Abstract

We theoretically investigate the generation of high harmonics and attosecond pulses by mid-infrared (IR) driving fields. Conditions for coherent build-up of high harmonics are revisited. We show that the coherence length dictated by ionization-induced dephasing does not constitute an ultimate limitation to the coherent growth of soft X-ray (> 100 eV) harmonics driven by few-cycle mid-IR driving pulses: perfect phase-matching, similar to non-adiabatic self-phase-matching, can be achieved even without non-linear deformation of the driving pulse. Our trajectory-based analysis of phase-matching reveals several important advantages of using longer laser wavelengths: conversion efficiency can be improved by orders of magnitude, phase-matched build-up of harmonics can be achieved in a jet with a high gas pressure, and isolated attosecond pulses can be extracted from plateau harmonics.

© 2007 Optical Society of America

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    [CrossRef] [PubMed]
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  4. G. Sansone, E. Benedetti, F. Calegari, C. Vozzi, L. Avaldi, R. Flammini, L. Poletto, P. Villoresi, C. Altucci, R. Velotta, S. Stagira, S. De Silvestri, M. Nisoli, "Isolated single-cycle attosecond pulses," Science 314, 443-446 (2006).
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    [CrossRef]
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    [CrossRef]
  24. T. Brabec and F. Krausz, "Nonlinear Optical Pulse Propagation in the Single-Cycle Regime," Phys. Rev. Lett. 78, 3282-3285 (1997).
    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
  31. P. Balcou, P. Salieres, A. LHuillier, M. Lewenstein, "Generalized phase-matching conditions for high harmonics: The role of field-gradient forces," Phys. Rev. A 55, 3204-3210 (1997).
    [CrossRef]
  32. M. Geissler, G. Tempea, and T. Brabec, "Phase-matched high-order harmonic generation in the nonadiabatic limit," Phys. Rev. A 62, 033817 (2000).
    [CrossRef]
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2007

P. B. Corkum, F. Krausz, "Attosecond science," Nat. Phys. 3, 381-387 (2007).
[CrossRef]

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

C. P. Hauri, R. B. Lopez-Martens, C. I. Blaga, K. D. Schultz, J. Cryan, R. Chirla, P. Colosimo, G. Doumy, A. M. March, C. Roedig, E. Sistrunk, J. Tate, J. Wheeler, L. F. DiMauro, E. P. Power, "Intense self-compressed, self-phase-stabilized few-cycle pulses at 2 μm from an optical filament," Opt. Lett. 32, 868-870 (2007).
[CrossRef] [PubMed]

2006

T. Fuji, N. Ishii, C. Y. Teisset, X. Gu, Th. Metzger, A. Baltuska, "Parametric amplification of few-cycle carrier-envelope phase-stable pulses at 2.1 μm," Opt. Lett. 31, 1103 (2006).
[CrossRef] [PubMed]

C. Vozzi, G. Cirmi, C. Manzoni, E. Benedetti, F. Calegari, G. Sansone, S. Stagira, O. Svelto, S. De Silvestri, M. Nisoli, G. Cerullo, "High-energy, few-optical-cycle pulses at 1.5 μm with passive carrier-envelope phase stabilization," Opt. Express 14, 10109-10116 (2006).
[CrossRef] [PubMed]

G. D. Tsakiris, K. Eidmann, J. Meyer-ter-Vehn, Ferenc Krausz, "Route to intense single attosecond pulses," New J. Phys. 8, 1-20 (2006).
[CrossRef]

G. Sansone, E. Benedetti, F. Calegari, C. Vozzi, L. Avaldi, R. Flammini, L. Poletto, P. Villoresi, C. Altucci, R. Velotta, S. Stagira, S. De Silvestri, M. Nisoli, "Isolated single-cycle attosecond pulses," Science 314, 443-446 (2006).
[CrossRef] [PubMed]

2005

J. Seres, E. Seres, A. J. Verhoef, G. Tempea, C. Streli, P. Wobrauschek, V. Yakovlev, A. Scrinzi, C. Spielmann, F. Krausz, "Source of coherent kiloelectronvolt X-rays," Nature 433, 596 (2005).
[CrossRef] [PubMed]

A. Gordon, F. X. Kärtner, "Scaling of keV HHG photon yield with drive wavelength," Opt. Express 13, 2941-2947 (2005).
[CrossRef] [PubMed]

2004

S. Gordienko, A. Pukhov, O. Shorokhov, T. Baeva, "Relativistic Doppler Effect: Universal Spectra and Zeptosecond Pulses", Phys. Rev. Lett. 93, 115002 (2004).
[CrossRef] [PubMed]

