Abstract

We introduce a new computational approach for femtosecond pulse propagation in the transparency region of gases that permits full resolution in three space dimensions plus time while fully incorporating quantum coherent effects such as high-harmonic generation and strong-field ionization in a holistic fashion. This is achieved by utilizing a one-dimensional model atom with a delta-function potential which allows for a closed-form solution for the nonlinear optical response due to ground-state to continuum transitions. It side-steps evaluation of the wave function, and offers more than one hundred-fold reduction in computation time in comparison to direct solution of the atomic Schrödinger equation. To illustrate the capability of our new computational approach, we apply it to the example of near-threshold harmonic generation in Xenon, and we also present a qualitative comparison between our model and results from an in-house experiment on extreme ultraviolet generation in a femtosecond enhancement cavity.

© 2012 OSA

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  1. A. Couairon and A. Mysyrowicz, “Femtosecond filamentation in transparent media,” Phys. Rep. 441, 47–189 (2007).
    [CrossRef]
  2. M. Lewenstein, P. Balcou, M. Y. Ivanov, A. L’Huillier, and P. B. Corkum, “Theory of high harmonics generation by low-frequency laser fields,” Phys. Rev. A 49, 2117–2132 (1994).
    [CrossRef] [PubMed]
  3. L. Bergé, S. Skupin, R. Nuter, J. Kasparian, and J. Wolf, “Ultrashort filaments of light in weakly ionized optically transparent media,” Rep. Prog. Phys. 70, 1633–1713 (2007).
    [CrossRef]
  4. M. Gaarde, J. Tate, and K. Schafer, “Macroscopic aspects of attosecond pulse generation,” J. Phys. B: At. Mol. Opt. Phys. 41, 132001 (2008).
    [CrossRef]
  5. M. Nurhuda, A. Suda, and K. Midorikawa, “Generalization of the Kerr effect for high intensity, ultrashort laser pulses,” New J. Phys. 10, 053006 (2008).
    [CrossRef]
  6. E. A. Volkova, A. M. Popov, and O. V. Tikhonova, “Nonlinear polarization response of an atomic gas medium in the field of a high-intensity femtosecond laser pulse,” JETP Lett. 94, 519–524 (2011).
    [CrossRef]
  7. I. Christov, “Propagation of ultrashort pulses in gaseous medium:breakdown of the quasistatic approximation,” Opt. Express 6, 34–39 (2000).
    [CrossRef] [PubMed]
  8. E. Lorin, S. Chelkowski, and A. D. Bandrauk, “The WASP model: A Micro-Macro system of Wave-Schrödinger-Plasma equations for filamentation,” Commun. Comput. Phys. 9, 406–440 (2011).
  9. Q. Su and J. Eberly, “Model atom for multiphoton physics,” Phys. Rev. A 44, 5997–6008 (1991).
    [CrossRef] [PubMed]
  10. G. P. Arrighini and M. Gavarini, “Ionization of a model atom by strong and superstrong electric fields,” Lett. Nuovo Cimento 33, 353–358 (1982).
    [CrossRef]
  11. W. Elberfeld and M. Kleber, “Tunneling from an ultrathin quantum well in a strong electrostatic field: A comparison of different methods,” Z. Phys. B: Cond. Matt. 73, 23–32 (1988).
    [CrossRef]
  12. R. M. Cavalcanti, P. Giacconi, and R. Soldati, “Decay in a uniform field: an exactly solvable model,” J. Phys. A: Math. Gen. 36, 12065–12080 (2003).
    [CrossRef]
  13. H. Uncu, H. Erkol, E. Demiralp, and H. Beker, “Solutions of the Schrödinger equation for dirac delta decorated linear potential,” C. Eur. J. Phys. 3, 303–323 (2005).
    [CrossRef]
  14. G. Álvarez and B. Sundaram, “Perturbation theory for the stark effect in a double quantum well,” J. Phys. A: Math. Gen. 37, 9735–9748 (2004).
    [CrossRef]
  15. V. M. Villalba and L. A. González-Díaz, “Particle resonance in the dirac equation in the presence of a delta interaction and a perturbative hyperbolic potential,” Eur. Phys. J. C 61, 519–525 (2009).
    [CrossRef]
  16. S. Geltman, “Ionisation dynamics of a model atom in an electrostatic field,” J. Phys. B: At. Mol. Phys. 11, 3323–3337 (1978).
    [CrossRef]
  17. G. V. Dunne and C. S. Gauthier, “Simple soluble molecular ionization model,” Phys. Rev. A 69, 053409 (2004).
    [CrossRef]
  18. Q. Su, B. P. Irving, C. W. Johnson, and J. H. Eberly, “Stabilization of a one-dimensional short-range model atom in intense laser fields,” J. Phys. B: At. Mol. Opt. 29, 5755–5764 (1996).
    [CrossRef]
  19. T. Dziubak and J. Matulewski, “Stabilization of one-dimensional soft-core and singular model atoms,” Eur. Phys. J. D 59, 321–327 (2010).
    [CrossRef]
  20. A. Sanpera, Q. Su, and L. Roso-Franco, “Ionization suppression in a very-short-range potential,” Phys. Rev. A 47, 2312–2318 (1993).
    [CrossRef] [PubMed]
  21. S. Geltman, “Short-pulse model-atom studies of ionization in intense laser fields,” J. Phys. B - At. Mol. Opt. 27, 1497–1514 (1994).
    [CrossRef]
  22. Z. X. Zhao, B. D. Esry, and C. D. Lin, “Boundary-free scaling calculation of the time-dependent Schrödinger equation for laser-atom interactions,” Phys. Rev. A 65, 023402 (2002).
    [CrossRef]
  23. A. Teleki, E. M. Wright, and M. Kolesik, “Microscopic model for the higher-order nonlinearity in optical filaments,” Phys. Rev. A 82, 065801 (2010).
    [CrossRef]
  24. J. M. Brown, E. M. Wright, J. V. Moloney, and M. Kolesik, “On the relative roles of higher-order nonlinearity and ionization in ultrafast light-matter interactions,” Opt. Lett. 37, 1604–1606 (2012).
    [CrossRef] [PubMed]
  25. J. Brown, A. Lotti, A. Teleki, and M. Kolesik, “Exactly solvable model for non-linear light-matter interaction in an arbitrary time-dependent field,” Phys. Rev. A 84, 063424 (2011).
    [CrossRef]
  26. J. Lee, D. R. Carlson, and R. J. Jones, “Optimizing intracavity high harmonic generation for xuv fs frequency combs,” Opt. Express 19, 23315–23326 (2011).
    [CrossRef] [PubMed]
  27. M. Kolesik and J. V. Moloney, “Nonlinear optical pulse propagation simulation: From Maxwell’s to unidirectional equations,” Phys. Rev. E 70, 036604 (2004).
    [CrossRef]
  28. A. Bideau-Mehu, Y. Guern, R. Abjean, and A. Johannin-Gilles, “Measurement of refractive indices of neon, argon, krypton and xenon in the 253.7—140.4 nm wavelength range. Dispersion relations and estimated oscillator strengths of the resonance lines,” J. Quant. Spect. Rad. Transfer 25, 395–402 (1981).
    [CrossRef]
  29. P. B. Corkum, “Plasma perspective on strong field multiphoton ionization,” Phys. Rev. Lett 71, 1994–1997 (1993).
    [CrossRef] [PubMed]
  30. K. J. 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]
  31. F. Schapper, M. Holler, T. Auguste, A. Zaïr, M. Weger, P. Salières, L. Gallmann, and U. Keller, “Spatial finger-print of quantum path interferences in high order harmonic generation,” Opt. Express 18, 2987–2994 (2010).
    [CrossRef] [PubMed]
  32. S. M. Teichmann, D. R. Austin, P. Bates, S. Cousin, A. Grün, M. Clerici, A. Lotti, D. Faccio, P. DiTrapani, A. Couairon, and J. Biegert, “Trajectory interferences in a semi-infinite gas cell,” Laser Phys. Lett. 9, 207–211 (2012).
    [CrossRef]
  33. A. L’Huillier, K.J. Schafer, and K.C. Kulander, “High-order harmonic generation in Xenon at 1064 nm: The role of phase matching,” Phys. Rev. Lett. 66, 2200–2203 (1991).
    [CrossRef]
  34. P. Salières, A. L’Huillier, and M. Lewenstein, “Coherence control of high-order harmonics,” Phys. Rev. Lett. 743776–3779 (1995).
    [CrossRef] [PubMed]
  35. E. Constant, D. Garzella, P. Breger, E. Mvel, C. Dorrer, C. Le Blanc, F. Sali, and P. Agostini, “Optimizing high harmonic generation in absorbing gases: Model and experiment,” Phys. Rev. Lett. 82, 1668–1671 (1999).
    [CrossRef]
  36. R. J. Jones, K. D. Moll, M. J. Thorpe, and J. Ye, “Phase-coherent frequency combs in the vacuum ultraviolet via high-harmonic generation inside a femtosecond enhancement cavity,” Phys. Rev. Lett. 94, 193201 (2005).
    [CrossRef] [PubMed]
  37. C. Gohle, T. Udem, M. Herrmann, J. Rauschenberger, R. Holzwarth, H. A. Schuessler, F. Krausz, and T. W. Hansch, “A frequency comb in the extreme ultraviolet,” Nature 436, 234–237 (2005).
    [CrossRef] [PubMed]
  38. D. R. Carlson, J. Lee, J. Mongelli, E. M. Wright, and R. J. Jones, “Intracavity ionization and pulse formation in femtosecond enhancement cavities,” Opt. Lett. 36, 2991–2993 (2011).
    [CrossRef] [PubMed]

