Abstract

We numerically investigate the influence of plasma defocusing in high harmonic generation (HHG) by solving the first-order wave equation in an ionized medium and defining an enhancement factor to quantitatively analyze the influence of plasma defocusing. While degrading the driver pulse intensity, plasma also has a strong impact on HHG phase-matching. Combined with the HHG wavelength scaling law, our results give an estimate of HHG efficiencies with different driver wavelengths and show a limited HHG efficiency in high density media.

© 2011 OSA

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  1. Ch. Spielmann, N. H. Burnett, S. Sartania, R. Koppitsch, M. Schnurer, 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(5338), 661–664 (1997).
    [CrossRef]
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    [CrossRef] [PubMed]
  3. M.-C. Chen, P. Arpin, T. Popmintchev, M. Gerrity, B. Zhang, M. Seaberg, D. Popmintchev, M. M. Murnane, and H. C. Kapteyn, “Bright, coherent, ultrafast soft X-ray harmonics spanning the water window from a tabletop light source,” Phys. Rev. Lett. 105(17), 173901 (2010).
    [CrossRef] [PubMed]
  4. T. Popmintchev, M.-C. Chen, A. Bahabad, M. Gerrity, P. Sidorenko, O. Cohen, I. P. Christov, M. M. Murnane, and H. C. Kapteyn, “Phase matching of high harmonic generation in the soft and hard X-ray regions of the spectrum,” Proc. Natl. Acad. Sci. U.S.A. 106(26), 10516–10521 (2009).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
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  14. H. Dachraoui, T. Auguste, A. Helmstedt, P. Bartz, M. Michelswirth, N. Mueller, W. Pfeiffer, P. Salieres, and U. Heinzmann, “Interplay between absorption, dispersion and refraction in high-order harmonic generation,” J. Phys. At. Mol. Opt. Phys. 42(17), 175402 (2009).
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    [CrossRef]
  18. M. Geissler, G. Tempea, A. Scrinzi, M. Schnurer, F. Krausz, and T. Brabec, “Light Propagation in Field-Ionizing Media: Extreme Nonlinear Optics,” Phys. Rev. Lett. 83(15), 2930–2933 (1999).
    [CrossRef]
  19. M. V. Ammosov, N. B. Delone, and V. P. Krainov, “Tunnel ionization of complex atoms and of atomic ions in an alternating electromagnetic field,” Sov. Phys. JETP 64(6), 1191–1194 (1986).
  20. A. Behjat, G. J. Tallents, and D. Neely, “The characterization of a high-density gas jet,” J. Phys. D Appl. Phys. 30(20), 2872–2879 (1997).
    [CrossRef]
  21. J.-S. Wu, S.-Y. Chou, U.-M. Lee, Y.-L. Shao, and Y.-Y. Lian, “Parallel DSMC Simulation of a Single Under-Expanded Free Orifice Jet From Transition to Near-Continuum Regime,” J. Fluids Eng. 127(6), 1161–1170 (2005).
    [CrossRef]
  22. E. J. Takahashi, Y. Nabekawa, H. Mashiko, H. Hasegawa, A. Suda, and K. Midorikawa, “Generation of Strong Optical Field in Soft X-ray Region by Using High-Order Harmonics,” IEEE J. Sel. Top. Quantum Electron. 10(6), 1315–1328 (2004).
    [CrossRef]
  23. S. Kazamias, S. Daboussi, O. Guilbaud, K. Cassou, D. Ros, B. Cros, and G. Maynard, “Pressure-induced phase matching in high-order harmonic generation,” Phys. Rev. A 83(6), 063405 (2011).
    [CrossRef]
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  25. M. Lewenstein, P. Salières, and A. L’Huillier, “Phase of the atomic polarization in high-order harmonic generation,” Phys. Rev. A 52(6), 4747–4754 (1995).
    [CrossRef] [PubMed]
  26. M. J. Weber, Handbook of Optical Materials (CRC Press, 2003), Chap. 6.
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    [CrossRef]
  28. I. J. Kim, C. M. Kim, H. T. Kim, G. H. Lee, Y. S. Lee, J. Y. Park, D. J. Cho, and C. H. Nam, “Highly Efficient High-Harmonic Generation in an Orthogonally Polarized Two-Color Laser Field,” Phys. Rev. Lett. 94, 243901 (2005).
  29. E. J. Takahashi, Y. Nabekawa, and K. Midorikawa, “Low-divergence coherent soft x-ray source at 13 nm by high-order harmonics,” Appl. Phys. Lett. 84(1), 4–6 (2004).
    [CrossRef]

2011 (1)

S. Kazamias, S. Daboussi, O. Guilbaud, K. Cassou, D. Ros, B. Cros, and G. Maynard, “Pressure-induced phase matching in high-order harmonic generation,” Phys. Rev. A 83(6), 063405 (2011).
[CrossRef]

2010 (2)

M.-C. Chen, P. Arpin, T. Popmintchev, M. Gerrity, B. Zhang, M. Seaberg, D. Popmintchev, M. M. Murnane, and H. C. Kapteyn, “Bright, coherent, ultrafast soft X-ray harmonics spanning the water window from a tabletop light source,” Phys. Rev. Lett. 105(17), 173901 (2010).
[CrossRef] [PubMed]

K.-H. Hong, J. T. Gopinath, D. Rand, A. M. Siddiqui, S.-W. Huang, E. Li, B. J. Eggleton, J. D. Hybl, T. Y. Fan, and F. X. Kartner, “High-energy, kHz-repetition-rate, ps cryogenic Yb:YAG chirped-pulse amplifier,” Opt. Lett. 35(11), 1752–1754 (2010).
[CrossRef] [PubMed]

2009 (7)

E. L. Falcao-Filho, M. Gkortsas, A. Gordon, and F. X. Kartner, “Analytic scaling analysis of high harmonic generation conversion efficiency,” Opt. Express 17(13), 11217–11229 (2009).
[CrossRef] [PubMed]

T. Popmintchev, M.-C. Chen, A. Bahabad, M. Gerrity, P. Sidorenko, O. Cohen, I. P. Christov, M. M. Murnane, and H. C. Kapteyn, “Phase matching of high harmonic generation in the soft and hard X-ray regions of the spectrum,” Proc. Natl. Acad. Sci. U.S.A. 106(26), 10516–10521 (2009).
[CrossRef] [PubMed]

J. Moses, S.-W. Huang, K.-H. Hong, O. D. Mucke, E. L. Falcao-Filho, A. Benedick, F. O. Ilday, A. Dergachev, J. A. Bolger, B. J. Eggleton, and F. X. Kartner, “Highly stable ultrabroadband mid-infrared optical parametric chirped pulse amplifier optimized for superfluorescence suppression,” Opt. Lett. 34(11), 1639–1641 (2009).
[CrossRef] [PubMed]

H. Dachraoui, T. Auguste, A. Helmstedt, P. Bartz, M. Michelswirth, N. Mueller, W. Pfeiffer, P. Salieres, and U. Heinzmann, “Interplay between absorption, dispersion and refraction in high-order harmonic generation,” J. Phys. At. Mol. Opt. Phys. 42(17), 175402 (2009).
[CrossRef]

V. Tosa, E. Balogh, and K. Kovács, “Phase-matched generation of water-window x rays,” Phys. Rev. A 80(4), 045801 (2009).
[CrossRef]

V. Tosa, K. T. Kim, and C. H. Nam, “Macroscopic generation of attosecond-pulse trains in strongly ionized media,” Phys. Rev. A 79(4), 043828 (2009).
[CrossRef]

A. D. Shiner, C. Trallero-Herrero, N. Kajumba, H.-C. Bandulet, D. Comtois, F. Legare, M. Giguere, J.-C. Kieffer, P. B. Corkum, and D. M. Villeneuve, “Wavelength scaling of high harmonic generation efficiency,” Phys. Rev. Lett. 103(7), 073902 (2009).
[CrossRef] [PubMed]

2008 (3)

I. Jong Kim, G. H. Lee, S. B. Park, Y. S. Lee, T. K. Kim, C. H. Nam, T. Mocek, and K. Jakubczak, “Generation of submicrojoule high harmonics using a long gas jet in a two-color laser field,” Appl. Phys. Lett. 92, 021125 (2008).