P. Agostini, L. F. DiMauro, "The physics of attosecond light pulses," Rep. Prog. Phys. 67, 813-855 (2004).
[CrossRef]

R. Kienberger, E. Goulielmakis, M. Uiberacker, A. Baltu¡ska, V. Yakovlev, F. Bammer, A. Scrinzi, Th. Westerwalbesloh, U. Kleineberg, U. Heinzmann, M. Drescher, F. Krausz, "Atomic transient recorder," Nature 427, 817-821 (2004).
[CrossRef] [PubMed]

2003

T. O. Clatterbuck, C. Lyngå, P. Colosimo, J. D. D. Marin, B. Sheehy, L. F. DiMauro, P. Agostini, K. C. KulanderJ. Mod. Opt. 50, 441-450 (2003).

M. Spanner, M. Pshenichnikov, V. Olvo, M. Yu. Ivanov, "Controlled supercontinuum generation for optimal pulse compression: A time-warp analysis of nonlinear propagation of ultrabroadband pulses," Appl. Phys. B 77, 329-336 (2003).
[CrossRef]

V. S. Yakovlev, A. Scrinzi, "High Harmonic Imaging of Few-Cycle Laser Pulses," Phys. Rev. Lett. 91, 153901 (2003).
[CrossRef] [PubMed]

Y. Mairesse, A. de Bohan, L. J. Frasinski, H. Merdji, L. C. Dinu, P. Monchicourt, P. Breger, M. Kovačev, R. Taïeb, B. Carré, H. G. Muller, P. Agostini, P. Salières, "Attosecond synchronization of high-harmonic soft Xrays," Science 302, 1540-1543 (2003).
[CrossRef] [PubMed]

2002

N. Milosevic, A. Scrinzi, T. Brabec, "Numerical characterisation of high harmonic attosecond pulses," Phys. Rev. Lett. 88, 093905 (2002).
[CrossRef] [PubMed]

2001

M. B. Gaarde, "Time-frequency representations of high order harmonics," Opt. Express 8, 529-536 (2001).
[CrossRef] [PubMed]

M. Hentschel, R. Kienberger, Ch. Spielmann, G. A. Reider, N. Milosevic, T. Brabec, P. Corkum, U. Heinzmann, M. Drescher, F. Krausz, "Attosecond metrology," Nature 414, 509-513 (2001).
[CrossRef] [PubMed]

2000

A. Scrinzi, "Ionization of multielectron atoms by strong static electric fields," Phys. Rev. A 61, 041402R (2000).
[CrossRef]

M. Geissler, G. Tempea, and T. Brabec, "Phase-matched high-order harmonic generation in the nonadiabatic limit," Phys. Rev. A 62, 033817 (2000).
[CrossRef]

1999

M. Geissler, G. Tempea, A. Scrinzi, M. Schn¨urer, F. Krausz, T. Brabec, "Light propagation in field-ionizing media: Extreme nonlinear optics," Phys. Rev. Lett. 83, 2930-2933 (1999).
[CrossRef]

1997

T. Brabec and F. Krausz, "Nonlinear Optical Pulse Propagation in the Single-Cycle Regime," Phys. Rev. Lett. 78, 3282-3285 (1997).
[CrossRef]

P. Balcou, P. Salieres, A. LHuillier, M. Lewenstein, "Generalized phase-matching conditions for high harmonics: The role of field-gradient forces," Phys. Rev. A 55, 3204-3210 (1997).
[CrossRef]

I. P. Christov, M. M. Murnane, H. C. Kapteyn, "High-Harmonic Generation of Attosecond Pulses in the Single-Cycle Regime," Phys. Rev. Lett. 78, 1251-1254 (1997).
[CrossRef]

1996

M. Yu. Ivanov, T. Brabec, and N. H. Burnett, "Coulomb corrections and polarization effects in high field high harmonic emission," Phys. Rev. A 54, 742-745 (1996).
[CrossRef] [PubMed]

P. Antoine, A. L’Huillier, M. Lewenstein, "Attosecond pulse trains using high-order harmonics," Phys. Rev. Lett. 77, 1234-1237 (1996).
[CrossRef] [PubMed]

1995

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

P. Salieres, A. L’Huillier, M. Lewenstein, "Coherence control of high-order harmonics," Phys. Rev. Lett. 74, 3776-3779 (1995).
[CrossRef] [PubMed]

1994

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

1993

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

1979

R. K. Bullough, P. M. Jack, P. W. Kitchenside, R. Saunders, Phys. Scr. 20, 364 (1979).
[CrossRef]

Agostini, P.

