Abstract

In this paper we propose and demonstrate that the ultrafast nonlinear optical response of atoms may be accurately calculated in terms of metastable states obtained as solutions of the stationary Schrödinger equation including the quasi-static applied electric field. We first develop the approach in the context of an exactly soluble one-dimensional atomic model with delta-function potential, as this allows comparison between the exact ultrafast nonlinear optical response and our approximate approach, both in adiabatic approximation and beyond. These ideas are then applied to a three-dimensional hydrogen-like atom and yield similar excellent agreement between the metastable state approach and simulations of the Schrödinger equation for off-resonant excitation. Finally, our approach yields a model for the ultrafast nonlinear optical response with no free parameters. It can potentially replace the light–matter interaction treatment currently used in optical filamentation, and we present a numerical example of application to femtosecond pulse propagation.

© 2014 Optical Society of America

Full Article  |  PDF Article

Corrections

M. Kolesik, J. M. Brown, A. Teleki, P. Jakobsen, J. V. Moloney, and E. M. Wright, "Metastable electronic states and nonlinear response for high-intensity optical pulses: erratum," Optica 2, 509-509 (2015)
http://proxy.osapublishing.org/optica/abstract.cfm?uri=optica-2-5-509

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References

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  1. T. Popmintchev, M.-C. Chen, P. Arpin, M. M. Murnane, H. C. Kapteyn, “The attosecond nonlinear optics of bright coherent x-ray generation,” Nat. Photonics 4, 822–832 (2010).
    [Crossref]
  2. F. Krausz, M. Ivanov, “Attosecond physics,” Rev. Mod. Phys. 81, 163–234 (2009).
    [Crossref]
  3. A. Couairon, A. Mysyrowicz, “Femtosecond filamentation in transparent media,” Phys. Rep. 441, 47–189 (2007).
    [Crossref]
  4. L. Bergé, S. Skupin, R. Nuter, J. Kasparian, J.-P. Wolf, “Ultrashort filaments of light in weakly ionized optically transparent media,” Rep. Prog. Phys. 70, 1633–1713 (2007).
    [Crossref]
  5. M. Nurhuda, A. Suda, 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, 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. E. A. Volkova, A. M. Popov, O. V. Tikhonova, “Polarization response of a gas medium in the field of a high-intensity ultrashort laser pulse: high order Kerr nonlinearities or plasma electron component?” Quantum Electron. 42, 680–686 (2012).
    [Crossref]
  8. A. M. Popov, O. V. Tikhonova, E. A. Volkova, “Polarization response of an atomic system in a strong mid-IR field,” Laser Phys. Lett. 10, 085303 (2013).
    [Crossref]
  9. P. Béjot, E. Cormier, E. Hertz, B. Lavorel, J. Kasparian, J.-P. Wolf, O. Faucher, “High-field quantum calculation reveals time-dependent negative Kerr contribution,” Phys. Rev. Lett. 110, 043902 (2013).
    [Crossref]
  10. C. Köhler, R. Guichard, E. Lorin, S. Chelkowski, A. D. Bandrauk, L. Bergé, S. Skupin, “Saturation of the nonlinear refractive index in atomic gases,” Phys. Rev. A 87, 043811 (2013).
    [Crossref]
  11. J. M. Brown, A. Lotti, A. Teleki, M. Kolesik, “Exactly solvable model for non-linear light-matter interaction in an arbitrary time-dependent field,” Phys. Rev. A 84, 063424 (2011).
    [Crossref]
  12. T. C. Rensink, T. M. Antonsen, J. P. Palastro, D. F. Gordon, “Model for atomic dielectric response in strong, time-dependent laser fields,” Phys. Rev. A 89, 033418 (2014).
    [Crossref]
  13. E. Lorin, S. Chelkowski, A. Bandrauk, “The WASP model: a micro–macro system of wave-Schrödinger-plasma equations for filamentation,” Commun. Comput. Phys. 9, 406–440 (2011).
  14. E. Lorin, S. Chelkowski, A. Bandrauk, “Maxwell-Schrödinger-Plasma (MASP) model for laser-molecule interactions: towards an understanding of filamentation with intense ultrashort pulses,” Physica D 241, 1059–1071 (2012).
    [Crossref]
  15. O. I. Tolstikhin, T. Morishita, S. Watanabe, “Adiabatic theory of ionization of atoms by intense laser pulses: one-dimensional zero-range-potential model,” Phys. Rev. A 81, 033415 (2010).
    [Crossref]
  16. R. M. Cavalcanti, P. Giacconi, R. Soldati, “Decay in a uniform field: an exactly solvable model,” J. Phys. A 36, 12065–12080 (2003).
    [Crossref]
  17. T. Berggren, “Expectation value of an operator in a resonant state,” Phys. Lett. B 373, 1–4 (1996).
    [Crossref]
  18. L. Hamonou, T. Morishita, O. I. Tolstikhin, S. Watanabe, “Siegert-state method for ionization of molecules in strong field,” J. Phys. Conf. Ser. 388, 032030 (2012).
    [Crossref]
  19. T. Berggren, “On the use of resonant states in eigenfunction expansions of scattering and reaction amplitudes,” Nucl. Phys. A 109, 265–287 (1968).
    [Crossref]
  20. A. Bahl, A. Teleki, P. Jakobsen, E. M. Wright, M. Kolesik, “Reflectionless beam propagation on a piecewise linear complex domain,” J. Lightwave Technol. 32, 3670–3676 (2014).
    [Crossref]
  21. D. C. Brody, “Biorthogonal quantum mechanics,” J. Phys. A 47, 035305 (2014).
    [Crossref]
  22. A. Couairon, E. Brambilla, T. Corti, D. Majus, O. J. Ramirez-Gongora, M. Kolesik, “Practitioner’s guide to laser pulse propagation models and simulation,” Eur. J. Phys. Special Topics 199, 5–76 (2011).
  23. J. Andreasen, M. Kolesik, “Nonlinear propagation of light in structured media: generalized unidirectional pulse propagation equations,” Phys. Rev. E 86, 036706 (2012).
    [Crossref]
  24. J. K. Wahlstrand, Y.-H. Cheng, H. M. Milchberg, “Absolute measurement of the transient optical nonlinearity in N2, O2, N2O, and Ar,” Phys. Rev. A 85, 043820 (2012).
  25. Y.-H. Chen, S. Varma, T. M. Antonsen, H. M. Milchberg, “Direct measurement of the electron density of extended femtosecond laser pulse-induced filaments,” Phys. Rev. Lett. 105, 215005 (2010).
    [Crossref]

