Abstract

Carrier-envelope-phase (CEP)-dependent modulation was measured in above-threshold ionization of xenon driven with 30-fs laser pulses. We showed the dependence from the asymmetry map obtained using a velocity map imaging spectrometer, up to 17 eV in photoelectron energy. The dependence appeared to be linear with a slope of one photon energy increase per CEP change of 2π and did not rely on the sign or the amount of laser chirp. Our results indicated the existence of the quantum interference between different multiphoton ionization paths.

© 2014 Optical Society of America

1. Introduction

Since its discovery, above-threshold ionization (ATI) has been extensively investigated to reveal the photoionization dynamics of atoms under intense laser fields [15]. Strong field ionization of atoms induces such interesting phenomena as high harmonic generation (HHG) [6, 7], nonsequential double ionization (NSDI) [810], and ATI. While all three phenomena are results of photoionization of atoms in a strong laser field, HHG emits harmonic photons due to the recombination of the released electron with its parent ion, and NSDI happens when the returning electron kicks out another electron from the ion. ATI produces photoelectrons separated by incident photon energy in a photoelectron spectrum due to the absorption of photons in excess of the minimum required to overcome the ionization threshold of an atom. The measurements of ATI spectra have revealed structural information on atomic bound states and the rescattering process of the freed electron [11, 12]. ATI is also useful in probing molecular structures from angle-resolved ATI spectra [13, 14]. In addition it has been known that the ATI process depends on the carrier-envelope phase (CEP) of few-cycle laser pulses [15, 16]. ATI is, thus, a fundamental process revealing the physics of strong field interaction in atoms and molecules.

As a sensitive measure of CEP, photoelectron emission has been investigated using few-cycle laser pulses. There exists an asymmetry in photoelectron yield along the polarization direction when a target atom is ionized by a linearly polarized few-cycle laser pulse, depending on CEP [16]. This asymmetric emission in ionization has been the key to devise measurement instruments and develop detection techniques as well as the stabilization scheme for CEP. A stereographic imaging technique is introduced with linearly polarized few-cycle pulses to investigate the asymmetric emission along the polarization direction by using a velocity map imaging spectrometer [17, 18]. In addition the stereo-ATI technique has been widely used to determine the CEP of a laser pulse from a two-dimensional parametric plot of asymmetry [19], proving the usefulness of ATI in measuring the CEP of few-cycle laser pulses.

Even the CEP of few-cycle laser pulses can be determined by these methods, it is still a meaningful question to ask the maximum pulse duration to observe the CEP effect and how to extract the absolute phase from multi-cycle pulses. The CEP of a femtosecond pulse could be a control parameter in investigating electronic transition processes in molecules coupled with multi-cycle laser [20] or molecular dynamics [21]. Photo-fragmentation, for example, was demonstrated for heavy molecules with CEP-controlled laser pulses [22]. With the single-shot CEP meter the upper limit to detect CEP effects was shown to be a pulse duration of around 12.5 fs [23]. Theoretical studies showed that the CEP effect could be observed even with multi-cycle laser pulses when quantum interference occurs between different ionization paths of an atom [24, 25], and another study demonstrated the CEP effect experimentally with multi-cycle RF pulses [26]. CEP dependence in HHG with multi-cycle laser pulses was shown by contribution of long electron trajectories [27]. The demonstration of CEP-dependent ATI with multi-cycle laser pulses would, thus, be a challenging task to reveal new physical processes.

In this investigation we present the experimental observation of CEP-sensitive ATI of xenon atoms exposed to 30-fs laser pulses containing more than 10 optical cycles. Since the CEP effects in ATI have been observed only with few-cycle pulses, our results indicate that an ionization process, occurring over many optical periods, can still be sensitive to CEP. The observed features of the CEP dependence shown here should provide the clues for finding such a new process.

2. Experimental setup for CEP-sensitive ATI measurement

We performed an ATI experiment with a CEP-controlled femtosecond Ti:sapphire laser centered at 820 nm and a velocity map imaging spectrometer (VMIS). As shown in Fig. 1(a), linearly polarized, 1-mJ, 30-fs laser pulses, after focused by a spherical mirror, irradiate at a repetition rate of 1 kHz the effused xenon atoms having a backing pressure of 10−7 Torr, and as a result free electrons are produced. These electrons are brought to the microchannel plate coupled with a phosphor screen by a set of the electrodes denoted by G, E, and R in Fig. 1(a). From the CCD image of the screen obtained after subtracting its background signal, the momentum distribution of electrons is reconstructed with the BASEX method [28], assuming cylindrical symmetry about the laser polarization axis. An example of the reconstructed momentum distribution is shown in Fig. 1(b). The CEP of the laser pulses was controlled by the direct locking method [29]. As the oscillator, stabilized by the direct locking method, produces pulses with identical CEP, any pulse selection was not required for amplifying pulses with identical CEP. The CEP was stabilized to a level of jitter below 200 mrad (over 10 consecutive laser shots) for more than several hours without any adjustment. Scanning over CEP was carried out with a phase step of π/12. Laser energy fluctuation was maintained within 2%. The CEP dependence of ATI in xenon atoms could, thus, be measured reliably while scanning CEP at different experimental parameters.

 figure: Fig. 1

Fig. 1 (a) Schematics of the experimental setup. CM: concave mirror (f=60 cm); ε̂: laser polarization; G: ground plate; E: extractor electrode; R: Repeller electrode; MCP+PS: dual microchannel plates assembled with a phosphor screen; CCD: charge-coupled device camera. (b) Reconstructed momentum distribution of the ATI electrons from xenon atoms irradiated by a 30-fs, 5 × 1013 W/cm2 laser pulse.

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To find the CEP dependence of ATI spectra, the difference between the spectra for positive momenta (py > 0) and that for negative momenta (py < 0) was considered. Here y refers to the laser polarization axis specified in Fig. 1(a). As a normalized measure of the difference, the asymmetry parameter [17], denoted by A(E, ϕ), was used:

A(E,ϕ)=P+(E,ϕ)P(E,ϕ)P+(E,ϕ)+P(E,ϕ),
where E is the electron energy, ϕ the CEP of the laser pulse, and P+ (P) the electron spectrum with the azimuthal angle of the momentum within 15° from the positive (negative) y-axis, respectively. Beyond this angle the asymmetry became weak with the increase of angle. Any variation of A(E, ϕ) over ϕ indicates the CEP dependence of ATI.

3. Experimental results and discussion

From the ATI spectra acquired with the VMIS an asymmetry map was obtained while changing CEP, as shown in Figs. 2(a) and 2(b). For the electron energy below 11ħω, where ħω=1.51 eV is the laser photon energy, the asymmetry map shows linear dependence on CEP with slopes of about ħω/2π. Even when other parameters such as laser chirp, intensity, and focusing position were varied, the slope did not change as far as the dependence was observed. The asymmetry was clearly observed in the intensity range from 3.5×1013 W/cm2 to 5.5×1013 W/cm2, while the maximum asymmetry value was 0.03 as shown in Fig. 2(a). For the electron energy above 11ħω, the CEP dependence was not observed while a modulation along the vertical axis was present. Such CEP-independent modulation might be attributed to the uneven gain of the spectrometer for the positive and negative directions or to some physical process. In contrast to the common understanding that CEP dependence appears only with few-cycle laser pulses, the ATI of xenon atoms clearly exhibited the dependence even with multi-cycle (30 fs) pulses.

 figure: Fig. 2

Fig. 2 (a) Asymmetry map as a function of CEP and electron energy and (b) electron spectra at the two directions along the laser polarization for the CEP, ϕ = π. The shortest 30-fs laser pulses with intensity of 5 × 1013 W/cm2 were applied.

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The effect of laser chirp on the CEP dependence was also examined, as shown in Fig. 3, with different amount of chirp as well as its sign. The shortest pulse had a temporal width of 30 fs and an intensity of 5.0 × 1013 W/cm2. The grating separation was adjusted in the pulse compressor to manipulate the chirp of the laser pulse. During the chirp control the laser intensity also changes due to the temporal broadening. The CEP dependence was observed for the cases shown in Figs. 3(a)–3(d) and disappeared outside this range. In Fig. 3(b) taken with 30-fs pulses, strong modulation in CEP change was observed. For the positively chirped 35-fs pulses shown in Fig. 3(a), the modulation became weaker than the case in Fig. 3(b), while the case for the negatively chirped 31-fs pulses still revealed the dependence in linear slopes as shown in Fig. 3(c). In Fig. 3(d), obtained with negatively chirped 35-fs pulses, the dependence became very weak at the low electron energy below 8ħω and disappeared at higher energy. From the comparison between Figs. 3(a) and 3(c), it was found that the slope in the asymmetry map was ħω/2π, maintaining the same value regardless of the amount of laser chirp and the slope did not change signs with chirp sign. It is contrary to the theoretical prediction by Abel et al. [18] based on the dispersion up to the second-order spectral phase.

 figure: Fig. 3

Fig. 3 Asymmetry maps obtained with various chirped laser pulses. The chirp was controlled by adjusting the grating separation. The sign of laser chirp, pulse width, and peak intensity are as follows: (a) (+)35 fs, 4.5 × 1013 W/cm2; (b) (+)30 fs, 5.0 × 1013 W/cm2; (c) (−)31 fs, 5.0×1013 W/cm2; and (d) (−)35 fs, 4.3×1013 W/cm2. Group delay dispersion (GDD) of each case is (a) +227 fs2, (b) +107 fs2, (c) −152 fs2, and (d) −206 fs2, respectively.

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To explain these results, we need to clarify the ionization regime by which the CEP dependence observed with multi-cycle laser pulses is governed. Because the laser intensity used in the experiment corresponds to the Keldysh parameter slightly larger than unity, the results could be affected by both tunneling ionization (TI) and multi-photon ionization (MPI). It has been known that, in the TI regime, the asymmetry in CEP-dependent events diminishes with the number of optical cycles contained in a laser pulse in theory [3, 30] and experiment [16, 23]. Although we can expect from Yudin et al. [31] that the relative contribution from TI could be slightly more than that of MPI in our intensity range, the sub-cycle nature of the electron emission through TI would have the CEP dependence averaged out for laser pulses longer than a few cycles. Especially rescattered electrons generated through TI might form the CEP-insensitive photoelectron spectra in high-energy part in Fig. 2(a). On the other hand, the low-energy part of ATI spectra might have contribution from MPI process. As a consequence, the CEP-dependent feature observed with multi-cycle laser pulses should be an event in the MPI regime.

For the description of the CEP dependence appearing in ATI with multi-cycle laser pulses of xenon, a multiphoton model, used by Abel et al. [18], was examined. This model is based on the interference between different quantum paths set by low and high frequency components of a driving laser. They reach the same final states with the number of absorbed photons differed by one, producing electron wave packets with opposite parities. This generates the asymmetry in ATI spectra as a result of the quantum interference between the two electron wave packets with different parities. The spectral phase of adjacent peaks in the photoelectron spectra contains a phase offset by the amount of the CEP of the pulse. Since the adjacent peaks in the asymmetry map can appear with the CEP shift of 2π, the slope ħω/2π can be formed. This concept might account for the CEP-dependent ATI observed up to 17 eV with the multi-cycle laser pulses.

The quantum interference between different ionization paths, giving the asymmetry of ATI spectra, can be conveniently described in the frequency domain. Several different ionization pathways are possible, as an atom can absorb excessive photons to produce ATI electrons at different frequencies. The laser spectrum used in our experiments extended from 0.94ħω to 1.07ħω, where ω is the central frequency of the laser pulse. For example, the components of 0.95ħω and 1.05ħω meet the interference condition at 0th-order in the ATI spectrum after absorbing 11 and 10 photons, respectively. Another example would be the components at 0.97ħω and 1.02ħω which have the same kinetic energy at 10th-order peak in the ATI spectrum with 21-and 20-photon absorption, respectively. Actual contributions are continuous around this transition, so the eventual asymmetry map is the sum of all possible sets of combinations. Within the laser intensity aforementioned the CEP dependence due to the interference can occur for the kinetic energy below 11ħω in the spectrum whenever the conditions are satisfied. Specifically for Figs. 3(b) and 3(c) where the asymmetry is prominent for the photoelectron energy between 3ħω and 9ħω, the conditions are met with considerable spectral intensities. Because the asymmetry parameter contains the term, e, where ϕ is the CEP, the change in CEP also follows the periodicity of 2π. Therefore, the CEP dependence observed using multi-cycle laser pulses could originate from the quantum interference between electron wave packets produced with opposite parities.