2012 (2)

S. M. Teichmann, D. R. Austin, P. Bates, S. Cousin, A. Grün, M. Clerici, A. Lotti, D. Faccio, P. DiTrapani, A. Couairon, and J. Biegert, “Trajectory interferences in a semi-infinite gas cell,” Laser Phys. Lett. 9, 207–211 (2012).
[CrossRef]

J. M. Brown, E. M. Wright, J. V. Moloney, and M. Kolesik, “On the relative roles of higher-order nonlinearity and ionization in ultrafast light-matter interactions,” Opt. Lett. 37, 1604–1606 (2012).
[CrossRef] [PubMed]

2011 (5)

D. R. Carlson, J. Lee, J. Mongelli, E. M. Wright, and R. J. Jones, “Intracavity ionization and pulse formation in femtosecond enhancement cavities,” Opt. Lett. 36, 2991–2993 (2011).
[CrossRef] [PubMed]

J. Lee, D. R. Carlson, and R. J. Jones, “Optimizing intracavity high harmonic generation for xuv fs frequency combs,” Opt. Express 19, 23315–23326 (2011).
[CrossRef] [PubMed]

E. A. Volkova, A. M. Popov, and O. V. Tikhonova, “Nonlinear polarization response of an atomic gas medium in the field of a high-intensity femtosecond laser pulse,” JETP Lett. 94, 519–524 (2011).
[CrossRef]

J. Brown, A. Lotti, A. Teleki, and M. Kolesik, “Exactly solvable model for non-linear light-matter interaction in an arbitrary time-dependent field,” Phys. Rev. A 84, 063424 (2011).
[CrossRef]

E. Lorin, S. Chelkowski, and A. D. Bandrauk, “The WASP model: A Micro-Macro system of Wave-Schrödinger-Plasma equations for filamentation,” Commun. Comput. Phys. 9, 406–440 (2011).

2010 (3)

T. Dziubak and J. Matulewski, “Stabilization of one-dimensional soft-core and singular model atoms,” Eur. Phys. J. D 59, 321–327 (2010).
[CrossRef]

A. Teleki, E. M. Wright, and M. Kolesik, “Microscopic model for the higher-order nonlinearity in optical filaments,” Phys. Rev. A 82, 065801 (2010).
[CrossRef]

F. Schapper, M. Holler, T. Auguste, A. Zaïr, M. Weger, P. Salières, L. Gallmann, and U. Keller, “Spatial finger-print of quantum path interferences in high order harmonic generation,” Opt. Express 18, 2987–2994 (2010).
[CrossRef] [PubMed]

2009 (1)

V. M. Villalba and L. A. González-Díaz, “Particle resonance in the dirac equation in the presence of a delta interaction and a perturbative hyperbolic potential,” Eur. Phys. J. C 61, 519–525 (2009).
[CrossRef]

2008 (2)

M. Gaarde, J. Tate, and K. Schafer, “Macroscopic aspects of attosecond pulse generation,” J. Phys. B: At. Mol. Opt. Phys. 41, 132001 (2008).
[CrossRef]

M. Nurhuda, A. Suda, and K. Midorikawa, “Generalization of the Kerr effect for high intensity, ultrashort laser pulses,” New J. Phys. 10, 053006 (2008).
[CrossRef]

2007 (2)

L. Bergé, S. Skupin, R. Nuter, J. Kasparian, and J. Wolf, “Ultrashort filaments of light in weakly ionized optically transparent media,” Rep. Prog. Phys. 70, 1633–1713 (2007).
[CrossRef]

A. Couairon and A. Mysyrowicz, “Femtosecond filamentation in transparent media,” Phys. Rep. 441, 47–189 (2007).
[CrossRef]

2005 (3)

H. Uncu, H. Erkol, E. Demiralp, and H. Beker, “Solutions of the Schrödinger equation for dirac delta decorated linear potential,” C. Eur. J. Phys. 3, 303–323 (2005).
[CrossRef]

R. J. Jones, K. D. Moll, M. J. Thorpe, and J. Ye, “Phase-coherent frequency combs in the vacuum ultraviolet via high-harmonic generation inside a femtosecond enhancement cavity,” Phys. Rev. Lett. 94, 193201 (2005).
[CrossRef] [PubMed]

C. Gohle, T. Udem, M. Herrmann, J. Rauschenberger, R. Holzwarth, H. A. Schuessler, F. Krausz, and T. W. Hansch, “A frequency comb in the extreme ultraviolet,” Nature 436, 234–237 (2005).
[CrossRef] [PubMed]

2004 (3)

M. Kolesik and J. V. Moloney, “Nonlinear optical pulse propagation simulation: From Maxwell’s to unidirectional equations,” Phys. Rev. E 70, 036604 (2004).
[CrossRef]

