2p sub-shell are accompanied by a low- energy background originating from various processes, including inelastic scattering, above-threshold ionization via the NIR field, contribution from a small satellite pulse and shakeup channels. The 2p spectrogram also slightly overlaps with that corresponding to 2s electrons. We subtracted this undesirable background in order to isolate the 2p spectrogram for a FROG analysis. The insets in Fig. 3 show the raw data before subtraction of that background. All features of the spectrograms remain obviously untouched. Thus the choice of the background function does not affect the qualitative result but has some influence on the details of the quantitative analyses. Using the FROG CRAB algorithm Attogram described in refs [33

33. J. Gagnon, E. Goulielmakis, and V. S. Yakovlev, “The accurate FROG characterization of attosecond pulses from streaking measurements,” Appl. Phys. B 92(1), 25–32 (2008). [CrossRef]

,34

34. J. Gagnon and V. S. Yakovlev, “The robustness of attosecond streaking measurements,” Opt. Express 17(20), 17678–17693 (2009). [CrossRef] [PubMed]

], we retrieved the vector potential of the streaking NIR laser field together with the spectral phase and intensity distribution of the attosecond XUV pulse. Figure 3(d)3(f) depict the corresponding streaking spectrograms calculated from the retrieved NIR waveform and XUV pulse. The calculated spectrograms appear to be in excellent agreement with the measured ones.

The spectrograms clearly reveal signatures of the chirp imposed to the XUV pulse after being reflected by the chirped XUV multilayer mirrors. In order to recognize these signatures, we analyse, with the help of Fig. 4
Fig. 4 Qualitative analysis of attosecond streak images of a linearly negatively-chirped attosecond pulse. For explanation, see text.
, qualitatively the implications of lowest-order (linear) frequency sweep of the attosecond XUV pulse on its streaking spectrogram recorded with a linearly polarized few-cycle field. The linear chirp causes a linear sweep of initial photoelectron momenta depicted by the slanted black straight lines in Fig. 4. The laser field transfers a momentum Δp to the XUV-released electron that is proportional to the vector potential AL(t) of the streaking field at the instant of release. As a consequence, AL(t) also sweeps the electron momentum near its zero crossings. This laser-induced sweep is positive (negative) at the positive (negative) slope of Δp(t), respectively. Depending on its sign, it increases or decreases the initial sweep of photoelectron momentum imposed by the chirp of the ionizing attosecond XUV pulse. This, in turn, gives rise to a broadening or narrowing of the corresponding final momentum (energy) distribution (streak image), respectively, which can be approximated at moderate streaking intensities as ΔE ~2ep(t0)AL(t0), where p(t 0 ) represents the electron momentum and AL(t0) the vector field amplitude of the streaking laser field at time t0 of its birth. Hence, a negatively-chirped pulse (taken in the example considered in Fig. 4) results in a streaking spectrogram exhibiting narrower/broader streaked spectra at the positive/negative slope of Δp(t), exactly as revealed by Fig. 3(c) and 3(f). Conversely, a positively-chirped pulse is predicted to produce a streaking spectrogram with broader/narrower streaked spectra at the positive/negative slope of Δp(t), as displayed by Fig. 3(a) and 3(d).