2014 (3)

T. C. Rensink, T. M. Antonsen, J. P. Palastro, D. F. Gordon, “Model for atomic dielectric response in strong, time-dependent laser fields,” Phys. Rev. A 89, 033418 (2014).
[Crossref]

D. C. Brody, “Biorthogonal quantum mechanics,” J. Phys. A 47, 035305 (2014).
[Crossref]

A. Bahl, A. Teleki, P. Jakobsen, E. M. Wright, M. Kolesik, “Reflectionless beam propagation on a piecewise linear complex domain,” J. Lightwave Technol. 32, 3670–3676 (2014).
[Crossref]

2013 (3)

A. M. Popov, O. V. Tikhonova, E. A. Volkova, “Polarization response of an atomic system in a strong mid-IR field,” Laser Phys. Lett. 10, 085303 (2013).
[Crossref]

P. Béjot, E. Cormier, E. Hertz, B. Lavorel, J. Kasparian, J.-P. Wolf, O. Faucher, “High-field quantum calculation reveals time-dependent negative Kerr contribution,” Phys. Rev. Lett. 110, 043902 (2013).
[Crossref]

C. Köhler, R. Guichard, E. Lorin, S. Chelkowski, A. D. Bandrauk, L. Bergé, S. Skupin, “Saturation of the nonlinear refractive index in atomic gases,” Phys. Rev. A 87, 043811 (2013).
[Crossref]

2012 (5)

E. Lorin, S. Chelkowski, A. Bandrauk, “Maxwell-Schrödinger-Plasma (MASP) model for laser-molecule interactions: towards an understanding of filamentation with intense ultrashort pulses,” Physica D 241, 1059–1071 (2012).
[Crossref]

E. A. Volkova, A. M. Popov, O. V. Tikhonova, “Polarization response of a gas medium in the field of a high-intensity ultrashort laser pulse: high order Kerr nonlinearities or plasma electron component?” Quantum Electron. 42, 680–686 (2012).
[Crossref]

J. Andreasen, M. Kolesik, “Nonlinear propagation of light in structured media: generalized unidirectional pulse propagation equations,” Phys. Rev. E 86, 036706 (2012).
[Crossref]

J. K. Wahlstrand, Y.-H. Cheng, H. M. Milchberg, “Absolute measurement of the transient optical nonlinearity in N2, O2, N2O, and Ar,” Phys. Rev. A 85, 043820 (2012).

