## Valley in the efficiency of the high-order harmonic yield at ultra-high laser intensities |

Optics Express, Vol. 19, Issue 20, pp. 19430-19439 (2011)

http://dx.doi.org/10.1364/OE.19.019430

Acrobat PDF (357 KB)

### Abstract

We study the process of high-order harmonic generation using laser pulses with non-adiabatic turn-on and intensities well above saturation. As a main point, we report the existence of a valley structure in the efficiency of single-atom high-order harmonic generation with increasing laser intensities. Consequently, after an initial decrease, the high-frequency radiation yield is shown to increase for higher intensities, returning to a level similar to the case below saturation. Such behavior contradicts the general belief of a progressive degradation of the harmonic emission at ultrahigh intensities, based on the experience with pulses with smoother turn-on. We shall show that this behavior corresponds to the emergence of a new pathway for high-order harmonic generation, which takes place during the pulse turn-on. Our study combines trajectory analysis, wavelet techniques and the numerical integration of 3-Dimensional Time Dependent Schrödinger Equation. The increase in efficiency raises the possibility of employing ultrahigh intensities to generate high-frequency radiation beyond the water window.

© 2011 OSA

## 1. Introduction

1. M. Ferray, A. L’Huillier, X. F. Li, L. A. Lompre, G. Mainfray, and C. Manus, “Multiple-harmonic conversion of 1064 nm radiation in rare gases,” J. Phys. B, At. Mol. Opt. Phys. **21**, L31–L35 (1998). [CrossRef]

*h̄ω*≃

_{c}*I*+ 3.17

_{p}*U*[2

_{p}2. J. L. Krause, K. J. Schafer, and K. C. Kulander, “High-order harmonic generation from atoms and ions in the high intensity regime,” Phys. Rev. Lett. **68**, 3535–3538 (1992). [CrossRef] [PubMed]

*I*is the ionization potential, and

_{p}*U*is the electron ponderomotive energy

_{p}*U*∝

_{p}*I*

*λ*

^{2}(

*I*being the laser intensity and

*λ*the wavelength). For the usual high-power laser wavelengths (≃ 800

*nm*) the spectral plateau extends to the XUV region, and beyond the water window [3

3. C. Spielmann, N. H. Burnett, S. Sartania, R. Koppitsch, M. Schnrer, C. Kan, M. Lenzner, P. Wobrauschek, and F. Krausz, “Generation of coherent X-rays in the water window using 5-femtosecond laser pulses,” Science **278**, 661–664 (1997). [CrossRef]

5. J. Seres, E. Seres, A. J. Verhoef, G. Tempea, C. Streli, P. Wobrauschek, V. Yakovlev, A. Scrinzi, C. Spielmann, and F. Krausz, “Laser technology: source of coherent kiloelectronvolt X-rays,” Nature **433**, 596 (2005). [CrossRef] [PubMed]

6. K. Schafer, B. Yang, L. F. DiMauro, and K. C. Kulander, “Above threshold ionization beyond the high harmonic cutoff,” Phys. Rev. Lett. **70**, 1599–1602 (1993). [CrossRef] [PubMed]

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

*U*). Consequently, the emission of higher frequencies requires either increasing the wavelength or increasing intensity of the driving laser. However, these two strategies are not equivalent as they affect differently the ionization process. On one hand, increasing the wavelength approaches the ideal tunnel ionization with static fields. Even though there is no fundamental limitation in this method, the harmonic yield is shown to decrease strongly with wavelength [8

_{p}8. J. Tate, T. Auguste, H. G. Muller, P. Salières, P. Agostini, and L. F. DiMauro, “Scaling of wave-packet dynamics in an intense midinfrared field,” Phys. Rev. Lett. **98**, 013901 (2007). [CrossRef] [PubMed]

10. J. A. Pérez-Hernández, J. Ramos, L. Roso, and L. Plaja, “Harmonic generation beyond the strong-field approximation: phase and temporal description,” Laser Phys. **20**, 1044–1050 (2010). [CrossRef]