We can now turn our attention to a quantitative evaluation of the chirp carried by the attosecond XUV pulse in the three experiments performed with the three different mirrors. Figure 5
Fig. 5 Retrieved spectral and temporal characteristics of the attosecond XUV pulse, upper row and lower row, respectively. Panels (a), (b) and (c) display the intensity spectrum (green dotted line) and group delay (red dashed line) of the attosecond XUV pulse reflected off the mirrors described in Fig. 2(a), 2(b), and 2(c), respectively, as retrieved from the measured streaking spectrograms shown in Fig. 3(a), 3(b), and 3(c), respectively. The black full lines depict the corresponding XUV spectra measured directly with an XUV spectrometer. The evaluated effective group-delay dispersions weighted by the final spectral XUV intensity are also shown. Panels (d), (e), (f) show the temporal intensity profile (black line) and temporal phase (red dashed line) retrieved from the streaking spectrograms of Fig. 3(a), 3(b), and 3(c), respectively. The XUV pulse duration (full width at intensity half maximum) has been evaluated and is displayed at the bottom of each panel.
shows the retrieved intensity and GD of the attosecond pulses after reflection off the XUV multilayer and filtering by the transmission filter as evaluated from the photo-electron spectrograms in Fig. 3. The solid black lines in Fig. 5(a)5(c) show a direct measurement of the XUV pulse spectrum at the target after passing the filter and the appropriate mirror. Comparison of the retrieved XUV spectra (green dotted lines) with those directly measured photon spectra shows remarkable agreement of the bandwidth, spectral profile and central energy position. This agreement between retrieved and measured spectra highlights the precision with which XUV mirrors are designed and manufactured and demonstrates the power of attosecond streaking measurements coupled with the FROG CRAB retrieval procedure.

Table 1

Table 1. Comparison of XUV mirror designed and FROG retrieved pulse parameters*

table-icon
View This Table
summarizes the evaluated pulse durations and the GDD carried by the reflected pulses, in comparison with the designed GDD of the mirrors. Small deviations from the average GDD influence the final pulse more if its spectral intensity is high at that energy. Thus, all GDD values in Table 1 have been weighted with the spectral profiles I(ω) of the final pulses for a more meaningful comparison: GDD average=∫I(ω)GDD ω dω/∫I(ω)dω. Comparing the retrieved averaged GDD values with the design goals shows an excellent quantitative agreement for two of the mirrors, namely the positive GDD (to within 20%), and the near zero GDD mirror (to within ≈2x103 as 2, causing negligible pulse broadening in the 100-as domain), while the quantitative agreement is compromised by the same layer thickness errors in the negative GDD mirror giving rise to the deviations in Fig. 2(c). Note that even thickness deviations on an atomic scale result in significant changes of the mirrors spectral phase response though the reflectance suffers only minor modifications.Uncertainties in the XUV optical constants of the multilayer materials Mo, B4C and Si in the 100-130 eV energy range may also contribute to the residual discrepancies between design and measurement, with dispersion of the Pd filter appearing to be less than 1.5x103 as 2 in the 100-130 eV photon energy range. The appearance of a single attosecond pulse in the fringe-less spectrograms (Fig. 3) ensures that our mirror reflectivity peak really coincides with the cut-off spectrum. The near-vanishing chirp of the attosecond pulse filtered from the cut-off range of the high-harmonic spectrum and reflected by the near-zero-GDD mirror (b) at the same time validates theoretical considerations that predict the attochirp to be negligible in the cut-off range [32

32. Y. Mairesse, A. de Bohan, L. J. Frasinski, H. Merdji, L. C. Dinu, P. Monchicourt, P. Breger, M. Kovačev, R. Taïeb, B. Carré, H. G. Muller, P. Agostini, and P. Salières, “Attosecond synchronization of high-harmonic soft x-rays,” Science 302(5650), 1540–1543 (2003). [CrossRef] [PubMed]

,12

12. F. Krausz and M. Ivanov, “Attosecond physics,” Rev. Mod. Phys. 81(1), 163–234 (2009). [CrossRef]

]. Finally the good agreement between the retrieved GDD values of the produced attosecond pulses and the designed mirror dispersion confirms that the chirp of the attosecond pulse is mainly affected by the mirror, while the intrinsic chirp of the high harmonic generation and the additional filter play subordinate roles.

