Abstract

We present a new interpretation of high-order optical harmonic generation (HHG) in atomic gases interacting with laser fields. The mechanism of harmonic generation is due to the temporal evolution of the atomic electron density spatial distribution in the external laser field, and the integral energy of a high harmonic emission and an electron excitation is equal to the work executed by the laser field for an electron motion in the intra-atomic potential field. The proposed interpretation is based on the use of the basis of eigenfunctions of the boundary value problem for “an atom in the external field.” As an illustration, we present the original results of computer simulations of an argon atom interaction with the two-color laser field formed by the fundamental and second harmonics of the Ti:sapphire laser.

© 2013 Optical Society of America

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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2012 (4)

D. Shafir, B. Fabre, J. Higuet, H. Soifer, M. Dagan, D. Descamps, E. Me’vel, S. Petit, H. J. Worner, B. Pons, N. Dudovich, and Y. Mairesse, “Role of the ionic potential in high harmonic generation,” Phys. Rev. Lett. 108, 203001 (2012).
[CrossRef]

E. Constant, A. Dubrouil, O. Hort, S. Petit, D. Descamps, and E. Mevel, “Spatial shaping of intense femtosecond beams for the generation of high-energy attosecond pulses,” J. Phys. B 45, 074018 (2012).
[CrossRef]

A. V. Andreev, S. Y. Stremoukhov, and O. A. Shoutova, “Light-induced anisotropy of atomic response: prospects for emission spectrum control,” Eur. Phys. J. D 66, 16 (2012).
[CrossRef]

V. V. Strelkov, M. A. Khokhlova, A. A. Gonoskov, I. A. Gonoskov, and M. Y. Ryabikin, “High-order harmonic generation by atoms in an elliptically polarized laser field: harmonic polarization properties and laser threshold ellipticity,” Phys. Rev. A 86, 013404 (2012).
[CrossRef]

2011 (2)

2010 (3)

H. Sofier, P. Botheron, D. Shafir, A. Diner, O. Raz, B. D. Bruner, Y. Mairesse, B. Pons, and N. Dubovich, “Near-threshold high-order harmonic spectroscopy with aligned molecules,” Phys. Rev. Lett. 105, 143904 (2010).
[CrossRef]

E. P. Power, A. M. March, F. Catoire, E. Sistrunk, K. Krushelnick, P. Agostini, and L. F. DiMauro, “XFROG phase measurement of threshold harmonics in Keldysh-scaled system,” Nat. Photonics 4, 352–356 (2010).
[CrossRef]

S. V. Popruzhenko, D. F. Zaretsky, and W. Becker, “High-order harmonic generation by an intense infrared laser pulse in the presence of a weak UV pulse,” Phys. Rev. A 81, 063417 (2010).
[CrossRef]

2009 (3)

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

M. V. Frolov, N. L. Manakov, T. S. Sarantseva, and A. F. Starace, “Analytic formulae for high harmonic generation,” J. Phys. B 42, 035601 (2009).
[CrossRef]

D. C. Yost, T. R. Schibli, J. Ye, J. L. Tate, J. Hostetter, M. B. Gaarde, and K. J. Schafer, “Vacuum-ultraviolet frequency combs from below-threshold harmonics,” Nat. Phys. 5, 815–820 (2009).
[CrossRef]

2008 (2)

G. Lambert, T. Hara, D. Garzella, T. Tanikawa, M. Labat, B. Carre, H. Kitamura, T. Shintake, M. Bougeard, T. Inoue, Y. Tanaka, P. Salieres, H. Merdji, O. Chubar, O. Gobert, K. Tahara, and M. E. Couprie, “Injection of harmonics generated in gas in a free-electron laser providing intense and coherent extreme-ultraviolet light,” Nat. Phys. 4, 296–300 (2008).
[CrossRef]

M. Kitzler, X. Xie, S. Roither, A. Scrinzi, and A. Baltuska, “Angular encoding in attosecond recollision,” New J. Phys. 10, 025029 (2008).
[CrossRef]

2007 (2)

M. Kitzler, X. Xie, S. Roither, A. Scrinzi, and A. Baltuska, “Optical attosecond mapping by polarization selective detection,” Phys. Rev. A 76, R011801 (2007).
[CrossRef]

P. B. Corkum and F. Krausz, “Attosecond science,” Nat. Phys. 3, 381–387 (2007).
[CrossRef]

2006 (1)

I. J. Sola, E. Mevel, L. Elouga, E. Constant, V. Strelkov, L. Poletto, P. Villoresi, E. Benedetti, J.-P. Caumes, S. Stagira, C. Vozzi, G. Sansone, and M. Nisoli, “Controlling attosecond electron dynamics by phase-stabilized polarization gating,” Nat. Phys. 2, 319–322 (2006).
[CrossRef]

2005 (1)

2001 (1)

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

1994 (1)

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

1993 (3)

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

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]

M. D. Perry and J. K. Crane, “High-order harmonic emission from mixed fields,” Phys. Rev. A 48, R4051 (1993).
[CrossRef]

1990 (1)

Agostini, P.

E. P. Power, A. M. March, F. Catoire, E. Sistrunk, K. Krushelnick, P. Agostini, and L. F. DiMauro, “XFROG phase measurement of threshold harmonics in Keldysh-scaled system,” Nat. Photonics 4, 352–356 (2010).
[CrossRef]

Andreev, A. V.

A. V. Andreev, S. Y. Stremoukhov, and O. A. Shoutova, “Light-induced anisotropy of atomic response: prospects for emission spectrum control,” Eur. Phys. J. D 66, 16 (2012).
[CrossRef]

A. V. Andreev, S. Y. Stremoukhov, and O. A. Shoutova, “Nonlinear optical response of an atom imposed on a laser pulse of near-atomic strength,” JETP Lett. 93, 476–486 (2011).
[CrossRef]

A. V. Andreev, S. Y. Stremoukhov, and O. A. Shoutova, Interaction of Atom With Laser Pulses of Intra-Atomic Field Strength, Anatoli V. Andreev, ed. (InTech, 2011), pp. 247–284.

Baba, M.

Balcou, P.

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

Baltuska, A.

M. Kitzler, X. Xie, S. Roither, A. Scrinzi, and A. Baltuska, “Angular encoding in attosecond recollision,” New J. Phys. 10, 025029 (2008).
[CrossRef]

M. Kitzler, X. Xie, S. Roither, A. Scrinzi, and A. Baltuska, “Optical attosecond mapping by polarization selective detection,” Phys. Rev. A 76, R011801 (2007).
[CrossRef]

Becker, W.

S. V. Popruzhenko, D. F. Zaretsky, and W. Becker, “High-order harmonic generation by an intense infrared laser pulse in the presence of a weak UV pulse,” Phys. Rev. A 81, 063417 (2010).
[CrossRef]

Benedetti, E.