11. T. Popmintchev, M. C. Chen, O. Cohen, M. E. Grisham, J. J. Rocca, M. M. Murnane, and H. C. Kapteyn, “Extended phase matching of high harmonics driven by mid-infrared light,” Opt. Lett. **33**, 2128–2130 (2008). [CrossRef] [PubMed]

12. P. Moreno, L. Plaja, V. Malyshev, and L. Roso, “Influence of barrier suppression in high-order harmonic generation,” Phys. Rev. A **51**, 4746–4753 (1995). [CrossRef] [PubMed]

13. V. V. Strelkov, A. F. Sterjantov, N. Yu Shubin, and V. T. Platonenko, “XUV generation with several-cycle laser pulse in barrier-suppression regime,” J. Phys. B, At. Mol. Opt. Phys. **39**, 577–589 (2006). [CrossRef]

14. H. Xiong, H. Xu, Y. Fu, J. Yao, B. Zeng, W. Chu, Y. Cheng, Z. Xu, E. J. Takahashi, K. Midorikawa, X. Liu, and J. Chen, “Generation of a coherent x ray in the water window region at 1 kHz repetition rate using a mid-infrared pump source,” Opt. Lett. **34**, 1747–1749 (2009). [CrossRef] [PubMed]

15. P. Arpin, T. Popmintchev, N. L. Wagner, A. L. Lytle, O. Cohen, H. C. Kapteyn, and M. M. Murnane, “Enhanced high harmonic generation from multiply ionized argon above 500 eV through laser pulse self-compression,” Phy. Rev. Lett. **103**, 143901 (2009). [CrossRef]

16. F. Ferrari, F. Calegari, M. Lucchini, C. Vozzi, S. Stagira, G. Sansone, and M. Nisoli, “High-energy isolated attosecond pulses generated by above-saturation few-cycle fields,” Nat. Photonics **4**, 875–879 (2010). [CrossRef]

19. M. Schnürer, Ch. Spielmann, P. Wobrauschek, C. Streli, N. H. Burnett, C. Kan, K. Ferencz, R. Koppitsch, Z. Cheng, T. Brabec, and F. Krausz, “Coherent 0.5-keV X-ray emission from helium driven by a sub-10-fs laser,” Phys. Rev. Lett. **80**, 3236–3239 (1998). [CrossRef]

20. M. Geissler, G. Tempea, and T. Brabec, “Phase-matched high-order harmonic generation in the nonadiabatic limit,” Phys. Rev. A **62**, 033817 (2000). [CrossRef]

16. F. Ferrari, F. Calegari, M. Lucchini, C. Vozzi, S. Stagira, G. Sansone, and M. Nisoli, “High-energy isolated attosecond pulses generated by above-saturation few-cycle fields,” Nat. Photonics **4**, 875–879 (2010). [CrossRef]

*nm*), reaching the present frontier of high-order harmonic generation [5

5. J. Seres, E. Seres, A. J. Verhoef, G. Tempea, C. Streli, P. Wobrauschek, V. Yakovlev, A. Scrinzi, C. Spielmann, and F. Krausz, “Laser technology: source of coherent kiloelectronvolt X-rays,” Nature **433**, 596 (2005). [CrossRef] [PubMed]

16. F. Ferrari, F. Calegari, M. Lucchini, C. Vozzi, S. Stagira, G. Sansone, and M. Nisoli, “High-energy isolated attosecond pulses generated by above-saturation few-cycle fields,” Nat. Photonics **4**, 875–879 (2010). [CrossRef]

21. J. Wu, H. Cai, A. Couairon, and H. Zeng, “Few-cycle shock X-wave generation by filamentation in prealigned molecules,” Phys. Rev. A **80**, 013828 (2009). [CrossRef]

24. H. Cai, J. Wu, X. Bai, H. Pan, and H Zeng, “Molecular-alignment-assisted high-energy supercontinuum pulse generation in air,” Opt. Lett. **35**, 49–51 (2010). [CrossRef] [PubMed]

## 2. Theoretical Approach

### 2.1. Trajectory Analysis

6. K. Schafer, B. Yang, L. F. DiMauro, and K. C. Kulander, “Above threshold ionization beyond the high harmonic cutoff,” Phys. Rev. Lett. **70**, 1599–1602 (1993). [CrossRef] [PubMed]

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

*et al*[6

6. K. Schafer, B. Yang, L. F. DiMauro, and K. C. Kulander, “Above threshold ionization beyond the high harmonic cutoff,” Phys. Rev. Lett. **70**, 1599–1602 (1993). [CrossRef] [PubMed]

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

*E*

_{0}is the field amplitude, and

*ϕ*is the carrier-envelope phase (in the following

*ϕ*= 0, unless otherwise is specified).