3. Conclusions

In summary, we have demonstrated control of the chirp and temporal profile of isolated attosecond XUV pulses with non-periodic multilayer mirrors in an energy range above 100 eV. This technique can be extended to third and higher order phase term treatment as well and is applicable to any spectral range were high reflecting multilayer mirrors are producible, it is important to mention that this range by far exceeds the photon energy range accessible with contemporary high-harmonic-sources. Precision control of the characteristics of attosecond pulses adds an important technical capability to the toolbox of attosecond technology, affording promise for pushing its frontiers to higher temporal resolutions down to the atomic unit of time (24 as) and extending coherent control from structural dynamics towards electronic motion in the valence band. High harmonic radiation contains, due to its generation process, intrinsically an essential amount of chirp in a spectral range out of the cut-off region. Precise dispersion control of attosecond pulses could allow us to push the limits to even shorter Fourier-limited pulses, taking spectral bandwidth exceeding the cut-off range and thus entering this temporal regime. Moreover, control over electronic motion in photo-ionization by chirped few-cycle attosecond pulses was recently predicted in a theoretical work by Peng et al. [35

35. L. Y. Peng, F. Tan, Q. Gong, E. A. Pronin, and A. F. Starace, “Few-cycle attosecond pulse chirp effects on asymmetries in ionized electron momentum distributions,” Phys. Rev. A 80(1), 013407 (2009). [CrossRef]

]. Furthermore important insight into fundamental electronic structures as the quantum phase can be gained from chirp analyses in electronic states via XUV streaking [36

36. V. S. Yakovlev, J. Gagnon, N. Karpowicz, and F. Krausz, “Attosecond streaking enables the measurement of quantum phase,” Phys. Rev. Lett. 105(7), 073001 (2010). [CrossRef] [PubMed]

]. Absolute control of the chirp of an attosecond pulse becomes even more interesting when we reach the regime of nonlinear processes in the XUV range, where for example coherent control by chirped pulses could be achieved. Future seeding of free electron lasers (FEL) in the XUV by coherent High Harmonic radiation allows for controlling the spectral and temporal FEL pulse output with sufficiently high photon numbers [37

37. Y. Li, J. Lewellen, Z. Huang, V. Sajaev, and S. V. Milton, “Time-resolved measurement of a self-amplified free-electron laser,” NIM A 507(1-2), 413–416 (2003). [CrossRef]

] and thus requires precise control over the spectral seed chirp as can be provided by the multilayer mirrors described in this paper.

Acknowledgements

This work was supported by the DFG Excellence Cluster “Munich Centre for Advanced Photonics” (MAP). R.K. acknowledges funding from the Sofja Kovalevskaja Award of the Alexander von Humboldt Foundation and an ERC Starting Grant.

References and links

1.

M. Drescher, M. Hentschel, R. Kienberger, G. Tempea, C. Spielmann, G. A. Reider, P. B. Corkum, and F. Krausz, “X-ray pulses approaching the attosecond frontier,” Science 291(5510), 1923–1927 (2001). [CrossRef] [PubMed]

2.

A. L. Cavalieri, N. Müller, T. 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(7165), 1029–1032 (2007). [CrossRef] [PubMed]

3.

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 tunnelling in atoms,” Nature 446(7136), 627–632 (2007). [CrossRef] [PubMed]

4.

M. Schultze, M. Fieß, N. Karpowicz, J. Gagnon, M. Korbman, M. Hofstetter, S. Neppl, A. L. Cavalieri, Y. Komninos, Th. 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(5986), 1658–1662 (2010). [CrossRef] [PubMed]

5.

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(7307), 739–743 (2010). [CrossRef] [PubMed]

6.

A. Wonisch, U. Neuhäusler, N. M. Kabachnik, T. Uphues, M. Uiberacker, V. Yakovlev, F. Krausz, M. Drescher, U. Kleineberg, and U. Heinzmann, “Design, fabrication, and analysis of chirped multilayer mirrors for reflection of extreme-ultraviolet attosecond pulses,” Appl. Opt. 45(17), 4147–4156 (2006). [CrossRef] [PubMed]

7.

A.-S. Morlens, P. Balcou, P. Zeitoun, C. Valentin, V. Laude, and S. Kazamias, “Compression of attosecond harmonic pulses by extreme-ultraviolet chirped mirrors,” Opt. Lett. 30(12), 1554–1556 (2005). [CrossRef] [PubMed]

8.