A feature of the chirp dependence in our results, however, requires different approach from the one by Abel et al. In their model, with consideration of the quadratic spectral phase of a few-cycle pulse, the change in CEP caused an offset of peaks in the asymmetry map. On the other hand, in our experiments with multi-cycle pulses the slopes did not change in the asymmetry map when the amount or even the sign of the chirp changes as shown in Fig. 3. The chirp-dependence of the CEP effect appeared in a simple pattern of linear slopes. For comparison, we analyzed the pulse by the FROG technique to estimate the group delay dispersion (GDD). Two asymmetry maps with GDD of about (+)230 fs2, (–)150 fs2, respectively, in Figs. 3(a) and 3(c), are shown to have no major difference regardless of the sign and the amount of the chirp of the laser pulse. This discrepancy might come from the existence of higher-order spectral phase terms. A new theoretical model is, thus, needed to rigorously explain our experimental results carried out with multi-cycle laser pulses.

4. Conclusion

We experimentally demonstrated the CEP-dependent ATI of atoms with multi-cycle laser pulses. In contrast to the substantial evidences obtained by others that CEP dependence should involve sub-cycle processes using few-cycle laser pulses, our results showed that the CEP of a laser pulse could clearly affect multi-cycle processes. The ATI spectra of xenon atoms exhibited CEP dependence even for 30-fs laser pulses. The CEP-dependent asymmetry, examined for laser intensity and chirp, could be qualitatively explained using the quantum interference occurring between the two electron wave packets formed from different multiphoton ionization paths with opposite parities. The observation that the slope of the asymmetry map did not change its sign with the change of laser chirp sign indicated that the multiphoton model by Abel et al. could not explain the experimental results; such effects would be clarified in successive investigations. Our results will push the investigation of CEP-dependent ATI phenomena one step forward by instigating a new theoretical development.

Acknowledgments

This work was supported by Institute for Basic Science and National Research Foundation, Korea. We appreciate helpful discussions with Chengpu Liu and Nark Nyul Choi.

References and links

1. P. Agostini, F. Fabre, G. Mainfray, G. Petite, and N. K. Rahman, “Free-free transitions following 6-photon ionization of xenon atoms,” Phys. Rev. Lett. 42, 1127–1130 (1979). [CrossRef]  

2. W. Becker, F. Grasbon, R. Kopold, D. B. Milošević, G. G. Paulus, and H. Walther, “Above-threshold ionization: From classical features to quantum effects,” Adv. Atom. Mol. Opt. Phys. 48, 35–98 (2002). [CrossRef]  

3. D. B. Milošević, G. G. Paulus, D. Bauer, and W. Becker, “Above-threshold ionization by few-cycle pulses,” J. Phys. B: At., Mol. Opt. Phys. 39, R203–R262 (2006). [CrossRef]  

4. G. G. Paulus, W. Nicklich, H. Xu, P. Lambropoulos, and H. Walther, “Plateau in above threshold ionization spectra,” Phys. Rev. Lett. 72, 2851–2854 (1994). [CrossRef]   [PubMed]  

5. B. Yang, K. J. Schafer, B. Walker, K. C. Kulander, P. Agostini, and L. F. DiMauro, “Intensity-dependent scattering rings in high order above-threshold ionization,” Phys. Rev. Lett. 71, 3770–3773 (1993). [CrossRef]   [PubMed]  

6. A. McPherson, G. Gibson, H. Jara, U. Johann, T. S. Luk, I. A. McIntyre, K. Boyer, and C. K. Rhodes, “Studies of multiphoton production of vacuum-ultraviolet radiation in the rare gases,” J. Opt. Soc. Am. B 4, 595–601 (1987). [CrossRef]  

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

8. A. l’Huillier, L. A. Lompre, G. Mainfray, and C. Manus, “Multiply charged ions induced by multiphoton absorption in rare gases at 0.53 m,” Phys. Rev. A 27, 2503–2512 (1983). [CrossRef]  

9. T. Weber, M. Weckenbrock, A. Staudte, L. Spielberger, O. Jagutzki, V. Mergel, F. Afaneh, G. Urbasch, M. Vollmer, H. Giessen, and R. Dörner, “Recoil-ion momentum distributions for single and double ionization of helium in strong laser fields,” Phys. Rev. Lett. 84, 443–446 (2000). [CrossRef]   [PubMed]  

10. X. Liu, H. Rottke, E. Eremina, W. Sandner, E. Goulielmakis, K. O. Keeffe, M. Lezius, F. Krausz, F. Lindner, M. G. Schätzel, G. G. Paulus, and H. Walther, “Nonsequential double ionization at the single-optical-cycle limit,” Phys. Rev. Lett. 93, 263001 (2004). [CrossRef]  

11. R. R. Freeman, P. H. Bucksbaum, H. Milchberg, S. Darack, D. Schumacher, and M. E. Geusic, “Above-threshold ionization with subpicosecond laser pulses,” Phys. Rev. Lett. 59, 1092–1095 (1987). [CrossRef]   [PubMed]  

12. G. G. Paulus, W. Becker, W. Nicklich, and H. Walther, “Rescattering effects in above-threshold ionization - a classical model,” J. Phys. B: At. Mol. Opt. Phys. 27, L703–L708 (1994). [CrossRef]  

13. H. Kang, W. Quan, Y. Wang, Z. Lin, M. Wu, H. Liu, X. Liu, B. B. Wang, H. J. Liu, Y. Q. Gu, X. Y. Jia, J. Liu, J. Chen, and Y. Cheng, “Structure effects in angle-resolved high-order above-threshold ionization of molecules,” Phys. Rev. Lett. 104, 203001 (2010). [CrossRef]   [PubMed]  

14. A. Gazibegović-Busuladžić, E. Hasović, M. Busuladžić, D. B. Milošević, F. Kelkensberg, W. K. Siu, M. J. J. Vrakking, F. Lépine, G. Sansone, M. Nisoli, I. Znakovskaya, and M. F. Kling, “Above-threshold ionization of diatomic molecules by few-cycle laser pulses,” Phys. Rev. A 84, 043426 (2011). [CrossRef]  

15. P. Dietrich, F. Krausz, and P. B. Corkum, “Determining the absolute carrier phase of a few-cycle laser pulse,” Opt. Lett. 25, 16–18 (2000). [CrossRef]  

16. G. G. Paulus, F. Grasbon, H. Walther, P. Villoresi, M. Nisoli, S. Stagira, E. Priori, and S. De Silvestri, “Absolute-phase phenomena in photoionization with few-cycle laser pulses,” Nature 414, 182–184 (2001). [CrossRef]   [PubMed]  

17. M. F. Kling, J. Rauschenberger, A. J. Verhoef, E. Hasović, T. Uphues, D. B. Milošević, H. G. Muller, and M. J. J. Vrakking, “Imaging of carrier-envelope phase effects in above-threshold ionization with intense few-cycle laser fields,” New J. Phys. 10, 025024 (2008). [CrossRef]  

18. M. J. Abel, T. Pfeifer, A. Jullien, P. M. Nagel, M. J. Bell, D. M. Neumark, and S. R. Leone, “Carrier-envelope phase-dependent quantum interferences in multiphoton ionization,” J. Phys. B: At., Mol. Opt. Phys. 42, 075601 (2009). [CrossRef]  

19. T. Wittmann, B. Horvath, W. Helml, M. G. Schätzel, X. Gu, A. L. Cavalieri, G. G. Paulus, and R. Kienberger, “Single-shot carrier-envelope phase measurement of few-cycle laser pulses,” Nat. Phys. 5, 357–362 (2009). [CrossRef]  

20. K. Renziehausen, K. Hader, W. Jakubetz, and V. Engel, “Weak-field, multiple-cycle carrier envelope phase effects in laser excitation,” ChemPhysChem 14, 1464–1470 (2013). [CrossRef]   [PubMed]  

21. P. Lan, E. J. Takahashi, K. Liu, Y. Fu, and K. Midorikawa, “Carrier envelope phase dependence of electron localization in the multicycle regime,” New J. Phys. 15, 063023 (2013). [CrossRef]  

22. X. Xie, K. Doblhoff-Dier, S. Roither, M. S. Schöffler, D. Kartashov, H. Xu, T. Rathje, G. G. Paulus, A. Baltuška, S. Gräfe, and M. Kitzler, “Attosecond-recollision-controlled selective fragmentation of polyatomic molecules,” Phys. Rev. Lett. 109, 243001 (2012). [CrossRef]  

23. M. Möller, A. M. Sayler, T. Rathje, M. Chini, Z. Chang, and G. G. Paulus, “Precise, real-time, single-shot carrier-envelope phase measurement in the multi-cycle regime,” Appl. Phys. Lett. 99, 121108 (2011). [CrossRef]  

24. V. Roudnev and B. D. Esry, “General theory of carrier-envelope phase effects,” Phys. Rev. Lett. 99, 220406 (2007). [CrossRef]  

25. X. Zhao, J. Chen, P. Fu, X. Liu, Z.-C. Yan, and B. Wang, “Carrier-envelope-phase effect in a long laser pulse with tens of optical cycles,” Phys. Rev. A 87, 043411 (2013). [CrossRef]  

26. P. K. Jha, Y. V. Rostovtsev, H. Li, V. A. Sautenkov, and M. O. Scully, “Experimental observation of carrier-envelope-phase effects by multicycle pulses,” Phys. Rev. A 83, 033404 (2011). [CrossRef]  

27. G. Sansone, C. Vozzi, S. Stagira, M. Pascolini, L. Poletto, P. Villoresi, G. Tondello, S. De Silvestri, and M. Nisoli, “Observation of carrier-envelope phase phenomena in the multi-optical-cycle regime,” Phys. Rev. Lett. 92, 113904 (2004). [CrossRef]   [PubMed]  

28. V. Dribinski, A. Ossadtchi, V. A. Mandelshtam, and H. Reisler, “Reconstruction of abel-transformable images: The gaussian basis-set expansion abel transform method,” Rev. Sci. Instrum. 73, 2634–2642 (2002). [CrossRef]  

29. J.-h. Lee, Y. S. Lee, J. Park, J. J. Park, D. S. Kim, T. J. Yu, and C. H. Nam, “Implementation of the direct locking method for long-term carrier-envelope-phase stabilization of a grating-based khz femtosecond laser,” Appl. Phys. B: Lasers Opt. 96, 287–291 (2009). [CrossRef]  

30. S. Chelkowski, A. D. Bandrauk, and A. Apolonski, “Phase-dependent asymmetries in strong-field photoionization by few-cycle laser pulses,” Phys. Rev. A 70, 013815 (2004). [CrossRef]  

31. G. L. Yudin and M. Y. Ivanov, “Nonadiabatic tunnel ionization: Looking inside a laser cycle,” Phys. Rev. A 64, 013409 (2001). [CrossRef]  