L. Hamonou, T. Morishita, O. I. Tolstikhin, S. Watanabe, “Siegert-state method for ionization of molecules in strong field,” J. Phys. Conf. Ser. 388, 032030 (2012).
[Crossref]

2011 (4)

A. Couairon, E. Brambilla, T. Corti, D. Majus, O. J. Ramirez-Gongora, M. Kolesik, “Practitioner’s guide to laser pulse propagation models and simulation,” Eur. J. Phys. Special Topics 199, 5–76 (2011).

E. Lorin, S. Chelkowski, A. Bandrauk, “The WASP model: a micro–macro system of wave-Schrödinger-plasma equations for filamentation,” Commun. Comput. Phys. 9, 406–440 (2011).

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

2010 (3)

T. Popmintchev, M.-C. Chen, P. Arpin, M. M. Murnane, H. C. Kapteyn, “The attosecond nonlinear optics of bright coherent x-ray generation,” Nat. Photonics 4, 822–832 (2010).
[Crossref]

O. I. Tolstikhin, T. Morishita, S. Watanabe, “Adiabatic theory of ionization of atoms by intense laser pulses: one-dimensional zero-range-potential model,” Phys. Rev. A 81, 033415 (2010).
[Crossref]

Y.-H. Chen, S. Varma, T. M. Antonsen, H. M. Milchberg, “Direct measurement of the electron density of extended femtosecond laser pulse-induced filaments,” Phys. Rev. Lett. 105, 215005 (2010).
[Crossref]

2009 (1)

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

2008 (1)

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

2007 (2)

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

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

2003 (1)

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

1996 (1)

T. Berggren, “Expectation value of an operator in a resonant state,” Phys. Lett. B 373, 1–4 (1996).
[Crossref]

1968 (1)

T. Berggren, “On the use of resonant states in eigenfunction expansions of scattering and reaction amplitudes,” Nucl. Phys. A 109, 265–287 (1968).
[Crossref]

Andreasen, J.

J. Andreasen, M. Kolesik, “Nonlinear propagation of light in structured media: generalized unidirectional pulse propagation equations,” Phys. Rev. E 86, 036706 (2012).
[Crossref]

Antonsen, T. M.

T. C. Rensink, T. M. Antonsen, J. P. Palastro, D. F. Gordon, “Model for atomic dielectric response in strong, time-dependent laser fields,” Phys. Rev. A 89, 033418 (2014).
[Crossref]

Y.-H. Chen, S. Varma, T. M. Antonsen, H. M. Milchberg, “Direct measurement of the electron density of extended femtosecond laser pulse-induced filaments,” Phys. Rev. Lett. 105, 215005 (2010).
[Crossref]

Arpin, P.

T. Popmintchev, M.-C. Chen, P. Arpin, M. M. Murnane, H. C. Kapteyn, “The attosecond nonlinear optics of bright coherent x-ray generation,” Nat. Photonics 4, 822–832 (2010).
[Crossref]

Bahl, A.

Bandrauk, A.

E. Lorin, S. Chelkowski, A. Bandrauk, “Maxwell-Schrödinger-Plasma (MASP) model for laser-molecule interactions: towards an understanding of filamentation with intense ultrashort pulses,” Physica D 241, 1059–1071 (2012).
[Crossref]

E. Lorin, S. Chelkowski, A. Bandrauk, “The WASP model: a micro–macro system of wave-Schrödinger-plasma equations for filamentation,” Commun. Comput. Phys. 9, 406–440 (2011).

Bandrauk, A. D.

C. Köhler, R. Guichard, E. Lorin, S. Chelkowski, A. D. Bandrauk, L. Bergé, S. Skupin, “Saturation of the nonlinear refractive index in atomic gases,” Phys. Rev. A 87, 043811 (2013).
[Crossref]

Béjot, P.

P. Béjot, E. Cormier, E. Hertz, B. Lavorel, J. Kasparian, J.-P. Wolf, O. Faucher, “High-field quantum calculation reveals time-dependent negative Kerr contribution,” Phys. Rev. Lett. 110, 043902 (2013).
[Crossref]

Bergé, L.

C. Köhler, R. Guichard, E. Lorin, S. Chelkowski, A. D. Bandrauk, L. Bergé, S. Skupin, “Saturation of the nonlinear refractive index in atomic gases,” Phys. Rev. A 87, 043811 (2013).
[Crossref]

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

Berggren, T.

T. Berggren, “Expectation value of an operator in a resonant state,” Phys. Lett. B 373, 1–4 (1996).
[Crossref]

T. Berggren, “On the use of resonant states in eigenfunction expansions of scattering and reaction amplitudes,” Nucl. Phys. A 109, 265–287 (1968).
[Crossref]

Brambilla, E.