M. Suman, G. Monaco, M.-G. Pelizzo, D. L. Windt, and P. Nicolosi, “Realization and characterization of an XUV multilayer coating for attosecond pulses,” Opt. Express 17(10), 7922–7932 (2009). [CrossRef] [PubMed]

9.

M. Hentschel, R. Kienberger, Ch. Spielmann, G. A. Reider, N. Milosevic, T. Brabec, P. Corkum, U. Heinzmann, M. Drescher, and F. Krausz, “Attosecond metrology,” Nature 414(6863), 509–513 (2001). [CrossRef] [PubMed]

10.

I. P. Christov, M. M. Murnane, and H. C. Kapteyn, “High-Harmonic Generation of Attosecond Pulses in the “Single-Cycle” Regime,” Phys. Rev. Lett. 78(7), 1251–1254 (1997). [CrossRef]

11.

R. Kienberger, E. Goulielmakis, M. Uiberacker, A. Baltuška, V. Yakovlev, F. Bammer, A. Scrinzi, Th. Westerwalbesloh, U. Kleineberg, U. Heinzmann, M. Drescher, and F. Krausz, “Atomic transient recorder,” Nature 427(6977), 817–821 (2004). [CrossRef] [PubMed]

12.

F. Krausz and M. Ivanov, “Attosecond physics,” Rev. Mod. Phys. 81(1), 163–234 (2009). [CrossRef]

13.

E. Goulielmakis, M. Uiberacker, R. Kienberger, A. Baltuška, V. Yakovlev, A. Scrinzi, Th. Westerwalbesloh, U. Kleineberg, U. Heinzmann, M. Drescher, and F. Krausz, “Direct measurement of light waves,” Science 305(5688), 1267–1269 (2004). [CrossRef] [PubMed]

14.

V. Pervak, A. V. Tikhonravov, M. K. Trubetskov, S. Naumov, F. Krausz, and A. Apolonski, “1.5-octave chirped mirror for pulse compression down to sub-3 fs,” Appl. Phys. B 87(1), 5–12 (2007). [CrossRef]

15.

E. Gustafsson, T. Ruchon, M. Swoboda, T. Remetter, E. Pourtal, R. López-Martens, Ph. Balcou, and A. L’Huillier, “Broadband attosecond pulse shaping,” Opt. Lett. 32(11), 1353–1355 (2007). [CrossRef] [PubMed]

16.

R. López-Martens, K. Varjú, P. Johnsson, J. Mauritsson, Y. Mairesse, P. Salières, M. B. Gaarde, K. J. Schafer, A. Persson, S. Svanberg, C.-G. Wahlström, and A. L’huillier, “Amplitude and phase control of attosecond light pulses,” Phys. Rev. Lett. 94(3), 033001 (2005). [CrossRef] [PubMed]

17.

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(5798), 443–446 (2006). [CrossRef] [PubMed]

18.

E. Goulielmakis, M. Schultze, M. Hofstetter, V. S. Yakovlev, J. Gagnon, M. Uiberacker, A. L. Aquila, E. M. Gullikson, D. T. Attwood, R. Kienberger, F. Krausz, and U. Kleineberg, “Single-cycle nonlinear optics,” Science 320(5883), 1614–1617 (2008). [CrossRef] [PubMed]

19.

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(6909), 803–807 (2002). [CrossRef] [PubMed]

20.

Y. Ménesguen, S. de Rossi, E. Meltchakov, and F. Delmotte, “Aperiodic multilayer mirrors for efficient broadband reflection in the extreme ultraviolet,” Appl. Phys., A Mater. Sci. Process. 98(2), 305–309 (2010). [CrossRef]

21.

M. Hofstetter, M. Schultze, M. Fieß, A. Guggenmos, J. Gagnon, E. Magerl, E. Botschafter, R. Ernstorfer, R. Kienberger, E. M. Gullikson, F. Krausz, and U. Kleineberg, “First attosecond pulse control by multilayer mirrors above 100 eV photon energy,“ in Ultrafast Phenomena XVII, 11.17, M. Chergui, D. Jonas, E. Riedle, B. Schönlein, A. Taylor (Oxford University Press, New York, 2010).