P. Colosimo, G. Doumy, C. I. Blaga, J. Wheeler, C. Hauri, F. Catoire, J. Tate, R. Chirla, A. M. March, G. G. Paulus, H. G. Muller, P. Agostini, and L. F. Dimauro, “Scaling strong-field interactions towards the classical limit,” Nat. Phys. 4(5), 386–389 (2008).
[CrossRef]

E. J. Takahashi, T. Kanai, K. L. Ishikawa, Y. Nabekawa, and K. Midorikawa, “Coherent water window x ray by phase-matched high-order harmonic generation in neutral media,” Phys. Rev. Lett. 101(25), 253901 (2008).
[CrossRef] [PubMed]

2007 (1)

J. Tate, T. Auguste, H. G. Muller, P. Salieres, P. Agostini, and L. F. DiMauro, “Scaling of wave-packet dynamics in an intense midinfrared field,” Phys. Rev. Lett. 98(1), 013901 (2007).
[CrossRef] [PubMed]

2005 (3)

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(7026), 596–596 (2005).
[CrossRef] [PubMed]

J.-S. Wu, S.-Y. Chou, U.-M. Lee, Y.-L. Shao, and Y.-Y. Lian, “Parallel DSMC Simulation of a Single Under-Expanded Free Orifice Jet From Transition to Near-Continuum Regime,” J. Fluids Eng. 127(6), 1161–1170 (2005).
[CrossRef]

I. J. Kim, C. M. Kim, H. T. Kim, G. H. Lee, Y. S. Lee, J. Y. Park, D. J. Cho, and C. H. Nam, “Highly Efficient High-Harmonic Generation in an Orthogonally Polarized Two-Color Laser Field,” Phys. Rev. Lett. 94, 243901 (2005).

2004 (2)

E. J. Takahashi, Y. Nabekawa, and K. Midorikawa, “Low-divergence coherent soft x-ray source at 13 nm by high-order harmonics,” Appl. Phys. Lett. 84(1), 4–6 (2004).
[CrossRef]

E. J. Takahashi, Y. Nabekawa, H. Mashiko, H. Hasegawa, A. Suda, and K. Midorikawa, “Generation of Strong Optical Field in Soft X-ray Region by Using High-Order Harmonics,” IEEE J. Sel. Top. Quantum Electron. 10(6), 1315–1328 (2004).
[CrossRef]

1999 (2)

E. Constant, D. Garzella, P. Breger, E. Mevel, Ch. Dorrer, C. Le Blanc, F. Salin, and P. Agostini, “Optimizing High Harmonic Generation in Absorbing Gases: Model and Experiment,” Phys. Rev. Lett. 82(8), 1668–1671 (1999).
[CrossRef]

M. Geissler, G. Tempea, A. Scrinzi, M. Schnurer, F. Krausz, and T. Brabec, “Light Propagation in Field-Ionizing Media: Extreme Nonlinear Optics,” Phys. Rev. Lett. 83(15), 2930–2933 (1999).
[CrossRef]

1997 (2)

A. Behjat, G. J. Tallents, and D. Neely, “The characterization of a high-density gas jet,” J. Phys. D Appl. Phys. 30(20), 2872–2879 (1997).
[CrossRef]

Ch. Spielmann, N. H. Burnett, S. Sartania, R. Koppitsch, M. Schnurer, 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(5338), 661–664 (1997).
[CrossRef]

1996 (1)

1995 (1)

M. Lewenstein, P. Salières, and A. L’Huillier, “Phase of the atomic polarization in high-order harmonic generation,” Phys. Rev. A 52(6), 4747–4754 (1995).
[CrossRef] [PubMed]

1993 (1)

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

1986 (1)

M. V. Ammosov, N. B. Delone, and V. P. Krainov, “Tunnel ionization of complex atoms and of atomic ions in an alternating electromagnetic field,” Sov. Phys. JETP 64(6), 1191–1194 (1986).

Agostini, P.

P. Colosimo, G. Doumy, C. I. Blaga, J. Wheeler, C. Hauri, F. Catoire, J. Tate, R. Chirla, A. M. March, G. G. Paulus, H. G. Muller, P. Agostini, and L. F. Dimauro, “Scaling strong-field interactions towards the classical limit,” Nat. Phys. 4(5), 386–389 (2008).
[CrossRef]

J. Tate, T. Auguste, H. G. Muller, P. Salieres, P. Agostini, and L. F. DiMauro, “Scaling of wave-packet dynamics in an intense midinfrared field,” Phys. Rev. Lett. 98(1), 013901 (2007).
[CrossRef] [PubMed]

E. Constant, D. Garzella, P. Breger, E. Mevel, Ch. Dorrer, C. Le Blanc, F. Salin, and P. Agostini, “Optimizing High Harmonic Generation in Absorbing Gases: Model and Experiment,” Phys. Rev. Lett. 82(8), 1668–1671 (1999).
[CrossRef]

Altucci, C.

Ammosov, M. V.

M. V. Ammosov, N. B. Delone, and V. P. Krainov, “Tunnel ionization of complex atoms and of atomic ions in an alternating electromagnetic field,” Sov. Phys. JETP 64(6), 1191–1194 (1986).

Arpin, P.

M.-C. Chen, P. Arpin, T. Popmintchev, M. Gerrity, B. Zhang, M. Seaberg, D. Popmintchev, M. M. Murnane, and H. C. Kapteyn, “Bright, coherent, ultrafast soft X-ray harmonics spanning the water window from a tabletop light source,” Phys. Rev. Lett. 105(17), 173901 (2010).
[CrossRef] [PubMed]

Auguste, T.

H. Dachraoui, T. Auguste, A. Helmstedt, P. Bartz, M. Michelswirth, N. Mueller, W. Pfeiffer, P. Salieres, and U. Heinzmann, “Interplay between absorption, dispersion and refraction in high-order harmonic generation,” J. Phys. At. Mol. Opt. Phys. 42(17), 175402 (2009).
[CrossRef]

J. Tate, T. Auguste, H. G. Muller, P. Salieres, P. Agostini, and L. F. DiMauro, “Scaling of wave-packet dynamics in an intense midinfrared field,” Phys. Rev. Lett. 98(1), 013901 (2007).
[CrossRef] [PubMed]

Bahabad, A.

T. Popmintchev, M.-C. Chen, A. Bahabad, M. Gerrity, P. Sidorenko, O. Cohen, I. P. Christov, M. M. Murnane, and H. C. Kapteyn, “Phase matching of high harmonic generation in the soft and hard X-ray regions of the spectrum,” Proc. Natl. Acad. Sci. U.S.A. 106(26), 10516–10521 (2009).
[CrossRef] [PubMed]

Balogh, E.

V. Tosa, E. Balogh, and K. Kovács, “Phase-matched generation of water-window x rays,” Phys. Rev. A 80(4), 045801 (2009).
[CrossRef]

Bandulet, H.-C.

A. D. Shiner, C. Trallero-Herrero, N. Kajumba, H.-C. Bandulet, D. Comtois, F. Legare, M. Giguere, J.-C. Kieffer, P. B. Corkum, and D. M. Villeneuve, “Wavelength scaling of high harmonic generation efficiency,” Phys. Rev. Lett. 103(7), 073902 (2009).
[CrossRef] [PubMed]

Bartz, P.

H. Dachraoui, T. Auguste, A. Helmstedt, P. Bartz, M. Michelswirth, N. Mueller, W. Pfeiffer, P. Salieres, and U. Heinzmann, “Interplay between absorption, dispersion and refraction in high-order harmonic generation,” J. Phys. At. Mol. Opt. Phys. 42(17), 175402 (2009).
[CrossRef]

Behjat, A.

A. Behjat, G. J. Tallents, and D. Neely, “The characterization of a high-density gas jet,” J. Phys. D Appl. Phys. 30(20), 2872–2879 (1997).
[CrossRef]

Benedick, A.

Blaga, C. I.

P. Colosimo, G. Doumy, C. I. Blaga, J. Wheeler, C. Hauri, F. Catoire, J. Tate, R. Chirla, A. M. March, G. G. Paulus, H. G. Muller, P. Agostini, and L. F. Dimauro, “Scaling strong-field interactions towards the classical limit,” Nat. Phys. 4(5), 386–389 (2008).
[CrossRef]

Bolger, J. A.

Brabec, T.

M. Geissler, G. Tempea, A. Scrinzi, M. Schnurer, F. Krausz, and T. Brabec, “Light Propagation in Field-Ionizing Media: Extreme Nonlinear Optics,” Phys. Rev. Lett. 83(15), 2930–2933 (1999).
[CrossRef]

Breger, P.

E. Constant, D. Garzella, P. Breger, E. Mevel, Ch. Dorrer, C. Le Blanc, F. Salin, and P. Agostini, “Optimizing High Harmonic Generation in Absorbing Gases: Model and Experiment,” Phys. Rev. Lett. 82(8), 1668–1671 (1999).
[CrossRef]

Burnett, N. H.

Ch. Spielmann, N. H. Burnett, S. Sartania, R. Koppitsch, M. Schnurer, 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(5338), 661–664 (1997).
[CrossRef]

Carre, B.

Cassou, K.