A. Couairon, E. Brambilla, T. Corti, D. Majus, O. J. Ramirez-Gongora, M. Kolesik, “Practitioner’s guide to laser pulse propagation models and simulation,” Eur. J. Phys. Special Topics 199, 5–76 (2011).

Brody, D. C.

D. C. Brody, “Biorthogonal quantum mechanics,” J. Phys. A 47, 035305 (2014).
[Crossref]

Brown, J. M.

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

Cavalcanti, R. M.

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

Chelkowski, S.

C. Köhler, R. Guichard, E. Lorin, S. Chelkowski, A. D. Bandrauk, L. Bergé, S. Skupin, “Saturation of the nonlinear refractive index in atomic gases,” Phys. Rev. A 87, 043811 (2013).
[Crossref]

E. Lorin, S. Chelkowski, A. Bandrauk, “Maxwell-Schrödinger-Plasma (MASP) model for laser-molecule interactions: towards an understanding of filamentation with intense ultrashort pulses,” Physica D 241, 1059–1071 (2012).
[Crossref]

E. Lorin, S. Chelkowski, A. Bandrauk, “The WASP model: a micro–macro system of wave-Schrödinger-plasma equations for filamentation,” Commun. Comput. Phys. 9, 406–440 (2011).

Chen, M.-C.

T. Popmintchev, M.-C. Chen, P. Arpin, M. M. Murnane, H. C. Kapteyn, “The attosecond nonlinear optics of bright coherent x-ray generation,” Nat. Photonics 4, 822–832 (2010).
[Crossref]

Chen, Y.-H.

Y.-H. Chen, S. Varma, T. M. Antonsen, H. M. Milchberg, “Direct measurement of the electron density of extended femtosecond laser pulse-induced filaments,” Phys. Rev. Lett. 105, 215005 (2010).
[Crossref]

Cheng, Y.-H.

J. K. Wahlstrand, Y.-H. Cheng, H. M. Milchberg, “Absolute measurement of the transient optical nonlinearity in N2, O2, N2O, and Ar,” Phys. Rev. A 85, 043820 (2012).

Cormier, E.

P. Béjot, E. Cormier, E. Hertz, B. Lavorel, J. Kasparian, J.-P. Wolf, O. Faucher, “High-field quantum calculation reveals time-dependent negative Kerr contribution,” Phys. Rev. Lett. 110, 043902 (2013).
[Crossref]

Corti, T.

A. Couairon, E. Brambilla, T. Corti, D. Majus, O. J. Ramirez-Gongora, M. Kolesik, “Practitioner’s guide to laser pulse propagation models and simulation,” Eur. J. Phys. Special Topics 199, 5–76 (2011).

Couairon, A.

A. Couairon, E. Brambilla, T. Corti, D. Majus, O. J. Ramirez-Gongora, M. Kolesik, “Practitioner’s guide to laser pulse propagation models and simulation,” Eur. J. Phys. Special Topics 199, 5–76 (2011).

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

Faucher, O.

P. Béjot, E. Cormier, E. Hertz, B. Lavorel, J. Kasparian, J.-P. Wolf, O. Faucher, “High-field quantum calculation reveals time-dependent negative Kerr contribution,” Phys. Rev. Lett. 110, 043902 (2013).
[Crossref]

Giacconi, P.

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

Gordon, D. F.

T. C. Rensink, T. M. Antonsen, J. P. Palastro, D. F. Gordon, “Model for atomic dielectric response in strong, time-dependent laser fields,” Phys. Rev. A 89, 033418 (2014).
[Crossref]

Guichard, R.

C. Köhler, R. Guichard, E. Lorin, S. Chelkowski, A. D. Bandrauk, L. Bergé, S. Skupin, “Saturation of the nonlinear refractive index in atomic gases,” Phys. Rev. A 87, 043811 (2013).
[Crossref]

Hamonou, L.

L. Hamonou, T. Morishita, O. I. Tolstikhin, S. Watanabe, “Siegert-state method for ionization of molecules in strong field,” J. Phys. Conf. Ser. 388, 032030 (2012).
[Crossref]

Hertz, E.

P. Béjot, E. Cormier, E. Hertz, B. Lavorel, J. Kasparian, J.-P. Wolf, O. Faucher, “High-field quantum calculation reveals time-dependent negative Kerr contribution,” Phys. Rev. Lett. 110, 043902 (2013).
[Crossref]

Ivanov, M.