References

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  1. P. Agostini, F. Fabre, G. Mainfray, G. Petite, and N. K. Rahman, “Free-free transitions following 6-photon ionization of xenon atoms,” Phys. Rev. Lett. 42, 1127–1130 (1979).
    [Crossref]
  2. W. Becker, F. Grasbon, R. Kopold, D. B. Milošević, G. G. Paulus, and H. Walther, “Above-threshold ionization: From classical features to quantum effects,” Adv. Atom. Mol. Opt. Phys. 48, 35–98 (2002).
    [Crossref]
  3. D. B. Milošević, G. G. Paulus, D. Bauer, and W. Becker, “Above-threshold ionization by few-cycle pulses,” J. Phys. B: At., Mol. Opt. Phys. 39, R203–R262 (2006).
    [Crossref]
  4. G. G. Paulus, W. Nicklich, H. Xu, P. Lambropoulos, and H. Walther, “Plateau in above threshold ionization spectra,” Phys. Rev. Lett. 72, 2851–2854 (1994).
    [Crossref] [PubMed]
  5. B. Yang, K. J. Schafer, B. Walker, K. C. Kulander, P. Agostini, and L. F. DiMauro, “Intensity-dependent scattering rings in high order above-threshold ionization,” Phys. Rev. Lett. 71, 3770–3773 (1993).
    [Crossref] [PubMed]
  6. A. McPherson, G. Gibson, H. Jara, U. Johann, T. S. Luk, I. A. McIntyre, K. Boyer, and C. K. Rhodes, “Studies of multiphoton production of vacuum-ultraviolet radiation in the rare gases,” J. Opt. Soc. Am. B 4, 595–601 (1987).
    [Crossref]
  7. P. B. Corkum, “Plasma perspective on strong field multiphoton ionization,” Phys. Rev. Lett. 71, 1994–1997 (1993).
    [Crossref] [PubMed]
  8. A. l’Huillier, L. A. Lompre, G. Mainfray, and C. Manus, “Multiply charged ions induced by multiphoton absorption in rare gases at 0.53 m,” Phys. Rev. A 27, 2503–2512 (1983).
    [Crossref]
  9. T. Weber, M. Weckenbrock, A. Staudte, L. Spielberger, O. Jagutzki, V. Mergel, F. Afaneh, G. Urbasch, M. Vollmer, H. Giessen, and R. Dörner, “Recoil-ion momentum distributions for single and double ionization of helium in strong laser fields,” Phys. Rev. Lett. 84, 443–446 (2000).
    [Crossref] [PubMed]
  10. X. Liu, H. Rottke, E. Eremina, W. Sandner, E. Goulielmakis, K. O. Keeffe, M. Lezius, F. Krausz, F. Lindner, M. G. Schätzel, G. G. Paulus, and H. Walther, “Nonsequential double ionization at the single-optical-cycle limit,” Phys. Rev. Lett. 93, 263001 (2004).
    [Crossref]
  11. R. R. Freeman, P. H. Bucksbaum, H. Milchberg, S. Darack, D. Schumacher, and M. E. Geusic, “Above-threshold ionization with subpicosecond laser pulses,” Phys. Rev. Lett. 59, 1092–1095 (1987).
    [Crossref] [PubMed]
  12. G. G. Paulus, W. Becker, W. Nicklich, and H. Walther, “Rescattering effects in above-threshold ionization - a classical model,” J. Phys. B: At. Mol. Opt. Phys. 27, L703–L708 (1994).
    [Crossref]
  13. H. Kang, W. Quan, Y. Wang, Z. Lin, M. Wu, H. Liu, X. Liu, B. B. Wang, H. J. Liu, Y. Q. Gu, X. Y. Jia, J. Liu, J. Chen, and Y. Cheng, “Structure effects in angle-resolved high-order above-threshold ionization of molecules,” Phys. Rev. Lett. 104, 203001 (2010).
    [Crossref] [PubMed]
  14. A. Gazibegović-Busuladžić, E. Hasović, M. Busuladžić, D. B. Milošević, F. Kelkensberg, W. K. Siu, M. J. J. Vrakking, F. Lépine, G. Sansone, M. Nisoli, I. Znakovskaya, and M. F. Kling, “Above-threshold ionization of diatomic molecules by few-cycle laser pulses,” Phys. Rev. A 84, 043426 (2011).
    [Crossref]
  15. P. Dietrich, F. Krausz, and P. B. Corkum, “Determining the absolute carrier phase of a few-cycle laser pulse,” Opt. Lett. 25, 16–18 (2000).
    [Crossref]
  16. G. G. Paulus, F. Grasbon, H. Walther, P. Villoresi, M. Nisoli, S. Stagira, E. Priori, and S. De Silvestri, “Absolute-phase phenomena in photoionization with few-cycle laser pulses,” Nature 414, 182–184 (2001).
    [Crossref] [PubMed]
  17. M. F. Kling, J. Rauschenberger, A. J. Verhoef, E. Hasović, T. Uphues, D. B. Milošević, H. G. Muller, and M. J. J. Vrakking, “Imaging of carrier-envelope phase effects in above-threshold ionization with intense few-cycle laser fields,” New J. Phys. 10, 025024 (2008).
    [Crossref]
  18. M. J. Abel, T. Pfeifer, A. Jullien, P. M. Nagel, M. J. Bell, D. M. Neumark, and S. R. Leone, “Carrier-envelope phase-dependent quantum interferences in multiphoton ionization,” J. Phys. B: At., Mol. Opt. Phys. 42, 075601 (2009).
    [Crossref]
  19. T. Wittmann, B. Horvath, W. Helml, M. G. Schätzel, X. Gu, A. L. Cavalieri, G. G. Paulus, and R. Kienberger, “Single-shot carrier-envelope phase measurement of few-cycle laser pulses,” Nat. Phys. 5, 357–362 (2009).
    [Crossref]
  20. K. Renziehausen, K. Hader, W. Jakubetz, and V. Engel, “Weak-field, multiple-cycle carrier envelope phase effects in laser excitation,” ChemPhysChem 14, 1464–1470 (2013).
    [Crossref] [PubMed]
  21. P. Lan, E. J. Takahashi, K. Liu, Y. Fu, and K. Midorikawa, “Carrier envelope phase dependence of electron localization in the multicycle regime,” New J. Phys. 15, 063023 (2013).
    [Crossref]
  22. X. Xie, K. Doblhoff-Dier, S. Roither, M. S. Schöffler, D. Kartashov, H. Xu, T. Rathje, G. G. Paulus, A. Baltuška, S. Gräfe, and M. Kitzler, “Attosecond-recollision-controlled selective fragmentation of polyatomic molecules,” Phys. Rev. Lett. 109, 243001 (2012).
    [Crossref]
  23. M. Möller, A. M. Sayler, T. Rathje, M. Chini, Z. Chang, and G. G. Paulus, “Precise, real-time, single-shot carrier-envelope phase measurement in the multi-cycle regime,” Appl. Phys. Lett. 99, 121108 (2011).
    [Crossref]
  24. V. Roudnev and B. D. Esry, “General theory of carrier-envelope phase effects,” Phys. Rev. Lett. 99, 220406 (2007).
    [Crossref]
  25. X. Zhao, J. Chen, P. Fu, X. Liu, Z.-C. Yan, and B. Wang, “Carrier-envelope-phase effect in a long laser pulse with tens of optical cycles,” Phys. Rev. A 87, 043411 (2013).
    [Crossref]
  26. P. K. Jha, Y. V. Rostovtsev, H. Li, V. A. Sautenkov, and M. O. Scully, “Experimental observation of carrier-envelope-phase effects by multicycle pulses,” Phys. Rev. A 83, 033404 (2011).
    [Crossref]
  27. G. Sansone, C. Vozzi, S. Stagira, M. Pascolini, L. Poletto, P. Villoresi, G. Tondello, S. De Silvestri, and M. Nisoli, “Observation of carrier-envelope phase phenomena in the multi-optical-cycle regime,” Phys. Rev. Lett. 92, 113904 (2004).
    [Crossref] [PubMed]
  28. V. Dribinski, A. Ossadtchi, V. A. Mandelshtam, and H. Reisler, “Reconstruction of abel-transformable images: The gaussian basis-set expansion abel transform method,” Rev. Sci. Instrum. 73, 2634–2642 (2002).
    [Crossref]
  29. J.-h. Lee, Y. S. Lee, J. Park, J. J. Park, D. S. Kim, T. J. Yu, and C. H. Nam, “Implementation of the direct locking method for long-term carrier-envelope-phase stabilization of a grating-based khz femtosecond laser,” Appl. Phys. B: Lasers Opt. 96, 287–291 (2009).
    [Crossref]
  30. S. Chelkowski, A. D. Bandrauk, and A. Apolonski, “Phase-dependent asymmetries in strong-field photoionization by few-cycle laser pulses,” Phys. Rev. A 70, 013815 (2004).
    [Crossref]
  31. G. L. Yudin and M. Y. Ivanov, “Nonadiabatic tunnel ionization: Looking inside a laser cycle,” Phys. Rev. A 64, 013409 (2001).
    [Crossref]

2013 (3)

K. Renziehausen, K. Hader, W. Jakubetz, and V. Engel, “Weak-field, multiple-cycle carrier envelope phase effects in laser excitation,” ChemPhysChem 14, 1464–1470 (2013).
[Crossref] [PubMed]

P. Lan, E. J. Takahashi, K. Liu, Y. Fu, and K. Midorikawa, “Carrier envelope phase dependence of electron localization in the multicycle regime,” New J. Phys. 15, 063023 (2013).
[Crossref]

X. Zhao, J. Chen, P. Fu, X. Liu, Z.-C. Yan, and B. Wang, “Carrier-envelope-phase effect in a long laser pulse with tens of optical cycles,” Phys. Rev. A 87, 043411 (2013).
[Crossref]

2012 (1)

X. Xie, K. Doblhoff-Dier, S. Roither, M. S. Schöffler, D. Kartashov, H. Xu, T. Rathje, G. G. Paulus, A. Baltuška, S. Gräfe, and M. Kitzler, “Attosecond-recollision-controlled selective fragmentation of polyatomic molecules,” Phys. Rev. Lett. 109, 243001 (2012).
[Crossref]

2011 (3)

M. Möller, A. M. Sayler, T. Rathje, M. Chini, Z. Chang, and G. G. Paulus, “Precise, real-time, single-shot carrier-envelope phase measurement in the multi-cycle regime,” Appl. Phys. Lett. 99, 121108 (2011).
[Crossref]

P. K. Jha, Y. V. Rostovtsev, H. Li, V. A. Sautenkov, and M. O. Scully, “Experimental observation of carrier-envelope-phase effects by multicycle pulses,” Phys. Rev. A 83, 033404 (2011).
[Crossref]

A. Gazibegović-Busuladžić, E. Hasović, M. Busuladžić, D. B. Milošević, F. Kelkensberg, W. K. Siu, M. J. J. Vrakking, F. Lépine, G. Sansone, M. Nisoli, I. Znakovskaya, and M. F. Kling, “Above-threshold ionization of diatomic molecules by few-cycle laser pulses,” Phys. Rev. A 84, 043426 (2011).
[Crossref]

2010 (1)

H. Kang, W. Quan, Y. Wang, Z. Lin, M. Wu, H. Liu, X. Liu, B. B. Wang, H. J. Liu, Y. Q. Gu, X. Y. Jia, J. Liu, J. Chen, and Y. Cheng, “Structure effects in angle-resolved high-order above-threshold ionization of molecules,” Phys. Rev. Lett. 104, 203001 (2010).
[Crossref] [PubMed]

2009 (3)

M. J. Abel, T. Pfeifer, A. Jullien, P. M. Nagel, M. J. Bell, D. M. Neumark, and S. R. Leone, “Carrier-envelope phase-dependent quantum interferences in multiphoton ionization,” J. Phys. B: At., Mol. Opt. Phys. 42, 075601 (2009).
[Crossref]

T. Wittmann, B. Horvath, W. Helml, M. G. Schätzel, X. Gu, A. L. Cavalieri, G. G. Paulus, and R. Kienberger, “Single-shot carrier-envelope phase measurement of few-cycle laser pulses,” Nat. Phys. 5, 357–362 (2009).
[Crossref]

J.-h. Lee, Y. S. Lee, J. Park, J. J. Park, D. S. Kim, T. J. Yu, and C. H. Nam, “Implementation of the direct locking method for long-term carrier-envelope-phase stabilization of a grating-based khz femtosecond laser,” Appl. Phys. B: Lasers Opt. 96, 287–291 (2009).
[Crossref]

2008 (1)

M. F. Kling, J. Rauschenberger, A. J. Verhoef, E. Hasović, T. Uphues, D. B. Milošević, H. G. Muller, and M. J. J. Vrakking, “Imaging of carrier-envelope phase effects in above-threshold ionization with intense few-cycle laser fields,” New J. Phys. 10, 025024 (2008).
[Crossref]

2007 (1)

V. Roudnev and B. D. Esry, “General theory of carrier-envelope phase effects,” Phys. Rev. Lett. 99, 220406 (2007).
[Crossref]

2006 (1)

D. B. Milošević, G. G. Paulus, D. Bauer, and W. Becker, “Above-threshold ionization by few-cycle pulses,” J. Phys. B: At., Mol. Opt. Phys. 39, R203–R262 (2006).
[Crossref]

2004 (3)

X. Liu, H. Rottke, E. Eremina, W. Sandner, E. Goulielmakis, K. O. Keeffe, M. Lezius, F. Krausz, F. Lindner, M. G. Schätzel, G. G. Paulus, and H. Walther, “Nonsequential double ionization at the single-optical-cycle limit,” Phys. Rev. Lett. 93, 263001 (2004).
[Crossref]

G. Sansone, C. Vozzi, S. Stagira, M. Pascolini, L. Poletto, P. Villoresi, G. Tondello, S. De Silvestri, and M. Nisoli, “Observation of carrier-envelope phase phenomena in the multi-optical-cycle regime,” Phys. Rev. Lett. 92, 113904 (2004).
[Crossref] [PubMed]

S. Chelkowski, A. D. Bandrauk, and A. Apolonski, “Phase-dependent asymmetries in strong-field photoionization by few-cycle laser pulses,” Phys. Rev. A 70, 013815 (2004).
[Crossref]

2002 (2)