12. P. Moreno, L. Plaja, V. Malyshev, and L. Roso, “Influence of barrier suppression in high-order harmonic generation,” Phys. Rev. A **51**, 4746–4753 (1995). [CrossRef] [PubMed]

13. V. V. Strelkov, A. F. Sterjantov, N. Yu Shubin, and V. T. Platonenko, “XUV generation with several-cycle laser pulse in barrier-suppression regime,” J. Phys. B, At. Mol. Opt. Phys. **39**, 577–589 (2006). [CrossRef]

*a*

_{0}(

*t*) is the probability amplitude of the ground state and

*a*

**(**

_{v}*t*) is the probability amplitude of the free electron state with velocity

*v*, at the time of rescattering

*t*. The values for the probability amplitudes are extracted from the results of the exact 3D numerical integration of the time-dependent Schrödinger equation (TDSE):

*|a*

_{0}(

*t*)| is found projecting of the total wavefunction on the ground state, and

*|a*(

_{v}*t*)| is estimated computing the ground-state depletion during a small time-window around the corresponding ionization time

*t*

_{0}(i.e. the initial time of the trajectory associated to the rescattering at time

*t*). Specifically with Δ

*t*being a small time interval, whose particular value is not important for the relative comparison between different trajectories, as long as it is kept unchanged. The values of the ionization and rescattering times (

*t*

_{0}and

*t*) for a particular trajectory are extracted from the classical analysis of Fig. 1. This permits us to associate each pair (

*t*

_{0},

*t*) to a well-defined trajectory of the NAT or SC type. In order to compare the harmonic efficiency at different laser intensities, we focus on the yield at a fixed energy,

*W*

_{0}.

*t*

_{0}, and the rescattering time

*t*corresponding to the electronic trajectories with recollision kinetic energy

*W*

_{0}–

*I*. We use

_{p}*W*

_{0}=73 eV, corresponding to the cut-off energy of the harmonic spectrum in hydrogen at the threshold intensity for saturation [13

13. V. V. Strelkov, A. F. Sterjantov, N. Yu Shubin, and V. T. Platonenko, “XUV generation with several-cycle laser pulse in barrier-suppression regime,” J. Phys. B, At. Mol. Opt. Phys. **39**, 577–589 (2006). [CrossRef]

*W*

_{0}using different laser intensities are shown in Fig. 2(a), for the short pulse considered in Fig. 1(b). SC curves in Fig. 2(a) show a descendent behavior with increasing field amplitude, which is connected with the degradation of the harmonic generation by these type of trajectories. The reason behind this can be found in the analysis of the probability amplitudes that conform the dipole transition, as written in Eq. (2). Figure 2(b) and Fig. 2(c) show the probability amplitudes of the ground and continuum states at rescattering,

*|a*

_{0}(

*t*)| and |

*a*(

_{v}*t*)|. As it is apparent, the decrease in the efficiency of the harmonics radiated by SC type trajectories is connected with the fast ionization of the ground state for intensities above saturation and, therefore, with the decrease of |

*a*

_{0}|. Despite the fact that depletion of the ground state population increases the population of electrons in the continuum, i.e. |

*a*

**| increases when |**

_{v}*a*

**| decreases, the product of both amplitudes has a net decrease and the efficiency of the dipole transition falls. In contrast, for the case of NAT trajectories, the behavior is the opposite: as they are originated at the first part of the turn-on, the ionization is moderate, even in the case of field amplitudes one order of magnitude above saturation (i.e. intensities two orders of magnitude above saturation). At rescattering, therefore, there is still a significant population in the ground state, and the product of probability amplitudes does not vanish. Therefore, the dipole amplitude is found to increase gradually with the field amplitude. As a result, the global behavior of the harmonic yield with the laser amplitude (Fig. 2(a)) follows the form of a valley: First, a decrease connected with the degradation of the efficiency of the SC trajectories, followed by an increase as the efficiency of the NAT trajectories becomes the relevant contribution to the dipole spectrum. NAT trajectories will eventually be degraded for ultraintense fields well above the atomic unit (3.51 × 10**