I. J. Sola, E. Mevel, L. Elouga, E. Constant, V. Strelkov, L. Poletto, P. Villoresi, E. Benedetti, J.-P. Caumes, S. Stagira, C. Vozzi, G. Sansone, and M. Nisoli, “Controlling attosecond electron dynamics by phase-stabilized polarization gating,” Nat. Phys. 2, 319–322 (2006).
[CrossRef]

Botheron, P.

H. Sofier, P. Botheron, D. Shafir, A. Diner, O. Raz, B. D. Bruner, Y. Mairesse, B. Pons, and N. Dubovich, “Near-threshold high-order harmonic spectroscopy with aligned molecules,” Phys. Rev. Lett. 105, 143904 (2010).
[CrossRef]

Bougeard, M.

G. Lambert, T. Hara, D. Garzella, T. Tanikawa, M. Labat, B. Carre, H. Kitamura, T. Shintake, M. Bougeard, T. Inoue, Y. Tanaka, P. Salieres, H. Merdji, O. Chubar, O. Gobert, K. Tahara, and M. E. Couprie, “Injection of harmonics generated in gas in a free-electron laser providing intense and coherent extreme-ultraviolet light,” Nat. Phys. 4, 296–300 (2008).
[CrossRef]

Bruner, B. D.

H. Sofier, P. Botheron, D. Shafir, A. Diner, O. Raz, B. D. Bruner, Y. Mairesse, B. Pons, and N. Dubovich, “Near-threshold high-order harmonic spectroscopy with aligned molecules,” Phys. Rev. Lett. 105, 143904 (2010).
[CrossRef]

Carre, B.

G. Lambert, T. Hara, D. Garzella, T. Tanikawa, M. Labat, B. Carre, H. Kitamura, T. Shintake, M. Bougeard, T. Inoue, Y. Tanaka, P. Salieres, H. Merdji, O. Chubar, O. Gobert, K. Tahara, and M. E. Couprie, “Injection of harmonics generated in gas in a free-electron laser providing intense and coherent extreme-ultraviolet light,” Nat. Phys. 4, 296–300 (2008).
[CrossRef]

Catoire, F.

E. P. Power, A. M. March, F. Catoire, E. Sistrunk, K. Krushelnick, P. Agostini, and L. F. DiMauro, “XFROG phase measurement of threshold harmonics in Keldysh-scaled system,” Nat. Photonics 4, 352–356 (2010).
[CrossRef]

Caumes, J.-P.

I. J. Sola, E. Mevel, L. Elouga, E. Constant, V. Strelkov, L. Poletto, P. Villoresi, E. Benedetti, J.-P. Caumes, S. Stagira, C. Vozzi, G. Sansone, and M. Nisoli, “Controlling attosecond electron dynamics by phase-stabilized polarization gating,” Nat. Phys. 2, 319–322 (2006).
[CrossRef]

Chubar, O.

G. Lambert, T. Hara, D. Garzella, T. Tanikawa, M. Labat, B. Carre, H. Kitamura, T. Shintake, M. Bougeard, T. Inoue, Y. Tanaka, P. Salieres, H. Merdji, O. Chubar, O. Gobert, K. Tahara, and M. E. Couprie, “Injection of harmonics generated in gas in a free-electron laser providing intense and coherent extreme-ultraviolet light,” Nat. Phys. 4, 296–300 (2008).
[CrossRef]

Clark, C. W.

Constant, E.

E. Constant, A. Dubrouil, O. Hort, S. Petit, D. Descamps, and E. Mevel, “Spatial shaping of intense femtosecond beams for the generation of high-energy attosecond pulses,” J. Phys. B 45, 074018 (2012).
[CrossRef]

I. J. Sola, E. Mevel, L. Elouga, E. Constant, V. Strelkov, L. Poletto, P. Villoresi, E. Benedetti, J.-P. Caumes, S. Stagira, C. Vozzi, G. Sansone, and M. Nisoli, “Controlling attosecond electron dynamics by phase-stabilized polarization gating,” Nat. Phys. 2, 319–322 (2006).
[CrossRef]

Corkum, P. B.

P. B. Corkum and F. Krausz, “Attosecond science,” Nat. Phys. 3, 381–387 (2007).
[CrossRef]

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

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

Couprie, M. E.

G. Lambert, T. Hara, D. Garzella, T. Tanikawa, M. Labat, B. Carre, H. Kitamura, T. Shintake, M. Bougeard, T. Inoue, Y. Tanaka, P. Salieres, H. Merdji, O. Chubar, O. Gobert, K. Tahara, and M. E. Couprie, “Injection of harmonics generated in gas in a free-electron laser providing intense and coherent extreme-ultraviolet light,” Nat. Phys. 4, 296–300 (2008).
[CrossRef]

Crane, J. K.

M. D. Perry and J. K. Crane, “High-order harmonic emission from mixed fields,” Phys. Rev. A 48, R4051 (1993).
[CrossRef]

Dagan, M.

D. Shafir, B. Fabre, J. Higuet, H. Soifer, M. Dagan, D. Descamps, E. Me’vel, S. Petit, H. J. Worner, B. Pons, N. Dudovich, and Y. Mairesse, “Role of the ionic potential in high harmonic generation,” Phys. Rev. Lett. 108, 203001 (2012).
[CrossRef]

Delmotte, F.

Descamps, D.

D. Shafir, B. Fabre, J. Higuet, H. Soifer, M. Dagan, D. Descamps, E. Me’vel, S. Petit, H. J. Worner, B. Pons, N. Dudovich, and Y. Mairesse, “Role of the ionic potential in high harmonic generation,” Phys. Rev. Lett. 108, 203001 (2012).
[CrossRef]

E. Constant, A. Dubrouil, O. Hort, S. Petit, D. Descamps, and E. Mevel, “Spatial shaping of intense femtosecond beams for the generation of high-energy attosecond pulses,” J. Phys. B 45, 074018 (2012).
[CrossRef]

DiMauro, L. F.

E. P. Power, A. M. March, F. Catoire, E. Sistrunk, K. Krushelnick, P. Agostini, and L. F. DiMauro, “XFROG phase measurement of threshold harmonics in Keldysh-scaled system,” Nat. Photonics 4, 352–356 (2010).
[CrossRef]

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]

Diner, A.

H. Sofier, P. Botheron, D. Shafir, A. Diner, O. Raz, B. D. Bruner, Y. Mairesse, B. Pons, and N. Dubovich, “Near-threshold high-order harmonic spectroscopy with aligned molecules,” Phys. Rev. Lett. 105, 143904 (2010).
[CrossRef]

Dubovich, N.

H. Sofier, P. Botheron, D. Shafir, A. Diner, O. Raz, B. D. Bruner, Y. Mairesse, B. Pons, and N. Dubovich, “Near-threshold high-order harmonic spectroscopy with aligned molecules,” Phys. Rev. Lett. 105, 143904 (2010).
[CrossRef]

Dubrouil, A.