V. Dribinski, A. Ossadtchi, V. A. Mandelshtam, and H. Reisler, “Reconstruction of abel-transformable images: The gaussian basis-set expansion abel transform method,” Rev. Sci. Instrum. 73, 2634–2642 (2002).
[Crossref]

W. Becker, F. Grasbon, R. Kopold, D. B. Milošević, G. G. Paulus, and H. Walther, “Above-threshold ionization: From classical features to quantum effects,” Adv. Atom. Mol. Opt. Phys. 48, 35–98 (2002).
[Crossref]

2001 (2)

G. G. Paulus, F. Grasbon, H. Walther, P. Villoresi, M. Nisoli, S. Stagira, E. Priori, and S. De Silvestri, “Absolute-phase phenomena in photoionization with few-cycle laser pulses,” Nature 414, 182–184 (2001).
[Crossref] [PubMed]

G. L. Yudin and M. Y. Ivanov, “Nonadiabatic tunnel ionization: Looking inside a laser cycle,” Phys. Rev. A 64, 013409 (2001).
[Crossref]

2000 (2)

P. Dietrich, F. Krausz, and P. B. Corkum, “Determining the absolute carrier phase of a few-cycle laser pulse,” Opt. Lett. 25, 16–18 (2000).
[Crossref]

T. Weber, M. Weckenbrock, A. Staudte, L. Spielberger, O. Jagutzki, V. Mergel, F. Afaneh, G. Urbasch, M. Vollmer, H. Giessen, and R. Dörner, “Recoil-ion momentum distributions for single and double ionization of helium in strong laser fields,” Phys. Rev. Lett. 84, 443–446 (2000).
[Crossref] [PubMed]

1994 (2)

G. G. Paulus, W. Becker, W. Nicklich, and H. Walther, “Rescattering effects in above-threshold ionization - a classical model,” J. Phys. B: At. Mol. Opt. Phys. 27, L703–L708 (1994).
[Crossref]

G. G. Paulus, W. Nicklich, H. Xu, P. Lambropoulos, and H. Walther, “Plateau in above threshold ionization spectra,” Phys. Rev. Lett. 72, 2851–2854 (1994).
[Crossref] [PubMed]

1993 (2)

B. Yang, K. J. Schafer, B. Walker, K. C. Kulander, P. Agostini, and L. F. DiMauro, “Intensity-dependent scattering rings in high order above-threshold ionization,” Phys. Rev. Lett. 71, 3770–3773 (1993).
[Crossref] [PubMed]

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

1987 (2)

A. McPherson, G. Gibson, H. Jara, U. Johann, T. S. Luk, I. A. McIntyre, K. Boyer, and C. K. Rhodes, “Studies of multiphoton production of vacuum-ultraviolet radiation in the rare gases,” J. Opt. Soc. Am. B 4, 595–601 (1987).
[Crossref]

R. R. Freeman, P. H. Bucksbaum, H. Milchberg, S. Darack, D. Schumacher, and M. E. Geusic, “Above-threshold ionization with subpicosecond laser pulses,” Phys. Rev. Lett. 59, 1092–1095 (1987).
[Crossref] [PubMed]

1983 (1)

A. l’Huillier, L. A. Lompre, G. Mainfray, and C. Manus, “Multiply charged ions induced by multiphoton absorption in rare gases at 0.53 m,” Phys. Rev. A 27, 2503–2512 (1983).
[Crossref]

1979 (1)

P. Agostini, F. Fabre, G. Mainfray, G. Petite, and N. K. Rahman, “Free-free transitions following 6-photon ionization of xenon atoms,” Phys. Rev. Lett. 42, 1127–1130 (1979).
[Crossref]

Abel, M. J.

M. J. Abel, T. Pfeifer, A. Jullien, P. M. Nagel, M. J. Bell, D. M. Neumark, and S. R. Leone, “Carrier-envelope phase-dependent quantum interferences in multiphoton ionization,” J. Phys. B: At., Mol. Opt. Phys. 42, 075601 (2009).
[Crossref]

Afaneh, F.

T. Weber, M. Weckenbrock, A. Staudte, L. Spielberger, O. Jagutzki, V. Mergel, F. Afaneh, G. Urbasch, M. Vollmer, H. Giessen, and R. Dörner, “Recoil-ion momentum distributions for single and double ionization of helium in strong laser fields,” Phys. Rev. Lett. 84, 443–446 (2000).
[Crossref] [PubMed]

Agostini, P.

B. Yang, K. J. Schafer, B. Walker, K. C. Kulander, P. Agostini, and L. F. DiMauro, “Intensity-dependent scattering rings in high order above-threshold ionization,” Phys. Rev. Lett. 71, 3770–3773 (1993).
[Crossref] [PubMed]

P. Agostini, F. Fabre, G. Mainfray, G. Petite, and N. K. Rahman, “Free-free transitions following 6-photon ionization of xenon atoms,” Phys. Rev. Lett. 42, 1127–1130 (1979).
[Crossref]

Apolonski, A.

S. Chelkowski, A. D. Bandrauk, and A. Apolonski, “Phase-dependent asymmetries in strong-field photoionization by few-cycle laser pulses,” Phys. Rev. A 70, 013815 (2004).
[Crossref]

Baltuška, A.

X. Xie, K. Doblhoff-Dier, S. Roither, M. S. Schöffler, D. Kartashov, H. Xu, T. Rathje, G. G. Paulus, A. Baltuška, S. Gräfe, and M. Kitzler, “Attosecond-recollision-controlled selective fragmentation of polyatomic molecules,” Phys. Rev. Lett. 109, 243001 (2012).
[Crossref]

Bandrauk, A. D.

S. Chelkowski, A. D. Bandrauk, and A. Apolonski, “Phase-dependent asymmetries in strong-field photoionization by few-cycle laser pulses,” Phys. Rev. A 70, 013815 (2004).
[Crossref]

Bauer, D.

D. B. Milošević, G. G. Paulus, D. Bauer, and W. Becker, “Above-threshold ionization by few-cycle pulses,” J. Phys. B: At., Mol. Opt. Phys. 39, R203–R262 (2006).
[Crossref]

Becker, W.

D. B. Milošević, G. G. Paulus, D. Bauer, and W. Becker, “Above-threshold ionization by few-cycle pulses,” J. Phys. B: At., Mol. Opt. Phys. 39, R203–R262 (2006).
[Crossref]

W. Becker, F. Grasbon, R. Kopold, D. B. Milošević, G. G. Paulus, and H. Walther, “Above-threshold ionization: From classical features to quantum effects,” Adv. Atom. Mol. Opt. Phys. 48, 35–98 (2002).
[Crossref]

G. G. Paulus, W. Becker, W. Nicklich, and H. Walther, “Rescattering effects in above-threshold ionization - a classical model,” J. Phys. B: At. Mol. Opt. Phys. 27, L703–L708 (1994).
[Crossref]

Bell, M. J.

M. J. Abel, T. Pfeifer, A. Jullien, P. M. Nagel, M. J. Bell, D. M. Neumark, and S. R. Leone, “Carrier-envelope phase-dependent quantum interferences in multiphoton ionization,” J. Phys. B: At., Mol. Opt. Phys. 42, 075601 (2009).
[Crossref]

Boyer, K.

Bucksbaum, P. H.

R. R. Freeman, P. H. Bucksbaum, H. Milchberg, S. Darack, D. Schumacher, and M. E. Geusic, “Above-threshold ionization with subpicosecond laser pulses,” Phys. Rev. Lett. 59, 1092–1095 (1987).
[Crossref] [PubMed]

Busuladžic, M.

A. Gazibegović-Busuladžić, E. Hasović, M. Busuladžić, D. B. Milošević, F. Kelkensberg, W. K. Siu, M. J. J. Vrakking, F. Lépine, G. Sansone, M. Nisoli, I. Znakovskaya, and M. F. Kling, “Above-threshold ionization of diatomic molecules by few-cycle laser pulses,” Phys. Rev. A 84, 043426 (2011).
[Crossref]

Cavalieri, A. L.

T. Wittmann, B. Horvath, W. Helml, M. G. Schätzel, X. Gu, A. L. Cavalieri, G. G. Paulus, and R. Kienberger, “Single-shot carrier-envelope phase measurement of few-cycle laser pulses,” Nat. Phys. 5, 357–362 (2009).
[Crossref]

Chang, Z.

M. Möller, A. M. Sayler, T. Rathje, M. Chini, Z. Chang, and G. G. Paulus, “Precise, real-time, single-shot carrier-envelope phase measurement in the multi-cycle regime,” Appl. Phys. Lett. 99, 121108 (2011).
[Crossref]

Chelkowski, S.

S. Chelkowski, A. D. Bandrauk, and A. Apolonski, “Phase-dependent asymmetries in strong-field photoionization by few-cycle laser pulses,” Phys. Rev. A 70, 013815 (2004).
[Crossref]

Chen, J.

X. Zhao, J. Chen, P. Fu, X. Liu, Z.-C. Yan, and B. Wang, “Carrier-envelope-phase effect in a long laser pulse with tens of optical cycles,” Phys. Rev. A 87, 043411 (2013).
[Crossref]

H. Kang, W. Quan, Y. Wang, Z. Lin, M. Wu, H. Liu, X. Liu, B. B. Wang, H. J. Liu, Y. Q. Gu, X. Y. Jia, J. Liu, J. Chen, and Y. Cheng, “Structure effects in angle-resolved high-order above-threshold ionization of molecules,” Phys. Rev. Lett. 104, 203001 (2010).
[Crossref] [PubMed]

Cheng, Y.

H. Kang, W. Quan, Y. Wang, Z. Lin, M. Wu, H. Liu, X. Liu, B. B. Wang, H. J. Liu, Y. Q. Gu, X. Y. Jia, J. Liu, J. Chen, and Y. Cheng, “Structure effects in angle-resolved high-order above-threshold ionization of molecules,” Phys. Rev. Lett. 104, 203001 (2010).
[Crossref] [PubMed]

Chini, M.

M. Möller, A. M. Sayler, T. Rathje, M. Chini, Z. Chang, and G. G. Paulus, “Precise, real-time, single-shot carrier-envelope phase measurement in the multi-cycle regime,” Appl. Phys. Lett. 99, 121108 (2011).
[Crossref]

Corkum, P. B.

P. Dietrich, F. Krausz, and P. B. Corkum, “Determining the absolute carrier phase of a few-cycle laser pulse,” Opt. Lett. 25, 16–18 (2000).
[Crossref]

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

Darack, S.

R. R. Freeman, P. H. Bucksbaum, H. Milchberg, S. Darack, D. Schumacher, and M. E. Geusic, “Above-threshold ionization with subpicosecond laser pulses,” Phys. Rev. Lett. 59, 1092–1095 (1987).
[Crossref] [PubMed]

De Silvestri, S.

G. Sansone, C. Vozzi, S. Stagira, M. Pascolini, L. Poletto, P. Villoresi, G. Tondello, S. De Silvestri, and M. Nisoli, “Observation of carrier-envelope phase phenomena in the multi-optical-cycle regime,” Phys. Rev. Lett. 92, 113904 (2004).
[Crossref] [PubMed]

G. G. Paulus, F. Grasbon, H. Walther, P. Villoresi, M. Nisoli, S. Stagira, E. Priori, and S. De Silvestri, “Absolute-phase phenomena in photoionization with few-cycle laser pulses,” Nature 414, 182–184 (2001).
[Crossref] [PubMed]

Dietrich, P.

DiMauro, L. F.

B. Yang, K. J. Schafer, B. Walker, K. C. Kulander, P. Agostini, and L. F. DiMauro, “Intensity-dependent scattering rings in high order above-threshold ionization,” Phys. Rev. Lett. 71, 3770–3773 (1993).
[Crossref] [PubMed]

Doblhoff-Dier, K.

X. Xie, K. Doblhoff-Dier, S. Roither, M. S. Schöffler, D. Kartashov, H. Xu, T. Rathje, G. G. Paulus, A. Baltuška, S. Gräfe, and M. Kitzler, “Attosecond-recollision-controlled selective fragmentation of polyatomic molecules,” Phys. Rev. Lett. 109, 243001 (2012).
[Crossref]

Dörner, R.

T. Weber, M. Weckenbrock, A. Staudte, L. Spielberger, O. Jagutzki, V. Mergel, F. Afaneh, G. Urbasch, M. Vollmer, H. Giessen, and R. Dörner, “Recoil-ion momentum distributions for single and double ionization of helium in strong laser fields,” Phys. Rev. Lett. 84, 443–446 (2000).
[Crossref] [PubMed]

Dribinski, V.