_{0}^{16}

*W/cm*

^{2}), however for these intensities we should expect also a decay connected with the breaking of the dipole approximation and the associated drift of the electron trajectories away from the ion due to the interaction with the magnetic field [25

25. J. Vazquez de Aldana and L. Roso, “Magnetic-field effect in atomic ionization by intense laser fields,” Opt. Express **5**, 144–148 (1999). [CrossRef] [PubMed]

### 2.2. Harmonic Spectrum and Synthesis of Attosecond Pulses

*I*≤ 3.51 × 10

^{14}W/cm

^{2}) the increase in laser intensity does not affect strongly the harmonic yield, although it extends the harmonic plateau accordingly to the cut-off law mentioned before. Above saturation the harmonic yield begins to decrease until a minimum is reached at

*I*≃ 5.6 × 10

^{15}W/cm

^{2}, corresponding to the bottom of the valley structure sketched in Fig. 2(a). For higher intensities the harmonic yield increases as a consequence of the emergence of the contribution of the NAT-type trajectories to the radiation spectrum.

*I*+ 0.5

_{p}*U*. A second characteristic is the absence of structure in the harmonic spectra above the saturation threshold. This is connected to the fact that for a given energy there is a single NAT trajectory, and therefore a single rescattering event generates the high-frequency radiation. This implies the generation of narrow isolated attosecond pulses as already pointed out in [16

_{p}**4**, 875–879 (2010). [CrossRef]

19. M. Schnürer, Ch. Spielmann, P. Wobrauschek, C. Streli, N. H. Burnett, C. Kan, K. Ferencz, R. Koppitsch, Z. Cheng, T. Brabec, and F. Krausz, “Coherent 0.5-keV X-ray emission from helium driven by a sub-10-fs laser,” Phys. Rev. Lett. **80**, 3236–3239 (1998). [CrossRef]

*I*= 4.2 × 10

^{16}W/cm

^{2}) of Fig. 3. The attosecond pulse is obtained filtering the harmonics below

*31st*, which corresponds to a photon energy of 46

*eV*(generated by a 800 nm fundamental field) in the spectrum of Fig. 3. Under these conditions a clean, narrow (FWHM≃ 50 attosecond) and intense attosecond pulse could be synthesized as it is shown in Fig. 4.

*ϕ*in Eq. (1). It is not surprising, therefore, that the above scenario changes for CEP different than 0. Fig. 1(c) shows the energy diagram for the trajectories corresponding to the laser pulse of Fig. 1(b), but with

*ϕ*=

*π*/2. In this case, the only relevant trajectories for harmonic generation are of the SC type. NAT trajectories are not useful, as the electron excursion is too short to acquire energy relevant for HHG. As a result, our 3D TDSE calculations for this case show an irreversible decay in yield when the field is increased above saturation.

### 2.3. Wavelet Analysis

## 3. Conclusion

## Acknowledgments

## References and links

1. | M. Ferray, A. L’Huillier, X. F. Li, L. A. Lompre, G. Mainfray, and C. Manus, “Multiple-harmonic conversion of 1064 nm radiation in rare gases,” J. Phys. B, At. Mol. Opt. Phys. |

2. | J. L. Krause, K. J. Schafer, and K. C. Kulander, “High-order harmonic generation from atoms and ions in the high intensity regime,” Phys. Rev. Lett. |

3. | C. Spielmann, N. H. Burnett, S. Sartania, R. Koppitsch, M. Schnrer, C. Kan, M. Lenzner, P. Wobrauschek, and F. Krausz, “Generation of coherent X-rays in the water window using 5-femtosecond laser pulses,” Science |

4. | Z. Chang, A. Rundquist, H. Wang, M. M. Murnane, and H. C. Kapteyn, “Generation of coherent soft X rays at 2.7 nm using high harmonics,” Phys. Rev. Lett. |

