Abstract

The physics of laser-mater interactions beyond the perturbative limit configures the field of extreme non-linear optics. Although most experiments have been done in the near infrared ( λ≤ 1μm), the situation is changing nowadays with the development of sources at longer wavelengths (<5μm), opening new perspectives in the synthesis of shorter XUV attosecond pulses and higher frequencies. The theory of intense-field interactions is based either on the exact numerical integration of the time-dependent Schrödinger equation or in the development of models, mostly based on the strong-field approximation. Recent studies in the short-wave infrared show a divergence between the predictions of these models and the exact results. In this paper we will show that this discrepancy reveals the incompleteness of our present understanding of high-order harmonic generation. We discuss the physical grounds, provide a theoretical framework beyond the standard approximations and develop a compact approach that accounts for the correct scaling of the harmonic yield.

© 2009 Optical Society of America

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2008 (1)

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

2007 (1)

2006 (2)

G. Sansone, E. Benedetti, F. Calegari, C. Vozzi, L. Avaldi, R. Flammini, L. Poletto, P. Villores, C. Altucci, R. Velotta, S. Stagira, S. De Silvestri, and M. Nisoli, "Isolated Single-Cycle Attosecond Pulses," Science 314, 443-446 (2006).
[CrossRef]

O. Smirnova, M. Spanner, and M. Ivanov, "Coulomb and polarization effects in sub-cycle dynamics of strong field ionization," J. Phys. B: At. Mol. Opt. Phys. 39, S307-321 (2006).
[CrossRef]

1997 (2)

W. Becker, A. Lohr, M. Kleber, and M. Lewenstein, "A unified theory of high-harmonic generation: application to polarization properties of the harmonics," Phys. Rev. A 56, 645-656 (1997).
[CrossRef]

V. P. Krainov, "Ionization rates and energy and angular distributions at the barrier-suppression ionization of complex atoms and atomic ions," J. Opt. Soc. Am. B 14, 425431 (1997).
[CrossRef]

1995 (1)

M. Lewenstein, P. Sali`eres, and A. L’Huiller, "Phase of the atomic polarization in high-order harmonic generation," Phys. Rev. A 52, 4747-4754 (1995).
[CrossRef]

1994 (1)

M. Lewenstein, Ph. Balcou, M. Yu. Ivanov, A. L’Huiller, and P. B. Corkum, "Theory of high-harmonic generation by low-frequency laser fields," Phys. Rev. A 49, 2117-2132 (1994).
[CrossRef]

1993 (1)

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

1990 (2)

1980 (1)

H. R. Reiss, "Effect of an intense electromagnetic field on a weakly bound system," Phys. Rev. A 22,1786-1813 (1980).
[CrossRef]

1973 (1)

F. H. M. Faisal, "Multiple Absorption of Laser Photons by Atoms," J. Phys. B 6, L89-L92 (1973).
[CrossRef]

1964 (1)

L. V. Keldysh, "Ionization in the field of a strong electromagnetic wave," Zh. Eksp. Teor. Fiz. 47, 1945-1956 (1964) [ Sov. Phys. JETP 20 1307-1314 (1965)].

Agostini, P.

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

Altucci, C.

G. Sansone, E. Benedetti, F. Calegari, C. Vozzi, L. Avaldi, R. Flammini, L. Poletto, P. Villores, C. Altucci, R. Velotta, S. Stagira, S. De Silvestri, and M. Nisoli, "Isolated Single-Cycle Attosecond Pulses," Science 314, 443-446 (2006).
[CrossRef]

Avaldi, L.

G. Sansone, E. Benedetti, F. Calegari, C. Vozzi, L. Avaldi, R. Flammini, L. Poletto, P. Villores, C. Altucci, R. Velotta, S. Stagira, S. De Silvestri, and M. Nisoli, "Isolated Single-Cycle Attosecond Pulses," Science 314, 443-446 (2006).
[CrossRef]

Balcou, Ph.

M. Lewenstein, Ph. Balcou, M. Yu. Ivanov, A. L’Huiller, and P. B. Corkum, "Theory of high-harmonic generation by low-frequency laser fields," Phys. Rev. A 49, 2117-2132 (1994).
[CrossRef]

Becker, W.

W. Becker, A. Lohr, M. Kleber, and M. Lewenstein, "A unified theory of high-harmonic generation: application to polarization properties of the harmonics," Phys. Rev. A 56, 645-656 (1997).
[CrossRef]

Benedetti, E.

G. Sansone, E. Benedetti, F. Calegari, C. Vozzi, L. Avaldi, R. Flammini, L. Poletto, P. Villores, C. Altucci, R. Velotta, S. Stagira, S. De Silvestri, and M. Nisoli, "Isolated Single-Cycle Attosecond Pulses," Science 314, 443-446 (2006).
[CrossRef]

Blaga, C. I.

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

Calegari, F.

