Abstract

A technique for enhanced generation of high harmonics and attosecond pulses in a gas medium, in a high ionization limit, is described theoretically. An aperiodic corrugated hollow-core waveguide modulates the intensity of the fundamental pulse along the direction of propagation, resulting in quasi-phase-matched harmonic emission at wavelengths close to the cutoff of the spectrum. For a few-cycle laser pulse, linearly chirped corrugation leads to a significant increase of the harmonic yield of a broad frequency band that corresponds to an ∼200-attosecond x-ray pulse. For longer driving pulses, appropriate corrugation permits flexible coherent control of the quasi-phase-matched emission of selected harmonics.

© 2001 Optical Society of America

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  1. A. L’Huillier, P. Balcou, and L. Lompre, “Coherence and resonance effects in high-order harmonic generation,” Phys. Rev. Lett. 68, 166–169 (1992).
    [CrossRef] [PubMed]
  2. J. Zhou, J. Peatross, M. Murnane, H. Kapteyn, and I. Christov, “Enhanced high-harmonic generation using 25 fs pulses,” Phys. Rev. Lett. 76, 752–755 (1996).
    [CrossRef] [PubMed]
  3. Z. Chang, A. Rundquist, H. Wang, M. M. Murnane, and H. C. Kapteyn, “Generation of coherent soft x rays at 2.7 nm using high harmonics,” Phys. Rev. Lett. 79, 2967–2970 (1997).
    [CrossRef]
  4. C. Spielman, N. Burnett, S. Sartania, R. Koppitsch, M. Schnurer, C. Kan, M. Lenzner, P. Wobrauschek, and F. Krausz, “Generation of coherent x-rays in the water window using 5-femtosecond laser pulses,” Science 278, 661–664 (1997).
    [CrossRef]
  5. A. Rundquist, C. Durfee, Z. Chang, C. Herne, S. Backus, M. Murnane, and H. Kapteyn, “Phase-matched generation of coherent soft x-rays,” Science 280, 1412–1415 (1998).
    [CrossRef] [PubMed]
  6. C. Durfee, A. Rundquist, S. Backus, C. Herne, M. M. Murnane, and H. C. Kapteyn, “Phase matching of high-order harmonics in hollow waveguides,” Phys. Rev. Lett. 83, 2187–2190 (1999).
    [CrossRef]
  7. I. P. Christov, H. C. Kapteyn, and M. M. Murnane, “Dispersion-controlled hollow core fiber for phase matched harmonic generation,” Opt. Express 3, 360–364 (1998), http://www.opticsexpress.org.
    [CrossRef] [PubMed]
  8. I. P. Christov, “Enhanced generation of attosecond pulses in dispersion-controlled hollow-core fiber,” Phys. Rev. A 60, 3244–3250 (1999).
    [CrossRef]
  9. I. P. Christov, H. C. Kapteyn, and M. M. Murnane, “Quasi-phase matching of high-harmonics and attosecond pulses in modulated waveguides,” Opt. Express 7, 362–367 (2000), http://www.opticsexpress.org.
    [CrossRef] [PubMed]
  10. P. L. Shkolnikov, A. E. Kaplan, and A. Lago, “Phase-matching optimization of large-scale nonlinear frequency upconversion in neutral and ionized gases,” J. Opt. Soc. Am. B 13, 412–423 (1996).
    [CrossRef]
  11. J. Peatross, S. Voronov, and I. Prokopovich, “Selective zoning of high harmonic emission using counter-propagating light,” Opt. Express 1, 114–125 (1997), http://www.opticsexpress.org.
    [CrossRef] [PubMed]
  12. H. R. Lange, A. Chiron, J.-F. Ripoche, A. Mysyrowicz, P. Breger, and P. Agostini, “High-order harmonic generation and quasiphase matching in xenon using self-guided femtosecond pulses,” Phys. Rev. Lett. 81, 1611–1613 (1998).
    [CrossRef]
  13. G. Tempea, M. Geissler, M. Schnürer, and T. Brabec, “Self-phase-matched high harmonic generation,” Phys. Rev. Lett. 84, 4329–4332 (2000).
    [CrossRef] [PubMed]
  14. I. P. Christov, M. M. Murnane, and H. C. Kapteyn, “High-harmonic generation of attosecond pulses in the ‘single-cycle’ regime,” Phys. Rev. Lett. 78, 1251–1254 (1997).
    [CrossRef]
  15. R. Bartels, S. Backus, E. Zeek, L. Misoguti, G. Vdovin, I. P. Christov, M. M. Murnane, and H. C. Kapteyn, “Shaped-pulse optimization of coherent emission of high-harmonic soft x-rays,” Nature 406, 164–166 (2000).
    [CrossRef] [PubMed]
  16. M. M. Fejer, G. A. Magel, D. H. Jundt, and R. L. Byer, “Quasi-phase-matched second harmonic generation: tuning and tolerances,” IEEE J. Quantum Electron. 28, 2631–2654 (1992).
    [CrossRef]
  17. K. Mizuuchi and K. Y. Yamamoto, “Waveguide second-harmonic generation device with broadened flat quasi-phase-matching response by use of a grating structure with located phase shifts,” Opt. Lett. 23, 1880–1882 (1998).
    [CrossRef]
  18. I. P. Christov, “Propagation of ultrashort pulses in gaseous medium: breakdown of the quasistatic approximation,” Opt. Express 6, 34–39 (2000), http://www.opticsexpress.org.
    [CrossRef] [PubMed]
  19. A. Delgarno and A. E. Kingston, “The refractive indices and Verdet constants of inert gases,” Proc. R. Soc. London Ser. A 259, 424–429 (1966).
    [CrossRef]
  20. M. Lewenstein, P. Salieres, and A. L’Huillier, “Phase of the atomic polarization in high-order harmonic generation,” Phys. Rev. A 52, 4747–4754 (1995).
    [CrossRef] [PubMed]
  21. A. Poppe, R. Holzwarth, A. Apolonski, G. Tempea, Ch. Spielmann, T. W. Hänsch, and F. Krausz, “Few-cycle optical waveform synthesis,” Appl. Phys. B 72, 373–376 (2000).
    [CrossRef]