5. | J. Seres, E. Seres, A. J. Verhoef, G. Tempea, C. Streli, P. Wobrauschek, V. Yakovlev, A. Scrinzi, C. Spielmann, and F. Krausz, “Laser technology: source of coherent kiloelectronvolt X-rays,” Nature |

6. | K. Schafer, B. Yang, L. F. DiMauro, and K. C. Kulander, “Above threshold ionization beyond the high harmonic cutoff,” Phys. Rev. Lett. |

7. | P. B. Corkum, “Plasma perspective on strong-field multiphoton ionization,” Phys. Rev. Lett. |

8. | J. Tate, T. Auguste, H. G. Muller, P. Salières, P. Agostini, and L. F. DiMauro, “Scaling of wave-packet dynamics in an intense midinfrared field,” Phys. Rev. Lett. |

9. | J. A. Pérez-Hernández, L. Roso, and L. Plaja, “Harmonic generation beyond the strong-field approximation: the physics behind the short-wave-infrared scaling laws,” Opt. Express |

10. | J. A. Pérez-Hernández, J. Ramos, L. Roso, and L. Plaja, “Harmonic generation beyond the strong-field approximation: phase and temporal description,” Laser Phys. |

11. | T. Popmintchev, M. C. Chen, O. Cohen, M. E. Grisham, J. J. Rocca, M. M. Murnane, and H. C. Kapteyn, “Extended phase matching of high harmonics driven by mid-infrared light,” Opt. Lett. |

12. | P. Moreno, L. Plaja, V. Malyshev, and L. Roso, “Influence of barrier suppression in high-order harmonic generation,” Phys. Rev. A |

13. | V. V. Strelkov, A. F. Sterjantov, N. Yu Shubin, and V. T. Platonenko, “XUV generation with several-cycle laser pulse in barrier-suppression regime,” J. Phys. B, At. Mol. Opt. Phys. |

14. | H. Xiong, H. Xu, Y. Fu, J. Yao, B. Zeng, W. Chu, Y. Cheng, Z. Xu, E. J. Takahashi, K. Midorikawa, X. Liu, and J. Chen, “Generation of a coherent x ray in the water window region at 1 kHz repetition rate using a mid-infrared pump source,” Opt. Lett. |

15. | P. Arpin, T. Popmintchev, N. L. Wagner, A. L. Lytle, O. Cohen, H. C. Kapteyn, and M. M. Murnane, “Enhanced high harmonic generation from multiply ionized argon above 500 eV through laser pulse self-compression,” Phy. Rev. Lett. |

16. | F. Ferrari, F. Calegari, M. Lucchini, C. Vozzi, S. Stagira, G. Sansone, and M. Nisoli, “High-energy isolated attosecond pulses generated by above-saturation few-cycle fields,” Nat. Photonics |

17. | K. T. Kim, C. M. Kim, M. G. Baik, G. Umesh, and C. H. Nam, “Single sub-50-attosecond pulse generation from chirp-compensated harmonic radiation using material dispersion,” Phys. Rev. A |

18. | T. Sekikawa, A. Kosuge, T. Kanai, and S. Watanabe, “Nonlinear optics in the extreme ultraviolet,” Nature |

19. | M. Schnürer, Ch. Spielmann, P. Wobrauschek, C. Streli, N. H. Burnett, C. Kan, K. Ferencz, R. Koppitsch, Z. Cheng, T. Brabec, and F. Krausz, “Coherent 0.5-keV X-ray emission from helium driven by a sub-10-fs laser,” Phys. Rev. Lett. |

20. | M. Geissler, G. Tempea, and T. Brabec, “Phase-matched high-order harmonic generation in the nonadiabatic limit,” Phys. Rev. A |

21. | J. Wu, H. Cai, A. Couairon, and H. Zeng, “Few-cycle shock X-wave generation by filamentation in prealigned molecules,” Phys. Rev. A |

22. | J. Wu, H. Cai, Y. Peng, and H. Zeng, “Controllable supercontinuum generation by the quantum wake of molecular alignment,” Phys. Rev. A |