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

P. Agostini, L. F. DiMauro, "The physics of attosecond light pulses," Rep. Prog. Phys. 67, 813-855 (2004).
[CrossRef]

T. O. Clatterbuck, C. Lyngå, P. Colosimo, J. D. D. Marin, B. Sheehy, L. F. DiMauro, P. Agostini, K. C. KulanderJ. Mod. Opt. 50, 441-450 (2003).

Y. Mairesse, A. de Bohan, L. J. Frasinski, H. Merdji, L. C. Dinu, P. Monchicourt, P. Breger, M. Kovačev, R. Taïeb, B. Carré, H. G. Muller, P. Agostini, P. Salières, "Attosecond synchronization of high-harmonic soft Xrays," Science 302, 1540-1543 (2003).
[CrossRef] [PubMed]

Altucci, C.

G. Sansone, E. Benedetti, F. Calegari, C. Vozzi, L. Avaldi, R. Flammini, L. Poletto, P. Villoresi, C. Altucci, R. Velotta, S. Stagira, S. De Silvestri, M. Nisoli, "Isolated single-cycle attosecond pulses," Science 314, 443-446 (2006).
[CrossRef] [PubMed]

Antoine, P.

P. Antoine, A. L’Huillier, M. Lewenstein, "Attosecond pulse trains using high-order harmonics," Phys. Rev. Lett. 77, 1234-1237 (1996).
[CrossRef] [PubMed]

Auguste, T.

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

Avaldi, L.

G. Sansone, E. Benedetti, F. Calegari, C. Vozzi, L. Avaldi, R. Flammini, L. Poletto, P. Villoresi, C. Altucci, R. Velotta, S. Stagira, S. De Silvestri, M. Nisoli, "Isolated single-cycle attosecond pulses," Science 314, 443-446 (2006).
[CrossRef] [PubMed]

Baeva, T.

S. Gordienko, A. Pukhov, O. Shorokhov, T. Baeva, "Relativistic Doppler Effect: Universal Spectra and Zeptosecond Pulses", Phys. Rev. Lett. 93, 115002 (2004).
[CrossRef] [PubMed]

Balcou, P.

P. Balcou, P. Salieres, A. LHuillier, M. Lewenstein, "Generalized phase-matching conditions for high harmonics: The role of field-gradient forces," Phys. Rev. A 55, 3204-3210 (1997).
[CrossRef]

Balcou, Ph.

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

Baltuska, A.

Benedetti, E.

C. Vozzi, G. Cirmi, C. Manzoni, E. Benedetti, F. Calegari, G. Sansone, S. Stagira, O. Svelto, S. De Silvestri, M. Nisoli, G. Cerullo, "High-energy, few-optical-cycle pulses at 1.5 μm with passive carrier-envelope phase stabilization," Opt. Express 14, 10109-10116 (2006).
[CrossRef] [PubMed]

G. Sansone, E. Benedetti, F. Calegari, C. Vozzi, L. Avaldi, R. Flammini, L. Poletto, P. Villoresi, C. Altucci, R. Velotta, S. Stagira, S. De Silvestri, M. Nisoli, "Isolated single-cycle attosecond pulses," Science 314, 443-446 (2006).
[CrossRef] [PubMed]

Blaga, C. I.

Brabec, T.

N. Milosevic, A. Scrinzi, T. Brabec, "Numerical characterisation of high harmonic attosecond pulses," Phys. Rev. Lett. 88, 093905 (2002).
[CrossRef] [PubMed]

M. Hentschel, R. Kienberger, Ch. Spielmann, G. A. Reider, N. Milosevic, T. Brabec, P. Corkum, U. Heinzmann, M. Drescher, F. Krausz, "Attosecond metrology," Nature 414, 509-513 (2001).
[CrossRef] [PubMed]

M. Geissler, G. Tempea, and T. Brabec, "Phase-matched high-order harmonic generation in the nonadiabatic limit," Phys. Rev. A 62, 033817 (2000).
[CrossRef]

T. Brabec and F. Krausz, "Nonlinear Optical Pulse Propagation in the Single-Cycle Regime," Phys. Rev. Lett. 78, 3282-3285 (1997).
[CrossRef]

M. Yu. Ivanov, T. Brabec, and N. H. Burnett, "Coulomb corrections and polarization effects in high field high harmonic emission," Phys. Rev. A 54, 742-745 (1996).
[CrossRef] [PubMed]

Breger, P.