E. Constant, A. Dubrouil, O. Hort, S. Petit, D. Descamps, and E. Mevel, “Spatial shaping of intense femtosecond beams for the generation of high-energy attosecond pulses,” J. Phys. B 45, 074018 (2012).
[CrossRef]

Dudovich, N.

D. Shafir, B. Fabre, J. Higuet, H. Soifer, M. Dagan, D. Descamps, E. Me’vel, S. Petit, H. J. Worner, B. Pons, N. Dudovich, and Y. Mairesse, “Role of the ionic potential in high harmonic generation,” Phys. Rev. Lett. 108, 203001 (2012).
[CrossRef]

Elouga, L.

I. J. Sola, E. Mevel, L. Elouga, E. Constant, V. Strelkov, L. Poletto, P. Villoresi, E. Benedetti, J.-P. Caumes, S. Stagira, C. Vozzi, G. Sansone, and M. Nisoli, “Controlling attosecond electron dynamics by phase-stabilized polarization gating,” Nat. Phys. 2, 319–322 (2006).
[CrossRef]

Fabre, B.

D. Shafir, B. Fabre, J. Higuet, H. Soifer, M. Dagan, D. Descamps, E. Me’vel, S. Petit, H. J. Worner, B. Pons, N. Dudovich, and Y. Mairesse, “Role of the ionic potential in high harmonic generation,” Phys. Rev. Lett. 108, 203001 (2012).
[CrossRef]

Frolov, M. V.

M. V. Frolov, N. L. Manakov, T. S. Sarantseva, and A. F. Starace, “Analytic formulae for high harmonic generation,” J. Phys. B 42, 035601 (2009).
[CrossRef]

Gaarde, M. B.

D. C. Yost, T. R. Schibli, J. Ye, J. L. Tate, J. Hostetter, M. B. Gaarde, and K. J. Schafer, “Vacuum-ultraviolet frequency combs from below-threshold harmonics,” Nat. Phys. 5, 815–820 (2009).
[CrossRef]

Ganeev, R. A.

Garzella, D.

G. Lambert, T. Hara, D. Garzella, T. Tanikawa, M. Labat, B. Carre, H. Kitamura, T. Shintake, M. Bougeard, T. Inoue, Y. Tanaka, P. Salieres, H. Merdji, O. Chubar, O. Gobert, K. Tahara, and M. E. Couprie, “Injection of harmonics generated in gas in a free-electron laser providing intense and coherent extreme-ultraviolet light,” Nat. Phys. 4, 296–300 (2008).
[CrossRef]

Gautier, J.

Georgiadou, E.

E. Georgiadou, Study of Harmonic Generation with a Two-Color Field (Lund Reports on Atomic Physics, 2007).

Gobert, O.

G. Lambert, T. Hara, D. Garzella, T. Tanikawa, M. Labat, B. Carre, H. Kitamura, T. Shintake, M. Bougeard, T. Inoue, Y. Tanaka, P. Salieres, H. Merdji, O. Chubar, O. Gobert, K. Tahara, and M. E. Couprie, “Injection of harmonics generated in gas in a free-electron laser providing intense and coherent extreme-ultraviolet light,” Nat. Phys. 4, 296–300 (2008).
[CrossRef]

Gonoskov, A. A.

V. V. Strelkov, M. A. Khokhlova, A. A. Gonoskov, I. A. Gonoskov, and M. Y. Ryabikin, “High-order harmonic generation by atoms in an elliptically polarized laser field: harmonic polarization properties and laser threshold ellipticity,” Phys. Rev. A 86, 013404 (2012).
[CrossRef]

Gonoskov, I. A.

V. V. Strelkov, M. A. Khokhlova, A. A. Gonoskov, I. A. Gonoskov, and M. Y. Ryabikin, “High-order harmonic generation by atoms in an elliptically polarized laser field: harmonic polarization properties and laser threshold ellipticity,” Phys. Rev. A 86, 013404 (2012).
[CrossRef]

Hara, T.

G. Lambert, T. Hara, D. Garzella, T. Tanikawa, M. Labat, B. Carre, H. Kitamura, T. Shintake, M. Bougeard, T. Inoue, Y. Tanaka, P. Salieres, H. Merdji, O. Chubar, O. Gobert, K. Tahara, and M. E. Couprie, “Injection of harmonics generated in gas in a free-electron laser providing intense and coherent extreme-ultraviolet light,” Nat. Phys. 4, 296–300 (2008).
[CrossRef]

Higuet, J.

D. Shafir, B. Fabre, J. Higuet, H. Soifer, M. Dagan, D. Descamps, E. Me’vel, S. Petit, H. J. Worner, B. Pons, N. Dudovich, and Y. Mairesse, “Role of the ionic potential in high harmonic generation,” Phys. Rev. Lett. 108, 203001 (2012).
[CrossRef]

Hort, O.

E. Constant, A. Dubrouil, O. Hort, S. Petit, D. Descamps, and E. Mevel, “Spatial shaping of intense femtosecond beams for the generation of high-energy attosecond pulses,” J. Phys. B 45, 074018 (2012).
[CrossRef]

Hostetter, J.

D. C. Yost, T. R. Schibli, J. Ye, J. L. Tate, J. Hostetter, M. B. Gaarde, and K. J. Schafer, “Vacuum-ultraviolet frequency combs from below-threshold harmonics,” Nat. Phys. 5, 815–820 (2009).
[CrossRef]

Iaquaniello, G.

Inoue, T.

G. Lambert, T. Hara, D. Garzella, T. Tanikawa, M. Labat, B. Carre, H. Kitamura, T. Shintake, M. Bougeard, T. Inoue, Y. Tanaka, P. Salieres, H. Merdji, O. Chubar, O. Gobert, K. Tahara, and M. E. Couprie, “Injection of harmonics generated in gas in a free-electron laser providing intense and coherent extreme-ultraviolet light,” Nat. Phys. 4, 296–300 (2008).
[CrossRef]

Ivanov, M.

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G. L. Yudin and M. Y. Ivanov, “Nonadiabatic tunnel ionization: looking inside a laser cycle,” Phys. Rev. A 64, 013409 (2001).
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M. Lewenstein, P. Balcou, M. Y. Ivanov, A. L’Huillier, and P. B. Corkum, “Theory of high-harmonic generation by low-frequency laser fields,” Phys. Rev. A 49, 2117–2132 (1994).
[CrossRef]

Khokhlova, M. A.

V. V. Strelkov, M. A. Khokhlova, A. A. Gonoskov, I. A. Gonoskov, and M. Y. Ryabikin, “High-order harmonic generation by atoms in an elliptically polarized laser field: harmonic polarization properties and laser threshold ellipticity,” Phys. Rev. A 86, 013404 (2012).
[CrossRef]

Kitamura, H.