2000 (5)

I. P. Christov, H. C. Kapteyn, and M. M. Murnane, “Quasi-phase matching of high-harmonics and attosecond pulses in modulated waveguides,” Opt. Express 7, 362–367 (2000), http://www.opticsexpress.org.
[CrossRef] [PubMed]

G. Tempea, M. Geissler, M. Schnürer, and T. Brabec, “Self-phase-matched high harmonic generation,” Phys. Rev. Lett. 84, 4329–4332 (2000).
[CrossRef] [PubMed]

R. Bartels, S. Backus, E. Zeek, L. Misoguti, G. Vdovin, I. P. Christov, M. M. Murnane, and H. C. Kapteyn, “Shaped-pulse optimization of coherent emission of high-harmonic soft x-rays,” Nature 406, 164–166 (2000).
[CrossRef] [PubMed]

I. P. Christov, “Propagation of ultrashort pulses in gaseous medium: breakdown of the quasistatic approximation,” Opt. Express 6, 34–39 (2000), http://www.opticsexpress.org.
[CrossRef] [PubMed]

A. Poppe, R. Holzwarth, A. Apolonski, G. Tempea, Ch. Spielmann, T. W. Hänsch, and F. Krausz, “Few-cycle optical waveform synthesis,” Appl. Phys. B 72, 373–376 (2000).
[CrossRef]

1999 (2)

C. Durfee, A. Rundquist, S. Backus, C. Herne, M. M. Murnane, and H. C. Kapteyn, “Phase matching of high-order harmonics in hollow waveguides,” Phys. Rev. Lett. 83, 2187–2190 (1999).
[CrossRef]

I. P. Christov, “Enhanced generation of attosecond pulses in dispersion-controlled hollow-core fiber,” Phys. Rev. A 60, 3244–3250 (1999).
[CrossRef]

1998 (4)

A. Rundquist, C. Durfee, Z. Chang, C. Herne, S. Backus, M. Murnane, and H. Kapteyn, “Phase-matched generation of coherent soft x-rays,” Science 280, 1412–1415 (1998).
[CrossRef] [PubMed]

I. P. Christov, H. C. Kapteyn, and M. M. Murnane, “Dispersion-controlled hollow core fiber for phase matched harmonic generation,” Opt. Express 3, 360–364 (1998), http://www.opticsexpress.org.
[CrossRef] [PubMed]

H. R. Lange, A. Chiron, J.-F. Ripoche, A. Mysyrowicz, P. Breger, and P. Agostini, “High-order harmonic generation and quasiphase matching in xenon using self-guided femtosecond pulses,” Phys. Rev. Lett. 81, 1611–1613 (1998).
[CrossRef]

K. Mizuuchi and K. Y. Yamamoto, “Waveguide second-harmonic generation device with broadened flat quasi-phase-matching response by use of a grating structure with located phase shifts,” Opt. Lett. 23, 1880–1882 (1998).
[CrossRef]

1997 (4)

J. Peatross, S. Voronov, and I. Prokopovich, “Selective zoning of high harmonic emission using counter-propagating light,” Opt. Express 1, 114–125 (1997), http://www.opticsexpress.org.
[CrossRef] [PubMed]

I. P. Christov, M. M. Murnane, and H. C. Kapteyn, “High-harmonic generation of attosecond pulses in the ‘single-cycle’ regime,” Phys. Rev. Lett. 78, 1251–1254 (1997).
[CrossRef]