Y. Mairesse, A. de Bohan, L. J. Frasinski, H. Merdji, L. C. Dinu, P. Monchicourt, P. Breger, M. Kovačev, R. Taïeb, B. Carré, H. G. Muller, P. Agostini, P. Salières, "Attosecond synchronization of high-harmonic soft Xrays," Science 302, 1540-1543 (2003).
[CrossRef] [PubMed]

Bullough, R. K.

R. K. Bullough, P. M. Jack, P. W. Kitchenside, R. Saunders, Phys. Scr. 20, 364 (1979).
[CrossRef]

Burnett, N. H.

M. Yu. Ivanov, T. Brabec, and N. H. Burnett, "Coulomb corrections and polarization effects in high field high harmonic emission," Phys. Rev. A 54, 742-745 (1996).
[CrossRef] [PubMed]

Calegari, F.

G. Sansone, E. Benedetti, F. Calegari, C. Vozzi, L. Avaldi, R. Flammini, L. Poletto, P. Villoresi, C. Altucci, R. Velotta, S. Stagira, S. De Silvestri, M. Nisoli, "Isolated single-cycle attosecond pulses," Science 314, 443-446 (2006).
[CrossRef] [PubMed]

C. Vozzi, G. Cirmi, C. Manzoni, E. Benedetti, F. Calegari, G. Sansone, S. Stagira, O. Svelto, S. De Silvestri, M. Nisoli, G. Cerullo, "High-energy, few-optical-cycle pulses at 1.5 μm with passive carrier-envelope phase stabilization," Opt. Express 14, 10109-10116 (2006).
[CrossRef] [PubMed]

Carré, B.

Y. Mairesse, A. de Bohan, L. J. Frasinski, H. Merdji, L. C. Dinu, P. Monchicourt, P. Breger, M. Kovačev, R. Taïeb, B. Carré, H. G. Muller, P. Agostini, P. Salières, "Attosecond synchronization of high-harmonic soft Xrays," Science 302, 1540-1543 (2003).
[CrossRef] [PubMed]

Cerullo, G.

Chirla, R.

Christov, I. P.

I. P. Christov, M. M. Murnane, H. C. Kapteyn, "High-Harmonic Generation of Attosecond Pulses in the Single-Cycle Regime," Phys. Rev. Lett. 78, 1251-1254 (1997).
[CrossRef]

Cirmi, G.

Clatterbuck, T. O.

T. O. Clatterbuck, C. Lyngå, P. Colosimo, J. D. D. Marin, B. Sheehy, L. F. DiMauro, P. Agostini, K. C. KulanderJ. Mod. Opt. 50, 441-450 (2003).

Colosimo, P.

Corkum, P.

M. Hentschel, R. Kienberger, Ch. Spielmann, G. A. Reider, N. Milosevic, T. Brabec, P. Corkum, U. Heinzmann, M. Drescher, F. Krausz, "Attosecond metrology," Nature 414, 509-513 (2001).
[CrossRef] [PubMed]

Corkum, P. B.

P. B. Corkum, F. Krausz, "Attosecond science," Nat. Phys. 3, 381-387 (2007).
[CrossRef]

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March, A. M.

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Y. Mairesse, A. de Bohan, L. J. Frasinski, H. Merdji, L. C. Dinu, P. Monchicourt, P. Breger, M. Kovačev, R. Taïeb, B. Carré, H. G. Muller, P. Agostini, P. Salières, "Attosecond synchronization of high-harmonic soft Xrays," Science 302, 1540-1543 (2003).
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N. Milosevic, A. Scrinzi, T. Brabec, "Numerical characterisation of high harmonic attosecond pulses," Phys. Rev. Lett. 88, 093905 (2002).
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M. Hentschel, R. Kienberger, Ch. Spielmann, G. A. Reider, N. Milosevic, T. Brabec, P. Corkum, U. Heinzmann, M. Drescher, F. Krausz, "Attosecond metrology," Nature 414, 509-513 (2001).
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Y. Mairesse, A. de Bohan, L. J. Frasinski, H. Merdji, L. C. Dinu, P. Monchicourt, P. Breger, M. Kovačev, R. Taïeb, B. Carré, H. G. Muller, P. Agostini, P. Salières, "Attosecond synchronization of high-harmonic soft Xrays," Science 302, 1540-1543 (2003).
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J. Tate, T. Auguste, H. G. Muller, P. Salieres, P. Agostini, L. F. DiMauro, "Scaling of wave-packet dynamics in an intense midinfrared field," Phys. Rev. Lett. 98, 013901 (2007).
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I. P. Christov, M. M. Murnane, H. C. Kapteyn, "High-Harmonic Generation of Attosecond Pulses in the Single-Cycle Regime," Phys. Rev. Lett. 78, 1251-1254 (1997).
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C. Vozzi, G. Cirmi, C. Manzoni, E. Benedetti, F. Calegari, G. Sansone, S. Stagira, O. Svelto, S. De Silvestri, M. Nisoli, G. Cerullo, "High-energy, few-optical-cycle pulses at 1.5 μm with passive carrier-envelope phase stabilization," Opt. Express 14, 10109-10116 (2006).
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G. Sansone, E. Benedetti, F. Calegari, C. Vozzi, L. Avaldi, R. Flammini, L. Poletto, P. Villoresi, C. Altucci, R. Velotta, S. Stagira, S. De Silvestri, M. Nisoli, "Isolated single-cycle attosecond pulses," Science 314, 443-446 (2006).
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M. Spanner, M. Pshenichnikov, V. Olvo, M. Yu. Ivanov, "Controlled supercontinuum generation for optimal pulse compression: A time-warp analysis of nonlinear propagation of ultrabroadband pulses," Appl. Phys. B 77, 329-336 (2003).
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G. Sansone, E. Benedetti, F. Calegari, C. Vozzi, L. Avaldi, R. Flammini, L. Poletto, P. Villoresi, C. Altucci, R. Velotta, S. Stagira, S. De Silvestri, M. Nisoli, "Isolated single-cycle attosecond pulses," Science 314, 443-446 (2006).
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Pshenichnikov, M.