G. Lambert, T. Hara, D. Garzella, T. Tanikawa, M. Labat, B. Carre, H. Kitamura, T. Shintake, M. Bougeard, T. Inoue, Y. Tanaka, P. Salieres, H. Merdji, O. Chubar, O. Gobert, K. Tahara, and M. E. Couprie, “Injection of harmonics generated in gas in a free-electron laser providing intense and coherent extreme-ultraviolet light,” Nat. Phys. 4, 296–300 (2008).
[CrossRef]

Kitzler, M.

M. Kitzler, X. Xie, S. Roither, A. Scrinzi, and A. Baltuska, “Angular encoding in attosecond recollision,” New J. Phys. 10, 025029 (2008).
[CrossRef]

M. Kitzler, X. Xie, S. Roither, A. Scrinzi, and A. Baltuska, “Optical attosecond mapping by polarization selective detection,” Phys. Rev. A 76, R011801 (2007).
[CrossRef]

Krausz, F.

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

P. B. Corkum and F. Krausz, “Attosecond science,” Nat. Phys. 3, 381–387 (2007).
[CrossRef]

Krushelnick, K.

E. P. Power, A. M. March, F. Catoire, E. Sistrunk, K. Krushelnick, P. Agostini, and L. F. DiMauro, “XFROG phase measurement of threshold harmonics in Keldysh-scaled system,” Nat. Photonics 4, 352–356 (2010).
[CrossRef]

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]

Kuroda, H.

L’Huillier, A.

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

Labat, M.

G. Lambert, T. Hara, D. Garzella, T. Tanikawa, M. Labat, B. Carre, H. Kitamura, T. Shintake, M. Bougeard, T. Inoue, Y. Tanaka, P. Salieres, H. Merdji, O. Chubar, O. Gobert, K. Tahara, and M. E. Couprie, “Injection of harmonics generated in gas in a free-electron laser providing intense and coherent extreme-ultraviolet light,” Nat. Phys. 4, 296–300 (2008).
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Lambert, G.

B. Vodungbo, A. B. Sardinha, J. Gautier, G. Lambert, C. Valentin, M. Lozano, G. Iaquaniello, F. Delmotte, S. Sebban, J. Luuning, and P. Zeitoun, “Polarization control of high order harmonics in the EUV photon energy range,” Opt. Express 19, 4346–4356 (2011).
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G. Lambert, T. Hara, D. Garzella, T. Tanikawa, M. Labat, B. Carre, H. Kitamura, T. Shintake, M. Bougeard, T. Inoue, Y. Tanaka, P. Salieres, H. Merdji, O. Chubar, O. Gobert, K. Tahara, and M. E. Couprie, “Injection of harmonics generated in gas in a free-electron laser providing intense and coherent extreme-ultraviolet light,” Nat. Phys. 4, 296–300 (2008).
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Landau, L. D.

L. D. Landau and E. M. Lifshitz, The Classical Theory of Fields (Pergamon, 1971), pp. 158–162.

Lewenstein, M.

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

Lifshitz, E. M.

L. D. Landau and E. M. Lifshitz, The Classical Theory of Fields (Pergamon, 1971), pp. 158–162.

Lozano, M.

Luuning, J.

Mairesse, Y.

D. Shafir, B. Fabre, J. Higuet, H. Soifer, M. Dagan, D. Descamps, E. Me’vel, S. Petit, H. J. Worner, B. Pons, N. Dudovich, and Y. Mairesse, “Role of the ionic potential in high harmonic generation,” Phys. Rev. Lett. 108, 203001 (2012).
[CrossRef]

H. Sofier, P. Botheron, D. Shafir, A. Diner, O. Raz, B. D. Bruner, Y. Mairesse, B. Pons, and N. Dubovich, “Near-threshold high-order harmonic spectroscopy with aligned molecules,” Phys. Rev. Lett. 105, 143904 (2010).
[CrossRef]

Manakov, N. L.

M. V. Frolov, N. L. Manakov, T. S. Sarantseva, and A. F. Starace, “Analytic formulae for high harmonic generation,” J. Phys. B 42, 035601 (2009).
[CrossRef]

March, A. M.

E. P. Power, A. M. March, F. Catoire, E. Sistrunk, K. Krushelnick, P. Agostini, and L. F. DiMauro, “XFROG phase measurement of threshold harmonics in Keldysh-scaled system,” Nat. Photonics 4, 352–356 (2010).
[CrossRef]

Me’vel, E.

D. Shafir, B. Fabre, J. Higuet, H. Soifer, M. Dagan, D. Descamps, E. Me’vel, S. Petit, H. J. Worner, B. Pons, N. Dudovich, and Y. Mairesse, “Role of the ionic potential in high harmonic generation,” Phys. Rev. Lett. 108, 203001 (2012).
[CrossRef]

Merdji, H.

G. Lambert, T. Hara, D. Garzella, T. Tanikawa, M. Labat, B. Carre, H. Kitamura, T. Shintake, M. Bougeard, T. Inoue, Y. Tanaka, P. Salieres, H. Merdji, O. Chubar, O. Gobert, K. Tahara, and M. E. Couprie, “Injection of harmonics generated in gas in a free-electron laser providing intense and coherent extreme-ultraviolet light,” Nat. Phys. 4, 296–300 (2008).
[CrossRef]

Mevel, E.

E. Constant, A. Dubrouil, O. Hort, S. Petit, D. Descamps, and E. Mevel, “Spatial shaping of intense femtosecond beams for the generation of high-energy attosecond pulses,” J. Phys. B 45, 074018 (2012).
[CrossRef]

I. J. Sola, E. Mevel, L. Elouga, E. Constant, V. Strelkov, L. Poletto, P. Villoresi, E. Benedetti, J.-P. Caumes, S. Stagira, C. Vozzi, G. Sansone, and M. Nisoli, “Controlling attosecond electron dynamics by phase-stabilized polarization gating,” Nat. Phys. 2, 319–322 (2006).
[CrossRef]

Nisoli, M.

I. J. Sola, E. Mevel, L. Elouga, E. Constant, V. Strelkov, L. Poletto, P. Villoresi, E. Benedetti, J.-P. Caumes, S. Stagira, C. Vozzi, G. Sansone, and M. Nisoli, “Controlling attosecond electron dynamics by phase-stabilized polarization gating,” Nat. Phys. 2, 319–322 (2006).
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Ozaki, T.

Pan, L.

Perry, M. D.

M. D. Perry and J. K. Crane, “High-order harmonic emission from mixed fields,” Phys. Rev. A 48, R4051 (1993).
[CrossRef]

Petit, S.