S. Kazamias, S. Daboussi, O. Guilbaud, K. Cassou, D. Ros, B. Cros, and G. Maynard, “Pressure-induced phase matching in high-order harmonic generation,” Phys. Rev. A 83(6), 063405 (2011).
[CrossRef]

Catoire, F.

P. Colosimo, G. Doumy, C. I. Blaga, J. Wheeler, C. Hauri, F. Catoire, J. Tate, R. Chirla, A. M. March, G. G. Paulus, H. G. Muller, P. Agostini, and L. F. Dimauro, “Scaling strong-field interactions towards the classical limit,” Nat. Phys. 4(5), 386–389 (2008).
[CrossRef]

Chen, M.-C.

M.-C. Chen, P. Arpin, T. Popmintchev, M. Gerrity, B. Zhang, M. Seaberg, D. Popmintchev, M. M. Murnane, and H. C. Kapteyn, “Bright, coherent, ultrafast soft X-ray harmonics spanning the water window from a tabletop light source,” Phys. Rev. Lett. 105(17), 173901 (2010).
[CrossRef] [PubMed]

T. Popmintchev, M.-C. Chen, A. Bahabad, M. Gerrity, P. Sidorenko, O. Cohen, I. P. Christov, M. M. Murnane, and H. C. Kapteyn, “Phase matching of high harmonic generation in the soft and hard X-ray regions of the spectrum,” Proc. Natl. Acad. Sci. U.S.A. 106(26), 10516–10521 (2009).
[CrossRef] [PubMed]

Chirla, R.

P. Colosimo, G. Doumy, C. I. Blaga, J. Wheeler, C. Hauri, F. Catoire, J. Tate, R. Chirla, A. M. March, G. G. Paulus, H. G. Muller, P. Agostini, and L. F. Dimauro, “Scaling strong-field interactions towards the classical limit,” Nat. Phys. 4(5), 386–389 (2008).
[CrossRef]

Cho, D. J.

I. J. Kim, C. M. Kim, H. T. Kim, G. H. Lee, Y. S. Lee, J. Y. Park, D. J. Cho, and C. H. Nam, “Highly Efficient High-Harmonic Generation in an Orthogonally Polarized Two-Color Laser Field,” Phys. Rev. Lett. 94, 243901 (2005).

Chou, S.-Y.

J.-S. Wu, S.-Y. Chou, U.-M. Lee, Y.-L. Shao, and Y.-Y. Lian, “Parallel DSMC Simulation of a Single Under-Expanded Free Orifice Jet From Transition to Near-Continuum Regime,” J. Fluids Eng. 127(6), 1161–1170 (2005).
[CrossRef]

Christov, I. P.

T. Popmintchev, M.-C. Chen, A. Bahabad, M. Gerrity, P. Sidorenko, O. Cohen, I. P. Christov, M. M. Murnane, and H. C. Kapteyn, “Phase matching of high harmonic generation in the soft and hard X-ray regions of the spectrum,” Proc. Natl. Acad. Sci. U.S.A. 106(26), 10516–10521 (2009).
[CrossRef] [PubMed]

Cohen, O.

T. Popmintchev, M.-C. Chen, A. Bahabad, M. Gerrity, P. Sidorenko, O. Cohen, I. P. Christov, M. M. Murnane, and H. C. Kapteyn, “Phase matching of high harmonic generation in the soft and hard X-ray regions of the spectrum,” Proc. Natl. Acad. Sci. U.S.A. 106(26), 10516–10521 (2009).
[CrossRef] [PubMed]

Colosimo, P.

P. Colosimo, G. Doumy, C. I. Blaga, J. Wheeler, C. Hauri, F. Catoire, J. Tate, R. Chirla, A. M. March, G. G. Paulus, H. G. Muller, P. Agostini, and L. F. Dimauro, “Scaling strong-field interactions towards the classical limit,” Nat. Phys. 4(5), 386–389 (2008).
[CrossRef]

Comtois, D.

A. D. Shiner, C. Trallero-Herrero, N. Kajumba, H.-C. Bandulet, D. Comtois, F. Legare, M. Giguere, J.-C. Kieffer, P. B. Corkum, and D. M. Villeneuve, “Wavelength scaling of high harmonic generation efficiency,” Phys. Rev. Lett. 103(7), 073902 (2009).
[CrossRef] [PubMed]

Constant, E.

E. Constant, D. Garzella, P. Breger, E. Mevel, Ch. Dorrer, C. Le Blanc, F. Salin, and P. Agostini, “Optimizing High Harmonic Generation in Absorbing Gases: Model and Experiment,” Phys. Rev. Lett. 82(8), 1668–1671 (1999).
[CrossRef]

Corkum, P. B.

A. D. Shiner, C. Trallero-Herrero, N. Kajumba, H.-C. Bandulet, D. Comtois, F. Legare, M. Giguere, J.-C. Kieffer, P. B. Corkum, and D. M. Villeneuve, “Wavelength scaling of high harmonic generation efficiency,” Phys. Rev. Lett. 103(7), 073902 (2009).
[CrossRef] [PubMed]

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S. Kazamias, S. Daboussi, O. Guilbaud, K. Cassou, D. Ros, B. Cros, and G. Maynard, “Pressure-induced phase matching in high-order harmonic generation,” Phys. Rev. A 83(6), 063405 (2011).
[CrossRef]

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S. Kazamias, S. Daboussi, O. Guilbaud, K. Cassou, D. Ros, B. Cros, and G. Maynard, “Pressure-induced phase matching in high-order harmonic generation,” Phys. Rev. A 83(6), 063405 (2011).
[CrossRef]

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H. Dachraoui, T. Auguste, A. Helmstedt, P. Bartz, M. Michelswirth, N. Mueller, W. Pfeiffer, P. Salieres, and U. Heinzmann, “Interplay between absorption, dispersion and refraction in high-order harmonic generation,” J. Phys. At. Mol. Opt. Phys. 42(17), 175402 (2009).
[CrossRef]

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

Delone, N. B.

M. V. Ammosov, N. B. Delone, and V. P. Krainov, “Tunnel ionization of complex atoms and of atomic ions in an alternating electromagnetic field,” Sov. Phys. JETP 64(6), 1191–1194 (1986).

Dergachev, A.

Dimauro, L. F.

P. Colosimo, G. Doumy, C. I. Blaga, J. Wheeler, C. Hauri, F. Catoire, J. Tate, R. Chirla, A. M. March, G. G. Paulus, H. G. Muller, P. Agostini, and L. F. Dimauro, “Scaling strong-field interactions towards the classical limit,” Nat. Phys. 4(5), 386–389 (2008).
[CrossRef]

J. Tate, T. Auguste, H. G. Muller, P. Salieres, P. Agostini, and L. F. DiMauro, “Scaling of wave-packet dynamics in an intense midinfrared field,” Phys. Rev. Lett. 98(1), 013901 (2007).
[CrossRef] [PubMed]

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E. Constant, D. Garzella, P. Breger, E. Mevel, Ch. Dorrer, C. Le Blanc, F. Salin, and P. Agostini, “Optimizing High Harmonic Generation in Absorbing Gases: Model and Experiment,” Phys. Rev. Lett. 82(8), 1668–1671 (1999).
[CrossRef]

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P. Colosimo, G. Doumy, C. I. Blaga, J. Wheeler, C. Hauri, F. Catoire, J. Tate, R. Chirla, A. M. March, G. G. Paulus, H. G. Muller, P. Agostini, and L. F. Dimauro, “Scaling strong-field interactions towards the classical limit,” Nat. Phys. 4(5), 386–389 (2008).
[CrossRef]

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Falcao-Filho, E. L.

Fan, T. Y.

Garzella, D.

E. Constant, D. Garzella, P. Breger, E. Mevel, Ch. Dorrer, C. Le Blanc, F. Salin, and P. Agostini, “Optimizing High Harmonic Generation in Absorbing Gases: Model and Experiment,” Phys. Rev. Lett. 82(8), 1668–1671 (1999).
[CrossRef]

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M. Geissler, G. Tempea, A. Scrinzi, M. Schnurer, F. Krausz, and T. Brabec, “Light Propagation in Field-Ionizing Media: Extreme Nonlinear Optics,” Phys. Rev. Lett. 83(15), 2930–2933 (1999).
[CrossRef]

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M.-C. Chen, P. Arpin, T. Popmintchev, M. Gerrity, B. Zhang, M. Seaberg, D. Popmintchev, M. M. Murnane, and H. C. Kapteyn, “Bright, coherent, ultrafast soft X-ray harmonics spanning the water window from a tabletop light source,” Phys. Rev. Lett. 105(17), 173901 (2010).
[CrossRef] [PubMed]

T. Popmintchev, M.-C. Chen, A. Bahabad, M. Gerrity, P. Sidorenko, O. Cohen, I. P. Christov, M. M. Murnane, and H. C. Kapteyn, “Phase matching of high harmonic generation in the soft and hard X-ray regions of the spectrum,” Proc. Natl. Acad. Sci. U.S.A. 106(26), 10516–10521 (2009).
[CrossRef] [PubMed]

Giguere, M.