M. Spanner, M. Pshenichnikov, V. Olvo, M. Yu. Ivanov, "Controlled supercontinuum generation for optimal pulse compression: A time-warp analysis of nonlinear propagation of ultrabroadband pulses," Appl. Phys. B 77, 329-336 (2003).
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S. Gordienko, A. Pukhov, O. Shorokhov, T. Baeva, "Relativistic Doppler Effect: Universal Spectra and Zeptosecond Pulses", Phys. Rev. Lett. 93, 115002 (2004).
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Reider, G. A.

M. Hentschel, R. Kienberger, Ch. Spielmann, G. A. Reider, N. Milosevic, T. Brabec, P. Corkum, U. Heinzmann, M. Drescher, F. Krausz, "Attosecond metrology," Nature 414, 509-513 (2001).
[CrossRef] [PubMed]

Roedig, C.

Salieres, P.

J. Tate, T. Auguste, H. G. Muller, P. Salieres, P. Agostini, L. F. DiMauro, "Scaling of wave-packet dynamics in an intense midinfrared field," Phys. Rev. Lett. 98, 013901 (2007).
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Y. Mairesse, A. de Bohan, L. J. Frasinski, H. Merdji, L. C. Dinu, P. Monchicourt, P. Breger, M. Kovačev, R. Taïeb, B. Carré, H. G. Muller, P. Agostini, P. Salières, "Attosecond synchronization of high-harmonic soft Xrays," Science 302, 1540-1543 (2003).
[CrossRef] [PubMed]

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

Sansone, G.

C. Vozzi, G. Cirmi, C. Manzoni, E. Benedetti, F. Calegari, G. Sansone, S. Stagira, O. Svelto, S. De Silvestri, M. Nisoli, G. Cerullo, "High-energy, few-optical-cycle pulses at 1.5 μm with passive carrier-envelope phase stabilization," Opt. Express 14, 10109-10116 (2006).
[CrossRef] [PubMed]

G. Sansone, E. Benedetti, F. Calegari, C. Vozzi, L. Avaldi, R. Flammini, L. Poletto, P. Villoresi, C. Altucci, R. Velotta, S. Stagira, S. De Silvestri, M. Nisoli, "Isolated single-cycle attosecond pulses," Science 314, 443-446 (2006).
[CrossRef] [PubMed]

Saunders, R.

R. K. Bullough, P. M. Jack, P. W. Kitchenside, R. Saunders, Phys. Scr. 20, 364 (1979).
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Schultz, K. D.

Scrinzi, A.

J. Seres, E. Seres, A. J. Verhoef, G. Tempea, C. Streli, P. Wobrauschek, V. Yakovlev, A. Scrinzi, C. Spielmann, F. Krausz, "Source of coherent kiloelectronvolt X-rays," Nature 433, 596 (2005).
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V. S. Yakovlev, A. Scrinzi, "High Harmonic Imaging of Few-Cycle Laser Pulses," Phys. Rev. Lett. 91, 153901 (2003).
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N. Milosevic, A. Scrinzi, T. Brabec, "Numerical characterisation of high harmonic attosecond pulses," Phys. Rev. Lett. 88, 093905 (2002).
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A. Scrinzi, "Ionization of multielectron atoms by strong static electric fields," Phys. Rev. A 61, 041402R (2000).
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M. Geissler, G. Tempea, A. Scrinzi, M. Schn¨urer, F. Krausz, T. Brabec, "Light propagation in field-ionizing media: Extreme nonlinear optics," Phys. Rev. Lett. 83, 2930-2933 (1999).
[CrossRef]

Seres, E.