D. Shafir, B. Fabre, J. Higuet, H. Soifer, M. Dagan, D. Descamps, E. Me’vel, S. Petit, H. J. Worner, B. Pons, N. Dudovich, and Y. Mairesse, “Role of the ionic potential in high harmonic generation,” Phys. Rev. Lett. 108, 203001 (2012).
[CrossRef]

E. Constant, A. Dubrouil, O. Hort, S. Petit, D. Descamps, and E. Mevel, “Spatial shaping of intense femtosecond beams for the generation of high-energy attosecond pulses,” J. Phys. B 45, 074018 (2012).
[CrossRef]

Poletto, L.

I. J. Sola, E. Mevel, L. Elouga, E. Constant, V. Strelkov, L. Poletto, P. Villoresi, E. Benedetti, J.-P. Caumes, S. Stagira, C. Vozzi, G. Sansone, and M. Nisoli, “Controlling attosecond electron dynamics by phase-stabilized polarization gating,” Nat. Phys. 2, 319–322 (2006).
[CrossRef]

Pons, B.

D. Shafir, B. Fabre, J. Higuet, H. Soifer, M. Dagan, D. Descamps, E. Me’vel, S. Petit, H. J. Worner, B. Pons, N. Dudovich, and Y. Mairesse, “Role of the ionic potential in high harmonic generation,” Phys. Rev. Lett. 108, 203001 (2012).
[CrossRef]

H. Sofier, P. Botheron, D. Shafir, A. Diner, O. Raz, B. D. Bruner, Y. Mairesse, B. Pons, and N. Dubovich, “Near-threshold high-order harmonic spectroscopy with aligned molecules,” Phys. Rev. Lett. 105, 143904 (2010).
[CrossRef]

Popruzhenko, S. V.

S. V. Popruzhenko, D. F. Zaretsky, and W. Becker, “High-order harmonic generation by an intense infrared laser pulse in the presence of a weak UV pulse,” Phys. Rev. A 81, 063417 (2010).
[CrossRef]

Power, E. P.

E. P. Power, A. M. March, F. Catoire, E. Sistrunk, K. Krushelnick, P. Agostini, and L. F. DiMauro, “XFROG phase measurement of threshold harmonics in Keldysh-scaled system,” Nat. Photonics 4, 352–356 (2010).
[CrossRef]

Raz, O.

H. Sofier, P. Botheron, D. Shafir, A. Diner, O. Raz, B. D. Bruner, Y. Mairesse, B. Pons, and N. Dubovich, “Near-threshold high-order harmonic spectroscopy with aligned molecules,” Phys. Rev. Lett. 105, 143904 (2010).
[CrossRef]

Roither, S.

M. Kitzler, X. Xie, S. Roither, A. Scrinzi, and A. Baltuska, “Angular encoding in attosecond recollision,” New J. Phys. 10, 025029 (2008).
[CrossRef]

M. Kitzler, X. Xie, S. Roither, A. Scrinzi, and A. Baltuska, “Optical attosecond mapping by polarization selective detection,” Phys. Rev. A 76, R011801 (2007).
[CrossRef]

Ryabikin, M. Y.

V. V. Strelkov, M. A. Khokhlova, A. A. Gonoskov, I. A. Gonoskov, and M. Y. Ryabikin, “High-order harmonic generation by atoms in an elliptically polarized laser field: harmonic polarization properties and laser threshold ellipticity,” Phys. Rev. A 86, 013404 (2012).
[CrossRef]

Salieres, P.

G. Lambert, T. Hara, D. Garzella, T. Tanikawa, M. Labat, B. Carre, H. Kitamura, T. Shintake, M. Bougeard, T. Inoue, Y. Tanaka, P. Salieres, H. Merdji, O. Chubar, O. Gobert, K. Tahara, and M. E. Couprie, “Injection of harmonics generated in gas in a free-electron laser providing intense and coherent extreme-ultraviolet light,” Nat. Phys. 4, 296–300 (2008).
[CrossRef]

Sansone, G.

I. J. Sola, E. Mevel, L. Elouga, E. Constant, V. Strelkov, L. Poletto, P. Villoresi, E. Benedetti, J.-P. Caumes, S. Stagira, C. Vozzi, G. Sansone, and M. Nisoli, “Controlling attosecond electron dynamics by phase-stabilized polarization gating,” Nat. Phys. 2, 319–322 (2006).
[CrossRef]

Sarantseva, T. S.

M. V. Frolov, N. L. Manakov, T. S. Sarantseva, and A. F. Starace, “Analytic formulae for high harmonic generation,” J. Phys. B 42, 035601 (2009).
[CrossRef]

Sardinha, A. B.

Schafer, K. J.

D. C. Yost, T. R. Schibli, J. Ye, J. L. Tate, J. Hostetter, M. B. Gaarde, and K. J. Schafer, “Vacuum-ultraviolet frequency combs from below-threshold harmonics,” Nat. Phys. 5, 815–820 (2009).
[CrossRef]

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]

Schibli, T. R.

D. C. Yost, T. R. Schibli, J. Ye, J. L. Tate, J. Hostetter, M. B. Gaarde, and K. J. Schafer, “Vacuum-ultraviolet frequency combs from below-threshold harmonics,” Nat. Phys. 5, 815–820 (2009).
[CrossRef]

Scrinzi, A.

M. Kitzler, X. Xie, S. Roither, A. Scrinzi, and A. Baltuska, “Angular encoding in attosecond recollision,” New J. Phys. 10, 025029 (2008).
[CrossRef]

M. Kitzler, X. Xie, S. Roither, A. Scrinzi, and A. Baltuska, “Optical attosecond mapping by polarization selective detection,” Phys. Rev. A 76, R011801 (2007).
[CrossRef]

Sebban, S.

Shafir, D.

D. Shafir, B. Fabre, J. Higuet, H. Soifer, M. Dagan, D. Descamps, E. Me’vel, S. Petit, H. J. Worner, B. Pons, N. Dudovich, and Y. Mairesse, “Role of the ionic potential in high harmonic generation,” Phys. Rev. Lett. 108, 203001 (2012).
[CrossRef]

H. Sofier, P. Botheron, D. Shafir, A. Diner, O. Raz, B. D. Bruner, Y. Mairesse, B. Pons, and N. Dubovich, “Near-threshold high-order harmonic spectroscopy with aligned molecules,” Phys. Rev. Lett. 105, 143904 (2010).
[CrossRef]

Shintake, T.

G. Lambert, T. Hara, D. Garzella, T. Tanikawa, M. Labat, B. Carre, H. Kitamura, T. Shintake, M. Bougeard, T. Inoue, Y. Tanaka, P. Salieres, H. Merdji, O. Chubar, O. Gobert, K. Tahara, and M. E. Couprie, “Injection of harmonics generated in gas in a free-electron laser providing intense and coherent extreme-ultraviolet light,” Nat. Phys. 4, 296–300 (2008).
[CrossRef]

Shoutova, O. A.