V. Dribinski, A. Ossadtchi, V. A. Mandelshtam, and H. Reisler, “Reconstruction of abel-transformable images: The gaussian basis-set expansion abel transform method,” Rev. Sci. Instrum. 73, 2634–2642 (2002).
[Crossref]

Engel, V.

K. Renziehausen, K. Hader, W. Jakubetz, and V. Engel, “Weak-field, multiple-cycle carrier envelope phase effects in laser excitation,” ChemPhysChem 14, 1464–1470 (2013).
[Crossref] [PubMed]

Eremina, E.

X. Liu, H. Rottke, E. Eremina, W. Sandner, E. Goulielmakis, K. O. Keeffe, M. Lezius, F. Krausz, F. Lindner, M. G. Schätzel, G. G. Paulus, and H. Walther, “Nonsequential double ionization at the single-optical-cycle limit,” Phys. Rev. Lett. 93, 263001 (2004).
[Crossref]

Esry, B. D.

V. Roudnev and B. D. Esry, “General theory of carrier-envelope phase effects,” Phys. Rev. Lett. 99, 220406 (2007).
[Crossref]

Fabre, F.

P. Agostini, F. Fabre, G. Mainfray, G. Petite, and N. K. Rahman, “Free-free transitions following 6-photon ionization of xenon atoms,” Phys. Rev. Lett. 42, 1127–1130 (1979).
[Crossref]

Freeman, R. R.

R. R. Freeman, P. H. Bucksbaum, H. Milchberg, S. Darack, D. Schumacher, and M. E. Geusic, “Above-threshold ionization with subpicosecond laser pulses,” Phys. Rev. Lett. 59, 1092–1095 (1987).
[Crossref] [PubMed]

Fu, P.

X. Zhao, J. Chen, P. Fu, X. Liu, Z.-C. Yan, and B. Wang, “Carrier-envelope-phase effect in a long laser pulse with tens of optical cycles,” Phys. Rev. A 87, 043411 (2013).
[Crossref]

Fu, Y.

P. Lan, E. J. Takahashi, K. Liu, Y. Fu, and K. Midorikawa, “Carrier envelope phase dependence of electron localization in the multicycle regime,” New J. Phys. 15, 063023 (2013).
[Crossref]

Gazibegovic-Busuladžic, A.

A. Gazibegović-Busuladžić, E. Hasović, M. Busuladžić, D. B. Milošević, F. Kelkensberg, W. K. Siu, M. J. J. Vrakking, F. Lépine, G. Sansone, M. Nisoli, I. Znakovskaya, and M. F. Kling, “Above-threshold ionization of diatomic molecules by few-cycle laser pulses,” Phys. Rev. A 84, 043426 (2011).
[Crossref]

Geusic, M. E.

R. R. Freeman, P. H. Bucksbaum, H. Milchberg, S. Darack, D. Schumacher, and M. E. Geusic, “Above-threshold ionization with subpicosecond laser pulses,” Phys. Rev. Lett. 59, 1092–1095 (1987).
[Crossref] [PubMed]

Gibson, G.

Giessen, H.

T. Weber, M. Weckenbrock, A. Staudte, L. Spielberger, O. Jagutzki, V. Mergel, F. Afaneh, G. Urbasch, M. Vollmer, H. Giessen, and R. Dörner, “Recoil-ion momentum distributions for single and double ionization of helium in strong laser fields,” Phys. Rev. Lett. 84, 443–446 (2000).
[Crossref] [PubMed]

Goulielmakis, E.

X. Liu, H. Rottke, E. Eremina, W. Sandner, E. Goulielmakis, K. O. Keeffe, M. Lezius, F. Krausz, F. Lindner, M. G. Schätzel, G. G. Paulus, and H. Walther, “Nonsequential double ionization at the single-optical-cycle limit,” Phys. Rev. Lett. 93, 263001 (2004).
[Crossref]

Gräfe, S.

X. Xie, K. Doblhoff-Dier, S. Roither, M. S. Schöffler, D. Kartashov, H. Xu, T. Rathje, G. G. Paulus, A. Baltuška, S. Gräfe, and M. Kitzler, “Attosecond-recollision-controlled selective fragmentation of polyatomic molecules,” Phys. Rev. Lett. 109, 243001 (2012).
[Crossref]

Grasbon, F.

W. Becker, F. Grasbon, R. Kopold, D. B. Milošević, G. G. Paulus, and H. Walther, “Above-threshold ionization: From classical features to quantum effects,” Adv. Atom. Mol. Opt. Phys. 48, 35–98 (2002).
[Crossref]

G. G. Paulus, F. Grasbon, H. Walther, P. Villoresi, M. Nisoli, S. Stagira, E. Priori, and S. De Silvestri, “Absolute-phase phenomena in photoionization with few-cycle laser pulses,” Nature 414, 182–184 (2001).
[Crossref] [PubMed]

Gu, X.

T. Wittmann, B. Horvath, W. Helml, M. G. Schätzel, X. Gu, A. L. Cavalieri, G. G. Paulus, and R. Kienberger, “Single-shot carrier-envelope phase measurement of few-cycle laser pulses,” Nat. Phys. 5, 357–362 (2009).
[Crossref]

Gu, Y. Q.

H. Kang, W. Quan, Y. Wang, Z. Lin, M. Wu, H. Liu, X. Liu, B. B. Wang, H. J. Liu, Y. Q. Gu, X. Y. Jia, J. Liu, J. Chen, and Y. Cheng, “Structure effects in angle-resolved high-order above-threshold ionization of molecules,” Phys. Rev. Lett. 104, 203001 (2010).
[Crossref] [PubMed]

Hader, K.

K. Renziehausen, K. Hader, W. Jakubetz, and V. Engel, “Weak-field, multiple-cycle carrier envelope phase effects in laser excitation,” ChemPhysChem 14, 1464–1470 (2013).
[Crossref] [PubMed]

Hasovic, E.

A. Gazibegović-Busuladžić, E. Hasović, M. Busuladžić, D. B. Milošević, F. Kelkensberg, W. K. Siu, M. J. J. Vrakking, F. Lépine, G. Sansone, M. Nisoli, I. Znakovskaya, and M. F. Kling, “Above-threshold ionization of diatomic molecules by few-cycle laser pulses,” Phys. Rev. A 84, 043426 (2011).
[Crossref]

M. F. Kling, J. Rauschenberger, A. J. Verhoef, E. Hasović, T. Uphues, D. B. Milošević, H. G. Muller, and M. J. J. Vrakking, “Imaging of carrier-envelope phase effects in above-threshold ionization with intense few-cycle laser fields,” New J. Phys. 10, 025024 (2008).
[Crossref]

Helml, W.

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G. G. Paulus, W. Nicklich, H. Xu, P. Lambropoulos, and H. Walther, “Plateau in above threshold ionization spectra,” Phys. Rev. Lett. 72, 2851–2854 (1994).
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J.-h. Lee, Y. S. Lee, J. Park, J. J. Park, D. S. Kim, T. J. Yu, and C. H. Nam, “Implementation of the direct locking method for long-term carrier-envelope-phase stabilization of a grating-based khz femtosecond laser,” Appl. Phys. B: Lasers Opt. 96, 287–291 (2009).
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M. J. Abel, T. Pfeifer, A. Jullien, P. M. Nagel, M. J. Bell, D. M. Neumark, and S. R. Leone, “Carrier-envelope phase-dependent quantum interferences in multiphoton ionization,” J. Phys. B: At., Mol. Opt. Phys. 42, 075601 (2009).
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X. Liu, H. Rottke, E. Eremina, W. Sandner, E. Goulielmakis, K. O. Keeffe, M. Lezius, F. Krausz, F. Lindner, M. G. Schätzel, G. G. Paulus, and H. Walther, “Nonsequential double ionization at the single-optical-cycle limit,” Phys. Rev. Lett. 93, 263001 (2004).
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P. K. Jha, Y. V. Rostovtsev, H. Li, V. A. Sautenkov, and M. O. Scully, “Experimental observation of carrier-envelope-phase effects by multicycle pulses,” Phys. Rev. A 83, 033404 (2011).
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H. Kang, W. Quan, Y. Wang, Z. Lin, M. Wu, H. Liu, X. Liu, B. B. Wang, H. J. Liu, Y. Q. Gu, X. Y. Jia, J. Liu, J. Chen, and Y. Cheng, “Structure effects in angle-resolved high-order above-threshold ionization of molecules,” Phys. Rev. Lett. 104, 203001 (2010).
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H. Kang, W. Quan, Y. Wang, Z. Lin, M. Wu, H. Liu, X. Liu, B. B. Wang, H. J. Liu, Y. Q. Gu, X. Y. Jia, J. Liu, J. Chen, and Y. Cheng, “Structure effects in angle-resolved high-order above-threshold ionization of molecules,” Phys. Rev. Lett. 104, 203001 (2010).
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H. Kang, W. Quan, Y. Wang, Z. Lin, M. Wu, H. Liu, X. Liu, B. B. Wang, H. J. Liu, Y. Q. Gu, X. Y. Jia, J. Liu, J. Chen, and Y. Cheng, “Structure effects in angle-resolved high-order above-threshold ionization of molecules,” Phys. Rev. Lett. 104, 203001 (2010).
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H. Kang, W. Quan, Y. Wang, Z. Lin, M. Wu, H. Liu, X. Liu, B. B. Wang, H. J. Liu, Y. Q. Gu, X. Y. Jia, J. Liu, J. Chen, and Y. Cheng, “Structure effects in angle-resolved high-order above-threshold ionization of molecules,” Phys. Rev. Lett. 104, 203001 (2010).
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P. Lan, E. J. Takahashi, K. Liu, Y. Fu, and K. Midorikawa, “Carrier envelope phase dependence of electron localization in the multicycle regime,” New J. Phys. 15, 063023 (2013).
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X. Liu, H. Rottke, E. Eremina, W. Sandner, E. Goulielmakis, K. O. Keeffe, M. Lezius, F. Krausz, F. Lindner, M. G. Schätzel, G. G. Paulus, and H. Walther, “Nonsequential double ionization at the single-optical-cycle limit,” Phys. Rev. Lett. 93, 263001 (2004).
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A. l’Huillier, L. A. Lompre, G. Mainfray, and C. Manus, “Multiply charged ions induced by multiphoton absorption in rare gases at 0.53 m,” Phys. Rev. A 27, 2503–2512 (1983).
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Luk, T. S.

Mainfray, G.

A. l’Huillier, L. A. Lompre, G. Mainfray, and C. Manus, “Multiply charged ions induced by multiphoton absorption in rare gases at 0.53 m,” Phys. Rev. A 27, 2503–2512 (1983).
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P. Agostini, F. Fabre, G. Mainfray, G. Petite, and N. K. Rahman, “Free-free transitions following 6-photon ionization of xenon atoms,” Phys. Rev. Lett. 42, 1127–1130 (1979).
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A. l’Huillier, L. A. Lompre, G. Mainfray, and C. Manus, “Multiply charged ions induced by multiphoton absorption in rare gases at 0.53 m,” Phys. Rev. A 27, 2503–2512 (1983).
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McPherson, A.

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P. Lan, E. J. Takahashi, K. Liu, Y. Fu, and K. Midorikawa, “Carrier envelope phase dependence of electron localization in the multicycle regime,” New J. Phys. 15, 063023 (2013).
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[Crossref]

M. F. Kling, J. Rauschenberger, A. J. Verhoef, E. Hasović, T. Uphues, D. B. Milošević, H. G. Muller, and M. J. J. Vrakking, “Imaging of carrier-envelope phase effects in above-threshold ionization with intense few-cycle laser fields,” New J. Phys. 10, 025024 (2008).
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D. B. Milošević, G. G. Paulus, D. Bauer, and W. Becker, “Above-threshold ionization by few-cycle pulses,” J. Phys. B: At., Mol. Opt. Phys. 39, R203–R262 (2006).
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W. Becker, F. Grasbon, R. Kopold, D. B. Milošević, G. G. Paulus, and H. Walther, “Above-threshold ionization: From classical features to quantum effects,” Adv. Atom. Mol. Opt. Phys. 48, 35–98 (2002).
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M. Möller, A. M. Sayler, T. Rathje, M. Chini, Z. Chang, and G. G. Paulus, “Precise, real-time, single-shot carrier-envelope phase measurement in the multi-cycle regime,” Appl. Phys. Lett. 99, 121108 (2011).
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M. F. Kling, J. Rauschenberger, A. J. Verhoef, E. Hasović, T. Uphues, D. B. Milošević, H. G. Muller, and M. J. J. Vrakking, “Imaging of carrier-envelope phase effects in above-threshold ionization with intense few-cycle laser fields,” New J. Phys. 10, 025024 (2008).
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M. J. Abel, T. Pfeifer, A. Jullien, P. M. Nagel, M. J. Bell, D. M. Neumark, and S. R. Leone, “Carrier-envelope phase-dependent quantum interferences in multiphoton ionization,” J. Phys. B: At., Mol. Opt. Phys. 42, 075601 (2009).
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Nam, C. H.