J. Seres, E. Seres, A. J. Verhoef, G. Tempea, C. Streli, P. Wobrauschek, V. Yakovlev, A. Scrinzi, C. Spielmann, F. Krausz, "Source of coherent kiloelectronvolt X-rays," Nature 433, 596 (2005).
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Seres, J.

J. Seres, E. Seres, A. J. Verhoef, G. Tempea, C. Streli, P. Wobrauschek, V. Yakovlev, A. Scrinzi, C. Spielmann, F. Krausz, "Source of coherent kiloelectronvolt X-rays," Nature 433, 596 (2005).
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Sheehy, B.

T. O. Clatterbuck, C. Lyngå, P. Colosimo, J. D. D. Marin, B. Sheehy, L. F. DiMauro, P. Agostini, K. C. KulanderJ. Mod. Opt. 50, 441-450 (2003).

Shorokhov, O.

S. Gordienko, A. Pukhov, O. Shorokhov, T. Baeva, "Relativistic Doppler Effect: Universal Spectra and Zeptosecond Pulses", Phys. Rev. Lett. 93, 115002 (2004).
[CrossRef] [PubMed]

Sistrunk, E.

Spanner, M.

M. Spanner, M. Pshenichnikov, V. Olvo, M. Yu. Ivanov, "Controlled supercontinuum generation for optimal pulse compression: A time-warp analysis of nonlinear propagation of ultrabroadband pulses," Appl. Phys. B 77, 329-336 (2003).
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Spielmann, C.

J. Seres, E. Seres, A. J. Verhoef, G. Tempea, C. Streli, P. Wobrauschek, V. Yakovlev, A. Scrinzi, C. Spielmann, F. Krausz, "Source of coherent kiloelectronvolt X-rays," Nature 433, 596 (2005).
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Spielmann, Ch.

M. Hentschel, R. Kienberger, Ch. Spielmann, G. A. Reider, N. Milosevic, T. Brabec, P. Corkum, U. Heinzmann, M. Drescher, F. Krausz, "Attosecond metrology," Nature 414, 509-513 (2001).
[CrossRef] [PubMed]

Stagira, S.

G. Sansone, E. Benedetti, F. Calegari, C. Vozzi, L. Avaldi, R. Flammini, L. Poletto, P. Villoresi, C. Altucci, R. Velotta, S. Stagira, S. De Silvestri, M. Nisoli, "Isolated single-cycle attosecond pulses," Science 314, 443-446 (2006).
[CrossRef] [PubMed]

C. Vozzi, G. Cirmi, C. Manzoni, E. Benedetti, F. Calegari, G. Sansone, S. Stagira, O. Svelto, S. De Silvestri, M. Nisoli, G. Cerullo, "High-energy, few-optical-cycle pulses at 1.5 μm with passive carrier-envelope phase stabilization," Opt. Express 14, 10109-10116 (2006).
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Streli, C.

J. Seres, E. Seres, A. J. Verhoef, G. Tempea, C. Streli, P. Wobrauschek, V. Yakovlev, A. Scrinzi, C. Spielmann, F. Krausz, "Source of coherent kiloelectronvolt X-rays," Nature 433, 596 (2005).
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Taïeb, R.