22.

A. V. Tikhonravov, M. K. Trubetskov, and G. W. DeBell, “Optical coating design approaches based on the needle optimization technique,” Appl. Opt. 46(5), 704–710 (2007). [CrossRef] [PubMed]

23.

B. L. Henke, E. M. Gullikson, and J. C. Davis, “X-ray interactions: photoabsorption, scattering, transmission, and reflection at E=50-30000 eV, Z=1-92,” At. Data Nucl. Data Tables 54(2), 181–342 (1993). [CrossRef]

24.

E. M. Gullikson, J. H. Underwood, P. Batson, and V. Nikitin, “A soft x-ray/EUV reflectometer based on a laser produced plasma source,” J. XRay Sci. Technol. 3(4), 283–299 (1992). [PubMed]

25.

A. Aquila, F. Salmassi, and E. Gullikson, “Metrologies for the phase characterization of attosecond extreme ultraviolet optics,” Opt. Lett. 33(5), 455–457 (2008). [CrossRef] [PubMed]

26.

M. Kitzler, N. Milosevic, A. Scrinzi, F. Krausz, and T. Brabec, “Quantum theory of attosecond XUV pulse measurement by laser dressed photoionization,” Phys. Rev. Lett. 88(17), 173904 (2002). [CrossRef] [PubMed]

27.

R. Kienberger, M. Hentschel, M. Uiberacker, Ch. Spielmann, M. Kitzler, A. Scrinzi, M. Wieland, Th. Westerwalbesloh, U. Kleineberg, U. Heinzmann, M. Drescher, and F. Krausz, “Steering attosecond electron wave packets with light,” Science 297(5584), 1144–1148 (2002). [CrossRef] [PubMed]

28.

M. Schultze, E. Goulielmakis, M. Uiberacker, M. Hofstetter, J. Kim, D. Kim, F. Krausz, and U. Kleineberg, “Powerful 170-attosecond XUV pulses generated with few-cycle laser pulses and broadband multilayer optics,” N. J. Phys. 9(7), 243 (2007). [CrossRef]

29.

M. Fieß, M. Schultze, E. Goulielmakis, B. Dennhardt, J. Gagnon, M. Hofstetter, R. Kienberger, and F. Krausz, “Versatile apparatus for attosecond metrology and spectroscopy,” Rev. Sci. Instrum. 81, 1 (2010). [CrossRef]

30.

R. Trebino, K. W. DeLong, D. N. Fittinghoff, J. N. Sweetser, M. A. Krumbügel, B. A. Richman, and D. J. Kane, “Measuring ultrashort laser pulses in the time-frequency domain using frequency-resolved optical gating,” Rev. Sci. Instrum. 68(9), 3277 (1997). [CrossRef]

31.

A download link of the program can be found at http://www.attoworld.de/Home/ourResearch/Downloads/index.html

32.

Y. Mairesse, A. de Bohan, L. J. Frasinski, H. Merdji, L. C. Dinu, P. Monchicourt, P. Breger, M. Kovačev, R. Taïeb, B. Carré, H. G. Muller, P. Agostini, and P. Salières, “Attosecond synchronization of high-harmonic soft x-rays,” Science 302(5650), 1540–1543 (2003). [CrossRef] [PubMed]

33.

J. Gagnon, E. Goulielmakis, and V. S. Yakovlev, “The accurate FROG characterization of attosecond pulses from streaking measurements,” Appl. Phys. B 92(1), 25–32 (2008). [CrossRef]

34.

J. Gagnon and V. S. Yakovlev, “The robustness of attosecond streaking measurements,” Opt. Express 17(20), 17678–17693 (2009). [CrossRef] [PubMed]

35.