23. | H. Cai, J. Wu, Y. Peng, and H. Zeng, “Comparison study of supercontinuum generationby molecular alignment of |

24. | H. Cai, J. Wu, X. Bai, H. Pan, and H Zeng, “Molecular-alignment-assisted high-energy supercontinuum pulse generation in air,” Opt. Lett. |

25. | J. Vazquez de Aldana and L. Roso, “Magnetic-field effect in atomic ionization by intense laser fields,” Opt. Express |

**OCIS Codes**

(020.4180) Atomic and molecular physics : Multiphoton processes

(190.2640) Nonlinear optics : Stimulated scattering, modulation, etc.

(190.4180) Nonlinear optics : Multiphoton processes

(320.2250) Ultrafast optics : Femtosecond phenomena

(320.5540) Ultrafast optics : Pulse shaping

(320.7110) Ultrafast optics : Ultrafast nonlinear optics

(340.7480) X-ray optics : X-rays, soft x-rays, extreme ultraviolet (EUV)

(020.2649) Atomic and molecular physics : Strong field laser physics

**ToC Category:**

Atomic and Molecular Physics

**History**

Original Manuscript: June 28, 2011

Revised Manuscript: July 28, 2011

Manuscript Accepted: July 28, 2011

Published: September 22, 2011

**Citation**

J. A. Pérez-Hernández, L. Roso, A. Zaïr, and L. Plaja, "Valley in the efficiency of the high-order harmonic yield at ultra-high laser intensities," Opt. Express **19**, 19430-19439 (2011)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-20-19430