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G. Sansone, E. Benedetti, F. Calegari, C. Vozzi, L. Avaldi, R. Flammini, L. Poletto, P. Villoresi, C. Altucci, R. Velotta, S. Stagira, S. De Silvestri, M. Nisoli, "Isolated single-cycle attosecond pulses," Science 314, 443-446 (2006).
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J. Seres, E. Seres, A. J. Verhoef, G. Tempea, C. Streli, P. Wobrauschek, V. Yakovlev, A. Scrinzi, C. Spielmann, F. Krausz, "Source of coherent kiloelectronvolt X-rays," Nature 433, 596 (2005).
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G. Sansone, E. Benedetti, F. Calegari, C. Vozzi, L. Avaldi, R. Flammini, L. Poletto, P. Villoresi, C. Altucci, R. Velotta, S. Stagira, S. De Silvestri, M. Nisoli, "Isolated single-cycle attosecond pulses," Science 314, 443-446 (2006).
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G. Sansone, E. Benedetti, F. Calegari, C. Vozzi, L. Avaldi, R. Flammini, L. Poletto, P. Villoresi, C. Altucci, R. Velotta, S. Stagira, S. De Silvestri, M. Nisoli, "Isolated single-cycle attosecond pulses," Science 314, 443-446 (2006).
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J. Seres, E. Seres, A. J. Verhoef, G. Tempea, C. Streli, P. Wobrauschek, V. Yakovlev, A. Scrinzi, C. Spielmann, F. Krausz, "Source of coherent kiloelectronvolt X-rays," Nature 433, 596 (2005).
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J. Seres, E. Seres, A. J. Verhoef, G. Tempea, C. Streli, P. Wobrauschek, V. Yakovlev, A. Scrinzi, C. Spielmann, F. Krausz, "Source of coherent kiloelectronvolt X-rays," Nature 433, 596 (2005).
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V. S. Yakovlev, A. Scrinzi, "High Harmonic Imaging of Few-Cycle Laser Pulses," Phys. Rev. Lett. 91, 153901 (2003).
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M. Spanner, M. Pshenichnikov, V. Olvo, M. Yu. Ivanov, "Controlled supercontinuum generation for optimal pulse compression: A time-warp analysis of nonlinear propagation of ultrabroadband pulses," Appl. Phys. B 77, 329-336 (2003).
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T. O. Clatterbuck, C. Lyngå, P. Colosimo, J. D. D. Marin, B. Sheehy, L. F. DiMauro, P. Agostini, K. C. KulanderJ. Mod. Opt. 50, 441-450 (2003).

Nat. Phys.

P. B. Corkum, F. Krausz, "Attosecond science," Nat. Phys. 3, 381-387 (2007).
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Nature

M. Hentschel, R. Kienberger, Ch. Spielmann, G. A. Reider, N. Milosevic, T. Brabec, P. Corkum, U. Heinzmann, M. Drescher, F. Krausz, "Attosecond metrology," Nature 414, 509-513 (2001).
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R. Kienberger, E. Goulielmakis, M. Uiberacker, A. Baltu¡ska, V. Yakovlev, F. Bammer, A. Scrinzi, Th. Westerwalbesloh, U. Kleineberg, U. Heinzmann, M. Drescher, F. Krausz, "Atomic transient recorder," Nature 427, 817-821 (2004).
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J. Seres, E. Seres, A. J. Verhoef, G. Tempea, C. Streli, P. Wobrauschek, V. Yakovlev, A. Scrinzi, C. Spielmann, F. Krausz, "Source of coherent kiloelectronvolt X-rays," Nature 433, 596 (2005).
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New J. Phys.

G. D. Tsakiris, K. Eidmann, J. Meyer-ter-Vehn, Ferenc Krausz, "Route to intense single attosecond pulses," New J. Phys. 8, 1-20 (2006).
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Y. Mairesse, A. de Bohan, L. J. Frasinski, H. Merdji, L. C. Dinu, P. Monchicourt, P. Breger, M. Kovačev, R. Taïeb, B. Carré, H. G. Muller, P. Agostini, P. Salières, "Attosecond synchronization of high-harmonic soft Xrays," Science 302, 1540-1543 (2003).
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Figures (5)

Fig. 1.
Fig. 1.

Contributions from different half-cycles of a 2-cycle laser pulse (inset in panel a) to high harmonics at 400 eV. For λ L = 0.75μm, a rapid increase of the harmonic signal (panel a) often coincides with a peak of the single-atom dipole response (panel b, solid lines). For λ L = 2.1μm (panels c and d), the observed highly efficient harmonic generation is due to phase-matching. In both simulations, the cut-off energy was equal to 700 eV at the beginning of propagation; cut-off energies of individual half-cycles are represented by dashed curves in panels b and d. Harmonic intensity in panels a and c is measured in the same units, propagation was simulated for a 100-mbar He jet starting from the focus of the laser beam. The dashed green line in panel c represents contribution from half-cycle 2 calculated with a non-divergent laser beam. In this case the harmonic generation is not phase-matched and a regular coherent ringing is observed.

Fig. 2.
Fig. 2.

Single-atom dipole response at the beginning of a 100-mbar He jet (a), and the far-field spectral intensity of high harmonics (b) generated by a 1-mJ 2-cycle pulse for different values of the laser wavelength λ L. In each simulation, the initial semi-classical cut-off energy was equal to 700 eV and the jet thickness L was chosen to reduce it by 10% (legend in panel b).

Fig. 3.
Fig. 3.