L. Y. Peng, F. Tan, Q. Gong, E. A. Pronin, and A. F. Starace, “Few-cycle attosecond pulse chirp effects on asymmetries in ionized electron momentum distributions,” Phys. Rev. A 80(1), 013407 (2009). [CrossRef]

36.

V. S. Yakovlev, J. Gagnon, N. Karpowicz, and F. Krausz, “Attosecond streaking enables the measurement of quantum phase,” Phys. Rev. Lett. 105(7), 073001 (2010). [CrossRef] [PubMed]

37.

Y. Li, J. Lewellen, Z. Huang, V. Sajaev, and S. V. Milton, “Time-resolved measurement of a self-amplified free-electron laser,” NIM A 507(1-2), 413–416 (2003). [CrossRef]

OCIS Codes
(320.0320) Ultrafast optics : Ultrafast optics
(320.1590) Ultrafast optics : Chirping
(320.5540) Ultrafast optics : Pulse shaping
(340.7480) X-ray optics : X-rays, soft x-rays, extreme ultraviolet (EUV)
(310.4165) Thin films : Multilayer design

ToC Category:
Ultrafast Optics

History
Original Manuscript: November 23, 2010
Revised Manuscript: December 31, 2010
Manuscript Accepted: January 3, 2011
Published: January 14, 2011

Citation
Michael Hofstetter, Martin Schultze, Markus Fieß, Benjamin Dennhardt, Alexander Guggenmos, Justin Gagnon, Vladislav S. Yakovlev, Eleftherios Goulielmakis, Reinhard Kienberger, Eric M. Gullikson, Ferenc Krausz, and Ulf Kleineberg, "Attosecond dispersion control by extreme ultraviolet multilayer mirrors," Opt. Express 19, 1767-1776 (2011)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-3-1767