G. Álvarez and B. Sundaram, “Perturbation theory for the stark effect in a double quantum well,” J. Phys. A: Math. Gen. 37, 9735–9748 (2004).
[CrossRef]

G. V. Dunne and C. S. Gauthier, “Simple soluble molecular ionization model,” Phys. Rev. A 69, 053409 (2004).
[CrossRef]

2003 (1)

R. M. Cavalcanti, P. Giacconi, and R. Soldati, “Decay in a uniform field: an exactly solvable model,” J. Phys. A: Math. Gen. 36, 12065–12080 (2003).
[CrossRef]

2002 (1)

Z. X. Zhao, B. D. Esry, and C. D. Lin, “Boundary-free scaling calculation of the time-dependent Schrödinger equation for laser-atom interactions,” Phys. Rev. A 65, 023402 (2002).
[CrossRef]

2000 (1)

1999 (1)

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

1996 (1)

Q. Su, B. P. Irving, C. W. Johnson, and J. H. Eberly, “Stabilization of a one-dimensional short-range model atom in intense laser fields,” J. Phys. B: At. Mol. Opt. 29, 5755–5764 (1996).
[CrossRef]

1995 (1)

P. Salières, A. L’Huillier, and M. Lewenstein, “Coherence control of high-order harmonics,” Phys. Rev. Lett. 743776–3779 (1995).
[CrossRef] [PubMed]

1994 (2)

S. Geltman, “Short-pulse model-atom studies of ionization in intense laser fields,” J. Phys. B - At. Mol. Opt. 27, 1497–1514 (1994).
[CrossRef]

M. Lewenstein, P. Balcou, M. Y. Ivanov, A. L’Huillier, and P. B. Corkum, “Theory of high harmonics generation by low-frequency laser fields,” Phys. Rev. A 49, 2117–2132 (1994).
[CrossRef] [PubMed]

1993 (3)

A. Sanpera, Q. Su, and L. Roso-Franco, “Ionization suppression in a very-short-range potential,” Phys. Rev. A 47, 2312–2318 (1993).
[CrossRef] [PubMed]

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

K. J. 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]

1991 (2)

A. L’Huillier, K.J. Schafer, and K.C. Kulander, “High-order harmonic generation in Xenon at 1064 nm: The role of phase matching,” Phys. Rev. Lett. 66, 2200–2203 (1991).
[CrossRef]

Q. Su and J. Eberly, “Model atom for multiphoton physics,” Phys. Rev. A 44, 5997–6008 (1991).
[CrossRef] [PubMed]

1988 (1)

W. Elberfeld and M. Kleber, “Tunneling from an ultrathin quantum well in a strong electrostatic field: A comparison of different methods,” Z. Phys. B: Cond. Matt. 73, 23–32 (1988).
[CrossRef]

1982 (1)

G. P. Arrighini and M. Gavarini, “Ionization of a model atom by strong and superstrong electric fields,” Lett. Nuovo Cimento 33, 353–358 (1982).
[CrossRef]

1981 (1)

A. Bideau-Mehu, Y. Guern, R. Abjean, and A. Johannin-Gilles, “Measurement of refractive indices of neon, argon, krypton and xenon in the 253.7—140.4 nm wavelength range. Dispersion relations and estimated oscillator strengths of the resonance lines,” J. Quant. Spect. Rad. Transfer 25, 395–402 (1981).
[CrossRef]

1978 (1)

S. Geltman, “Ionisation dynamics of a model atom in an electrostatic field,” J. Phys. B: At. Mol. Phys. 11, 3323–3337 (1978).
[CrossRef]

Abjean, R.

A. Bideau-Mehu, Y. Guern, R. Abjean, and A. Johannin-Gilles, “Measurement of refractive indices of neon, argon, krypton and xenon in the 253.7—140.4 nm wavelength range. Dispersion relations and estimated oscillator strengths of the resonance lines,” J. Quant. Spect. Rad. Transfer 25, 395–402 (1981).
[CrossRef]

Agostini, P.

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

Álvarez, G.

G. Álvarez and B. Sundaram, “Perturbation theory for the stark effect in a double quantum well,” J. Phys. A: Math. Gen. 37, 9735–9748 (2004).
[CrossRef]

Arrighini, G. P.

G. P. Arrighini and M. Gavarini, “Ionization of a model atom by strong and superstrong electric fields,” Lett. Nuovo Cimento 33, 353–358 (1982).
[CrossRef]

Auguste, T.

Austin, D. R.

S. M. Teichmann, D. R. Austin, P. Bates, S. Cousin, A. Grün, M. Clerici, A. Lotti, D. Faccio, P. DiTrapani, A. Couairon, and J. Biegert, “Trajectory interferences in a semi-infinite gas cell,” Laser Phys. Lett. 9, 207–211 (2012).
[CrossRef]

Balcou, P.

M. Lewenstein, P. Balcou, M. Y. Ivanov, A. L’Huillier, and P. B. Corkum, “Theory of high harmonics generation by low-frequency laser fields,” Phys. Rev. A 49, 2117–2132 (1994).
[CrossRef] [PubMed]

Bandrauk, A. D.

E. Lorin, S. Chelkowski, and A. D. Bandrauk, “The WASP model: A Micro-Macro system of Wave-Schrödinger-Plasma equations for filamentation,” Commun. Comput. Phys. 9, 406–440 (2011).

Bates, P.

S. M. Teichmann, D. R. Austin, P. Bates, S. Cousin, A. Grün, M. Clerici, A. Lotti, D. Faccio, P. DiTrapani, A. Couairon, and J. Biegert, “Trajectory interferences in a semi-infinite gas cell,” Laser Phys. Lett. 9, 207–211 (2012).
[CrossRef]

Beker, H.

H. Uncu, H. Erkol, E. Demiralp, and H. Beker, “Solutions of the Schrödinger equation for dirac delta decorated linear potential,” C. Eur. J. Phys. 3, 303–323 (2005).
[CrossRef]

Bergé, L.

L. Bergé, S. Skupin, R. Nuter, J. Kasparian, and J. Wolf, “Ultrashort filaments of light in weakly ionized optically transparent media,” Rep. Prog. Phys. 70, 1633–1713 (2007).
[CrossRef]

Bideau-Mehu, A.

A. Bideau-Mehu, Y. Guern, R. Abjean, and A. Johannin-Gilles, “Measurement of refractive indices of neon, argon, krypton and xenon in the 253.7—140.4 nm wavelength range. Dispersion relations and estimated oscillator strengths of the resonance lines,” J. Quant. Spect. Rad. Transfer 25, 395–402 (1981).
[CrossRef]

Biegert, J.

S. M. Teichmann, D. R. Austin, P. Bates, S. Cousin, A. Grün, M. Clerici, A. Lotti, D. Faccio, P. DiTrapani, A. Couairon, and J. Biegert, “Trajectory interferences in a semi-infinite gas cell,” Laser Phys. Lett. 9, 207–211 (2012).
[CrossRef]

Breger, P.

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

Brown, J.

J. Brown, A. Lotti, A. Teleki, and M. Kolesik, “Exactly solvable model for non-linear light-matter interaction in an arbitrary time-dependent field,” Phys. Rev. A 84, 063424 (2011).
[CrossRef]

Brown, J. M.