J.-h. Lee, Y. S. Lee, J. Park, J. J. Park, D. S. Kim, T. J. Yu, and C. H. Nam, “Implementation of the direct locking method for long-term carrier-envelope-phase stabilization of a grating-based khz femtosecond laser,” Appl. Phys. B: Lasers Opt. 96, 287–291 (2009).
[Crossref]

Neumark, D. M.

M. J. Abel, T. Pfeifer, A. Jullien, P. M. Nagel, M. J. Bell, D. M. Neumark, and S. R. Leone, “Carrier-envelope phase-dependent quantum interferences in multiphoton ionization,” J. Phys. B: At., Mol. Opt. Phys. 42, 075601 (2009).
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G. G. Paulus, W. Nicklich, H. Xu, P. Lambropoulos, and H. Walther, “Plateau in above threshold ionization spectra,” Phys. Rev. Lett. 72, 2851–2854 (1994).
[Crossref] [PubMed]

G. G. Paulus, W. Becker, W. Nicklich, and H. Walther, “Rescattering effects in above-threshold ionization - a classical model,” J. Phys. B: At. Mol. Opt. Phys. 27, L703–L708 (1994).
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Nisoli, M.

A. Gazibegović-Busuladžić, E. Hasović, M. Busuladžić, D. B. Milošević, F. Kelkensberg, W. K. Siu, M. J. J. Vrakking, F. Lépine, G. Sansone, M. Nisoli, I. Znakovskaya, and M. F. Kling, “Above-threshold ionization of diatomic molecules by few-cycle laser pulses,” Phys. Rev. A 84, 043426 (2011).
[Crossref]

G. Sansone, C. Vozzi, S. Stagira, M. Pascolini, L. Poletto, P. Villoresi, G. Tondello, S. De Silvestri, and M. Nisoli, “Observation of carrier-envelope phase phenomena in the multi-optical-cycle regime,” Phys. Rev. Lett. 92, 113904 (2004).
[Crossref] [PubMed]

G. G. Paulus, F. Grasbon, H. Walther, P. Villoresi, M. Nisoli, S. Stagira, E. Priori, and S. De Silvestri, “Absolute-phase phenomena in photoionization with few-cycle laser pulses,” Nature 414, 182–184 (2001).
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V. Dribinski, A. Ossadtchi, V. A. Mandelshtam, and H. Reisler, “Reconstruction of abel-transformable images: The gaussian basis-set expansion abel transform method,” Rev. Sci. Instrum. 73, 2634–2642 (2002).
[Crossref]

Park, J.

J.-h. Lee, Y. S. Lee, J. Park, J. J. Park, D. S. Kim, T. J. Yu, and C. H. Nam, “Implementation of the direct locking method for long-term carrier-envelope-phase stabilization of a grating-based khz femtosecond laser,” Appl. Phys. B: Lasers Opt. 96, 287–291 (2009).
[Crossref]

Park, J. J.

J.-h. Lee, Y. S. Lee, J. Park, J. J. Park, D. S. Kim, T. J. Yu, and C. H. Nam, “Implementation of the direct locking method for long-term carrier-envelope-phase stabilization of a grating-based khz femtosecond laser,” Appl. Phys. B: Lasers Opt. 96, 287–291 (2009).
[Crossref]

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G. Sansone, C. Vozzi, S. Stagira, M. Pascolini, L. Poletto, P. Villoresi, G. Tondello, S. De Silvestri, and M. Nisoli, “Observation of carrier-envelope phase phenomena in the multi-optical-cycle regime,” Phys. Rev. Lett. 92, 113904 (2004).
[Crossref] [PubMed]

Paulus, G. G.

X. Xie, K. Doblhoff-Dier, S. Roither, M. S. Schöffler, D. Kartashov, H. Xu, T. Rathje, G. G. Paulus, A. Baltuška, S. Gräfe, and M. Kitzler, “Attosecond-recollision-controlled selective fragmentation of polyatomic molecules,” Phys. Rev. Lett. 109, 243001 (2012).
[Crossref]

M. Möller, A. M. Sayler, T. Rathje, M. Chini, Z. Chang, and G. G. Paulus, “Precise, real-time, single-shot carrier-envelope phase measurement in the multi-cycle regime,” Appl. Phys. Lett. 99, 121108 (2011).
[Crossref]

T. Wittmann, B. Horvath, W. Helml, M. G. Schätzel, X. Gu, A. L. Cavalieri, G. G. Paulus, and R. Kienberger, “Single-shot carrier-envelope phase measurement of few-cycle laser pulses,” Nat. Phys. 5, 357–362 (2009).
[Crossref]

D. B. Milošević, G. G. Paulus, D. Bauer, and W. Becker, “Above-threshold ionization by few-cycle pulses,” J. Phys. B: At., Mol. Opt. Phys. 39, R203–R262 (2006).
[Crossref]

X. Liu, H. Rottke, E. Eremina, W. Sandner, E. Goulielmakis, K. O. Keeffe, M. Lezius, F. Krausz, F. Lindner, M. G. Schätzel, G. G. Paulus, and H. Walther, “Nonsequential double ionization at the single-optical-cycle limit,” Phys. Rev. Lett. 93, 263001 (2004).
[Crossref]

W. Becker, F. Grasbon, R. Kopold, D. B. Milošević, G. G. Paulus, and H. Walther, “Above-threshold ionization: From classical features to quantum effects,” Adv. Atom. Mol. Opt. Phys. 48, 35–98 (2002).
[Crossref]

G. G. Paulus, F. Grasbon, H. Walther, P. Villoresi, M. Nisoli, S. Stagira, E. Priori, and S. De Silvestri, “Absolute-phase phenomena in photoionization with few-cycle laser pulses,” Nature 414, 182–184 (2001).
[Crossref] [PubMed]

G. G. Paulus, W. Nicklich, H. Xu, P. Lambropoulos, and H. Walther, “Plateau in above threshold ionization spectra,” Phys. Rev. Lett. 72, 2851–2854 (1994).
[Crossref] [PubMed]

G. G. Paulus, W. Becker, W. Nicklich, and H. Walther, “Rescattering effects in above-threshold ionization - a classical model,” J. Phys. B: At. Mol. Opt. Phys. 27, L703–L708 (1994).
[Crossref]

Petite, G.

P. Agostini, F. Fabre, G. Mainfray, G. Petite, and N. K. Rahman, “Free-free transitions following 6-photon ionization of xenon atoms,” Phys. Rev. Lett. 42, 1127–1130 (1979).
[Crossref]

Pfeifer, T.

M. J. Abel, T. Pfeifer, A. Jullien, P. M. Nagel, M. J. Bell, D. M. Neumark, and S. R. Leone, “Carrier-envelope phase-dependent quantum interferences in multiphoton ionization,” J. Phys. B: At., Mol. Opt. Phys. 42, 075601 (2009).
[Crossref]

Poletto, L.

G. Sansone, C. Vozzi, S. Stagira, M. Pascolini, L. Poletto, P. Villoresi, G. Tondello, S. De Silvestri, and M. Nisoli, “Observation of carrier-envelope phase phenomena in the multi-optical-cycle regime,” Phys. Rev. Lett. 92, 113904 (2004).
[Crossref] [PubMed]

Priori, E.

G. G. Paulus, F. Grasbon, H. Walther, P. Villoresi, M. Nisoli, S. Stagira, E. Priori, and S. De Silvestri, “Absolute-phase phenomena in photoionization with few-cycle laser pulses,” Nature 414, 182–184 (2001).
[Crossref] [PubMed]

Quan, W.

H. Kang, W. Quan, Y. Wang, Z. Lin, M. Wu, H. Liu, X. Liu, B. B. Wang, H. J. Liu, Y. Q. Gu, X. Y. Jia, J. Liu, J. Chen, and Y. Cheng, “Structure effects in angle-resolved high-order above-threshold ionization of molecules,” Phys. Rev. Lett. 104, 203001 (2010).
[Crossref] [PubMed]

Rahman, N. K.

P. Agostini, F. Fabre, G. Mainfray, G. Petite, and N. K. Rahman, “Free-free transitions following 6-photon ionization of xenon atoms,” Phys. Rev. Lett. 42, 1127–1130 (1979).
[Crossref]

Rathje, T.

X. Xie, K. Doblhoff-Dier, S. Roither, M. S. Schöffler, D. Kartashov, H. Xu, T. Rathje, G. G. Paulus, A. Baltuška, S. Gräfe, and M. Kitzler, “Attosecond-recollision-controlled selective fragmentation of polyatomic molecules,” Phys. Rev. Lett. 109, 243001 (2012).
[Crossref]

M. Möller, A. M. Sayler, T. Rathje, M. Chini, Z. Chang, and G. G. Paulus, “Precise, real-time, single-shot carrier-envelope phase measurement in the multi-cycle regime,” Appl. Phys. Lett. 99, 121108 (2011).
[Crossref]

Rauschenberger, J.

M. F. Kling, J. Rauschenberger, A. J. Verhoef, E. Hasović, T. Uphues, D. B. Milošević, H. G. Muller, and M. J. J. Vrakking, “Imaging of carrier-envelope phase effects in above-threshold ionization with intense few-cycle laser fields,” New J. Phys. 10, 025024 (2008).
[Crossref]

Reisler, H.

V. Dribinski, A. Ossadtchi, V. A. Mandelshtam, and H. Reisler, “Reconstruction of abel-transformable images: The gaussian basis-set expansion abel transform method,” Rev. Sci. Instrum. 73, 2634–2642 (2002).
[Crossref]

Renziehausen, K.

K. Renziehausen, K. Hader, W. Jakubetz, and V. Engel, “Weak-field, multiple-cycle carrier envelope phase effects in laser excitation,” ChemPhysChem 14, 1464–1470 (2013).
[Crossref] [PubMed]

Rhodes, C. K.

Roither, S.

X. Xie, K. Doblhoff-Dier, S. Roither, M. S. Schöffler, D. Kartashov, H. Xu, T. Rathje, G. G. Paulus, A. Baltuška, S. Gräfe, and M. Kitzler, “Attosecond-recollision-controlled selective fragmentation of polyatomic molecules,” Phys. Rev. Lett. 109, 243001 (2012).
[Crossref]

Rostovtsev, Y. V.

P. K. Jha, Y. V. Rostovtsev, H. Li, V. A. Sautenkov, and M. O. Scully, “Experimental observation of carrier-envelope-phase effects by multicycle pulses,” Phys. Rev. A 83, 033404 (2011).
[Crossref]

Rottke, H.

X. Liu, H. Rottke, E. Eremina, W. Sandner, E. Goulielmakis, K. O. Keeffe, M. Lezius, F. Krausz, F. Lindner, M. G. Schätzel, G. G. Paulus, and H. Walther, “Nonsequential double ionization at the single-optical-cycle limit,” Phys. Rev. Lett. 93, 263001 (2004).
[Crossref]

Roudnev, V.

V. Roudnev and B. D. Esry, “General theory of carrier-envelope phase effects,” Phys. Rev. Lett. 99, 220406 (2007).
[Crossref]

Sandner, W.

X. Liu, H. Rottke, E. Eremina, W. Sandner, E. Goulielmakis, K. O. Keeffe, M. Lezius, F. Krausz, F. Lindner, M. G. Schätzel, G. G. Paulus, and H. Walther, “Nonsequential double ionization at the single-optical-cycle limit,” Phys. Rev. Lett. 93, 263001 (2004).
[Crossref]

Sansone, G.

A. Gazibegović-Busuladžić, E. Hasović, M. Busuladžić, D. B. Milošević, F. Kelkensberg, W. K. Siu, M. J. J. Vrakking, F. Lépine, G. Sansone, M. Nisoli, I. Znakovskaya, and M. F. Kling, “Above-threshold ionization of diatomic molecules by few-cycle laser pulses,” Phys. Rev. A 84, 043426 (2011).
[Crossref]

G. Sansone, C. Vozzi, S. Stagira, M. Pascolini, L. Poletto, P. Villoresi, G. Tondello, S. De Silvestri, and M. Nisoli, “Observation of carrier-envelope phase phenomena in the multi-optical-cycle regime,” Phys. Rev. Lett. 92, 113904 (2004).
[Crossref] [PubMed]

Sautenkov, V. A.