A. D. Shiner, C. Trallero-Herrero, N. Kajumba, H.-C. Bandulet, D. Comtois, F. Legare, M. Giguere, J.-C. Kieffer, P. B. Corkum, and D. M. Villeneuve, “Wavelength scaling of high harmonic generation efficiency,” Phys. Rev. Lett. 103(7), 073902 (2009).
[CrossRef] [PubMed]

Gkortsas, M.

Gopinath, J. T.

Gordon, A.

Guilbaud, O.

S. Kazamias, S. Daboussi, O. Guilbaud, K. Cassou, D. Ros, B. Cros, and G. Maynard, “Pressure-induced phase matching in high-order harmonic generation,” Phys. Rev. A 83(6), 063405 (2011).
[CrossRef]

Gullikson, E. M.

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

Hasegawa, H.

E. J. Takahashi, Y. Nabekawa, H. Mashiko, H. Hasegawa, A. Suda, and K. Midorikawa, “Generation of Strong Optical Field in Soft X-ray Region by Using High-Order Harmonics,” IEEE J. Sel. Top. Quantum Electron. 10(6), 1315–1328 (2004).
[CrossRef]

Hauri, C.

P. Colosimo, G. Doumy, C. I. Blaga, J. Wheeler, C. Hauri, F. Catoire, J. Tate, R. Chirla, A. M. March, G. G. Paulus, H. G. Muller, P. Agostini, and L. F. Dimauro, “Scaling strong-field interactions towards the classical limit,” Nat. Phys. 4(5), 386–389 (2008).
[CrossRef]

Heinzmann, U.

H. Dachraoui, T. Auguste, A. Helmstedt, P. Bartz, M. Michelswirth, N. Mueller, W. Pfeiffer, P. Salieres, and U. Heinzmann, “Interplay between absorption, dispersion and refraction in high-order harmonic generation,” J. Phys. At. Mol. Opt. Phys. 42(17), 175402 (2009).
[CrossRef]

Helmstedt, A.

H. Dachraoui, T. Auguste, A. Helmstedt, P. Bartz, M. Michelswirth, N. Mueller, W. Pfeiffer, P. Salieres, and U. Heinzmann, “Interplay between absorption, dispersion and refraction in high-order harmonic generation,” J. Phys. At. Mol. Opt. Phys. 42(17), 175402 (2009).
[CrossRef]

Henke, B. L.

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

Hong, K.-H.

Huang, S.-W.

Hybl, J. D.

Ilday, F. O.

Ishikawa, K. L.

E. J. Takahashi, T. Kanai, K. L. Ishikawa, Y. Nabekawa, and K. Midorikawa, “Coherent water window x ray by phase-matched high-order harmonic generation in neutral media,” Phys. Rev. Lett. 101(25), 253901 (2008).
[CrossRef] [PubMed]

Jakubczak, K.

I. Jong Kim, G. H. Lee, S. B. Park, Y. S. Lee, T. K. Kim, C. H. Nam, T. Mocek, and K. Jakubczak, “Generation of submicrojoule high harmonics using a long gas jet in a two-color laser field,” Appl. Phys. Lett. 92, 021125 (2008).

Jong Kim, I.

I. Jong Kim, G. H. Lee, S. B. Park, Y. S. Lee, T. K. Kim, C. H. Nam, T. Mocek, and K. Jakubczak, “Generation of submicrojoule high harmonics using a long gas jet in a two-color laser field,” Appl. Phys. Lett. 92, 021125 (2008).

Kajumba, N.

A. D. Shiner, C. Trallero-Herrero, N. Kajumba, H.-C. Bandulet, D. Comtois, F. Legare, M. Giguere, J.-C. Kieffer, P. B. Corkum, and D. M. Villeneuve, “Wavelength scaling of high harmonic generation efficiency,” Phys. Rev. Lett. 103(7), 073902 (2009).
[CrossRef] [PubMed]

Kan, C.

Ch. Spielmann, N. H. Burnett, S. Sartania, R. Koppitsch, M. Schnurer, 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(5338), 661–664 (1997).
[CrossRef]

Kanai, T.

E. J. Takahashi, T. Kanai, K. L. Ishikawa, Y. Nabekawa, and K. Midorikawa, “Coherent water window x ray by phase-matched high-order harmonic generation in neutral media,” Phys. Rev. Lett. 101(25), 253901 (2008).
[CrossRef] [PubMed]

Kapteyn, H. C.

M.-C. Chen, P. Arpin, T. Popmintchev, M. Gerrity, B. Zhang, M. Seaberg, D. Popmintchev, M. M. Murnane, and H. C. Kapteyn, “Bright, coherent, ultrafast soft X-ray harmonics spanning the water window from a tabletop light source,” Phys. Rev. Lett. 105(17), 173901 (2010).
[CrossRef] [PubMed]

T. Popmintchev, M.-C. Chen, A. Bahabad, M. Gerrity, P. Sidorenko, O. Cohen, I. P. Christov, M. M. Murnane, and H. C. Kapteyn, “Phase matching of high harmonic generation in the soft and hard X-ray regions of the spectrum,” Proc. Natl. Acad. Sci. U.S.A. 106(26), 10516–10521 (2009).
[CrossRef] [PubMed]

Kartner, F. X.

Kazamias, S.

S. Kazamias, S. Daboussi, O. Guilbaud, K. Cassou, D. Ros, B. Cros, and G. Maynard, “Pressure-induced phase matching in high-order harmonic generation,” Phys. Rev. A 83(6), 063405 (2011).
[CrossRef]

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A. D. Shiner, C. Trallero-Herrero, N. Kajumba, H.-C. Bandulet, D. Comtois, F. Legare, M. Giguere, J.-C. Kieffer, P. B. Corkum, and D. M. Villeneuve, “Wavelength scaling of high harmonic generation efficiency,” Phys. Rev. Lett. 103(7), 073902 (2009).
[CrossRef] [PubMed]

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I. J. Kim, C. M. Kim, H. T. Kim, G. H. Lee, Y. S. Lee, J. Y. Park, D. J. Cho, and C. H. Nam, “Highly Efficient High-Harmonic Generation in an Orthogonally Polarized Two-Color Laser Field,” Phys. Rev. Lett. 94, 243901 (2005).

Kim, H. T.

I. J. Kim, C. M. Kim, H. T. Kim, G. H. Lee, Y. S. Lee, J. Y. Park, D. J. Cho, and C. H. Nam, “Highly Efficient High-Harmonic Generation in an Orthogonally Polarized Two-Color Laser Field,” Phys. Rev. Lett. 94, 243901 (2005).

Kim, I. J.

I. J. Kim, C. M. Kim, H. T. Kim, G. H. Lee, Y. S. Lee, J. Y. Park, D. J. Cho, and C. H. Nam, “Highly Efficient High-Harmonic Generation in an Orthogonally Polarized Two-Color Laser Field,” Phys. Rev. Lett. 94, 243901 (2005).

Kim, K. T.

V. Tosa, K. T. Kim, and C. H. Nam, “Macroscopic generation of attosecond-pulse trains in strongly ionized media,” Phys. Rev. A 79(4), 043828 (2009).
[CrossRef]

Kim, T. K.

I. Jong Kim, G. H. Lee, S. B. Park, Y. S. Lee, T. K. Kim, C. H. Nam, T. Mocek, and K. Jakubczak, “Generation of submicrojoule high harmonics using a long gas jet in a two-color laser field,” Appl. Phys. Lett. 92, 021125 (2008).

Koppitsch, R.

Ch. Spielmann, N. H. Burnett, S. Sartania, R. Koppitsch, M. Schnurer, 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(5338), 661–664 (1997).
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V. Tosa, E. Balogh, and K. Kovács, “Phase-matched generation of water-window x rays,” Phys. Rev. A 80(4), 045801 (2009).
[CrossRef]

Krainov, V. P.

M. V. Ammosov, N. B. Delone, and V. P. Krainov, “Tunnel ionization of complex atoms and of atomic ions in an alternating electromagnetic field,” Sov. Phys. JETP 64(6), 1191–1194 (1986).

Krausz, F.

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(7026), 596–596 (2005).
[CrossRef] [PubMed]

M. Geissler, G. Tempea, A. Scrinzi, M. Schnurer, F. Krausz, and T. Brabec, “Light Propagation in Field-Ionizing Media: Extreme Nonlinear Optics,” Phys. Rev. Lett. 83(15), 2930–2933 (1999).
[CrossRef]

Ch. Spielmann, N. H. Burnett, S. Sartania, R. Koppitsch, M. Schnurer, 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(5338), 661–664 (1997).
[CrossRef]

L’Huillier, A.