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### References

- M. Ferray, A. L’Huillier, X. F. Li, L. A. Lompre, G. Mainfray, and C. Manus, “Multiple-harmonic conversion of 1064 nm radiation in rare gases,” J. Phys. B, At. Mol. Opt. Phys. 21, L31–L35 (1998). [CrossRef]
- J. L. Krause, K. J. Schafer, and K. C. Kulander, “High-order harmonic generation from atoms and ions in the high intensity regime,” Phys. Rev. Lett. 68, 3535–3538 (1992). [CrossRef] [PubMed]
- C. Spielmann, N. H. Burnett, S. Sartania, R. Koppitsch, M. Schnrer, C. Kan, M. Lenzner, P. Wobrauschek, and F. Krausz, “Generation of coherent X-rays in the water window using 5-femtosecond laser pulses,” Science 278, 661–664 (1997). [CrossRef]
- Z. Chang, A. Rundquist, H. Wang, M. M. Murnane, and H. C. Kapteyn, “Generation of coherent soft X rays at 2.7 nm using high harmonics,” Phys. Rev. Lett. 79, 2967–2970 (1997). [CrossRef]
- J. Seres, E. Seres, A. J. Verhoef, G. Tempea, C. Streli, P. Wobrauschek, V. Yakovlev, A. Scrinzi, C. Spielmann, and F. Krausz, “Laser technology: source of coherent kiloelectronvolt X-rays,” Nature 433, 596 (2005). [CrossRef] [PubMed]
- K. Schafer, B. Yang, L. F. DiMauro, and K. C. Kulander, “Above threshold ionization beyond the high harmonic cutoff,” Phys. Rev. Lett. 70, 1599–1602 (1993). [CrossRef] [PubMed]
- P. B. Corkum, “Plasma perspective on strong-field multiphoton ionization,” Phys. Rev. Lett. 71, 1994–1997 (1993). [CrossRef] [PubMed]
- J. Tate, T. Auguste, H. G. Muller, P. Salières, P. Agostini, and L. F. DiMauro, “Scaling of wave-packet dynamics in an intense midinfrared field,” Phys. Rev. Lett. 98, 013901 (2007). [CrossRef] [PubMed]
- J. A. Pérez-Hernández, L. Roso, and L. Plaja, “Harmonic generation beyond the strong-field approximation: the physics behind the short-wave-infrared scaling laws,” Opt. Express 17, 9891–9903 (2009). [CrossRef] [PubMed]
- J. A. Pérez-Hernández, J. Ramos, L. Roso, and L. Plaja, “Harmonic generation beyond the strong-field approximation: phase and temporal description,” Laser Phys. 20, 1044–1050 (2010). [CrossRef]
- T. Popmintchev, M. C. Chen, O. Cohen, M. E. Grisham, J. J. Rocca, M. M. Murnane, and H. C. Kapteyn, “Extended phase matching of high harmonics driven by mid-infrared light,” Opt. Lett. 33, 2128–2130 (2008). [CrossRef] [PubMed]
- P. Moreno, L. Plaja, V. Malyshev, and L. Roso, “Influence of barrier suppression in high-order harmonic generation,” Phys. Rev. A 51, 4746–4753 (1995). [CrossRef] [PubMed]
- V. V. Strelkov, A. F. Sterjantov, N. Yu Shubin, and V. T. Platonenko, “XUV generation with several-cycle laser pulse in barrier-suppression regime,” J. Phys. B, At. Mol. Opt. Phys. 39, 577–589 (2006). [CrossRef]
- H. Xiong, H. Xu, Y. Fu, J. Yao, B. Zeng, W. Chu, Y. Cheng, Z. Xu, E. J. Takahashi, K. Midorikawa, X. Liu, and J. Chen, “Generation of a coherent x ray in the water window region at 1 kHz repetition rate using a mid-infrared pump source,” Opt. Lett. 34, 1747–1749 (2009). [CrossRef] [PubMed]
- P. Arpin, T. Popmintchev, N. L. Wagner, A. L. Lytle, O. Cohen, H. C. Kapteyn, and M. M. Murnane, “Enhanced high harmonic generation from multiply ionized argon above 500 eV through laser pulse self-compression,” Phy. Rev. Lett. 103, 143901 (2009). [CrossRef]
- F. Ferrari, F. Calegari, M. Lucchini, C. Vozzi, S. Stagira, G. Sansone, and M. Nisoli, “High-energy isolated attosecond pulses generated by above-saturation few-cycle fields,” Nat. Photonics 4, 875–879 (2010). [CrossRef]
- K. T. Kim, C. M. Kim, M. G. Baik, G. Umesh, and C. H. Nam, “Single sub-50-attosecond pulse generation from chirp-compensated harmonic radiation using material dispersion,” Phys. Rev. A 69, 051805 (2004). [CrossRef]
- T. Sekikawa, A. Kosuge, T. Kanai, and S. Watanabe, “Nonlinear optics in the extreme ultraviolet,” Nature 432, 605–608 (2004). [CrossRef] [PubMed]
- M. Schnürer, Ch. Spielmann, P. Wobrauschek, C. Streli, N. H. Burnett, C. Kan, K. Ferencz, R. Koppitsch, Z. Cheng, T. Brabec, and F. Krausz, “Coherent 0.5-keV X-ray emission from helium driven by a sub-10-fs laser,” Phys. Rev. Lett. 80, 3236–3239 (1998). [CrossRef]
- M. Geissler, G. Tempea, and T. Brabec, “Phase-matched high-order harmonic generation in the nonadiabatic limit,” Phys. Rev. A 62, 033817 (2000). [CrossRef]
- J. Wu, H. Cai, A. Couairon, and H. Zeng, “Few-cycle shock X-wave generation by filamentation in prealigned molecules,” Phys. Rev. A 80, 013828 (2009). [CrossRef]
- J. Wu, H. Cai, Y. Peng, and H. Zeng, “Controllable supercontinuum generation by the quantum wake of molecular alignment,” Phys. Rev. A 79, 041404 (2009). [CrossRef]
- H. Cai, J. Wu, Y. Peng, and H. Zeng, “Comparison study of supercontinuum generationby molecular alignment of N2 and O2,” Opt. Express 17, 5822–5828 (2009). [PubMed]
- H. Cai, J. Wu, X. Bai, H. Pan, and H Zeng, “Molecular-alignment-assisted high-energy supercontinuum pulse generation in air,” Opt. Lett. 35, 49–51 (2010). [CrossRef] [PubMed]
- J. Vazquez de Aldana and L. Roso, “Magnetic-field effect in atomic ionization by intense laser fields,” Opt. Express 5, 144–148 (1999). [CrossRef] [PubMed]

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