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References

  1. M. Drescher, M. Hentschel, R. Kienberger, G. Tempea, C. Spielmann, G. A. Reider, P. B. Corkum, and F. Krausz, “X-ray pulses approaching the attosecond frontier,” Science 291(5510), 1923–1927 (2001). [CrossRef] [PubMed]
  2. A. L. Cavalieri, N. Müller, T. 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(7165), 1029–1032 (2007). [CrossRef] [PubMed]
  3. 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 tunnelling in atoms,” Nature 446(7136), 627–632 (2007). [CrossRef] [PubMed]
  4. M. Schultze, M. Fieß, N. Karpowicz, J. Gagnon, M. Korbman, M. Hofstetter, S. Neppl, A. L. Cavalieri, Y. Komninos, Th. 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(5986), 1658–1662 (2010). [CrossRef] [PubMed]
  5. 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(7307), 739–743 (2010). [CrossRef] [PubMed]
  6. A. Wonisch, U. Neuhäusler, N. M. Kabachnik, T. Uphues, M. Uiberacker, V. Yakovlev, F. Krausz, M. Drescher, U. Kleineberg, and U. Heinzmann, “Design, fabrication, and analysis of chirped multilayer mirrors for reflection of extreme-ultraviolet attosecond pulses,” Appl. Opt. 45(17), 4147–4156 (2006). [CrossRef] [PubMed]
  7. A.-S. Morlens, P. Balcou, P. Zeitoun, C. Valentin, V. Laude, and S. Kazamias, “Compression of attosecond harmonic pulses by extreme-ultraviolet chirped mirrors,” Opt. Lett. 30(12), 1554–1556 (2005). [CrossRef] [PubMed]
  8. M. Suman, G. Monaco, M.-G. Pelizzo, D. L. Windt, and P. Nicolosi, “Realization and characterization of an XUV multilayer coating for attosecond pulses,” Opt. Express 17(10), 7922–7932 (2009). [CrossRef] [PubMed]
  9. M. Hentschel, R. Kienberger, Ch. Spielmann, G. A. Reider, N. Milosevic, T. Brabec, P. Corkum, U. Heinzmann, M. Drescher, and F. Krausz, “Attosecond metrology,” Nature 414(6863), 509–513 (2001). [CrossRef] [PubMed]
  10. I. P. Christov, M. M. Murnane, and H. C. Kapteyn, “High-Harmonic Generation of Attosecond Pulses in the “Single-Cycle” Regime,” Phys. Rev. Lett. 78(7), 1251–1254 (1997). [CrossRef]
  11. R. Kienberger, E. Goulielmakis, M. Uiberacker, A. Baltuška, V. Yakovlev, F. Bammer, A. Scrinzi, Th. Westerwalbesloh, U. Kleineberg, U. Heinzmann, M. Drescher, and F. Krausz, “Atomic transient recorder,” Nature 427(6977), 817–821 (2004). [CrossRef] [PubMed]
  12. F. Krausz and M. Ivanov, “Attosecond physics,” Rev. Mod. Phys. 81(1), 163–234 (2009). [CrossRef]
  13. E. Goulielmakis, M. Uiberacker, R. Kienberger, A. Baltuška, V. Yakovlev, A. Scrinzi, Th. Westerwalbesloh, U. Kleineberg, U. Heinzmann, M. Drescher, and F. Krausz, “Direct measurement of light waves,” Science 305(5688), 1267–1269 (2004). [CrossRef] [PubMed]
  14. V. Pervak, A. V. Tikhonravov, M. K. Trubetskov, S. Naumov, F. Krausz, and A. Apolonski, “1.5-octave chirped mirror for pulse compression down to sub-3 fs,” Appl. Phys. B 87(1), 5–12 (2007). [CrossRef]
  15. E. Gustafsson, T. Ruchon, M. Swoboda, T. Remetter, E. Pourtal, R. López-Martens, Ph. Balcou, and A. L’Huillier, “Broadband attosecond pulse shaping,” Opt. Lett. 32(11), 1353–1355 (2007). [CrossRef] [PubMed]
  16. R. López-Martens, K. Varjú, P. Johnsson, J. Mauritsson, Y. Mairesse, P. Salières, M. B. Gaarde, K. J. Schafer, A. Persson, S. Svanberg, C.-G. Wahlström, and A. L’huillier, “Amplitude and phase control of attosecond light pulses,” Phys. Rev. Lett. 94(3), 033001 (2005). [CrossRef] [PubMed]
  17. 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(5798), 443–446 (2006). [CrossRef] [PubMed]
  18. E. Goulielmakis, M. Schultze, M. Hofstetter, V. S. Yakovlev, J. Gagnon, M. Uiberacker, A. L. Aquila, E. M. Gullikson, D. T. Attwood, R. Kienberger, F. Krausz, and U. Kleineberg, “Single-cycle nonlinear optics,” Science 320(5883), 1614–1617 (2008). [CrossRef] [PubMed]
  19. 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(6909), 803–807 (2002). [CrossRef] [PubMed]