C. Altucci, T. Starczewski, E. Mevel, C.-G. Wahlstrom, B. Carre, and A. L’Huillier, “Influence of atomic density in high-order harmonic generation,” J. Opt. Soc. Am. B 13(1), 148–156 (1996).
[CrossRef]

M. Lewenstein, P. Salières, and A. L’Huillier, “Phase of the atomic polarization in high-order harmonic generation,” Phys. Rev. A 52(6), 4747–4754 (1995).
[CrossRef] [PubMed]

Le Blanc, C.

E. Constant, D. Garzella, P. Breger, E. Mevel, Ch. Dorrer, C. Le Blanc, F. Salin, and P. Agostini, “Optimizing High Harmonic Generation in Absorbing Gases: Model and Experiment,” Phys. Rev. Lett. 82(8), 1668–1671 (1999).
[CrossRef]

Lee, G. H.

I. Jong Kim, G. H. Lee, S. B. Park, Y. S. Lee, T. K. Kim, C. H. Nam, T. Mocek, and K. Jakubczak, “Generation of submicrojoule high harmonics using a long gas jet in a two-color laser field,” Appl. Phys. Lett. 92, 021125 (2008).

I. J. Kim, C. M. Kim, H. T. Kim, G. H. Lee, Y. S. Lee, J. Y. Park, D. J. Cho, and C. H. Nam, “Highly Efficient High-Harmonic Generation in an Orthogonally Polarized Two-Color Laser Field,” Phys. Rev. Lett. 94, 243901 (2005).

Lee, U.-M.

J.-S. Wu, S.-Y. Chou, U.-M. Lee, Y.-L. Shao, and Y.-Y. Lian, “Parallel DSMC Simulation of a Single Under-Expanded Free Orifice Jet From Transition to Near-Continuum Regime,” J. Fluids Eng. 127(6), 1161–1170 (2005).
[CrossRef]

Lee, Y. S.

I. Jong Kim, G. H. Lee, S. B. Park, Y. S. Lee, T. K. Kim, C. H. Nam, T. Mocek, and K. Jakubczak, “Generation of submicrojoule high harmonics using a long gas jet in a two-color laser field,” Appl. Phys. Lett. 92, 021125 (2008).

I. J. Kim, C. M. Kim, H. T. Kim, G. H. Lee, Y. S. Lee, J. Y. Park, D. J. Cho, and C. H. Nam, “Highly Efficient High-Harmonic Generation in an Orthogonally Polarized Two-Color Laser Field,” Phys. Rev. Lett. 94, 243901 (2005).

Legare, F.

A. D. Shiner, C. Trallero-Herrero, N. Kajumba, H.-C. Bandulet, D. Comtois, F. Legare, M. Giguere, J.-C. Kieffer, P. B. Corkum, and D. M. Villeneuve, “Wavelength scaling of high harmonic generation efficiency,” Phys. Rev. Lett. 103(7), 073902 (2009).
[CrossRef] [PubMed]

Lenzner, M.

Ch. Spielmann, N. H. Burnett, S. Sartania, R. Koppitsch, M. Schnurer, 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(5338), 661–664 (1997).
[CrossRef]

Lewenstein, M.

M. Lewenstein, P. Salières, and A. L’Huillier, “Phase of the atomic polarization in high-order harmonic generation,” Phys. Rev. A 52(6), 4747–4754 (1995).
[CrossRef] [PubMed]

Li, E.

Lian, Y.-Y.

J.-S. Wu, S.-Y. Chou, U.-M. Lee, Y.-L. Shao, and Y.-Y. Lian, “Parallel DSMC Simulation of a Single Under-Expanded Free Orifice Jet From Transition to Near-Continuum Regime,” J. Fluids Eng. 127(6), 1161–1170 (2005).
[CrossRef]

March, A. M.

P. Colosimo, G. Doumy, C. I. Blaga, J. Wheeler, C. Hauri, F. Catoire, J. Tate, R. Chirla, A. M. March, G. G. Paulus, H. G. Muller, P. Agostini, and L. F. Dimauro, “Scaling strong-field interactions towards the classical limit,” Nat. Phys. 4(5), 386–389 (2008).
[CrossRef]

Mashiko, H.

E. J. Takahashi, Y. Nabekawa, H. Mashiko, H. Hasegawa, A. Suda, and K. Midorikawa, “Generation of Strong Optical Field in Soft X-ray Region by Using High-Order Harmonics,” IEEE J. Sel. Top. Quantum Electron. 10(6), 1315–1328 (2004).
[CrossRef]

Maynard, G.

S. Kazamias, S. Daboussi, O. Guilbaud, K. Cassou, D. Ros, B. Cros, and G. Maynard, “Pressure-induced phase matching in high-order harmonic generation,” Phys. Rev. A 83(6), 063405 (2011).
[CrossRef]

Mevel, E.

E. Constant, D. Garzella, P. Breger, E. Mevel, Ch. Dorrer, C. Le Blanc, F. Salin, and P. Agostini, “Optimizing High Harmonic Generation in Absorbing Gases: Model and Experiment,” Phys. Rev. Lett. 82(8), 1668–1671 (1999).
[CrossRef]

C. Altucci, T. Starczewski, E. Mevel, C.-G. Wahlstrom, B. Carre, and A. L’Huillier, “Influence of atomic density in high-order harmonic generation,” J. Opt. Soc. Am. B 13(1), 148–156 (1996).
[CrossRef]

Michelswirth, M.

H. Dachraoui, T. Auguste, A. Helmstedt, P. Bartz, M. Michelswirth, N. Mueller, W. Pfeiffer, P. Salieres, and U. Heinzmann, “Interplay between absorption, dispersion and refraction in high-order harmonic generation,” J. Phys. At. Mol. Opt. Phys. 42(17), 175402 (2009).
[CrossRef]

Midorikawa, K.

E. J. Takahashi, T. Kanai, K. L. Ishikawa, Y. Nabekawa, and K. Midorikawa, “Coherent water window x ray by phase-matched high-order harmonic generation in neutral media,” Phys. Rev. Lett. 101(25), 253901 (2008).
[CrossRef] [PubMed]

E. J. Takahashi, Y. Nabekawa, H. Mashiko, H. Hasegawa, A. Suda, and K. Midorikawa, “Generation of Strong Optical Field in Soft X-ray Region by Using High-Order Harmonics,” IEEE J. Sel. Top. Quantum Electron. 10(6), 1315–1328 (2004).
[CrossRef]

E. J. Takahashi, Y. Nabekawa, and K. Midorikawa, “Low-divergence coherent soft x-ray source at 13 nm by high-order harmonics,” Appl. Phys. Lett. 84(1), 4–6 (2004).
[CrossRef]

Mocek, T.

I. Jong Kim, G. H. Lee, S. B. Park, Y. S. Lee, T. K. Kim, C. H. Nam, T. Mocek, and K. Jakubczak, “Generation of submicrojoule high harmonics using a long gas jet in a two-color laser field,” Appl. Phys. Lett. 92, 021125 (2008).

Moses, J.

Mucke, O. D.

Mueller, N.

H. Dachraoui, T. Auguste, A. Helmstedt, P. Bartz, M. Michelswirth, N. Mueller, W. Pfeiffer, P. Salieres, and U. Heinzmann, “Interplay between absorption, dispersion and refraction in high-order harmonic generation,” J. Phys. At. Mol. Opt. Phys. 42(17), 175402 (2009).
[CrossRef]

Muller, H. G.

P. Colosimo, G. Doumy, C. I. Blaga, J. Wheeler, C. Hauri, F. Catoire, J. Tate, R. Chirla, A. M. March, G. G. Paulus, H. G. Muller, P. Agostini, and L. F. Dimauro, “Scaling strong-field interactions towards the classical limit,” Nat. Phys. 4(5), 386–389 (2008).
[CrossRef]

J. Tate, T. Auguste, H. G. Muller, P. Salieres, P. Agostini, and L. F. DiMauro, “Scaling of wave-packet dynamics in an intense midinfrared field,” Phys. Rev. Lett. 98(1), 013901 (2007).
[CrossRef] [PubMed]

Murnane, M. M.

M.-C. Chen, P. Arpin, T. Popmintchev, M. Gerrity, B. Zhang, M. Seaberg, D. Popmintchev, M. M. Murnane, and H. C. Kapteyn, “Bright, coherent, ultrafast soft X-ray harmonics spanning the water window from a tabletop light source,” Phys. Rev. Lett. 105(17), 173901 (2010).
[CrossRef] [PubMed]

T. Popmintchev, M.-C. Chen, A. Bahabad, M. Gerrity, P. Sidorenko, O. Cohen, I. P. Christov, M. M. Murnane, and H. C. Kapteyn, “Phase matching of high harmonic generation in the soft and hard X-ray regions of the spectrum,” Proc. Natl. Acad. Sci. U.S.A. 106(26), 10516–10521 (2009).
[CrossRef] [PubMed]

Nabekawa, Y.