Z. Chang, A. Rundquist, H. Wang, M. M. Murnane, and H. C. Kapteyn, “Generation of coherent soft x rays at 2.7 nm using high harmonics,” Phys. Rev. Lett. 79, 2967–2970 (1997).
[CrossRef]

C. Spielman, N. Burnett, S. Sartania, R. Koppitsch, M. Schnurer, C. Kan, M. Lenzner, P. Wobrauschek, and F. Krausz, “Generation of coherent x-rays in the water window using 5-femtosecond laser pulses,” Science 278, 661–664 (1997).
[CrossRef]

1996 (2)

J. Zhou, J. Peatross, M. Murnane, H. Kapteyn, and I. Christov, “Enhanced high-harmonic generation using 25 fs pulses,” Phys. Rev. Lett. 76, 752–755 (1996).
[CrossRef] [PubMed]

P. L. Shkolnikov, A. E. Kaplan, and A. Lago, “Phase-matching optimization of large-scale nonlinear frequency upconversion in neutral and ionized gases,” J. Opt. Soc. Am. B 13, 412–423 (1996).
[CrossRef]

1995 (1)

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

1992 (2)

M. M. Fejer, G. A. Magel, D. H. Jundt, and R. L. Byer, “Quasi-phase-matched second harmonic generation: tuning and tolerances,” IEEE J. Quantum Electron. 28, 2631–2654 (1992).
[CrossRef]

A. L’Huillier, P. Balcou, and L. Lompre, “Coherence and resonance effects in high-order harmonic generation,” Phys. Rev. Lett. 68, 166–169 (1992).
[CrossRef] [PubMed]

1966 (1)

A. Delgarno and A. E. Kingston, “The refractive indices and Verdet constants of inert gases,” Proc. R. Soc. London Ser. A 259, 424–429 (1966).
[CrossRef]

Agostini, P.

H. R. Lange, A. Chiron, J.-F. Ripoche, A. Mysyrowicz, P. Breger, and P. Agostini, “High-order harmonic generation and quasiphase matching in xenon using self-guided femtosecond pulses,” Phys. Rev. Lett. 81, 1611–1613 (1998).
[CrossRef]

Apolonski, A.

A. Poppe, R. Holzwarth, A. Apolonski, G. Tempea, Ch. Spielmann, T. W. Hänsch, and F. Krausz, “Few-cycle optical waveform synthesis,” Appl. Phys. B 72, 373–376 (2000).
[CrossRef]

Backus, S.

R. Bartels, S. Backus, E. Zeek, L. Misoguti, G. Vdovin, I. P. Christov, M. M. Murnane, and H. C. Kapteyn, “Shaped-pulse optimization of coherent emission of high-harmonic soft x-rays,” Nature 406, 164–166 (2000).
[CrossRef] [PubMed]

C. Durfee, A. Rundquist, S. Backus, C. Herne, M. M. Murnane, and H. C. Kapteyn, “Phase matching of high-order harmonics in hollow waveguides,” Phys. Rev. Lett. 83, 2187–2190 (1999).
[CrossRef]

A. Rundquist, C. Durfee, Z. Chang, C. Herne, S. Backus, M. Murnane, and H. Kapteyn, “Phase-matched generation of coherent soft x-rays,” Science 280, 1412–1415 (1998).
[CrossRef] [PubMed]

Balcou, P.

A. L’Huillier, P. Balcou, and L. Lompre, “Coherence and resonance effects in high-order harmonic generation,” Phys. Rev. Lett. 68, 166–169 (1992).
[CrossRef] [PubMed]

Bartels, R.

R. Bartels, S. Backus, E. Zeek, L. Misoguti, G. Vdovin, I. P. Christov, M. M. Murnane, and H. C. Kapteyn, “Shaped-pulse optimization of coherent emission of high-harmonic soft x-rays,” Nature 406, 164–166 (2000).
[CrossRef] [PubMed]

Brabec, T.

G. Tempea, M. Geissler, M. Schnürer, and T. Brabec, “Self-phase-matched high harmonic generation,” Phys. Rev. Lett. 84, 4329–4332 (2000).
[CrossRef] [PubMed]

Breger, P.

H. R. Lange, A. Chiron, J.-F. Ripoche, A. Mysyrowicz, P. Breger, and P. Agostini, “High-order harmonic generation and quasiphase matching in xenon using self-guided femtosecond pulses,” Phys. Rev. Lett. 81, 1611–1613 (1998).
[CrossRef]

Burnett, N.

C. Spielman, N. Burnett, S. Sartania, R. Koppitsch, M. Schnurer, C. Kan, M. Lenzner, P. Wobrauschek, and F. Krausz, “Generation of coherent x-rays in the water window using 5-femtosecond laser pulses,” Science 278, 661–664 (1997).
[CrossRef]

Byer, R. L.