P. K. Jha, Y. V. Rostovtsev, H. Li, V. A. Sautenkov, and M. O. Scully, “Experimental observation of carrier-envelope-phase effects by multicycle pulses,” Phys. Rev. A 83, 033404 (2011).
[Crossref]

Sayler, A. M.

M. Möller, A. M. Sayler, T. Rathje, M. Chini, Z. Chang, and G. G. Paulus, “Precise, real-time, single-shot carrier-envelope phase measurement in the multi-cycle regime,” Appl. Phys. Lett. 99, 121108 (2011).
[Crossref]

Schafer, K. J.

B. Yang, K. J. Schafer, B. Walker, K. C. Kulander, P. Agostini, and L. F. DiMauro, “Intensity-dependent scattering rings in high order above-threshold ionization,” Phys. Rev. Lett. 71, 3770–3773 (1993).
[Crossref] [PubMed]

Schätzel, M. G.

T. Wittmann, B. Horvath, W. Helml, M. G. Schätzel, X. Gu, A. L. Cavalieri, G. G. Paulus, and R. Kienberger, “Single-shot carrier-envelope phase measurement of few-cycle laser pulses,” Nat. Phys. 5, 357–362 (2009).
[Crossref]

X. Liu, H. Rottke, E. Eremina, W. Sandner, E. Goulielmakis, K. O. Keeffe, M. Lezius, F. Krausz, F. Lindner, M. G. Schätzel, G. G. Paulus, and H. Walther, “Nonsequential double ionization at the single-optical-cycle limit,” Phys. Rev. Lett. 93, 263001 (2004).
[Crossref]

Schöffler, M. S.

X. Xie, K. Doblhoff-Dier, S. Roither, M. S. Schöffler, D. Kartashov, H. Xu, T. Rathje, G. G. Paulus, A. Baltuška, S. Gräfe, and M. Kitzler, “Attosecond-recollision-controlled selective fragmentation of polyatomic molecules,” Phys. Rev. Lett. 109, 243001 (2012).
[Crossref]

Schumacher, D.

R. R. Freeman, P. H. Bucksbaum, H. Milchberg, S. Darack, D. Schumacher, and M. E. Geusic, “Above-threshold ionization with subpicosecond laser pulses,” Phys. Rev. Lett. 59, 1092–1095 (1987).
[Crossref] [PubMed]

Scully, M. O.

P. K. Jha, Y. V. Rostovtsev, H. Li, V. A. Sautenkov, and M. O. Scully, “Experimental observation of carrier-envelope-phase effects by multicycle pulses,” Phys. Rev. A 83, 033404 (2011).
[Crossref]

Siu, W. K.

A. Gazibegović-Busuladžić, E. Hasović, M. Busuladžić, D. B. Milošević, F. Kelkensberg, W. K. Siu, M. J. J. Vrakking, F. Lépine, G. Sansone, M. Nisoli, I. Znakovskaya, and M. F. Kling, “Above-threshold ionization of diatomic molecules by few-cycle laser pulses,” Phys. Rev. A 84, 043426 (2011).
[Crossref]

Spielberger, L.

T. Weber, M. Weckenbrock, A. Staudte, L. Spielberger, O. Jagutzki, V. Mergel, F. Afaneh, G. Urbasch, M. Vollmer, H. Giessen, and R. Dörner, “Recoil-ion momentum distributions for single and double ionization of helium in strong laser fields,” Phys. Rev. Lett. 84, 443–446 (2000).
[Crossref] [PubMed]

Stagira, S.

G. Sansone, C. Vozzi, S. Stagira, M. Pascolini, L. Poletto, P. Villoresi, G. Tondello, S. De Silvestri, and M. Nisoli, “Observation of carrier-envelope phase phenomena in the multi-optical-cycle regime,” Phys. Rev. Lett. 92, 113904 (2004).
[Crossref] [PubMed]

G. G. Paulus, F. Grasbon, H. Walther, P. Villoresi, M. Nisoli, S. Stagira, E. Priori, and S. De Silvestri, “Absolute-phase phenomena in photoionization with few-cycle laser pulses,” Nature 414, 182–184 (2001).
[Crossref] [PubMed]

Staudte, A.

T. Weber, M. Weckenbrock, A. Staudte, L. Spielberger, O. Jagutzki, V. Mergel, F. Afaneh, G. Urbasch, M. Vollmer, H. Giessen, and R. Dörner, “Recoil-ion momentum distributions for single and double ionization of helium in strong laser fields,” Phys. Rev. Lett. 84, 443–446 (2000).
[Crossref] [PubMed]

Takahashi, E. J.

P. Lan, E. J. Takahashi, K. Liu, Y. Fu, and K. Midorikawa, “Carrier envelope phase dependence of electron localization in the multicycle regime,” New J. Phys. 15, 063023 (2013).
[Crossref]

Tondello, G.

G. Sansone, C. Vozzi, S. Stagira, M. Pascolini, L. Poletto, P. Villoresi, G. Tondello, S. De Silvestri, and M. Nisoli, “Observation of carrier-envelope phase phenomena in the multi-optical-cycle regime,” Phys. Rev. Lett. 92, 113904 (2004).
[Crossref] [PubMed]

Uphues, T.

M. F. Kling, J. Rauschenberger, A. J. Verhoef, E. Hasović, T. Uphues, D. B. Milošević, H. G. Muller, and M. J. J. Vrakking, “Imaging of carrier-envelope phase effects in above-threshold ionization with intense few-cycle laser fields,” New J. Phys. 10, 025024 (2008).
[Crossref]

Urbasch, G.

T. Weber, M. Weckenbrock, A. Staudte, L. Spielberger, O. Jagutzki, V. Mergel, F. Afaneh, G. Urbasch, M. Vollmer, H. Giessen, and R. Dörner, “Recoil-ion momentum distributions for single and double ionization of helium in strong laser fields,” Phys. Rev. Lett. 84, 443–446 (2000).
[Crossref] [PubMed]

Verhoef, A. J.

M. F. Kling, J. Rauschenberger, A. J. Verhoef, E. Hasović, T. Uphues, D. B. Milošević, H. G. Muller, and M. J. J. Vrakking, “Imaging of carrier-envelope phase effects in above-threshold ionization with intense few-cycle laser fields,” New J. Phys. 10, 025024 (2008).
[Crossref]

Villoresi, P.

G. Sansone, C. Vozzi, S. Stagira, M. Pascolini, L. Poletto, P. Villoresi, G. Tondello, S. De Silvestri, and M. Nisoli, “Observation of carrier-envelope phase phenomena in the multi-optical-cycle regime,” Phys. Rev. Lett. 92, 113904 (2004).
[Crossref] [PubMed]

G. G. Paulus, F. Grasbon, H. Walther, P. Villoresi, M. Nisoli, S. Stagira, E. Priori, and S. De Silvestri, “Absolute-phase phenomena in photoionization with few-cycle laser pulses,” Nature 414, 182–184 (2001).
[Crossref] [PubMed]

Vollmer, M.

T. Weber, M. Weckenbrock, A. Staudte, L. Spielberger, O. Jagutzki, V. Mergel, F. Afaneh, G. Urbasch, M. Vollmer, H. Giessen, and R. Dörner, “Recoil-ion momentum distributions for single and double ionization of helium in strong laser fields,” Phys. Rev. Lett. 84, 443–446 (2000).
[Crossref] [PubMed]

Vozzi, C.

G. Sansone, C. Vozzi, S. Stagira, M. Pascolini, L. Poletto, P. Villoresi, G. Tondello, S. De Silvestri, and M. Nisoli, “Observation of carrier-envelope phase phenomena in the multi-optical-cycle regime,” Phys. Rev. Lett. 92, 113904 (2004).
[Crossref] [PubMed]

Vrakking, M. J. J.

A. Gazibegović-Busuladžić, E. Hasović, M. Busuladžić, D. B. Milošević, F. Kelkensberg, W. K. Siu, M. J. J. Vrakking, F. Lépine, G. Sansone, M. Nisoli, I. Znakovskaya, and M. F. Kling, “Above-threshold ionization of diatomic molecules by few-cycle laser pulses,” Phys. Rev. A 84, 043426 (2011).
[Crossref]

M. F. Kling, J. Rauschenberger, A. J. Verhoef, E. Hasović, T. Uphues, D. B. Milošević, H. G. Muller, and M. J. J. Vrakking, “Imaging of carrier-envelope phase effects in above-threshold ionization with intense few-cycle laser fields,” New J. Phys. 10, 025024 (2008).
[Crossref]

Walker, B.

B. Yang, K. J. Schafer, B. Walker, K. C. Kulander, P. Agostini, and L. F. DiMauro, “Intensity-dependent scattering rings in high order above-threshold ionization,” Phys. Rev. Lett. 71, 3770–3773 (1993).
[Crossref] [PubMed]

Walther, H.

X. Liu, H. Rottke, E. Eremina, W. Sandner, E. Goulielmakis, K. O. Keeffe, M. Lezius, F. Krausz, F. Lindner, M. G. Schätzel, G. G. Paulus, and H. Walther, “Nonsequential double ionization at the single-optical-cycle limit,” Phys. Rev. Lett. 93, 263001 (2004).
[Crossref]

W. Becker, F. Grasbon, R. Kopold, D. B. Milošević, G. G. Paulus, and H. Walther, “Above-threshold ionization: From classical features to quantum effects,” Adv. Atom. Mol. Opt. Phys. 48, 35–98 (2002).
[Crossref]

G. G. Paulus, F. Grasbon, H. Walther, P. Villoresi, M. Nisoli, S. Stagira, E. Priori, and S. De Silvestri, “Absolute-phase phenomena in photoionization with few-cycle laser pulses,” Nature 414, 182–184 (2001).
[Crossref] [PubMed]

G. G. Paulus, W. Nicklich, H. Xu, P. Lambropoulos, and H. Walther, “Plateau in above threshold ionization spectra,” Phys. Rev. Lett. 72, 2851–2854 (1994).
[Crossref] [PubMed]

G. G. Paulus, W. Becker, W. Nicklich, and H. Walther, “Rescattering effects in above-threshold ionization - a classical model,” J. Phys. B: At. Mol. Opt. Phys. 27, L703–L708 (1994).
[Crossref]

Wang, B.

X. Zhao, J. Chen, P. Fu, X. Liu, Z.-C. Yan, and B. Wang, “Carrier-envelope-phase effect in a long laser pulse with tens of optical cycles,” Phys. Rev. A 87, 043411 (2013).
[Crossref]

Wang, B. B.

H. Kang, W. Quan, Y. Wang, Z. Lin, M. Wu, H. Liu, X. Liu, B. B. Wang, H. J. Liu, Y. Q. Gu, X. Y. Jia, J. Liu, J. Chen, and Y. Cheng, “Structure effects in angle-resolved high-order above-threshold ionization of molecules,” Phys. Rev. Lett. 104, 203001 (2010).
[Crossref] [PubMed]

Wang, Y.

H. Kang, W. Quan, Y. Wang, Z. Lin, M. Wu, H. Liu, X. Liu, B. B. Wang, H. J. Liu, Y. Q. Gu, X. Y. Jia, J. Liu, J. Chen, and Y. Cheng, “Structure effects in angle-resolved high-order above-threshold ionization of molecules,” Phys. Rev. Lett. 104, 203001 (2010).
[Crossref] [PubMed]

Weber, T.

T. Weber, M. Weckenbrock, A. Staudte, L. Spielberger, O. Jagutzki, V. Mergel, F. Afaneh, G. Urbasch, M. Vollmer, H. Giessen, and R. Dörner, “Recoil-ion momentum distributions for single and double ionization of helium in strong laser fields,” Phys. Rev. Lett. 84, 443–446 (2000).
[Crossref] [PubMed]

Weckenbrock, M.

T. Weber, M. Weckenbrock, A. Staudte, L. Spielberger, O. Jagutzki, V. Mergel, F. Afaneh, G. Urbasch, M. Vollmer, H. Giessen, and R. Dörner, “Recoil-ion momentum distributions for single and double ionization of helium in strong laser fields,” Phys. Rev. Lett. 84, 443–446 (2000).
[Crossref] [PubMed]

Wittmann, T.

T. Wittmann, B. Horvath, W. Helml, M. G. Schätzel, X. Gu, A. L. Cavalieri, G. G. Paulus, and R. Kienberger, “Single-shot carrier-envelope phase measurement of few-cycle laser pulses,” Nat. Phys. 5, 357–362 (2009).
[Crossref]

Wu, M.