E. J. Takahashi, T. Kanai, K. L. Ishikawa, Y. Nabekawa, and K. Midorikawa, “Coherent water window x ray by phase-matched high-order harmonic generation in neutral media,” Phys. Rev. Lett. 101(25), 253901 (2008).
[CrossRef] [PubMed]

E. J. Takahashi, Y. Nabekawa, H. Mashiko, H. Hasegawa, A. Suda, and K. Midorikawa, “Generation of Strong Optical Field in Soft X-ray Region by Using High-Order Harmonics,” IEEE J. Sel. Top. Quantum Electron. 10(6), 1315–1328 (2004).
[CrossRef]

E. J. Takahashi, Y. Nabekawa, and K. Midorikawa, “Low-divergence coherent soft x-ray source at 13 nm by high-order harmonics,” Appl. Phys. Lett. 84(1), 4–6 (2004).
[CrossRef]

Nam, C. H.

V. Tosa, K. T. Kim, and C. H. Nam, “Macroscopic generation of attosecond-pulse trains in strongly ionized media,” Phys. Rev. A 79(4), 043828 (2009).
[CrossRef]

I. Jong Kim, G. H. Lee, S. B. Park, Y. S. Lee, T. K. Kim, C. H. Nam, T. Mocek, and K. Jakubczak, “Generation of submicrojoule high harmonics using a long gas jet in a two-color laser field,” Appl. Phys. Lett. 92, 021125 (2008).

I. J. Kim, C. M. Kim, H. T. Kim, G. H. Lee, Y. S. Lee, J. Y. Park, D. J. Cho, and C. H. Nam, “Highly Efficient High-Harmonic Generation in an Orthogonally Polarized Two-Color Laser Field,” Phys. Rev. Lett. 94, 243901 (2005).

Neely, D.

A. Behjat, G. J. Tallents, and D. Neely, “The characterization of a high-density gas jet,” J. Phys. D Appl. Phys. 30(20), 2872–2879 (1997).
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Park, J. Y.

I. J. Kim, C. M. Kim, H. T. Kim, G. H. Lee, Y. S. Lee, J. Y. Park, D. J. Cho, and C. H. Nam, “Highly Efficient High-Harmonic Generation in an Orthogonally Polarized Two-Color Laser Field,” Phys. Rev. Lett. 94, 243901 (2005).

Park, S. B.

I. Jong Kim, G. H. Lee, S. B. Park, Y. S. Lee, T. K. Kim, C. H. Nam, T. Mocek, and K. Jakubczak, “Generation of submicrojoule high harmonics using a long gas jet in a two-color laser field,” Appl. Phys. Lett. 92, 021125 (2008).

Paulus, G. G.

P. Colosimo, G. Doumy, C. I. Blaga, J. Wheeler, C. Hauri, F. Catoire, J. Tate, R. Chirla, A. M. March, G. G. Paulus, H. G. Muller, P. Agostini, and L. F. Dimauro, “Scaling strong-field interactions towards the classical limit,” Nat. Phys. 4(5), 386–389 (2008).
[CrossRef]

Pfeiffer, W.

H. Dachraoui, T. Auguste, A. Helmstedt, P. Bartz, M. Michelswirth, N. Mueller, W. Pfeiffer, P. Salieres, and U. Heinzmann, “Interplay between absorption, dispersion and refraction in high-order harmonic generation,” J. Phys. At. Mol. Opt. Phys. 42(17), 175402 (2009).
[CrossRef]

Popmintchev, D.

M.-C. Chen, P. Arpin, T. Popmintchev, M. Gerrity, B. Zhang, M. Seaberg, D. Popmintchev, M. M. Murnane, and H. C. Kapteyn, “Bright, coherent, ultrafast soft X-ray harmonics spanning the water window from a tabletop light source,” Phys. Rev. Lett. 105(17), 173901 (2010).
[CrossRef] [PubMed]

Popmintchev, T.

M.-C. Chen, P. Arpin, T. Popmintchev, M. Gerrity, B. Zhang, M. Seaberg, D. Popmintchev, M. M. Murnane, and H. C. Kapteyn, “Bright, coherent, ultrafast soft X-ray harmonics spanning the water window from a tabletop light source,” Phys. Rev. Lett. 105(17), 173901 (2010).
[CrossRef] [PubMed]

T. Popmintchev, M.-C. Chen, A. Bahabad, M. Gerrity, P. Sidorenko, O. Cohen, I. P. Christov, M. M. Murnane, and H. C. Kapteyn, “Phase matching of high harmonic generation in the soft and hard X-ray regions of the spectrum,” Proc. Natl. Acad. Sci. U.S.A. 106(26), 10516–10521 (2009).
[CrossRef] [PubMed]

Rand, D.

Ros, D.

S. Kazamias, S. Daboussi, O. Guilbaud, K. Cassou, D. Ros, B. Cros, and G. Maynard, “Pressure-induced phase matching in high-order harmonic generation,” Phys. Rev. A 83(6), 063405 (2011).
[CrossRef]

Salieres, P.

H. Dachraoui, T. Auguste, A. Helmstedt, P. Bartz, M. Michelswirth, N. Mueller, W. Pfeiffer, P. Salieres, and U. Heinzmann, “Interplay between absorption, dispersion and refraction in high-order harmonic generation,” J. Phys. At. Mol. Opt. Phys. 42(17), 175402 (2009).
[CrossRef]

J. Tate, T. Auguste, H. G. Muller, P. Salieres, P. Agostini, and L. F. DiMauro, “Scaling of wave-packet dynamics in an intense midinfrared field,” Phys. Rev. Lett. 98(1), 013901 (2007).
[CrossRef] [PubMed]

Salières, P.

M. Lewenstein, P. Salières, and A. L’Huillier, “Phase of the atomic polarization in high-order harmonic generation,” Phys. Rev. A 52(6), 4747–4754 (1995).
[CrossRef] [PubMed]

Salin, F.

E. Constant, D. Garzella, P. Breger, E. Mevel, Ch. Dorrer, C. Le Blanc, F. Salin, and P. Agostini, “Optimizing High Harmonic Generation in Absorbing Gases: Model and Experiment,” Phys. Rev. Lett. 82(8), 1668–1671 (1999).
[CrossRef]

Sartania, S.

Ch. Spielmann, N. H. Burnett, S. Sartania, R. Koppitsch, M. Schnurer, 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(5338), 661–664 (1997).
[CrossRef]

Schnurer, M.

M. Geissler, G. Tempea, A. Scrinzi, M. Schnurer, F. Krausz, and T. Brabec, “Light Propagation in Field-Ionizing Media: Extreme Nonlinear Optics,” Phys. Rev. Lett. 83(15), 2930–2933 (1999).
[CrossRef]

Ch. Spielmann, N. H. Burnett, S. Sartania, R. Koppitsch, M. Schnurer, 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(5338), 661–664 (1997).
[CrossRef]

Scrinzi, A.

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(7026), 596–596 (2005).
[CrossRef] [PubMed]

M. Geissler, G. Tempea, A. Scrinzi, M. Schnurer, F. Krausz, and T. Brabec, “Light Propagation in Field-Ionizing Media: Extreme Nonlinear Optics,” Phys. Rev. Lett. 83(15), 2930–2933 (1999).
[CrossRef]

Seaberg, M.

M.-C. Chen, P. Arpin, T. Popmintchev, M. Gerrity, B. Zhang, M. Seaberg, D. Popmintchev, M. M. Murnane, and H. C. Kapteyn, “Bright, coherent, ultrafast soft X-ray harmonics spanning the water window from a tabletop light source,” Phys. Rev. Lett. 105(17), 173901 (2010).
[CrossRef] [PubMed]

Seres, E.

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(7026), 596–596 (2005).
[CrossRef] [PubMed]

Seres, J.

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(7026), 596–596 (2005).
[CrossRef] [PubMed]

Shao, Y.-L.

J.-S. Wu, S.-Y. Chou, U.-M. Lee, Y.-L. Shao, and Y.-Y. Lian, “Parallel DSMC Simulation of a Single Under-Expanded Free Orifice Jet From Transition to Near-Continuum Regime,” J. Fluids Eng. 127(6), 1161–1170 (2005).
[CrossRef]

Shiner, A. D.

A. D. Shiner, C. Trallero-Herrero, N. Kajumba, H.-C. Bandulet, D. Comtois, F. Legare, M. Giguere, J.-C. Kieffer, P. B. Corkum, and D. M. Villeneuve, “Wavelength scaling of high harmonic generation efficiency,” Phys. Rev. Lett. 103(7), 073902 (2009).
[CrossRef] [PubMed]

Siddiqui, A. M.