Carlson, D. R.

Cavalcanti, R. M.

R. M. Cavalcanti, P. Giacconi, and R. Soldati, “Decay in a uniform field: an exactly solvable model,” J. Phys. A: Math. Gen. 36, 12065–12080 (2003).
[CrossRef]

Chelkowski, S.

E. Lorin, S. Chelkowski, and A. D. Bandrauk, “The WASP model: A Micro-Macro system of Wave-Schrödinger-Plasma equations for filamentation,” Commun. Comput. Phys. 9, 406–440 (2011).

Christov, I.

Clerici, M.

S. M. Teichmann, D. R. Austin, P. Bates, S. Cousin, A. Grün, M. Clerici, A. Lotti, D. Faccio, P. DiTrapani, A. Couairon, and J. Biegert, “Trajectory interferences in a semi-infinite gas cell,” Laser Phys. Lett. 9, 207–211 (2012).
[CrossRef]

Constant, E.

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

Corkum, P. B.

M. Lewenstein, P. Balcou, M. Y. Ivanov, A. L’Huillier, and P. B. Corkum, “Theory of high harmonics generation by low-frequency laser fields,” Phys. Rev. A 49, 2117–2132 (1994).
[CrossRef] [PubMed]

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

Couairon, A.

S. M. Teichmann, D. R. Austin, P. Bates, S. Cousin, A. Grün, M. Clerici, A. Lotti, D. Faccio, P. DiTrapani, A. Couairon, and J. Biegert, “Trajectory interferences in a semi-infinite gas cell,” Laser Phys. Lett. 9, 207–211 (2012).
[CrossRef]

A. Couairon and A. Mysyrowicz, “Femtosecond filamentation in transparent media,” Phys. Rep. 441, 47–189 (2007).
[CrossRef]

Cousin, S.

S. M. Teichmann, D. R. Austin, P. Bates, S. Cousin, A. Grün, M. Clerici, A. Lotti, D. Faccio, P. DiTrapani, A. Couairon, and J. Biegert, “Trajectory interferences in a semi-infinite gas cell,” Laser Phys. Lett. 9, 207–211 (2012).
[CrossRef]

Demiralp, E.

H. Uncu, H. Erkol, E. Demiralp, and H. Beker, “Solutions of the Schrödinger equation for dirac delta decorated linear potential,” C. Eur. J. Phys. 3, 303–323 (2005).
[CrossRef]

DiMauro, L. F.

K. J. 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]

DiTrapani, P.

S. M. Teichmann, D. R. Austin, P. Bates, S. Cousin, A. Grün, M. Clerici, A. Lotti, D. Faccio, P. DiTrapani, A. Couairon, and J. Biegert, “Trajectory interferences in a semi-infinite gas cell,” Laser Phys. Lett. 9, 207–211 (2012).
[CrossRef]

Dorrer, C.

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

Dunne, G. V.

G. V. Dunne and C. S. Gauthier, “Simple soluble molecular ionization model,” Phys. Rev. A 69, 053409 (2004).
[CrossRef]

Dziubak, T.

T. Dziubak and J. Matulewski, “Stabilization of one-dimensional soft-core and singular model atoms,” Eur. Phys. J. D 59, 321–327 (2010).
[CrossRef]

Eberly, J.

Q. Su and J. Eberly, “Model atom for multiphoton physics,” Phys. Rev. A 44, 5997–6008 (1991).
[CrossRef] [PubMed]

Eberly, J. H.

Q. Su, B. P. Irving, C. W. Johnson, and J. H. Eberly, “Stabilization of a one-dimensional short-range model atom in intense laser fields,” J. Phys. B: At. Mol. Opt. 29, 5755–5764 (1996).
[CrossRef]

Elberfeld, W.

W. Elberfeld and M. Kleber, “Tunneling from an ultrathin quantum well in a strong electrostatic field: A comparison of different methods,” Z. Phys. B: Cond. Matt. 73, 23–32 (1988).
[CrossRef]

Erkol, H.

H. Uncu, H. Erkol, E. Demiralp, and H. Beker, “Solutions of the Schrödinger equation for dirac delta decorated linear potential,” C. Eur. J. Phys. 3, 303–323 (2005).
[CrossRef]

Esry, B. D.

Z. X. Zhao, B. D. Esry, and C. D. Lin, “Boundary-free scaling calculation of the time-dependent Schrödinger equation for laser-atom interactions,” Phys. Rev. A 65, 023402 (2002).
[CrossRef]

Faccio, D.

S. M. Teichmann, D. R. Austin, P. Bates, S. Cousin, A. Grün, M. Clerici, A. Lotti, D. Faccio, P. DiTrapani, A. Couairon, and J. Biegert, “Trajectory interferences in a semi-infinite gas cell,” Laser Phys. Lett. 9, 207–211 (2012).
[CrossRef]

Gaarde, M.

M. Gaarde, J. Tate, and K. Schafer, “Macroscopic aspects of attosecond pulse generation,” J. Phys. B: At. Mol. Opt. Phys. 41, 132001 (2008).
[CrossRef]

Gallmann, L.

Garzella, D.

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

Gauthier, C. S.

G. V. Dunne and C. S. Gauthier, “Simple soluble molecular ionization model,” Phys. Rev. A 69, 053409 (2004).
[CrossRef]

Gavarini, M.

G. P. Arrighini and M. Gavarini, “Ionization of a model atom by strong and superstrong electric fields,” Lett. Nuovo Cimento 33, 353–358 (1982).
[CrossRef]

Geltman, S.

S. Geltman, “Short-pulse model-atom studies of ionization in intense laser fields,” J. Phys. B - At. Mol. Opt. 27, 1497–1514 (1994).
[CrossRef]

S. Geltman, “Ionisation dynamics of a model atom in an electrostatic field,” J. Phys. B: At. Mol. Phys. 11, 3323–3337 (1978).
[CrossRef]

Giacconi, P.

R. M. Cavalcanti, P. Giacconi, and R. Soldati, “Decay in a uniform field: an exactly solvable model,” J. Phys. A: Math. Gen. 36, 12065–12080 (2003).
[CrossRef]

Gohle, C.

C. Gohle, T. Udem, M. Herrmann, J. Rauschenberger, R. Holzwarth, H. A. Schuessler, F. Krausz, and T. W. Hansch, “A frequency comb in the extreme ultraviolet,” Nature 436, 234–237 (2005).
[CrossRef] [PubMed]

González-Díaz, L. A.

V. M. Villalba and L. A. González-Díaz, “Particle resonance in the dirac equation in the presence of a delta interaction and a perturbative hyperbolic potential,” Eur. Phys. J. C 61, 519–525 (2009).
[CrossRef]

Grün, A.

S. M. Teichmann, D. R. Austin, P. Bates, S. Cousin, A. Grün, M. Clerici, A. Lotti, D. Faccio, P. DiTrapani, A. Couairon, and J. Biegert, “Trajectory interferences in a semi-infinite gas cell,” Laser Phys. Lett. 9, 207–211 (2012).
[CrossRef]

Guern, Y.