  20. Y. Ménesguen, S. de Rossi, E. Meltchakov, and F. Delmotte, “Aperiodic multilayer mirrors for efficient broadband reflection in the extreme ultraviolet,” Appl. Phys., A Mater. Sci. Process. 98(2), 305–309 (2010). [CrossRef]
  21. M. Hofstetter, M. Schultze, M. Fieß, A. Guggenmos, J. Gagnon, E. Magerl, E. Botschafter, R. Ernstorfer, R. Kienberger, E. M. Gullikson, F. Krausz, and U. Kleineberg, “First attosecond pulse control by multilayer mirrors above 100 eV photon energy,“ in Ultrafast Phenomena XVII, 11.17, M. Chergui, D. Jonas, E. Riedle, B. Schönlein, A. Taylor (Oxford University Press, New York, 2010).
  22. A. V. Tikhonravov, M. K. Trubetskov, and G. W. DeBell, “Optical coating design approaches based on the needle optimization technique,” Appl. Opt. 46(5), 704–710 (2007). [CrossRef] [PubMed]
  23. B. L. Henke, E. M. Gullikson, and J. C. Davis, “X-ray interactions: photoabsorption, scattering, transmission, and reflection at E=50-30000 eV, Z=1-92,” At. Data Nucl. Data Tables 54(2), 181–342 (1993). [CrossRef]
  24. E. M. Gullikson, J. H. Underwood, P. Batson, and V. Nikitin, “A soft x-ray/EUV reflectometer based on a laser produced plasma source,” J. XRay Sci. Technol. 3(4), 283–299 (1992). [PubMed]
  25. A. Aquila, F. Salmassi, and E. Gullikson, “Metrologies for the phase characterization of attosecond extreme ultraviolet optics,” Opt. Lett. 33(5), 455–457 (2008). [CrossRef] [PubMed]
  26. M. Kitzler, N. Milosevic, A. Scrinzi, F. Krausz, and T. Brabec, “Quantum theory of attosecond XUV pulse measurement by laser dressed photoionization,” Phys. Rev. Lett. 88(17), 173904 (2002). [CrossRef] [PubMed]
  27. R. Kienberger, M. Hentschel, M. Uiberacker, Ch. Spielmann, M. Kitzler, A. Scrinzi, M. Wieland, Th. Westerwalbesloh, U. Kleineberg, U. Heinzmann, M. Drescher, and F. Krausz, “Steering attosecond electron wave packets with light,” Science 297(5584), 1144–1148 (2002). [CrossRef] [PubMed]
  28. M. Schultze, E. Goulielmakis, M. Uiberacker, M. Hofstetter, J. Kim, D. Kim, F. Krausz, and U. Kleineberg, “Powerful 170-attosecond XUV pulses generated with few-cycle laser pulses and broadband multilayer optics,” N. J. Phys. 9(7), 243 (2007). [CrossRef]
  29. M. Fieß, M. Schultze, E. Goulielmakis, B. Dennhardt, J. Gagnon, M. Hofstetter, R. Kienberger, and F. Krausz, “Versatile apparatus for attosecond metrology and spectroscopy,” Rev. Sci. Instrum. 81, 1 (2010). [CrossRef]
  30. R. Trebino, K. W. DeLong, D. N. Fittinghoff, J. N. Sweetser, M. A. Krumbügel, B. A. Richman, and D. J. Kane, “Measuring ultrashort laser pulses in the time-frequency domain using frequency-resolved optical gating,” Rev. Sci. Instrum. 68(9), 3277 (1997). [CrossRef]
  31. A download link of the program can be found at http://www.attoworld.de/Home/ourResearch/Downloads/index.html
  32. Y. Mairesse, A. de Bohan, L. J. Frasinski, H. Merdji, L. C. Dinu, P. Monchicourt, P. Breger, M. Kovačev, R. Taïeb, B. Carré, H. G. Muller, P. Agostini, and P. Salières, “Attosecond synchronization of high-harmonic soft x-rays,” Science 302(5650), 1540–1543 (2003). [CrossRef] [PubMed]
  33. J. Gagnon, E. Goulielmakis, and V. S. Yakovlev, “The accurate FROG characterization of attosecond pulses from streaking measurements,” Appl. Phys. B 92(1), 25–32 (2008). [CrossRef]
  34. J. Gagnon and V. S. Yakovlev, “The robustness of attosecond streaking measurements,” Opt. Express 17(20), 17678–17693 (2009). [CrossRef] [PubMed]
  35. L. Y. Peng, F. Tan, Q. Gong, E. A. Pronin, and A. F. Starace, “Few-cycle attosecond pulse chirp effects on asymmetries in ionized electron momentum distributions,” Phys. Rev. A 80(1), 013407 (2009). [CrossRef]
  36. V. S. Yakovlev, J. Gagnon, N. Karpowicz, and F. Krausz, “Attosecond streaking enables the measurement of quantum phase,” Phys. Rev. Lett. 105(7), 073001 (2010). [CrossRef] [PubMed]
  37. Y. Li, J. Lewellen, Z. Huang, V. Sajaev, and S. V. Milton, “Time-resolved measurement of a self-amplified free-electron laser,” NIM A 507(1-2), 413–416 (2003). [CrossRef]

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