Sidorenko, P.

T. Popmintchev, M.-C. Chen, A. Bahabad, M. Gerrity, P. Sidorenko, O. Cohen, I. P. Christov, M. M. Murnane, and H. C. Kapteyn, “Phase matching of high harmonic generation in the soft and hard X-ray regions of the spectrum,” Proc. Natl. Acad. Sci. U.S.A. 106(26), 10516–10521 (2009).
[CrossRef] [PubMed]

Spielmann, C.

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(7026), 596–596 (2005).
[CrossRef] [PubMed]

Spielmann, Ch.

Ch. Spielmann, N. H. Burnett, S. Sartania, R. Koppitsch, M. Schnurer, 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(5338), 661–664 (1997).
[CrossRef]

Starczewski, T.

Streli, C.

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(7026), 596–596 (2005).
[CrossRef] [PubMed]

Suda, A.

E. J. Takahashi, Y. Nabekawa, H. Mashiko, H. Hasegawa, A. Suda, and K. Midorikawa, “Generation of Strong Optical Field in Soft X-ray Region by Using High-Order Harmonics,” IEEE J. Sel. Top. Quantum Electron. 10(6), 1315–1328 (2004).
[CrossRef]

Takahashi, E. J.

E. J. Takahashi, T. Kanai, K. L. Ishikawa, Y. Nabekawa, and K. Midorikawa, “Coherent water window x ray by phase-matched high-order harmonic generation in neutral media,” Phys. Rev. Lett. 101(25), 253901 (2008).
[CrossRef] [PubMed]

E. J. Takahashi, Y. Nabekawa, H. Mashiko, H. Hasegawa, A. Suda, and K. Midorikawa, “Generation of Strong Optical Field in Soft X-ray Region by Using High-Order Harmonics,” IEEE J. Sel. Top. Quantum Electron. 10(6), 1315–1328 (2004).
[CrossRef]

E. J. Takahashi, Y. Nabekawa, and K. Midorikawa, “Low-divergence coherent soft x-ray source at 13 nm by high-order harmonics,” Appl. Phys. Lett. 84(1), 4–6 (2004).
[CrossRef]

Tallents, G. J.

A. Behjat, G. J. Tallents, and D. Neely, “The characterization of a high-density gas jet,” J. Phys. D Appl. Phys. 30(20), 2872–2879 (1997).
[CrossRef]

Tate, J.

P. Colosimo, G. Doumy, C. I. Blaga, J. Wheeler, C. Hauri, F. Catoire, J. Tate, R. Chirla, A. M. March, G. G. Paulus, H. G. Muller, P. Agostini, and L. F. Dimauro, “Scaling strong-field interactions towards the classical limit,” Nat. Phys. 4(5), 386–389 (2008).
[CrossRef]

J. Tate, T. Auguste, H. G. Muller, P. Salieres, P. Agostini, and L. F. DiMauro, “Scaling of wave-packet dynamics in an intense midinfrared field,” Phys. Rev. Lett. 98(1), 013901 (2007).
[CrossRef] [PubMed]

Tempea, G.

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(7026), 596–596 (2005).
[CrossRef] [PubMed]

M. Geissler, G. Tempea, A. Scrinzi, M. Schnurer, F. Krausz, and T. Brabec, “Light Propagation in Field-Ionizing Media: Extreme Nonlinear Optics,” Phys. Rev. Lett. 83(15), 2930–2933 (1999).
[CrossRef]

Tosa, V.

V. Tosa, K. T. Kim, and C. H. Nam, “Macroscopic generation of attosecond-pulse trains in strongly ionized media,” Phys. Rev. A 79(4), 043828 (2009).
[CrossRef]

V. Tosa, E. Balogh, and K. Kovács, “Phase-matched generation of water-window x rays,” Phys. Rev. A 80(4), 045801 (2009).
[CrossRef]

Trallero-Herrero, C.

A. D. Shiner, C. Trallero-Herrero, N. Kajumba, H.-C. Bandulet, D. Comtois, F. Legare, M. Giguere, J.-C. Kieffer, P. B. Corkum, and D. M. Villeneuve, “Wavelength scaling of high harmonic generation efficiency,” Phys. Rev. Lett. 103(7), 073902 (2009).
[CrossRef] [PubMed]

Verhoef, A. J.

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(7026), 596–596 (2005).
[CrossRef] [PubMed]

Villeneuve, D. M.

A. D. Shiner, C. Trallero-Herrero, N. Kajumba, H.-C. Bandulet, D. Comtois, F. Legare, M. Giguere, J.-C. Kieffer, P. B. Corkum, and D. M. Villeneuve, “Wavelength scaling of high harmonic generation efficiency,” Phys. Rev. Lett. 103(7), 073902 (2009).
[CrossRef] [PubMed]

Wahlstrom, C.-G.

Wheeler, J.

P. Colosimo, G. Doumy, C. I. Blaga, J. Wheeler, C. Hauri, F. Catoire, J. Tate, R. Chirla, A. M. March, G. G. Paulus, H. G. Muller, P. Agostini, and L. F. Dimauro, “Scaling strong-field interactions towards the classical limit,” Nat. Phys. 4(5), 386–389 (2008).
[CrossRef]

Wobrauschek, P.

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(7026), 596–596 (2005).
[CrossRef] [PubMed]

Ch. Spielmann, N. H. Burnett, S. Sartania, R. Koppitsch, M. Schnurer, 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(5338), 661–664 (1997).
[CrossRef]

Wu, J.-S.

J.-S. Wu, S.-Y. Chou, U.-M. Lee, Y.-L. Shao, and Y.-Y. Lian, “Parallel DSMC Simulation of a Single Under-Expanded Free Orifice Jet From Transition to Near-Continuum Regime,” J. Fluids Eng. 127(6), 1161–1170 (2005).
[CrossRef]

Yakovlev, V.

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(7026), 596–596 (2005).
[CrossRef] [PubMed]

Zhang, B.

M.-C. Chen, P. Arpin, T. Popmintchev, M. Gerrity, B. Zhang, M. Seaberg, D. Popmintchev, M. M. Murnane, and H. C. Kapteyn, “Bright, coherent, ultrafast soft X-ray harmonics spanning the water window from a tabletop light source,” Phys. Rev. Lett. 105(17), 173901 (2010).
[CrossRef] [PubMed]

Appl. Phys. Lett. (2)

I. Jong Kim, G. H. Lee, S. B. Park, Y. S. Lee, T. K. Kim, C. H. Nam, T. Mocek, and K. Jakubczak, “Generation of submicrojoule high harmonics using a long gas jet in a two-color laser field,” Appl. Phys. Lett. 92, 021125 (2008).

E. J. Takahashi, Y. Nabekawa, and K. Midorikawa, “Low-divergence coherent soft x-ray source at 13 nm by high-order harmonics,” Appl. Phys. Lett. 84(1), 4–6 (2004).
[CrossRef]

At. Data Nucl. Data Tables (1)

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

IEEE J. Sel. Top. Quantum Electron. (1)

E. J. Takahashi, Y. Nabekawa, H. Mashiko, H. Hasegawa, A. Suda, and K. Midorikawa, “Generation of Strong Optical Field in Soft X-ray Region by Using High-Order Harmonics,” IEEE J. Sel. Top. Quantum Electron. 10(6), 1315–1328 (2004).
[CrossRef]

J. Fluids Eng. (1)

J.-S. Wu, S.-Y. Chou, U.-M. Lee, Y.-L. Shao, and Y.-Y. Lian, “Parallel DSMC Simulation of a Single Under-Expanded Free Orifice Jet From Transition to Near-Continuum Regime,” J. Fluids Eng. 127(6), 1161–1170 (2005).
[CrossRef]

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

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

H. Dachraoui, T. Auguste, A. Helmstedt, P. Bartz, M. Michelswirth, N. Mueller, W. Pfeiffer, P. Salieres, and U. Heinzmann, “Interplay between absorption, dispersion and refraction in high-order harmonic generation,” J. Phys. At. Mol. Opt. Phys. 42(17), 175402 (2009).
[CrossRef]

J. Phys. D Appl. Phys. (1)

A. Behjat, G. J. Tallents, and D. Neely, “The characterization of a high-density gas jet,” J. Phys. D Appl. Phys. 30(20), 2872–2879 (1997).
[CrossRef]

Nat. Phys. (1)

P. Colosimo, G. Doumy, C. I. Blaga, J. Wheeler, C. Hauri, F. Catoire, J. Tate, R. Chirla, A. M. March, G. G. Paulus, H. G. Muller, P. Agostini, and L. F. Dimauro, “Scaling strong-field interactions towards the classical limit,” Nat. Phys. 4(5), 386–389 (2008).
[CrossRef]