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

Jakobsen, P.

Kapteyn, H. C.

T. Popmintchev, M.-C. Chen, P. Arpin, M. M. Murnane, H. C. Kapteyn, “The attosecond nonlinear optics of bright coherent x-ray generation,” Nat. Photonics 4, 822–832 (2010).
[Crossref]

Kasparian, J.

P. Béjot, E. Cormier, E. Hertz, B. Lavorel, J. Kasparian, J.-P. Wolf, O. Faucher, “High-field quantum calculation reveals time-dependent negative Kerr contribution,” Phys. Rev. Lett. 110, 043902 (2013).
[Crossref]

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

Köhler, C.

C. Köhler, R. Guichard, E. Lorin, S. Chelkowski, A. D. Bandrauk, L. Bergé, S. Skupin, “Saturation of the nonlinear refractive index in atomic gases,” Phys. Rev. A 87, 043811 (2013).
[Crossref]

Kolesik, M.

A. Bahl, A. Teleki, P. Jakobsen, E. M. Wright, M. Kolesik, “Reflectionless beam propagation on a piecewise linear complex domain,” J. Lightwave Technol. 32, 3670–3676 (2014).
[Crossref]

J. Andreasen, M. Kolesik, “Nonlinear propagation of light in structured media: generalized unidirectional pulse propagation equations,” Phys. Rev. E 86, 036706 (2012).
[Crossref]

A. Couairon, E. Brambilla, T. Corti, D. Majus, O. J. Ramirez-Gongora, M. Kolesik, “Practitioner’s guide to laser pulse propagation models and simulation,” Eur. J. Phys. Special Topics 199, 5–76 (2011).

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

Krausz, F.

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

Lavorel, B.

P. Béjot, E. Cormier, E. Hertz, B. Lavorel, J. Kasparian, J.-P. Wolf, O. Faucher, “High-field quantum calculation reveals time-dependent negative Kerr contribution,” Phys. Rev. Lett. 110, 043902 (2013).
[Crossref]

Lorin, E.

C. Köhler, R. Guichard, E. Lorin, S. Chelkowski, A. D. Bandrauk, L. Bergé, S. Skupin, “Saturation of the nonlinear refractive index in atomic gases,” Phys. Rev. A 87, 043811 (2013).
[Crossref]

E. Lorin, S. Chelkowski, A. Bandrauk, “Maxwell-Schrödinger-Plasma (MASP) model for laser-molecule interactions: towards an understanding of filamentation with intense ultrashort pulses,” Physica D 241, 1059–1071 (2012).
[Crossref]

E. Lorin, S. Chelkowski, A. Bandrauk, “The WASP model: a micro–macro system of wave-Schrödinger-plasma equations for filamentation,” Commun. Comput. Phys. 9, 406–440 (2011).

Lotti, A.

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

Majus, D.

A. Couairon, E. Brambilla, T. Corti, D. Majus, O. J. Ramirez-Gongora, M. Kolesik, “Practitioner’s guide to laser pulse propagation models and simulation,” Eur. J. Phys. Special Topics 199, 5–76 (2011).

Midorikawa, K.

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

Milchberg, H. M.

J. K. Wahlstrand, Y.-H. Cheng, H. M. Milchberg, “Absolute measurement of the transient optical nonlinearity in N2, O2, N2O, and Ar,” Phys. Rev. A 85, 043820 (2012).

Y.-H. Chen, S. Varma, T. M. Antonsen, H. M. Milchberg, “Direct measurement of the electron density of extended femtosecond laser pulse-induced filaments,” Phys. Rev. Lett. 105, 215005 (2010).
[Crossref]

Morishita, T.

L. Hamonou, T. Morishita, O. I. Tolstikhin, S. Watanabe, “Siegert-state method for ionization of molecules in strong field,” J. Phys. Conf. Ser. 388, 032030 (2012).
[Crossref]

O. I. Tolstikhin, T. Morishita, S. Watanabe, “Adiabatic theory of ionization of atoms by intense laser pulses: one-dimensional zero-range-potential model,” Phys. Rev. A 81, 033415 (2010).
[Crossref]

Murnane, M. M.

T. Popmintchev, M.-C. Chen, P. Arpin, M. M. Murnane, H. C. Kapteyn, “The attosecond nonlinear optics of bright coherent x-ray generation,” Nat. Photonics 4, 822–832 (2010).
[Crossref]

Mysyrowicz, A.

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

Nurhuda, M.