A. Bideau-Mehu, Y. Guern, R. Abjean, and A. Johannin-Gilles, “Measurement of refractive indices of neon, argon, krypton and xenon in the 253.7—140.4 nm wavelength range. Dispersion relations and estimated oscillator strengths of the resonance lines,” J. Quant. Spect. Rad. Transfer 25, 395–402 (1981).
[CrossRef]

Hansch, T. W.

C. Gohle, T. Udem, M. Herrmann, J. Rauschenberger, R. Holzwarth, H. A. Schuessler, F. Krausz, and T. W. Hansch, “A frequency comb in the extreme ultraviolet,” Nature 436, 234–237 (2005).
[CrossRef] [PubMed]

Herrmann, M.

C. Gohle, T. Udem, M. Herrmann, J. Rauschenberger, R. Holzwarth, H. A. Schuessler, F. Krausz, and T. W. Hansch, “A frequency comb in the extreme ultraviolet,” Nature 436, 234–237 (2005).
[CrossRef] [PubMed]

Holler, M.

Holzwarth, R.

C. Gohle, T. Udem, M. Herrmann, J. Rauschenberger, R. Holzwarth, H. A. Schuessler, F. Krausz, and T. W. Hansch, “A frequency comb in the extreme ultraviolet,” Nature 436, 234–237 (2005).
[CrossRef] [PubMed]

Irving, B. P.

Q. Su, B. P. Irving, C. W. Johnson, and J. H. Eberly, “Stabilization of a one-dimensional short-range model atom in intense laser fields,” J. Phys. B: At. Mol. Opt. 29, 5755–5764 (1996).
[CrossRef]

Ivanov, M. Y.

M. Lewenstein, P. Balcou, M. Y. Ivanov, A. L’Huillier, and P. B. Corkum, “Theory of high harmonics generation by low-frequency laser fields,” Phys. Rev. A 49, 2117–2132 (1994).
[CrossRef] [PubMed]

Johannin-Gilles, A.

A. Bideau-Mehu, Y. Guern, R. Abjean, and A. Johannin-Gilles, “Measurement of refractive indices of neon, argon, krypton and xenon in the 253.7—140.4 nm wavelength range. Dispersion relations and estimated oscillator strengths of the resonance lines,” J. Quant. Spect. Rad. Transfer 25, 395–402 (1981).
[CrossRef]

Johnson, C. W.

Q. Su, B. P. Irving, C. W. Johnson, and J. H. Eberly, “Stabilization of a one-dimensional short-range model atom in intense laser fields,” J. Phys. B: At. Mol. Opt. 29, 5755–5764 (1996).
[CrossRef]

Jones, R. J.

Kasparian, J.

L. Bergé, S. Skupin, R. Nuter, J. Kasparian, and J. Wolf, “Ultrashort filaments of light in weakly ionized optically transparent media,” Rep. Prog. Phys. 70, 1633–1713 (2007).
[CrossRef]

Keller, U.

Kleber, M.

W. Elberfeld and M. Kleber, “Tunneling from an ultrathin quantum well in a strong electrostatic field: A comparison of different methods,” Z. Phys. B: Cond. Matt. 73, 23–32 (1988).
[CrossRef]

Kolesik, M.

J. M. Brown, E. M. Wright, J. V. Moloney, and M. Kolesik, “On the relative roles of higher-order nonlinearity and ionization in ultrafast light-matter interactions,” Opt. Lett. 37, 1604–1606 (2012).
[CrossRef] [PubMed]

J. Brown, A. Lotti, A. Teleki, and M. Kolesik, “Exactly solvable model for non-linear light-matter interaction in an arbitrary time-dependent field,” Phys. Rev. A 84, 063424 (2011).
[CrossRef]

A. Teleki, E. M. Wright, and M. Kolesik, “Microscopic model for the higher-order nonlinearity in optical filaments,” Phys. Rev. A 82, 065801 (2010).
[CrossRef]

M. Kolesik and J. V. Moloney, “Nonlinear optical pulse propagation simulation: From Maxwell’s to unidirectional equations,” Phys. Rev. E 70, 036604 (2004).
[CrossRef]

Krausz, F.

C. Gohle, T. Udem, M. Herrmann, J. Rauschenberger, R. Holzwarth, H. A. Schuessler, F. Krausz, and T. W. Hansch, “A frequency comb in the extreme ultraviolet,” Nature 436, 234–237 (2005).
[CrossRef] [PubMed]

Kulander, K. C.

K. J. 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]

Kulander, K.C.

A. L’Huillier, K.J. Schafer, and K.C. Kulander, “High-order harmonic generation in Xenon at 1064 nm: The role of phase matching,” Phys. Rev. Lett. 66, 2200–2203 (1991).
[CrossRef]

L’Huillier, A.

P. Salières, A. L’Huillier, and M. Lewenstein, “Coherence control of high-order harmonics,” Phys. Rev. Lett. 743776–3779 (1995).
[CrossRef] [PubMed]

M. Lewenstein, P. Balcou, M. Y. Ivanov, A. L’Huillier, and P. B. Corkum, “Theory of high harmonics generation by low-frequency laser fields,” Phys. Rev. A 49, 2117–2132 (1994).
[CrossRef] [PubMed]

A. L’Huillier, K.J. Schafer, and K.C. Kulander, “High-order harmonic generation in Xenon at 1064 nm: The role of phase matching,” Phys. Rev. Lett. 66, 2200–2203 (1991).
[CrossRef]

Le Blanc, C.

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

Lee, J.

Lewenstein, M.

P. Salières, A. L’Huillier, and M. Lewenstein, “Coherence control of high-order harmonics,” Phys. Rev. Lett. 743776–3779 (1995).
[CrossRef] [PubMed]

M. Lewenstein, P. Balcou, M. Y. Ivanov, A. L’Huillier, and P. B. Corkum, “Theory of high harmonics generation by low-frequency laser fields,” Phys. Rev. A 49, 2117–2132 (1994).
[CrossRef] [PubMed]

Lin, C. D.

Z. X. Zhao, B. D. Esry, and C. D. Lin, “Boundary-free scaling calculation of the time-dependent Schrödinger equation for laser-atom interactions,” Phys. Rev. A 65, 023402 (2002).
[CrossRef]

Lorin, E.

E. Lorin, S. Chelkowski, and A. D. Bandrauk, “The WASP model: A Micro-Macro system of Wave-Schrödinger-Plasma equations for filamentation,” Commun. Comput. Phys. 9, 406–440 (2011).

Lotti, A.

S. M. Teichmann, D. R. Austin, P. Bates, S. Cousin, A. Grün, M. Clerici, A. Lotti, D. Faccio, P. DiTrapani, A. Couairon, and J. Biegert, “Trajectory interferences in a semi-infinite gas cell,” Laser Phys. Lett. 9, 207–211 (2012).
[CrossRef]

J. Brown, A. Lotti, A. Teleki, and M. Kolesik, “Exactly solvable model for non-linear light-matter interaction in an arbitrary time-dependent field,” Phys. Rev. A 84, 063424 (2011).
[CrossRef]

Matulewski, J.

T. Dziubak and J. Matulewski, “Stabilization of one-dimensional soft-core and singular model atoms,” Eur. Phys. J. D 59, 321–327 (2010).
[CrossRef]

Midorikawa, K.