G. Sansone, E. Benedetti, F. Calegari, C. Vozzi, L. Avaldi, R. Flammini, L. Poletto, P. Villores, C. Altucci, R. Velotta, S. Stagira, S. De Silvestri, and M. Nisoli, "Isolated Single-Cycle Attosecond Pulses," Science 314, 443-446 (2006).
[CrossRef]

Catoire, F.

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

Chirla, R.

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

Colosimo, P.

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

Corkum, P. B.

M. Lewenstein, Ph. Balcou, M. Yu. Ivanov, A. L’Huiller, 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]

De Silvestri, S.

G. Sansone, E. Benedetti, F. Calegari, C. Vozzi, L. Avaldi, R. Flammini, L. Poletto, P. Villores, C. Altucci, R. Velotta, S. Stagira, S. De Silvestri, and M. Nisoli, "Isolated Single-Cycle Attosecond Pulses," Science 314, 443-446 (2006).
[CrossRef]

Di Mauro, L. F.

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

Doumy, G.

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

Faisal, F. H. M.

F. H. M. Faisal, "Multiple Absorption of Laser Photons by Atoms," J. Phys. B 6, L89-L92 (1973).
[CrossRef]

Flammini, R.

G. Sansone, E. Benedetti, F. Calegari, C. Vozzi, L. Avaldi, R. Flammini, L. Poletto, P. Villores, C. Altucci, R. Velotta, S. Stagira, S. De Silvestri, and M. Nisoli, "Isolated Single-Cycle Attosecond Pulses," Science 314, 443-446 (2006).
[CrossRef]

Hahn, Y.

Hauri, C.

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

Ivanov, M.

O. Smirnova, M. Spanner, and M. Ivanov, "Coulomb and polarization effects in sub-cycle dynamics of strong field ionization," J. Phys. B: At. Mol. Opt. Phys. 39, S307-321 (2006).
[CrossRef]

Ivanov, M. Yu.

M. Lewenstein, Ph. Balcou, M. Yu. Ivanov, A. L’Huiller, and P. B. Corkum, "Theory of high-harmonic generation by low-frequency laser fields," Phys. Rev. A 49, 2117-2132 (1994).
[CrossRef]

Janjusevic, M.

Keldysh, L. V.

L. V. Keldysh, "Ionization in the field of a strong electromagnetic wave," Zh. Eksp. Teor. Fiz. 47, 1945-1956 (1964) [ Sov. Phys. JETP 20 1307-1314 (1965)].

Kleber, M.

W. Becker, A. Lohr, M. Kleber, and M. Lewenstein, "A unified theory of high-harmonic generation: application to polarization properties of the harmonics," Phys. Rev. A 56, 645-656 (1997).
[CrossRef]

Krainov, V. P.

V. P. Krainov, "Ionization rates and energy and angular distributions at the barrier-suppression ionization of complex atoms and atomic ions," J. Opt. Soc. Am. B 14, 425431 (1997).
[CrossRef]

L’Huiller, A.

M. Lewenstein, P. Sali`eres, and A. L’Huiller, "Phase of the atomic polarization in high-order harmonic generation," Phys. Rev. A 52, 4747-4754 (1995).
[CrossRef]

M. Lewenstein, Ph. Balcou, M. Yu. Ivanov, A. L’Huiller, and P. B. Corkum, "Theory of high-harmonic generation by low-frequency laser fields," Phys. Rev. A 49, 2117-2132 (1994).
[CrossRef]

Lewenstein, M.

W. Becker, A. Lohr, M. Kleber, and M. Lewenstein, "A unified theory of high-harmonic generation: application to polarization properties of the harmonics," Phys. Rev. A 56, 645-656 (1997).
[CrossRef]

M. Lewenstein, P. Sali`eres, and A. L’Huiller, "Phase of the atomic polarization in high-order harmonic generation," Phys. Rev. A 52, 4747-4754 (1995).
[CrossRef]

M. Lewenstein, Ph. Balcou, M. Yu. Ivanov, A. L’Huiller, and P. B. Corkum, "Theory of high-harmonic generation by low-frequency laser fields," Phys. Rev. A 49, 2117-2132 (1994).
[CrossRef]

Lohr, A.

W. Becker, A. Lohr, M. Kleber, and M. Lewenstein, "A unified theory of high-harmonic generation: application to polarization properties of the harmonics," Phys. Rev. A 56, 645-656 (1997).
[CrossRef]

March, A. M.

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

Muller, H. G.

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

Nisoli, M.

G. Sansone, E. Benedetti, F. Calegari, C. Vozzi, L. Avaldi, R. Flammini, L. Poletto, P. Villores, C. Altucci, R. Velotta, S. Stagira, S. De Silvestri, and M. Nisoli, "Isolated Single-Cycle Attosecond Pulses," Science 314, 443-446 (2006).
[CrossRef]

Paulus, G. G.

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

Plaja, L.

Poletto, L.