A. V. Andreev, S. Y. Stremoukhov, and O. A. Shoutova, “Light-induced anisotropy of atomic response: prospects for emission spectrum control,” Eur. Phys. J. D 66, 16 (2012).
[CrossRef]

A. V. Andreev, S. Y. Stremoukhov, and O. A. Shoutova, “Nonlinear optical response of an atom imposed on a laser pulse of near-atomic strength,” JETP Lett. 93, 476–486 (2011).
[CrossRef]

A. V. Andreev, S. Y. Stremoukhov, and O. A. Shoutova, Interaction of Atom With Laser Pulses of Intra-Atomic Field Strength, Anatoli V. Andreev, ed. (InTech, 2011), pp. 247–284.

Sistrunk, E.

E. P. Power, A. M. March, F. Catoire, E. Sistrunk, K. Krushelnick, P. Agostini, and L. F. DiMauro, “XFROG phase measurement of threshold harmonics in Keldysh-scaled system,” Nat. Photonics 4, 352–356 (2010).
[CrossRef]

Sofier, H.

H. Sofier, P. Botheron, D. Shafir, A. Diner, O. Raz, B. D. Bruner, Y. Mairesse, B. Pons, and N. Dubovich, “Near-threshold high-order harmonic spectroscopy with aligned molecules,” Phys. Rev. Lett. 105, 143904 (2010).
[CrossRef]

Soifer, H.

D. Shafir, B. Fabre, J. Higuet, H. Soifer, M. Dagan, D. Descamps, E. Me’vel, S. Petit, H. J. Worner, B. Pons, N. Dudovich, and Y. Mairesse, “Role of the ionic potential in high harmonic generation,” Phys. Rev. Lett. 108, 203001 (2012).
[CrossRef]

Sola, I. J.

I. J. Sola, E. Mevel, L. Elouga, E. Constant, V. Strelkov, L. Poletto, P. Villoresi, E. Benedetti, J.-P. Caumes, S. Stagira, C. Vozzi, G. Sansone, and M. Nisoli, “Controlling attosecond electron dynamics by phase-stabilized polarization gating,” Nat. Phys. 2, 319–322 (2006).
[CrossRef]

Stagira, S.

I. J. Sola, E. Mevel, L. Elouga, E. Constant, V. Strelkov, L. Poletto, P. Villoresi, E. Benedetti, J.-P. Caumes, S. Stagira, C. Vozzi, G. Sansone, and M. Nisoli, “Controlling attosecond electron dynamics by phase-stabilized polarization gating,” Nat. Phys. 2, 319–322 (2006).
[CrossRef]

Starace, A. F.

M. V. Frolov, N. L. Manakov, T. S. Sarantseva, and A. F. Starace, “Analytic formulae for high harmonic generation,” J. Phys. B 42, 035601 (2009).
[CrossRef]

Strelkov, V.

I. J. Sola, E. Mevel, L. Elouga, E. Constant, V. Strelkov, L. Poletto, P. Villoresi, E. Benedetti, J.-P. Caumes, S. Stagira, C. Vozzi, G. Sansone, and M. Nisoli, “Controlling attosecond electron dynamics by phase-stabilized polarization gating,” Nat. Phys. 2, 319–322 (2006).
[CrossRef]

Strelkov, V. V.

V. V. Strelkov, M. A. Khokhlova, A. A. Gonoskov, I. A. Gonoskov, and M. Y. Ryabikin, “High-order harmonic generation by atoms in an elliptically polarized laser field: harmonic polarization properties and laser threshold ellipticity,” Phys. Rev. A 86, 013404 (2012).
[CrossRef]

Stremoukhov, S. Y.

A. V. Andreev, S. Y. Stremoukhov, and O. A. Shoutova, “Light-induced anisotropy of atomic response: prospects for emission spectrum control,” Eur. Phys. J. D 66, 16 (2012).
[CrossRef]

A. V. Andreev, S. Y. Stremoukhov, and O. A. Shoutova, “Nonlinear optical response of an atom imposed on a laser pulse of near-atomic strength,” JETP Lett. 93, 476–486 (2011).
[CrossRef]

A. V. Andreev, S. Y. Stremoukhov, and O. A. Shoutova, Interaction of Atom With Laser Pulses of Intra-Atomic Field Strength, Anatoli V. Andreev, ed. (InTech, 2011), pp. 247–284.

Suzuki, M.

Tahara, K.

G. Lambert, T. Hara, D. Garzella, T. Tanikawa, M. Labat, B. Carre, H. Kitamura, T. Shintake, M. Bougeard, T. Inoue, Y. Tanaka, P. Salieres, H. Merdji, O. Chubar, O. Gobert, K. Tahara, and M. E. Couprie, “Injection of harmonics generated in gas in a free-electron laser providing intense and coherent extreme-ultraviolet light,” Nat. Phys. 4, 296–300 (2008).
[CrossRef]

Tanaka, Y.

G. Lambert, T. Hara, D. Garzella, T. Tanikawa, M. Labat, B. Carre, H. Kitamura, T. Shintake, M. Bougeard, T. Inoue, Y. Tanaka, P. Salieres, H. Merdji, O. Chubar, O. Gobert, K. Tahara, and M. E. Couprie, “Injection of harmonics generated in gas in a free-electron laser providing intense and coherent extreme-ultraviolet light,” Nat. Phys. 4, 296–300 (2008).
[CrossRef]

Tanikawa, T.

G. Lambert, T. Hara, D. Garzella, T. Tanikawa, M. Labat, B. Carre, H. Kitamura, T. Shintake, M. Bougeard, T. Inoue, Y. Tanaka, P. Salieres, H. Merdji, O. Chubar, O. Gobert, K. Tahara, and M. E. Couprie, “Injection of harmonics generated in gas in a free-electron laser providing intense and coherent extreme-ultraviolet light,” Nat. Phys. 4, 296–300 (2008).
[CrossRef]

Tate, J. L.

D. C. Yost, T. R. Schibli, J. Ye, J. L. Tate, J. Hostetter, M. B. Gaarde, and K. J. Schafer, “Vacuum-ultraviolet frequency combs from below-threshold harmonics,” Nat. Phys. 5, 815–820 (2009).
[CrossRef]

Taylor, K. T.

Valentin, C.

Villoresi, P.

I. J. Sola, E. Mevel, L. Elouga, E. Constant, V. Strelkov, L. Poletto, P. Villoresi, E. Benedetti, J.-P. Caumes, S. Stagira, C. Vozzi, G. Sansone, and M. Nisoli, “Controlling attosecond electron dynamics by phase-stabilized polarization gating,” Nat. Phys. 2, 319–322 (2006).
[CrossRef]

Vodungbo, B.

Vozzi, C.

I. J. Sola, E. Mevel, L. Elouga, E. Constant, V. Strelkov, L. Poletto, P. Villoresi, E. Benedetti, J.-P. Caumes, S. Stagira, C. Vozzi, G. Sansone, and M. Nisoli, “Controlling attosecond electron dynamics by phase-stabilized polarization gating,” Nat. Phys. 2, 319–322 (2006).
[CrossRef]

Worner, H. J.