M. Nurhuda, A. Suda, and K. Midorikawa, “Generalization of the Kerr effect for high intensity, ultrashort laser pulses,” New J. Phys. 10, 053006 (2008).
[CrossRef]

Moll, K. D.

R. J. Jones, K. D. Moll, M. J. Thorpe, and J. Ye, “Phase-coherent frequency combs in the vacuum ultraviolet via high-harmonic generation inside a femtosecond enhancement cavity,” Phys. Rev. Lett. 94, 193201 (2005).
[CrossRef] [PubMed]

Moloney, J. V.

J. M. Brown, E. M. Wright, J. V. Moloney, and M. Kolesik, “On the relative roles of higher-order nonlinearity and ionization in ultrafast light-matter interactions,” Opt. Lett. 37, 1604–1606 (2012).
[CrossRef] [PubMed]

M. Kolesik and J. V. Moloney, “Nonlinear optical pulse propagation simulation: From Maxwell’s to unidirectional equations,” Phys. Rev. E 70, 036604 (2004).
[CrossRef]

Mongelli, J.

Mvel, E.

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

Mysyrowicz, A.

A. Couairon and A. Mysyrowicz, “Femtosecond filamentation in transparent media,” Phys. Rep. 441, 47–189 (2007).
[CrossRef]

Nurhuda, M.

M. Nurhuda, A. Suda, and K. Midorikawa, “Generalization of the Kerr effect for high intensity, ultrashort laser pulses,” New J. Phys. 10, 053006 (2008).
[CrossRef]

Nuter, R.

L. Bergé, S. Skupin, R. Nuter, J. Kasparian, and J. Wolf, “Ultrashort filaments of light in weakly ionized optically transparent media,” Rep. Prog. Phys. 70, 1633–1713 (2007).
[CrossRef]

Popov, A. M.

E. A. Volkova, A. M. Popov, and O. V. Tikhonova, “Nonlinear polarization response of an atomic gas medium in the field of a high-intensity femtosecond laser pulse,” JETP Lett. 94, 519–524 (2011).
[CrossRef]

Rauschenberger, J.

C. Gohle, T. Udem, M. Herrmann, J. Rauschenberger, R. Holzwarth, H. A. Schuessler, F. Krausz, and T. W. Hansch, “A frequency comb in the extreme ultraviolet,” Nature 436, 234–237 (2005).
[CrossRef] [PubMed]

Roso-Franco, L.

A. Sanpera, Q. Su, and L. Roso-Franco, “Ionization suppression in a very-short-range potential,” Phys. Rev. A 47, 2312–2318 (1993).
[CrossRef] [PubMed]

Sali, F.

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

Salières, P.

Sanpera, A.

A. Sanpera, Q. Su, and L. Roso-Franco, “Ionization suppression in a very-short-range potential,” Phys. Rev. A 47, 2312–2318 (1993).
[CrossRef] [PubMed]

Schafer, K.

M. Gaarde, J. Tate, and K. Schafer, “Macroscopic aspects of attosecond pulse generation,” J. Phys. B: At. Mol. Opt. Phys. 41, 132001 (2008).
[CrossRef]

Schafer, K. J.

K. J. 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]

Schafer, K.J.

A. L’Huillier, K.J. Schafer, and K.C. Kulander, “High-order harmonic generation in Xenon at 1064 nm: The role of phase matching,” Phys. Rev. Lett. 66, 2200–2203 (1991).
[CrossRef]

Schapper, F.

Schuessler, H. A.

C. Gohle, T. Udem, M. Herrmann, J. Rauschenberger, R. Holzwarth, H. A. Schuessler, F. Krausz, and T. W. Hansch, “A frequency comb in the extreme ultraviolet,” Nature 436, 234–237 (2005).
[CrossRef] [PubMed]

Skupin, S.

L. Bergé, S. Skupin, R. Nuter, J. Kasparian, and J. Wolf, “Ultrashort filaments of light in weakly ionized optically transparent media,” Rep. Prog. Phys. 70, 1633–1713 (2007).
[CrossRef]

Soldati, R.

R. M. Cavalcanti, P. Giacconi, and R. Soldati, “Decay in a uniform field: an exactly solvable model,” J. Phys. A: Math. Gen. 36, 12065–12080 (2003).
[CrossRef]

Su, Q.

Q. Su, B. P. Irving, C. W. Johnson, and J. H. Eberly, “Stabilization of a one-dimensional short-range model atom in intense laser fields,” J. Phys. B: At. Mol. Opt. 29, 5755–5764 (1996).
[CrossRef]

A. Sanpera, Q. Su, and L. Roso-Franco, “Ionization suppression in a very-short-range potential,” Phys. Rev. A 47, 2312–2318 (1993).
[CrossRef] [PubMed]

Q. Su and J. Eberly, “Model atom for multiphoton physics,” Phys. Rev. A 44, 5997–6008 (1991).
[CrossRef] [PubMed]

Suda, A.

M. Nurhuda, A. Suda, and K. Midorikawa, “Generalization of the Kerr effect for high intensity, ultrashort laser pulses,” New J. Phys. 10, 053006 (2008).
[CrossRef]

Sundaram, B.

G. Álvarez and B. Sundaram, “Perturbation theory for the stark effect in a double quantum well,” J. Phys. A: Math. Gen. 37, 9735–9748 (2004).
[CrossRef]

Tate, J.

M. Gaarde, J. Tate, and K. Schafer, “Macroscopic aspects of attosecond pulse generation,” J. Phys. B: At. Mol. Opt. Phys. 41, 132001 (2008).
[CrossRef]

Teichmann, S. M.

S. M. Teichmann, D. R. Austin, P. Bates, S. Cousin, A. Grün, M. Clerici, A. Lotti, D. Faccio, P. DiTrapani, A. Couairon, and J. Biegert, “Trajectory interferences in a semi-infinite gas cell,” Laser Phys. Lett. 9, 207–211 (2012).
[CrossRef]

Teleki, A.

J. Brown, A. Lotti, A. Teleki, and M. Kolesik, “Exactly solvable model for non-linear light-matter interaction in an arbitrary time-dependent field,” Phys. Rev. A 84, 063424 (2011).
[CrossRef]

A. Teleki, E. M. Wright, and M. Kolesik, “Microscopic model for the higher-order nonlinearity in optical filaments,” Phys. Rev. A 82, 065801 (2010).
[CrossRef]

Thorpe, M. J.

R. J. Jones, K. D. Moll, M. J. Thorpe, and J. Ye, “Phase-coherent frequency combs in the vacuum ultraviolet via high-harmonic generation inside a femtosecond enhancement cavity,” Phys. Rev. Lett. 94, 193201 (2005).
[CrossRef] [PubMed]

Tikhonova, O. V.

E. A. Volkova, A. M. Popov, and O. V. Tikhonova, “Nonlinear polarization response of an atomic gas medium in the field of a high-intensity femtosecond laser pulse,” JETP Lett. 94, 519–524 (2011).
[CrossRef]

Udem, T.

C. Gohle, T. Udem, M. Herrmann, J. Rauschenberger, R. Holzwarth, H. A. Schuessler, F. Krausz, and T. W. Hansch, “A frequency comb in the extreme ultraviolet,” Nature 436, 234–237 (2005).
[CrossRef] [PubMed]

Uncu, H.