H. Kang, W. Quan, Y. Wang, Z. Lin, M. Wu, H. Liu, X. Liu, B. B. Wang, H. J. Liu, Y. Q. Gu, X. Y. Jia, J. Liu, J. Chen, and Y. Cheng, “Structure effects in angle-resolved high-order above-threshold ionization of molecules,” Phys. Rev. Lett. 104, 203001 (2010).
[Crossref] [PubMed]

Xie, X.

X. Xie, K. Doblhoff-Dier, S. Roither, M. S. Schöffler, D. Kartashov, H. Xu, T. Rathje, G. G. Paulus, A. Baltuška, S. Gräfe, and M. Kitzler, “Attosecond-recollision-controlled selective fragmentation of polyatomic molecules,” Phys. Rev. Lett. 109, 243001 (2012).
[Crossref]

Xu, H.

X. Xie, K. Doblhoff-Dier, S. Roither, M. S. Schöffler, D. Kartashov, H. Xu, T. Rathje, G. G. Paulus, A. Baltuška, S. Gräfe, and M. Kitzler, “Attosecond-recollision-controlled selective fragmentation of polyatomic molecules,” Phys. Rev. Lett. 109, 243001 (2012).
[Crossref]

G. G. Paulus, W. Nicklich, H. Xu, P. Lambropoulos, and H. Walther, “Plateau in above threshold ionization spectra,” Phys. Rev. Lett. 72, 2851–2854 (1994).
[Crossref] [PubMed]

Yan, Z.-C.

X. Zhao, J. Chen, P. Fu, X. Liu, Z.-C. Yan, and B. Wang, “Carrier-envelope-phase effect in a long laser pulse with tens of optical cycles,” Phys. Rev. A 87, 043411 (2013).
[Crossref]

Yang, B.

B. Yang, K. J. Schafer, B. Walker, K. C. Kulander, P. Agostini, and L. F. DiMauro, “Intensity-dependent scattering rings in high order above-threshold ionization,” Phys. Rev. Lett. 71, 3770–3773 (1993).
[Crossref] [PubMed]

Yu, T. J.

J.-h. Lee, Y. S. Lee, J. Park, J. J. Park, D. S. Kim, T. J. Yu, and C. H. Nam, “Implementation of the direct locking method for long-term carrier-envelope-phase stabilization of a grating-based khz femtosecond laser,” Appl. Phys. B: Lasers Opt. 96, 287–291 (2009).
[Crossref]

Yudin, G. L.

G. L. Yudin and M. Y. Ivanov, “Nonadiabatic tunnel ionization: Looking inside a laser cycle,” Phys. Rev. A 64, 013409 (2001).
[Crossref]

Zhao, X.

X. Zhao, J. Chen, P. Fu, X. Liu, Z.-C. Yan, and B. Wang, “Carrier-envelope-phase effect in a long laser pulse with tens of optical cycles,” Phys. Rev. A 87, 043411 (2013).
[Crossref]

Znakovskaya, I.

A. Gazibegović-Busuladžić, E. Hasović, M. Busuladžić, D. B. Milošević, F. Kelkensberg, W. K. Siu, M. J. J. Vrakking, F. Lépine, G. Sansone, M. Nisoli, I. Znakovskaya, and M. F. Kling, “Above-threshold ionization of diatomic molecules by few-cycle laser pulses,” Phys. Rev. A 84, 043426 (2011).
[Crossref]

Adv. Atom. Mol. Opt. Phys. (1)

W. Becker, F. Grasbon, R. Kopold, D. B. Milošević, G. G. Paulus, and H. Walther, “Above-threshold ionization: From classical features to quantum effects,” Adv. Atom. Mol. Opt. Phys. 48, 35–98 (2002).
[Crossref]

Appl. Phys. B: Lasers Opt. (1)

J.-h. Lee, Y. S. Lee, J. Park, J. J. Park, D. S. Kim, T. J. Yu, and C. H. Nam, “Implementation of the direct locking method for long-term carrier-envelope-phase stabilization of a grating-based khz femtosecond laser,” Appl. Phys. B: Lasers Opt. 96, 287–291 (2009).
[Crossref]

Appl. Phys. Lett. (1)

M. Möller, A. M. Sayler, T. Rathje, M. Chini, Z. Chang, and G. G. Paulus, “Precise, real-time, single-shot carrier-envelope phase measurement in the multi-cycle regime,” Appl. Phys. Lett. 99, 121108 (2011).
[Crossref]

ChemPhysChem (1)

K. Renziehausen, K. Hader, W. Jakubetz, and V. Engel, “Weak-field, multiple-cycle carrier envelope phase effects in laser excitation,” ChemPhysChem 14, 1464–1470 (2013).
[Crossref] [PubMed]

J. Opt. Soc. Am. B (1)

J. Phys. B: At. Mol. Opt. Phys. (1)

G. G. Paulus, W. Becker, W. Nicklich, and H. Walther, “Rescattering effects in above-threshold ionization - a classical model,” J. Phys. B: At. Mol. Opt. Phys. 27, L703–L708 (1994).
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J. Phys. B: At., Mol. Opt. Phys. (2)

D. B. Milošević, G. G. Paulus, D. Bauer, and W. Becker, “Above-threshold ionization by few-cycle pulses,” J. Phys. B: At., Mol. Opt. Phys. 39, R203–R262 (2006).
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Nat. Phys. (1)

T. Wittmann, B. Horvath, W. Helml, M. G. Schätzel, X. Gu, A. L. Cavalieri, G. G. Paulus, and R. Kienberger, “Single-shot carrier-envelope phase measurement of few-cycle laser pulses,” Nat. Phys. 5, 357–362 (2009).
[Crossref]

Nature (1)

G. G. Paulus, F. Grasbon, H. Walther, P. Villoresi, M. Nisoli, S. Stagira, E. Priori, and S. De Silvestri, “Absolute-phase phenomena in photoionization with few-cycle laser pulses,” Nature 414, 182–184 (2001).
[Crossref] [PubMed]

New J. Phys. (2)

M. F. Kling, J. Rauschenberger, A. J. Verhoef, E. Hasović, T. Uphues, D. B. Milošević, H. G. Muller, and M. J. J. Vrakking, “Imaging of carrier-envelope phase effects in above-threshold ionization with intense few-cycle laser fields,” New J. Phys. 10, 025024 (2008).
[Crossref]

P. Lan, E. J. Takahashi, K. Liu, Y. Fu, and K. Midorikawa, “Carrier envelope phase dependence of electron localization in the multicycle regime,” New J. Phys. 15, 063023 (2013).
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Opt. Lett. (1)

Phys. Rev. A (6)

S. Chelkowski, A. D. Bandrauk, and A. Apolonski, “Phase-dependent asymmetries in strong-field photoionization by few-cycle laser pulses,” Phys. Rev. A 70, 013815 (2004).
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G. L. Yudin and M. Y. Ivanov, “Nonadiabatic tunnel ionization: Looking inside a laser cycle,” Phys. Rev. A 64, 013409 (2001).
[Crossref]

X. Zhao, J. Chen, P. Fu, X. Liu, Z.-C. Yan, and B. Wang, “Carrier-envelope-phase effect in a long laser pulse with tens of optical cycles,” Phys. Rev. A 87, 043411 (2013).
[Crossref]

P. K. Jha, Y. V. Rostovtsev, H. Li, V. A. Sautenkov, and M. O. Scully, “Experimental observation of carrier-envelope-phase effects by multicycle pulses,” Phys. Rev. A 83, 033404 (2011).
[Crossref]

A. Gazibegović-Busuladžić, E. Hasović, M. Busuladžić, D. B. Milošević, F. Kelkensberg, W. K. Siu, M. J. J. Vrakking, F. Lépine, G. Sansone, M. Nisoli, I. Znakovskaya, and M. F. Kling, “Above-threshold ionization of diatomic molecules by few-cycle laser pulses,” Phys. Rev. A 84, 043426 (2011).
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T. Weber, M. Weckenbrock, A. Staudte, L. Spielberger, O. Jagutzki, V. Mergel, F. Afaneh, G. Urbasch, M. Vollmer, H. Giessen, and R. Dörner, “Recoil-ion momentum distributions for single and double ionization of helium in strong laser fields,” Phys. Rev. Lett. 84, 443–446 (2000).
[Crossref] [PubMed]

X. Liu, H. Rottke, E. Eremina, W. Sandner, E. Goulielmakis, K. O. Keeffe, M. Lezius, F. Krausz, F. Lindner, M. G. Schätzel, G. G. Paulus, and H. Walther, “Nonsequential double ionization at the single-optical-cycle limit,” Phys. Rev. Lett. 93, 263001 (2004).
[Crossref]

R. R. Freeman, P. H. Bucksbaum, H. Milchberg, S. Darack, D. Schumacher, and M. E. Geusic, “Above-threshold ionization with subpicosecond laser pulses,” Phys. Rev. Lett. 59, 1092–1095 (1987).
[Crossref] [PubMed]

G. G. Paulus, W. Nicklich, H. Xu, P. Lambropoulos, and H. Walther, “Plateau in above threshold ionization spectra,” Phys. Rev. Lett. 72, 2851–2854 (1994).
[Crossref] [PubMed]

B. Yang, K. J. Schafer, B. Walker, K. C. Kulander, P. Agostini, and L. F. DiMauro, “Intensity-dependent scattering rings in high order above-threshold ionization,” Phys. Rev. Lett. 71, 3770–3773 (1993).
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H. Kang, W. Quan, Y. Wang, Z. Lin, M. Wu, H. Liu, X. Liu, B. B. Wang, H. J. Liu, Y. Q. Gu, X. Y. Jia, J. Liu, J. Chen, and Y. Cheng, “Structure effects in angle-resolved high-order above-threshold ionization of molecules,” Phys. Rev. Lett. 104, 203001 (2010).
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G. Sansone, C. Vozzi, S. Stagira, M. Pascolini, L. Poletto, P. Villoresi, G. Tondello, S. De Silvestri, and M. Nisoli, “Observation of carrier-envelope phase phenomena in the multi-optical-cycle regime,” Phys. Rev. Lett. 92, 113904 (2004).
[Crossref] [PubMed]

X. Xie, K. Doblhoff-Dier, S. Roither, M. S. Schöffler, D. Kartashov, H. Xu, T. Rathje, G. G. Paulus, A. Baltuška, S. Gräfe, and M. Kitzler, “Attosecond-recollision-controlled selective fragmentation of polyatomic molecules,” Phys. Rev. Lett. 109, 243001 (2012).
[Crossref]

V. Roudnev and B. D. Esry, “General theory of carrier-envelope phase effects,” Phys. Rev. Lett. 99, 220406 (2007).
[Crossref]

Rev. Sci. Instrum. (1)

V. Dribinski, A. Ossadtchi, V. A. Mandelshtam, and H. Reisler, “Reconstruction of abel-transformable images: The gaussian basis-set expansion abel transform method,” Rev. Sci. Instrum. 73, 2634–2642 (2002).
[Crossref]

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Figures (3)

Fig. 1
Fig. 1 (a) Schematics of the experimental setup. CM: concave mirror (f=60 cm); ε̂: laser polarization; G: ground plate; E: extractor electrode; R: Repeller electrode; MCP+PS: dual microchannel plates assembled with a phosphor screen; CCD: charge-coupled device camera. (b) Reconstructed momentum distribution of the ATI electrons from xenon atoms irradiated by a 30-fs, 5 × 1013 W/cm2 laser pulse.
Fig. 2
Fig. 2 (a) Asymmetry map as a function of CEP and electron energy and (b) electron spectra at the two directions along the laser polarization for the CEP, ϕ = π. The shortest 30-fs laser pulses with intensity of 5 × 1013 W/cm2 were applied.
Fig. 3
Fig. 3 Asymmetry maps obtained with various chirped laser pulses. The chirp was controlled by adjusting the grating separation. The sign of laser chirp, pulse width, and peak intensity are as follows: (a) (+)35 fs, 4.5 × 1013 W/cm2; (b) (+)30 fs, 5.0 × 1013 W/cm2; (c) (−)31 fs, 5.0×1013 W/cm2; and (d) (−)35 fs, 4.3×1013 W/cm2. Group delay dispersion (GDD) of each case is (a) +227 fs2, (b) +107 fs2, (c) −152 fs2, and (d) −206 fs2, respectively.

Equations (1)

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A ( E , ϕ ) = P + ( E , ϕ ) P ( E , ϕ ) P + ( E , ϕ ) + P ( E , ϕ ) ,

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