M. Nurhuda, A. Suda, 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, J.-P. Wolf, “Ultrashort filaments of light in weakly ionized optically transparent media,” Rep. Prog. Phys. 70, 1633–1713 (2007).
[Crossref]

Palastro, J. P.

T. C. Rensink, T. M. Antonsen, J. P. Palastro, D. F. Gordon, “Model for atomic dielectric response in strong, time-dependent laser fields,” Phys. Rev. A 89, 033418 (2014).
[Crossref]

Popmintchev, T.

T. Popmintchev, M.-C. Chen, P. Arpin, M. M. Murnane, H. C. Kapteyn, “The attosecond nonlinear optics of bright coherent x-ray generation,” Nat. Photonics 4, 822–832 (2010).
[Crossref]

Popov, A. M.

A. M. Popov, O. V. Tikhonova, E. A. Volkova, “Polarization response of an atomic system in a strong mid-IR field,” Laser Phys. Lett. 10, 085303 (2013).
[Crossref]

E. A. Volkova, A. M. Popov, O. V. Tikhonova, “Polarization response of a gas medium in the field of a high-intensity ultrashort laser pulse: high order Kerr nonlinearities or plasma electron component?” Quantum Electron. 42, 680–686 (2012).
[Crossref]

E. A. Volkova, A. M. Popov, 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]

Ramirez-Gongora, O. J.

A. Couairon, E. Brambilla, T. Corti, D. Majus, O. J. Ramirez-Gongora, M. Kolesik, “Practitioner’s guide to laser pulse propagation models and simulation,” Eur. J. Phys. Special Topics 199, 5–76 (2011).

Rensink, T. C.

T. C. Rensink, T. M. Antonsen, J. P. Palastro, D. F. Gordon, “Model for atomic dielectric response in strong, time-dependent laser fields,” Phys. Rev. A 89, 033418 (2014).
[Crossref]

Skupin, S.

C. Köhler, R. Guichard, E. Lorin, S. Chelkowski, A. D. Bandrauk, L. Bergé, S. Skupin, “Saturation of the nonlinear refractive index in atomic gases,” Phys. Rev. A 87, 043811 (2013).
[Crossref]

L. Bergé, S. Skupin, R. Nuter, J. Kasparian, J.-P. 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, R. Soldati, “Decay in a uniform field: an exactly solvable model,” J. Phys. A 36, 12065–12080 (2003).
[Crossref]

Suda, A.

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

Teleki, A.

A. Bahl, A. Teleki, P. Jakobsen, E. M. Wright, M. Kolesik, “Reflectionless beam propagation on a piecewise linear complex domain,” J. Lightwave Technol. 32, 3670–3676 (2014).
[Crossref]

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

Tikhonova, O. V.

A. M. Popov, O. V. Tikhonova, E. A. Volkova, “Polarization response of an atomic system in a strong mid-IR field,” Laser Phys. Lett. 10, 085303 (2013).
[Crossref]

E. A. Volkova, A. M. Popov, O. V. Tikhonova, “Polarization response of a gas medium in the field of a high-intensity ultrashort laser pulse: high order Kerr nonlinearities or plasma electron component?” Quantum Electron. 42, 680–686 (2012).
[Crossref]

E. A. Volkova, A. M. Popov, 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]

Tolstikhin, O. I.

L. Hamonou, T. Morishita, O. I. Tolstikhin, S. Watanabe, “Siegert-state method for ionization of molecules in strong field,” J. Phys. Conf. Ser. 388, 032030 (2012).
[Crossref]

O. I. Tolstikhin, T. Morishita, S. Watanabe, “Adiabatic theory of ionization of atoms by intense laser pulses: one-dimensional zero-range-potential model,” Phys. Rev. A 81, 033415 (2010).
[Crossref]

Varma, S.

Y.-H. Chen, S. Varma, T. M. Antonsen, H. M. Milchberg, “Direct measurement of the electron density of extended femtosecond laser pulse-induced filaments,” Phys. Rev. Lett. 105, 215005 (2010).
[Crossref]

Volkova, E. A.

A. M. Popov, O. V. Tikhonova, E. A. Volkova, “Polarization response of an atomic system in a strong mid-IR field,” Laser Phys. Lett. 10, 085303 (2013).
[Crossref]

E. A. Volkova, A. M. Popov, O. V. Tikhonova, “Polarization response of a gas medium in the field of a high-intensity ultrashort laser pulse: high order Kerr nonlinearities or plasma electron component?” Quantum Electron. 42, 680–686 (2012).
[Crossref]

E. A. Volkova, A. M. Popov, 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]

Wahlstrand, J. K.