H. Uncu, H. Erkol, E. Demiralp, and H. Beker, “Solutions of the Schrödinger equation for dirac delta decorated linear potential,” C. Eur. J. Phys. 3, 303–323 (2005).
[CrossRef]

Villalba, V. M.

V. M. Villalba and L. A. González-Díaz, “Particle resonance in the dirac equation in the presence of a delta interaction and a perturbative hyperbolic potential,” Eur. Phys. J. C 61, 519–525 (2009).
[CrossRef]

Volkova, E. A.

E. A. Volkova, A. M. Popov, and O. V. Tikhonova, “Nonlinear polarization response of an atomic gas medium in the field of a high-intensity femtosecond laser pulse,” JETP Lett. 94, 519–524 (2011).
[CrossRef]

Weger, M.

Wolf, J.

L. Bergé, S. Skupin, R. Nuter, J. Kasparian, and J. Wolf, “Ultrashort filaments of light in weakly ionized optically transparent media,” Rep. Prog. Phys. 70, 1633–1713 (2007).
[CrossRef]

Wright, E. M.

Yang, B.

K. J. 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]

Ye, J.

R. J. Jones, K. D. Moll, M. J. Thorpe, and J. Ye, “Phase-coherent frequency combs in the vacuum ultraviolet via high-harmonic generation inside a femtosecond enhancement cavity,” Phys. Rev. Lett. 94, 193201 (2005).
[CrossRef] [PubMed]

Zaïr, A.

Zhao, Z. X.

Z. X. Zhao, B. D. Esry, and C. D. Lin, “Boundary-free scaling calculation of the time-dependent Schrödinger equation for laser-atom interactions,” Phys. Rev. A 65, 023402 (2002).
[CrossRef]

C. Eur. J. Phys. (1)

H. Uncu, H. Erkol, E. Demiralp, and H. Beker, “Solutions of the Schrödinger equation for dirac delta decorated linear potential,” C. Eur. J. Phys. 3, 303–323 (2005).
[CrossRef]

Commun. Comput. Phys. (1)

E. Lorin, S. Chelkowski, and A. D. Bandrauk, “The WASP model: A Micro-Macro system of Wave-Schrödinger-Plasma equations for filamentation,” Commun. Comput. Phys. 9, 406–440 (2011).

Eur. Phys. J. C (1)

V. M. Villalba and L. A. González-Díaz, “Particle resonance in the dirac equation in the presence of a delta interaction and a perturbative hyperbolic potential,” Eur. Phys. J. C 61, 519–525 (2009).
[CrossRef]

Eur. Phys. J. D (1)

T. Dziubak and J. Matulewski, “Stabilization of one-dimensional soft-core and singular model atoms,” Eur. Phys. J. D 59, 321–327 (2010).
[CrossRef]

J. Phys. A: Math. Gen. (2)

R. M. Cavalcanti, P. Giacconi, and R. Soldati, “Decay in a uniform field: an exactly solvable model,” J. Phys. A: Math. Gen. 36, 12065–12080 (2003).
[CrossRef]

G. Álvarez and B. Sundaram, “Perturbation theory for the stark effect in a double quantum well,” J. Phys. A: Math. Gen. 37, 9735–9748 (2004).
[CrossRef]

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

S. Geltman, “Short-pulse model-atom studies of ionization in intense laser fields,” J. Phys. B - At. Mol. Opt. 27, 1497–1514 (1994).
[CrossRef]

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

Q. Su, B. P. Irving, C. W. Johnson, and J. H. Eberly, “Stabilization of a one-dimensional short-range model atom in intense laser fields,” J. Phys. B: At. Mol. Opt. 29, 5755–5764 (1996).
[CrossRef]

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

M. Gaarde, J. Tate, and K. Schafer, “Macroscopic aspects of attosecond pulse generation,” J. Phys. B: At. Mol. Opt. Phys. 41, 132001 (2008).
[CrossRef]

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

S. Geltman, “Ionisation dynamics of a model atom in an electrostatic field,” J. Phys. B: At. Mol. Phys. 11, 3323–3337 (1978).
[CrossRef]

J. Quant. Spect. Rad. Transfer (1)

A. Bideau-Mehu, Y. Guern, R. Abjean, and A. Johannin-Gilles, “Measurement of refractive indices of neon, argon, krypton and xenon in the 253.7—140.4 nm wavelength range. Dispersion relations and estimated oscillator strengths of the resonance lines,” J. Quant. Spect. Rad. Transfer 25, 395–402 (1981).
[CrossRef]

JETP Lett. (1)

E. A. Volkova, A. M. Popov, and O. V. Tikhonova, “Nonlinear polarization response of an atomic gas medium in the field of a high-intensity femtosecond laser pulse,” JETP Lett. 94, 519–524 (2011).
[CrossRef]

Laser Phys. Lett. (1)

S. M. Teichmann, D. R. Austin, P. Bates, S. Cousin, A. Grün, M. Clerici, A. Lotti, D. Faccio, P. DiTrapani, A. Couairon, and J. Biegert, “Trajectory interferences in a semi-infinite gas cell,” Laser Phys. Lett. 9, 207–211 (2012).
[CrossRef]

Lett. Nuovo Cimento (1)

G. P. Arrighini and M. Gavarini, “Ionization of a model atom by strong and superstrong electric fields,” Lett. Nuovo Cimento 33, 353–358 (1982).
[CrossRef]

Nature (1)

C. Gohle, T. Udem, M. Herrmann, J. Rauschenberger, R. Holzwarth, H. A. Schuessler, F. Krausz, and T. W. Hansch, “A frequency comb in the extreme ultraviolet,” Nature 436, 234–237 (2005).
[CrossRef] [PubMed]

New J. Phys. (1)

M. Nurhuda, A. Suda, and K. Midorikawa, “Generalization of the Kerr effect for high intensity, ultrashort laser pulses,” New J. Phys. 10, 053006 (2008).
[CrossRef]

Opt. Express (3)

Opt. Lett. (2)

Phys. Rep. (1)

A. Couairon and A. Mysyrowicz, “Femtosecond filamentation in transparent media,” Phys. Rep. 441, 47–189 (2007).
[CrossRef]

Phys. Rev. A (7)

M. Lewenstein, P. Balcou, M. Y. Ivanov, A. L’Huillier, and P. B. Corkum, “Theory of high harmonics generation by low-frequency laser fields,” Phys. Rev. A 49, 2117–2132 (1994).
[CrossRef] [PubMed]

Z. X. Zhao, B. D. Esry, and C. D. Lin, “Boundary-free scaling calculation of the time-dependent Schrödinger equation for laser-atom interactions,” Phys. Rev. A 65, 023402 (2002).
[CrossRef]

A. Teleki, E. M. Wright, and M. Kolesik, “Microscopic model for the higher-order nonlinearity in optical filaments,” Phys. Rev. A 82, 065801 (2010).
[CrossRef]

A. Sanpera, Q. Su, and L. Roso-Franco, “Ionization suppression in a very-short-range potential,” Phys. Rev. A 47, 2312–2318 (1993).
[CrossRef] [PubMed]