D. Shafir, B. Fabre, J. Higuet, H. Soifer, M. Dagan, D. Descamps, E. Me’vel, S. Petit, H. J. Worner, B. Pons, N. Dudovich, and Y. Mairesse, “Role of the ionic potential in high harmonic generation,” Phys. Rev. Lett. 108, 203001 (2012).
[CrossRef]

Xie, X.

M. Kitzler, X. Xie, S. Roither, A. Scrinzi, and A. Baltuska, “Angular encoding in attosecond recollision,” New J. Phys. 10, 025029 (2008).
[CrossRef]

M. Kitzler, X. Xie, S. Roither, A. Scrinzi, and A. Baltuska, “Optical attosecond mapping by polarization selective detection,” Phys. Rev. A 76, R011801 (2007).
[CrossRef]

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]

Ye, J.

D. C. Yost, T. R. Schibli, J. Ye, J. L. Tate, J. Hostetter, M. B. Gaarde, and K. J. Schafer, “Vacuum-ultraviolet frequency combs from below-threshold harmonics,” Nat. Phys. 5, 815–820 (2009).
[CrossRef]

Yost, D. C.

D. C. Yost, T. R. Schibli, J. Ye, J. L. Tate, J. Hostetter, M. B. Gaarde, and K. J. Schafer, “Vacuum-ultraviolet frequency combs from below-threshold harmonics,” Nat. Phys. 5, 815–820 (2009).
[CrossRef]

Yudin, G. L.

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

Zaretsky, D. F.

S. V. Popruzhenko, D. F. Zaretsky, and W. Becker, “High-order harmonic generation by an intense infrared laser pulse in the presence of a weak UV pulse,” Phys. Rev. A 81, 063417 (2010).
[CrossRef]

Zeitoun, P.

Eur. Phys. J. D (1)

A. V. Andreev, S. Y. Stremoukhov, and O. A. Shoutova, “Light-induced anisotropy of atomic response: prospects for emission spectrum control,” Eur. Phys. J. D 66, 16 (2012).
[CrossRef]

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

J. Phys. B (2)

E. Constant, A. Dubrouil, O. Hort, S. Petit, D. Descamps, and E. Mevel, “Spatial shaping of intense femtosecond beams for the generation of high-energy attosecond pulses,” J. Phys. B 45, 074018 (2012).
[CrossRef]

M. V. Frolov, N. L. Manakov, T. S. Sarantseva, and A. F. Starace, “Analytic formulae for high harmonic generation,” J. Phys. B 42, 035601 (2009).
[CrossRef]

JETP Lett. (1)

A. V. Andreev, S. Y. Stremoukhov, and O. A. Shoutova, “Nonlinear optical response of an atom imposed on a laser pulse of near-atomic strength,” JETP Lett. 93, 476–486 (2011).
[CrossRef]

Nat. Photonics (1)

E. P. Power, A. M. March, F. Catoire, E. Sistrunk, K. Krushelnick, P. Agostini, and L. F. DiMauro, “XFROG phase measurement of threshold harmonics in Keldysh-scaled system,” Nat. Photonics 4, 352–356 (2010).
[CrossRef]

Nat. Phys. (4)

D. C. Yost, T. R. Schibli, J. Ye, J. L. Tate, J. Hostetter, M. B. Gaarde, and K. J. Schafer, “Vacuum-ultraviolet frequency combs from below-threshold harmonics,” Nat. Phys. 5, 815–820 (2009).
[CrossRef]

I. J. Sola, E. Mevel, L. Elouga, E. Constant, V. Strelkov, L. Poletto, P. Villoresi, E. Benedetti, J.-P. Caumes, S. Stagira, C. Vozzi, G. Sansone, and M. Nisoli, “Controlling attosecond electron dynamics by phase-stabilized polarization gating,” Nat. Phys. 2, 319–322 (2006).
[CrossRef]

P. B. Corkum and F. Krausz, “Attosecond science,” Nat. Phys. 3, 381–387 (2007).
[CrossRef]

G. Lambert, T. Hara, D. Garzella, T. Tanikawa, M. Labat, B. Carre, H. Kitamura, T. Shintake, M. Bougeard, T. Inoue, Y. Tanaka, P. Salieres, H. Merdji, O. Chubar, O. Gobert, K. Tahara, and M. E. Couprie, “Injection of harmonics generated in gas in a free-electron laser providing intense and coherent extreme-ultraviolet light,” Nat. Phys. 4, 296–300 (2008).
[CrossRef]

New J. Phys. (1)

M. Kitzler, X. Xie, S. Roither, A. Scrinzi, and A. Baltuska, “Angular encoding in attosecond recollision,” New J. Phys. 10, 025029 (2008).
[CrossRef]

Opt. Express (1)

Opt. Lett. (1)

Phys. Rev. A (6)

S. V. Popruzhenko, D. F. Zaretsky, and W. Becker, “High-order harmonic generation by an intense infrared laser pulse in the presence of a weak UV pulse,” Phys. Rev. A 81, 063417 (2010).
[CrossRef]

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

V. V. Strelkov, M. A. Khokhlova, A. A. Gonoskov, I. A. Gonoskov, and M. Y. Ryabikin, “High-order harmonic generation by atoms in an elliptically polarized laser field: harmonic polarization properties and laser threshold ellipticity,” Phys. Rev. A 86, 013404 (2012).
[CrossRef]

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

M. D. Perry and J. K. Crane, “High-order harmonic emission from mixed fields,” Phys. Rev. A 48, R4051 (1993).
[CrossRef]

M. Kitzler, X. Xie, S. Roither, A. Scrinzi, and A. Baltuska, “Optical attosecond mapping by polarization selective detection,” Phys. Rev. A 76, R011801 (2007).
[CrossRef]

Phys. Rev. Lett. (4)

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

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]

H. Sofier, P. Botheron, D. Shafir, A. Diner, O. Raz, B. D. Bruner, Y. Mairesse, B. Pons, and N. Dubovich, “Near-threshold high-order harmonic spectroscopy with aligned molecules,” Phys. Rev. Lett. 105, 143904 (2010).
[CrossRef]

D. Shafir, B. Fabre, J. Higuet, H. Soifer, M. Dagan, D. Descamps, E. Me’vel, S. Petit, H. J. Worner, B. Pons, N. Dudovich, and Y. Mairesse, “Role of the ionic potential in high harmonic generation,” Phys. Rev. Lett. 108, 203001 (2012).
[CrossRef]

Rev. Mod. Phys. (1)

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

Other (3)

A. V. Andreev, S. Y. Stremoukhov, and O. A. Shoutova, Interaction of Atom With Laser Pulses of Intra-Atomic Field Strength, Anatoli V. Andreev, ed. (InTech, 2011), pp. 247–284.