Nature (1)

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(7026), 596–596 (2005).
[CrossRef] [PubMed]

Opt. Express (1)

Opt. Lett. (2)

Phys. Rev. A (4)

V. Tosa, E. Balogh, and K. Kovács, “Phase-matched generation of water-window x rays,” Phys. Rev. A 80(4), 045801 (2009).
[CrossRef]

V. Tosa, K. T. Kim, and C. H. Nam, “Macroscopic generation of attosecond-pulse trains in strongly ionized media,” Phys. Rev. A 79(4), 043828 (2009).
[CrossRef]

S. Kazamias, S. Daboussi, O. Guilbaud, K. Cassou, D. Ros, B. Cros, and G. Maynard, “Pressure-induced phase matching in high-order harmonic generation,” Phys. Rev. A 83(6), 063405 (2011).
[CrossRef]

M. Lewenstein, P. Salières, and A. L’Huillier, “Phase of the atomic polarization in high-order harmonic generation,” Phys. Rev. A 52(6), 4747–4754 (1995).
[CrossRef] [PubMed]

Phys. Rev. Lett. (7)

I. J. Kim, C. M. Kim, H. T. Kim, G. H. Lee, Y. S. Lee, J. Y. Park, D. J. Cho, and C. H. Nam, “Highly Efficient High-Harmonic Generation in an Orthogonally Polarized Two-Color Laser Field,” Phys. Rev. Lett. 94, 243901 (2005).

E. Constant, D. Garzella, P. Breger, E. Mevel, Ch. Dorrer, C. Le Blanc, F. Salin, and P. Agostini, “Optimizing High Harmonic Generation in Absorbing Gases: Model and Experiment,” Phys. Rev. Lett. 82(8), 1668–1671 (1999).
[CrossRef]

M. Geissler, G. Tempea, A. Scrinzi, M. Schnurer, F. Krausz, and T. Brabec, “Light Propagation in Field-Ionizing Media: Extreme Nonlinear Optics,” Phys. Rev. Lett. 83(15), 2930–2933 (1999).
[CrossRef]

M.-C. Chen, P. Arpin, T. Popmintchev, M. Gerrity, B. Zhang, M. Seaberg, D. Popmintchev, M. M. Murnane, and H. C. Kapteyn, “Bright, coherent, ultrafast soft X-ray harmonics spanning the water window from a tabletop light source,” Phys. Rev. Lett. 105(17), 173901 (2010).
[CrossRef] [PubMed]

J. Tate, T. Auguste, H. G. Muller, P. Salieres, P. Agostini, and L. F. DiMauro, “Scaling of wave-packet dynamics in an intense midinfrared field,” Phys. Rev. Lett. 98(1), 013901 (2007).
[CrossRef] [PubMed]

A. D. Shiner, C. Trallero-Herrero, N. Kajumba, H.-C. Bandulet, D. Comtois, F. Legare, M. Giguere, J.-C. Kieffer, P. B. Corkum, and D. M. Villeneuve, “Wavelength scaling of high harmonic generation efficiency,” Phys. Rev. Lett. 103(7), 073902 (2009).
[CrossRef] [PubMed]

E. J. Takahashi, T. Kanai, K. L. Ishikawa, Y. Nabekawa, and K. Midorikawa, “Coherent water window x ray by phase-matched high-order harmonic generation in neutral media,” Phys. Rev. Lett. 101(25), 253901 (2008).
[CrossRef] [PubMed]

Proc. Natl. Acad. Sci. U.S.A. (1)

T. Popmintchev, M.-C. Chen, A. Bahabad, M. Gerrity, P. Sidorenko, O. Cohen, I. P. Christov, M. M. Murnane, and H. C. Kapteyn, “Phase matching of high harmonic generation in the soft and hard X-ray regions of the spectrum,” Proc. Natl. Acad. Sci. U.S.A. 106(26), 10516–10521 (2009).
[CrossRef] [PubMed]

Science (1)

Ch. Spielmann, N. H. Burnett, S. Sartania, R. Koppitsch, M. Schnurer, 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(5338), 661–664 (1997).
[CrossRef]

Sov. Phys. JETP (1)

M. V. Ammosov, N. B. Delone, and V. P. Krainov, “Tunnel ionization of complex atoms and of atomic ions in an alternating electromagnetic field,” Sov. Phys. JETP 64(6), 1191–1194 (1986).

Other (2)

M. J. Weber, Handbook of Optical Materials (CRC Press, 2003), Chap. 6.

Pascal Salières and Ivan Christov, “Macroscopic Effects in High-Order Harmonic Generation,” in Strong Field Laser Physics, Thomas Brabec, ed. (Springer, 2008).

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Figures (8)

Fig. 1
Fig. 1

Numerical results of the 2μm laser pulse propagation toward the + z direction through a He gas jet. The upper row shows the peak intensity when the peak pressure at the jet is (a) 0.1bar, (b) 1bar, and (c) 10bar. The Gaussian curves illustrate the relative pressure profile of the jet. The lower row shows the ionization level when the pressure is (d) 0.1bar, (e) 1bar, and (f) 10bar. The color scales of the intensity and the ionization level are shown on the side.

Fig. 2
Fig. 2

Numerical results of the 2μm laser pulse propagation toward the + z direction through a He cell. The upper row shows the peak intensity when the pressure is (a) 0.1bar, (b) 1bar, and (c) 10bar. The relative pressure is shown by the flat-top curve. The lower row shows the ionization level when the pressure is (d) 0.1bar, (e) 1bar, and (f) 10bar. The color scales of the intensity and the ionization level are shown on the side.

Fig. 3
Fig. 3

The wave-vector mismatches in a He jet at r = 0 and τ = 0 (pulse peak). The laser pulse and medium conditions are the same as Fig. 1, and the medium pressures are (a) 0.1bar, (b) 1bar, and (c) 10bar respectively. The harmonic energy considered here is 500eV. In each plot, the blue, green, red, and yellow curves show the mismatch due to neutral atom dispersion, plasma dispersion, geometric phase, and dipole phase respectively. The black curve shows the total wave-vector mismatch that is the sum of the above four curves.

Fig. 4
Fig. 4

The wave-vector mismatches in a He cell at r = 0 and τ = 0 (pulse peak). The laser pulse and medium conditions are the same as Fig. 2, and the medium pressure is (a) 0.1bar, (b) 1bar, and (c) 10bar respectively. The harmonic energy considered here is 500eV. In each plot, the blue, green, red, and yellow curves show the mismatch due to neutral atom dispersion, plasma dispersion, geometric phase, and dipole phase respectively. The black curve shows the total wave-vector mismatch that is the sum of the above four curves.

Fig. 5
Fig. 5

Enhancement factor ξ for He. (a) and (b) show the enhancement of a 1mm He jet and a 1cm He cell respectively. For each driver wavelength, the curve is intentionally shifted for clarity. The number near each curve indicates the driver wavelength in units of 1μm. For comparison, the dashed lines show a parabolic dependence on pressure.

Fig. 6
Fig. 6

Enhancement factor ξ for Ne. (a) and (b) show the enhancement of a 1mm Ne jet and a 1cm Ne cell respectively. For each driver wavelength, the curve is intentionally shifted for clarity. The number near each curve indicates the driver wavelength in units of 1μm. For comparison, the dashed lines show a parabolic dependence on pressure.

Fig. 7
Fig. 7

Enhancement factor for 0.8μm driver wavelength with high pulse energy and loose focusing. For (a) He, a 130mJ pulse is focused into a 5cm-long gas cell with 590μm beam radius. For (b) Ne, a 50mJ pulse is focused into a 4cm-long gas cell with 360μm beam radius [22]. The solid curves consider plasma defocusing, while the dashed ones don’t.

Fig. 8
Fig. 8

Calculated HHG efficiency for optimal pressures in (a) He and (b) Ne. The black dotted curves also show a λ1−5.5 dependence starting from the efficiency reference point. For different driver wavelengths, different photon energies that are near the corresponding cutoffs are considered, as labeled.

Equations (5)

Equations on this page are rendered with MathJax. Learn more.

E z = i 2k 2 E+i k 2 n 2 ε 0 c | E | 2 E 1 2c τ ω p 2 Ed τ I p 2c ε 0 Re ( E ) 2 ρ τ E,
E q =Aη( q, λ 1 ) 2πrdr dτ × | L/2 L/2 w P( z )exp[ izΔ k q ( r,z,τ ) ]exp[ β( z )( Lz ) ]dz | 2 ,
ξ 2πrdr dτ | L/2 L/2 w P( z )exp[ izΔ k q ( r,z,τ ) ]exp[ β( Lz ) ]dz | 2 ,
E q =Aηξ.
Δ k q =δ k a +δ k p +δ k g +δ k d .

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