Generation of a single attosecond pulse in the plateau region. Panel a shows the far-field on-axis harmonic signal generated with λ L = 1.5μm (green dashed line in Fig. 2b) after it was transmitted through a filter made of 0.1 μm of Cu and 0.1 μm of Pd. The filter suppresses harmonics below 100 eV, its transmittance is shown by the inset in panel a. Panel b shows the time-domain intensity of the harmonic field after the filter.

Fig. 4.
Fig. 4.

Scaling of harmonic output with gas pressure p for λ L = 2.1 μm. Propagation of the laser pulse was simulated in all spatial dimensions, HHG was simulated on axis only. At small values of p the harmonic output grows quadratically with pressure. Due to SPM, the overall output becomes pressure-independent at large values of p in agreement with Eq. (26). The inset shows the dependence of the cut-off energy on the propagation distance.

Fig. 5.
Fig. 5.

Scaling law given by Eq. (32). The ionization rate of helium was calculated for a 2-cycle Gaussian laser pulse with a peak intensity adjusted to have a required value of the cut-off energy Ωcutoff. Only simulations with an ionization probability between 0.1% and 10% are shown in this plot.

Equations (32)

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d ( t ) = Re [ e i π 4 trajectories a ion ( t ) a pr ( t ) a rec ( t ) ] .
t b t A L ( t ) d t = ( t t b ) A L ( t b ) ,
A L ( t ) = t E L ( t ) dt′
a ion = ( dn ( t b ) dt ) 1 2 ,
a pr ( t ) = ( 2 π t t b ) 3 2 ( 2 W b ) 1 4 E L ( t b ) exp [ i ( t t b ) W b iS ( t ) ] and
a rec ( t ) = n ( t r ) A L ( t b ) A L ( t ) [ 2 W b + { A L ( t b ) A L ( t ) } 2 ] 3 ,
S ( t ) = 1 2 t b t [ A L ( t ) A L ( t b ) ] 2 dt .
d ˜ ( Ω ) = e i π 4 bursts a ion ( t ) a pr ( t ) a rec ( t ) exp ( i Ω t ) dt = k d ˜ k ( Ω )
E H z ρ Ω z = ( α ( Ω ) + ic 2 Ω 2 ) E H z ρ Ω + k s k z ρ Ω .
s k z ρ Ω = 2 πi Ω n a e a 0 c 1 d ˜ k ( Ω ) ,
arg [ s k ] φ ( t r ( k ) ) = Ω t r ( k ) S ( t r ( k ) ) ( t r ( k ) t b ( k ) ) W b + π 2 ,
Ω = W b + W kin
dz = Ω d t r dz dS dz ( d t r dz d t b dz ) W b .
dz = W b d t b ( z ) dz S z = W b d t b ( z ) dz t b ( z ) t r ( z ) dt [ A L z t A L ( z , t b ( z ) ) ] A L z t z ,
A L z t = f ( z ) g ( t τ ( z ) ) ,
E L z t = f ( z ) g ( t τ ( z ) ) ,
dz = Ω τ ( z ) 2 f ( z ) f ( z ) S ( t r ( z ) ) .
2 f ( z ) f ( z ) 1 τ′ ( z ) = Ω S ( t r ( z ) ) .
2 f ( z ) f ( z ) ~ τ′ ( z ) ω L .
φ ( z ) φ ( z 0 ) + 1 2 φ″ ( z 0 ) ( z z 0 ) 2 .
L eff = ( 2 π φ″ ( z 0 ) ) 1 2 .
φ″ ( z 0 ) = Ω τ″ ( z 0 ) Ω τ′ ( z 0 ) ( f″ ( z 0 ) f′ ( z 0 ) f′ ( z 0 ) f ( z 0 ) ) W b 2 f′ ( z 0 ) f ( z 0 ) τ′ ( z 0 ) .
L eff ~ 2 τ′ ( z 0 ) ( π ω L Ω ) 1 2 .
L eff L c ~ ( 4 Ω π ω L ) 1 2 ~ q ,
s ( z 0 ) L eff 2 n a 2 τ′ ( z 0 ) 2 p 2 1 c 1 ν ph ( z 0 ) 2 ,
s ( z 0 ) L eff 2 n a 2 n e 2 = const .
s 2 n a ( t b ) n a ( t r ) Γ ( t b ) ( t r t b ) 3 E L ( t b ) 2 S″ ( t r ) .
s 2 n a 2 Γ ( t b ) ω L 3 E 0 3
s 2 n a 2 Γ ( t b ) ω L 3 E 0 2 [ E 0 ω L ] 2 3
s 2 n a 2 Γ ( t b ) ω L δ ,
L eff ω L 3 2 n e ω L 5 2 n a Γ ( t b ) .
I H s 2 L eff ω L 5 Γ ( t b ) .

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