E. Georgiadou, Study of Harmonic Generation with a Two-Color Field (Lund Reports on Atomic Physics, 2007).

L. D. Landau and E. M. Lifshitz, The Classical Theory of Fields (Pergamon, 1971), pp. 158–162.

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Figures (6)

Fig. 1.
Fig. 1.

First nine components of the sum in (a) Eq. (18), (b) Eq. (19), and (c) Eq. (20) calculated for μ0=0.1 (circles) and μ0=2 (squares).

Fig. 2.
Fig. 2.

Sums S1(N) as functions of the laser field intensity multiplied by the square of its wavelength in the cases in which the following states are taken into account: the 13 low-lying states of the discrete band S1(13) (squares) and the only ground state S1(1) (circles). The arrow marks the point where I1=6.77×1012W/cm2 for λ=800nm and I2=2.7×1013W/cm2 for λ=400nm.

Fig. 3.
Fig. 3.

Photoemission spectra of an argon atom interacting with a single-color field of Ti:sapphire laser, I1=6.77×1012W/cm2, τ=26.6fs.

Fig. 4.
Fig. 4.

Photoemission spectra of an argon atom interacting with the two-color laser field (I1=6.77×1012W/cm2, I2=2.7×1013W/cm2, τ1,2=26.6fs, t01t02=0) for different values of (a) θ: 21π/48 and (b) π/2.

Fig. 5.
Fig. 5.

Photoemission spectra of an argon atom interacting with the two-color laser field: (a) I2=0 (squares), I2=2.7×1011W/cm2 (circles), and I2=2.7×1013W/cm2 (triangles); (b) t02t01=13.3fs (circles) and t02t01=0 (squares); (c) τ1=τ2=26.6fs (squares) and τ1=τ2=13.3fs (circles); (d) α1=1.02029·105 (circles) and α1=1.7151·105 (squares); and (e) θ=5π/24 (squares) and θ=21π/48 (circles). Other parameters are presented in the insets of the figures.

Fig. 6.
Fig. 6.

Yield of the sixth, ninth, and tenth harmonics as a function of the angle between the polarization vectors of the components of the two-color laser field: I1=6.77×1012W/cm2, I2=2.7×1013W/cm2, t02t01=0, τ1=τ2=26.6fs. The tenth efficiency is multiplied by a factor of 3 for more convenient presentation.

Equations (33)

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iψ(r⃗,t)t=[12m(p⃗qcA⃗(t))2+U(r)]ψ(r⃗,t),
[12m(p⃗qcA⃗(t))2+U(r)]φN(r⃗,t)=ENφN(r⃗,t).
EN=En,
φN(r⃗,t)=un(r⃗)exp(iqcA⃗(t)·r⃗),
unlm(r⃗)=Rnl(r)Ylm(θ,φ).
φn*(r⃗,t)φm(r⃗,t)dr⃗=un*(r⃗)um(r⃗)dr⃗=δnm,
nφn*(r⃗,t)φn(r⃗,t)=exp[iqcA⃗(t)·(r⃗r⃗)]nun*(r⃗)un(r⃗)=δ(r⃗r⃗).
φn(r⃗,t)=mVnm1(t)um(r⃗),un(r⃗)=mVnm(t)φm(r⃗,t),
V(t)=exp(iqcA⃗(t)·r⃗).
ψ(r⃗,t)=nan(t)un(r⃗),
idan(t)dt=m,kVnk1(t)EkVkm(t)am(t).
A⃗r(r⃗,ω)=exp(ikr)rcj⃗(r⃗,ω)exp(ik⃗·r⃗)dr⃗
dI(ω)dω=ω24c3|[J⃗(ω)×n⃗]|2do,
J⃗(ω)=j⃗(r⃗,ω)dr⃗.
j⃗(r⃗,t)=q2m[ψ*(r⃗,t)·(p⃗qcA⃗(t))ψ(r⃗,t)+((p⃗qcA⃗(t))ψ(r⃗,t))*·ψ(r⃗,t)].
J⃗(t)=qmn,m,p,qan*(t)am(t)Vnp1(t)p⃗pqVqm(t).
pVpn(t)Vpm*(t)=δnm.
Sn(N)=m=1N|Vmn(t0)|2,
Sn(N)=m=1N|Vmn(t0)|2=1
A(t)=A0exp[(tt0)2τ2]sin((ω+αt)t),
V=eiqcA⃗(t)r⃗=n=0(i)nn!(qA⃗(t)·r⃗c)n.
V(t)=n=0inn!(qE⃗0·r⃗ωcos(ωt))n.
μ0=qA0aBc=2U0ωE0Eat,
J⃗(t)=i(a1s*(t)a1s(t)(V1s1s1(t)ω1s2pd⃗1s2pV2p1s(t)+V1s2p1(t)ω2p1sd⃗2p1sV1s1s(t))+a1s*(t)a2p(t)(V1s1s1(t)ω1s2pd⃗1s2pV2p2p(t)+V1s2p1(t)ω2p1sd⃗2p1sV1s2p(t))+a2p*(t)a1s(t)(V2p2p1(t)ω2p1sd⃗2p1sV1s1s(t)+V2p1s1(t)ω1s2pd⃗1s2pV2p1s(t))+a2p*(t)a2p(t)(V2p2p1(t)ω2p1sd⃗2p1sV1s2p(t)+V2p1s1(t)ω1s2pd⃗1s2pV2p2p(t))),
V1s1s1(t)16(4+(μ0cos(ωt))2)2=n=02n2Γ(n+3)n!2cos(nπ2)n+1(μ0cos(ωt))n.
V1s2p1(t)3842μ0cos(ωt)(9+4(μ0cos(ωt))2)2=n=0(32)n4Γ(n+4)i(i)n(1(1)n)22(n+2)n!(μ0cos(ωt))n.
j1s1s(t)=V1s1s1(t)ω1s2pd1s2pV2p1s(t)+V1s2p1(t)ω2p1sd2p1sV1s1s(t)=RyaBq81ωn=023nΓ(n+3)n!(n+1)cos(nπ2)(μ0cos(ωt))nn=0(32)n4(i)n(1(1)n)Γ(n+4)n!(n+2)(μ0cos(ωt))n,
P⃗(t)=n,man*(t)am(t)d⃗nm,
J⃗(t)=P⃗(t)tinman*(t)am(t)ωnmd⃗nm=qnman*(t)am(t)g⃗nm,
J⃗(t)=in,m,p,qan*(t)am(t)Vnp1(t)ωpqd⃗pqVqm(t)=qn,m,p,qan*(t)am(t)G⃗nm(t).
G⃗nm(t)=ip,qVnp1(t)ωpqr⃗pqVqm(t)=p,qVnp1(t)g⃗pqVqm(t).
G⃗00(t)=ip,qV0p1(t)ωpqr⃗pqVq0(t).
J⃗(t)=qG⃗00(t).

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