G. Sansone, E. Benedetti, F. Calegari, C. Vozzi, L. Avaldi, R. Flammini, L. Poletto, P. Villores, C. Altucci, R. Velotta, S. Stagira, S. De Silvestri, and M. Nisoli, "Isolated Single-Cycle Attosecond Pulses," Science 314, 443-446 (2006).
[CrossRef]

Reiss, H. R.

H. R. Reiss, "Effect of an intense electromagnetic field on a weakly bound system," Phys. Rev. A 22,1786-1813 (1980).
[CrossRef]

Sali`eres, P.

M. Lewenstein, P. Sali`eres, and A. L’Huiller, "Phase of the atomic polarization in high-order harmonic generation," Phys. Rev. A 52, 4747-4754 (1995).
[CrossRef]

Sansone, G.

G. Sansone, E. Benedetti, F. Calegari, C. Vozzi, L. Avaldi, R. Flammini, L. Poletto, P. Villores, C. Altucci, R. Velotta, S. Stagira, S. De Silvestri, and M. Nisoli, "Isolated Single-Cycle Attosecond Pulses," Science 314, 443-446 (2006).
[CrossRef]

Smirnova, O.

O. Smirnova, M. Spanner, and M. Ivanov, "Coulomb and polarization effects in sub-cycle dynamics of strong field ionization," J. Phys. B: At. Mol. Opt. Phys. 39, S307-321 (2006).
[CrossRef]

Spanner, M.

O. Smirnova, M. Spanner, and M. Ivanov, "Coulomb and polarization effects in sub-cycle dynamics of strong field ionization," J. Phys. B: At. Mol. Opt. Phys. 39, S307-321 (2006).
[CrossRef]

Stagira, S.

G. Sansone, E. Benedetti, F. Calegari, C. Vozzi, L. Avaldi, R. Flammini, L. Poletto, P. Villores, C. Altucci, R. Velotta, S. Stagira, S. De Silvestri, and M. Nisoli, "Isolated Single-Cycle Attosecond Pulses," Science 314, 443-446 (2006).
[CrossRef]

Tate, J.

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

Velotta, R.

G. Sansone, E. Benedetti, F. Calegari, C. Vozzi, L. Avaldi, R. Flammini, L. Poletto, P. Villores, C. Altucci, R. Velotta, S. Stagira, S. De Silvestri, and M. Nisoli, "Isolated Single-Cycle Attosecond Pulses," Science 314, 443-446 (2006).
[CrossRef]

Villores, P.

G. Sansone, E. Benedetti, F. Calegari, C. Vozzi, L. Avaldi, R. Flammini, L. Poletto, P. Villores, C. Altucci, R. Velotta, S. Stagira, S. De Silvestri, and M. Nisoli, "Isolated Single-Cycle Attosecond Pulses," Science 314, 443-446 (2006).
[CrossRef]

Vozzi, C.

G. Sansone, E. Benedetti, F. Calegari, C. Vozzi, L. Avaldi, R. Flammini, L. Poletto, P. Villores, C. Altucci, R. Velotta, S. Stagira, S. De Silvestri, and M. Nisoli, "Isolated Single-Cycle Attosecond Pulses," Science 314, 443-446 (2006).
[CrossRef]

Wheeler, J.

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

J. Opt. Soc. Am. B (3)

V. P. Krainov, "Ionization rates and energy and angular distributions at the barrier-suppression ionization of complex atoms and atomic ions," J. Opt. Soc. Am. B 14, 425431 (1997).
[CrossRef]

P. Krsti’c and M. H. Mittleman, "S-matrix theory of multiphoton ionization," J. Opt. Soc. Am. B 7, 587-591 (1990).
[CrossRef]

M. Janjusevic and Y. Hahn, "Testing of laser-dressed atomic states," J. Opt. Soc. Am. B 7, 592-597 (1990).
[CrossRef]

J. Phys. B (1)

F. H. M. Faisal, "Multiple Absorption of Laser Photons by Atoms," J. Phys. B 6, L89-L92 (1973).
[CrossRef]

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

O. Smirnova, M. Spanner, and M. Ivanov, "Coulomb and polarization effects in sub-cycle dynamics of strong field ionization," J. Phys. B: At. Mol. Opt. Phys. 39, S307-321 (2006).
[CrossRef]

Nature Phys. (1)

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

Opt. Express (1)

Phys. Rev. A (4)

H. R. Reiss, "Effect of an intense electromagnetic field on a weakly bound system," Phys. Rev. A 22,1786-1813 (1980).
[CrossRef]

M. Lewenstein, Ph. Balcou, M. Yu. Ivanov, A. L’Huiller, and P. B. Corkum, "Theory of high-harmonic generation by low-frequency laser fields," Phys. Rev. A 49, 2117-2132 (1994).
[CrossRef]

M. Lewenstein, P. Sali`eres, and A. L’Huiller, "Phase of the atomic polarization in high-order harmonic generation," Phys. Rev. A 52, 4747-4754 (1995).
[CrossRef]

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