Q. Su and J. Eberly, “Model atom for multiphoton physics,” Phys. Rev. A 44, 5997–6008 (1991).
[CrossRef] [PubMed]

G. V. Dunne and C. S. Gauthier, “Simple soluble molecular ionization model,” Phys. Rev. A 69, 053409 (2004).
[CrossRef]

J. Brown, A. Lotti, A. Teleki, and M. Kolesik, “Exactly solvable model for non-linear light-matter interaction in an arbitrary time-dependent field,” Phys. Rev. A 84, 063424 (2011).
[CrossRef]

Phys. Rev. E (1)

M. Kolesik and J. V. Moloney, “Nonlinear optical pulse propagation simulation: From Maxwell’s to unidirectional equations,” Phys. Rev. E 70, 036604 (2004).
[CrossRef]

Phys. Rev. Lett (1)

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

Phys. Rev. Lett. (5)

K. J. 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]

A. L’Huillier, K.J. Schafer, and K.C. Kulander, “High-order harmonic generation in Xenon at 1064 nm: The role of phase matching,” Phys. Rev. Lett. 66, 2200–2203 (1991).
[CrossRef]

P. Salières, A. L’Huillier, and M. Lewenstein, “Coherence control of high-order harmonics,” Phys. Rev. Lett. 743776–3779 (1995).
[CrossRef] [PubMed]

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

R. J. Jones, K. D. Moll, M. J. Thorpe, and J. Ye, “Phase-coherent frequency combs in the vacuum ultraviolet via high-harmonic generation inside a femtosecond enhancement cavity,” Phys. Rev. Lett. 94, 193201 (2005).
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[CrossRef]

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Figures (9)

Fig. 1
Fig. 1

Real (dark lines) and imaginary (red line) parts of the linear susceptibility of Xenon as employed in the numerical simulations in this paper. The vertical dashed lines mark the fundamental wavelength of the fundamental field at 800 nm, and several of its harmonic are also indicated.

Fig. 2
Fig. 2

High-harmonics in the spectrum of the dipole moment induced by a pulse at λ = 800nm. The intensity was 1.5 × 1018W/m2, kept constant over duration of ten optical cycles. The arrow marks the location of cut-off energy calculated for these conditions.

Fig. 3
Fig. 3

For the sake of comparison, we examine four cases of focusing geometry. Here, A and B denote geometric focus after and before the center of the gas jet. The nominal maximal intensity is kept constant.

Fig. 4
Fig. 4

Angularly resolved spectra of the 9th, 11th, and 13th harmonics at three different propagation distances through the gas jet for w0 = 7 μm. Each panel shows a frequency region (vertical axis) corresponding to one half of the harmonic order, centered at the given harmonic frequency. The horizontal extent of each panel corresponds to the transverse wave-number and thus represents the angle of propagation.

Fig. 5
Fig. 5

Evolution of the conversion efficiency versus propagation distance in the gas jet for two different beam focusing conditions. The gas density is a smooth flat-top profile with a roughly constant pressure region between 100 and 300 micron. The pulse intensities are comparable in both cases, with their maxima approximately located at z = 300 and z = 100 micron in case a) and b), respectively.

Fig. 6
Fig. 6

On-axis and off-axis propagating harmonic components exhibit different phase-matching behavior. The top panel show the angularly resolved spectra of the 9th harmonic at the beginning, in the middle and at the end of the gas jet corresponding to case (b) from Fig. 4. Energy accumulates preferentially in the off-axis (conical) components during the propagation in the center of the jet. Later, the on-axis component becomes relatively stronger, as the pulse starts to exit from the jet and the gas pressure it experiences starts to decrease. This behavior correlates with the evolution of the energy accumulated in the 9th harmonic (shown as the red line in the lower panel). Note that this is the harmonic which suffers the strongest losses.

Fig. 7
Fig. 7

As expected, for a wider beam (w0 = 15μm), the precise location of the beam focus is less important. Angularly resolved spectra are shown for the 9th, 11th, and 13th harmonics at three different propagation distances through the gas jet. Each panel shows a frequency region (vertical axis) corresponding to one half of the harmonic order, centered at the given harmonic frequency. The horizontal extent of each panel corresponds to the transverse wave-number and thus represents the angle of propagation.

Fig. 8
Fig. 8

Evolution of the conversion efficiency versus propagation distance in the gas jet for two different beam focusing conditions. The gas density is a smooth flat-top profile with a roughly constant pressure region between 100 and 300 micron. The pulse intensities are comparable in both cases, with their maxima approximately located at z = 300 and z = 100 micron in case a) and b), respectively.

Fig. 9
Fig. 9

Harmonic spectrum calculated (left panels) for conditions reflecting those in the femtosecond enhancement cavity. Dashed and full line compare results for simulation with and without inclusion of losses. Left most panel: beam focus at the “entrance” into the gas jet. Middle panel: beam focus at the “exit” from the gas jet. Experimental spectrum shown in the right panel, with an account for the grating efficiency.

Equations (11)

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z E k ( ω , z ) = i k z E k ( ω , z ) + i ω 2 2 ε 0 c 2 k z P k ( ω , z , { E } ) ω 2 ε 0 c 2 k z J k ( ω , z , { E } ) ,
k z ( ω , k ) = ω 2 ( 1 + χ ( ω ) ) / c 2 k 2 .
[ i τ + 1 2 s 2 + B δ ( s ) s F ( τ ) ] ψ ( s , τ ) = 0.
J ( τ ) d s ψ * ( s , τ ) ( i s ) ψ ( s , τ ) ,
P ( t ) = 2 ε 0 n b n ¯ 2 E 2 ( t ) E ( t ) ,
p c l ( t ) = 0 t F ( τ ) d τ , x c l ( t ) = 0 t p c l ( τ ) d τ .
A ( t ) = ψ R ( x c l ( t ) , t ) + i B 2 π i 0 t d t e + i B 2 2 ( t t ) t t exp [ i ( x c l ( t ) x c l ( t ) ) 2 2 ( t t ) ] A ( t ) ,
ψ R ( x , t ) e + B x 2 erfc ( i B t + x 2 i t ) + e B x 2 erfc ( i B t x 2 i t ) .
J ( n l ) = J S S ( n l ) + J F S ( n l ) ,
J S S ( n l ) = 2 Im { 0 t d t 1 0 t 1 d t 2 ( i ) 3 2 B 3 2 π e + i B 2 2 ( t 2 t 1 ) t 1 t 2 [ e i [ x c l ( t 1 ) x c l ( t 2 ) ] 2 2 ( t 1 t 2 ) A * ( t 1 ) A ( t 2 ) 1 ] x c l ( t 1 ) x c l ( t 2 ) t 1 t 2 }
J F S ( n l ) = Im { i B 3 0 t d t 1 A * ( t 1 ) e + B x c l ( t 1 ) erfc ( ( 1 + i ) ( B t 1 i x c l ( t 1 ) ) 2 t 1 ) } Im { i B 3 0 t d t 1 A * ( t 1 ) e B x c l ( t 1 ) erfc ( ( 1 + i ) ( B t 1 + i x c l ( t 1 ) ) 2 t 1 ) } Im { 2 B 3 0 t d t 1 x c l ( t 1 ) ( i B erfc ( ( 1 + i ) B t 1 2 ) 1 + i π t 1 e i B 2 2 t 1 ) }

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