J. K. Wahlstrand, Y.-H. Cheng, H. M. Milchberg, “Absolute measurement of the transient optical nonlinearity in N2, O2, N2O, and Ar,” Phys. Rev. A 85, 043820 (2012).

Watanabe, S.

L. Hamonou, T. Morishita, O. I. Tolstikhin, S. Watanabe, “Siegert-state method for ionization of molecules in strong field,” J. Phys. Conf. Ser. 388, 032030 (2012).
[Crossref]

O. I. Tolstikhin, T. Morishita, S. Watanabe, “Adiabatic theory of ionization of atoms by intense laser pulses: one-dimensional zero-range-potential model,” Phys. Rev. A 81, 033415 (2010).
[Crossref]

Wolf, J.-P.

P. Béjot, E. Cormier, E. Hertz, B. Lavorel, J. Kasparian, J.-P. Wolf, O. Faucher, “High-field quantum calculation reveals time-dependent negative Kerr contribution,” Phys. Rev. Lett. 110, 043902 (2013).
[Crossref]

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

Wright, E. M.

Commun. Comput. Phys. (1)

E. Lorin, S. Chelkowski, A. Bandrauk, “The WASP model: a micro–macro system of wave-Schrödinger-plasma equations for filamentation,” Commun. Comput. Phys. 9, 406–440 (2011).

Eur. J. Phys. Special Topics (1)

A. Couairon, E. Brambilla, T. Corti, D. Majus, O. J. Ramirez-Gongora, M. Kolesik, “Practitioner’s guide to laser pulse propagation models and simulation,” Eur. J. Phys. Special Topics 199, 5–76 (2011).

J. Lightwave Technol. (1)

J. Phys. A (2)

D. C. Brody, “Biorthogonal quantum mechanics,” J. Phys. A 47, 035305 (2014).
[Crossref]

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

J. Phys. Conf. Ser. (1)

L. Hamonou, T. Morishita, O. I. Tolstikhin, S. Watanabe, “Siegert-state method for ionization of molecules in strong field,” J. Phys. Conf. Ser. 388, 032030 (2012).
[Crossref]

JETP Lett. (1)

E. A. Volkova, A. M. Popov, 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)

A. M. Popov, O. V. Tikhonova, E. A. Volkova, “Polarization response of an atomic system in a strong mid-IR field,” Laser Phys. Lett. 10, 085303 (2013).
[Crossref]

Nat. Photonics (1)

T. Popmintchev, M.-C. Chen, P. Arpin, M. M. Murnane, H. C. Kapteyn, “The attosecond nonlinear optics of bright coherent x-ray generation,” Nat. Photonics 4, 822–832 (2010).
[Crossref]

New J. Phys. (1)

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

Nucl. Phys. A (1)

T. Berggren, “On the use of resonant states in eigenfunction expansions of scattering and reaction amplitudes,” Nucl. Phys. A 109, 265–287 (1968).
[Crossref]

Phys. Lett. B (1)

T. Berggren, “Expectation value of an operator in a resonant state,” Phys. Lett. B 373, 1–4 (1996).
[Crossref]

Phys. Rep. (1)

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

Phys. Rev. A (5)

O. I. Tolstikhin, T. Morishita, S. Watanabe, “Adiabatic theory of ionization of atoms by intense laser pulses: one-dimensional zero-range-potential model,” Phys. Rev. A 81, 033415 (2010).
[Crossref]

C. Köhler, R. Guichard, E. Lorin, S. Chelkowski, A. D. Bandrauk, L. Bergé, S. Skupin, “Saturation of the nonlinear refractive index in atomic gases,” Phys. Rev. A 87, 043811 (2013).
[Crossref]

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

T. C. Rensink, T. M. Antonsen, J. P. Palastro, D. F. Gordon, “Model for atomic dielectric response in strong, time-dependent laser fields,” Phys. Rev. A 89, 033418 (2014).
[Crossref]

J. K. Wahlstrand, Y.-H. Cheng, H. M. Milchberg, “Absolute measurement of the transient optical nonlinearity in N2, O2, N2O, and Ar,” Phys. Rev. A 85, 043820 (2012).

Phys. Rev. E (1)

J. Andreasen, M. Kolesik, “Nonlinear propagation of light in structured media: generalized unidirectional pulse propagation equations,” Phys. Rev. E 86, 036706 (2012).
[Crossref]

Phys. Rev. Lett. (2)

Y.-H. Chen, S. Varma, T. M. Antonsen, H. M. Milchberg, “Direct measurement of the electron density of extended femtosecond laser pulse-induced filaments,” Phys. Rev. Lett. 105, 215005 (2010).
[Crossref]

P. Béjot, E. Cormier, E. Hertz, B. Lavorel, J. Kasparian, J.-P. Wolf, O. Faucher, “High-field quantum calculation reveals time-dependent negative Kerr contribution,” Phys. Rev. Lett. 110, 043902 (2013).
[Crossref]

Physica D (1)

E. Lorin, S. Chelkowski, A. Bandrauk, “Maxwell-Schrödinger-Plasma (MASP) model for laser-molecule interactions: towards an understanding of filamentation with intense ultrashort pulses,” Physica D 241, 1059–1071 (2012).
[Crossref]

Quantum Electron. (1)

E. A. Volkova, A. M. Popov, O. V. Tikhonova, “Polarization response of a gas medium in the field of a high-intensity ultrashort laser pulse: high order Kerr nonlinearities or plasma electron component?” Quantum Electron. 42, 680–686 (2012).
[Crossref]

Rep. Prog. Phys. (1)

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

Rev. Mod. Phys. (1)

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

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Figures (8)

Fig. 1.
Fig. 1. Complex-valued expectation value of the dipole moment in the metastable ground state as a function of the external field strength. The fine dashed line indicates the linear susceptibility. The gap between the thin dashed and the thick black line represents the nonlinear response Eq. (11).
Fig. 2.
Fig. 2. Ionization yield as a function of the intensity of the driving pulse. Exact, adiabatic, and corrected solutions are compared. The top and bottom panels correspond to wavelengths of λ=2400nm and λ=800nm, respectively.
Fig. 3.
Fig. 3. Nonlinear response of the Dirac-delta system to a λ=2.5μm driving pulse indicated by the thin dashed line. The exact response is shown as a blue solid line, and the resonant-response model result is shown in thick red. The top panel zooms in to highlight that our response model “filters out” very-high-frequency components. The bottom panel demonstrates accurate overall agreement between approximate and exact solutions.
Fig. 4.
Fig. 4. Complex-valued dipole moment of a 3D hydrogen-like model atom, measured in the metastable state born from the ground-state as a function of the external field strength. Data obtained for two computational domain size L are shown, indicating fast convergence.
Fig. 5.
Fig. 5. Nonlinear response of a hydrogen-like system to a λ=2μm driving pulse indicated by the shaded area(s). The exact TDSE response is shown by the blue dashed line, and the resonant-response model result is shown in red.
Fig. 6.
Fig. 6. On-axis energy fluence in a filament created by a 30 fs, λ=2.0μm pulse. The two curves represent simulations with the indicated initial intensity.
Fig. 7.
Fig. 7. Free electrons generated per unit of propagation length.
Fig. 8.
Fig. 8. Supercontinuum generation in a femtosecond filament. The spectrum before the collapse exhibits well-separated harmonic orders.

Equations (18)

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[it+12x2+Bδ(x)+xF(t)]ψ(x,t)=0,
ψ(λ,x)={Ci(ξ0)Ai(ξ)x<0Ai(ξ0)Ci(ξ)x>0,
1=2πB(2F)1/3Ai(2λ(2F)2/3)[iAi(2λ(2F)2/3)+Bi(2λ(2F)2/3)].
ψi|ψj=Cψi(z)ψj(z)dz=Ni2(F)δij,
X0(F)=N02(F)Cψ0(z)zψ0(z)dz.
1=n|ψnψn|+Ldλ|ϕλϕλ|,
itψM=H^(F(t))ψM(x,t),ψM=ici(t)ψi(F(t),x),
H^(F)ψi(F,x)=Ei(F)ψi(F,x),
cn(t)=icnEn(F(t))kck(t)F(t)ψn|Fψk(F(t),x).
c0(a)(t)=exp{iEGtit[E0(F(τ))EG]dτ},
P(nl)(F(t))=P(F(t))limϵ01ϵP(ϵF(t)),
tρ(t)=[1ρ(t)]I{2E0(F(t))}.
tJ(t)=ρ(t)F(t).
E0(R)(F(t))=E0(F(t))n0(F(t))2(ψ0|Fψn(F(t)))2[En(F(t))E0(F(t))].
E0(R)(F(t))=E0(F(t))+(F(t))2E0(F(t))Fψ0(F(t))|Fψ0(F(t)).
PNL(corr)(t)1EGI{tψ0(F(t))|X|ψ0(F(t))}.
tJ(t)=ρ(t)F(t)+vitρ(t),
H=12Δ1a2+x2+y2+z2xF(t),

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