M. M. Fejer, G. A. Magel, D. H. Jundt, and R. L. Byer, “Quasi-phase-matched second harmonic generation: tuning and tolerances,” IEEE J. Quantum Electron. 28, 2631–2654 (1992).
[CrossRef]

Chang, Z.

A. Rundquist, C. Durfee, Z. Chang, C. Herne, S. Backus, M. Murnane, and H. Kapteyn, “Phase-matched generation of coherent soft x-rays,” Science 280, 1412–1415 (1998).
[CrossRef] [PubMed]

Z. Chang, A. Rundquist, H. Wang, M. M. Murnane, and H. C. Kapteyn, “Generation of coherent soft x rays at 2.7 nm using high harmonics,” Phys. Rev. Lett. 79, 2967–2970 (1997).
[CrossRef]

Chiron, A.

H. R. Lange, A. Chiron, J.-F. Ripoche, A. Mysyrowicz, P. Breger, and P. Agostini, “High-order harmonic generation and quasiphase matching in xenon using self-guided femtosecond pulses,” Phys. Rev. Lett. 81, 1611–1613 (1998).
[CrossRef]

Christov, I.

J. Zhou, J. Peatross, M. Murnane, H. Kapteyn, and I. Christov, “Enhanced high-harmonic generation using 25 fs pulses,” Phys. Rev. Lett. 76, 752–755 (1996).
[CrossRef] [PubMed]

Christov, I. P.

I. P. Christov, H. C. Kapteyn, and M. M. Murnane, “Quasi-phase matching of high-harmonics and attosecond pulses in modulated waveguides,” Opt. Express 7, 362–367 (2000), http://www.opticsexpress.org.
[CrossRef] [PubMed]

R. Bartels, S. Backus, E. Zeek, L. Misoguti, G. Vdovin, I. P. Christov, M. M. Murnane, and H. C. Kapteyn, “Shaped-pulse optimization of coherent emission of high-harmonic soft x-rays,” Nature 406, 164–166 (2000).
[CrossRef] [PubMed]

I. P. Christov, “Propagation of ultrashort pulses in gaseous medium: breakdown of the quasistatic approximation,” Opt. Express 6, 34–39 (2000), http://www.opticsexpress.org.
[CrossRef] [PubMed]

I. P. Christov, “Enhanced generation of attosecond pulses in dispersion-controlled hollow-core fiber,” Phys. Rev. A 60, 3244–3250 (1999).
[CrossRef]

I. P. Christov, H. C. Kapteyn, and M. M. Murnane, “Dispersion-controlled hollow core fiber for phase matched harmonic generation,” Opt. Express 3, 360–364 (1998), http://www.opticsexpress.org.
[CrossRef] [PubMed]

I. P. Christov, M. M. Murnane, and H. C. Kapteyn, “High-harmonic generation of attosecond pulses in the ‘single-cycle’ regime,” Phys. Rev. Lett. 78, 1251–1254 (1997).
[CrossRef]

Delgarno, A.

A. Delgarno and A. E. Kingston, “The refractive indices and Verdet constants of inert gases,” Proc. R. Soc. London Ser. A 259, 424–429 (1966).
[CrossRef]

Durfee, C.

C. Durfee, A. Rundquist, S. Backus, C. Herne, M. M. Murnane, and H. C. Kapteyn, “Phase matching of high-order harmonics in hollow waveguides,” Phys. Rev. Lett. 83, 2187–2190 (1999).
[CrossRef]

A. Rundquist, C. Durfee, Z. Chang, C. Herne, S. Backus, M. Murnane, and H. Kapteyn, “Phase-matched generation of coherent soft x-rays,” Science 280, 1412–1415 (1998).
[CrossRef] [PubMed]

Fejer, M. M.

M. M. Fejer, G. A. Magel, D. H. Jundt, and R. L. Byer, “Quasi-phase-matched second harmonic generation: tuning and tolerances,” IEEE J. Quantum Electron. 28, 2631–2654 (1992).
[CrossRef]

Geissler, M.

G. Tempea, M. Geissler, M. Schnürer, and T. Brabec, “Self-phase-matched high harmonic generation,” Phys. Rev. Lett. 84, 4329–4332 (2000).
[CrossRef] [PubMed]

Hänsch, T. W.

A. Poppe, R. Holzwarth, A. Apolonski, G. Tempea, Ch. Spielmann, T. W. Hänsch, and F. Krausz, “Few-cycle optical waveform synthesis,” Appl. Phys. B 72, 373–376 (2000).
[CrossRef]

Herne, C.

C. Durfee, A. Rundquist, S. Backus, C. Herne, M. M. Murnane, and H. C. Kapteyn, “Phase matching of high-order harmonics in hollow waveguides,” Phys. Rev. Lett. 83, 2187–2190 (1999).
[CrossRef]

A. Rundquist, C. Durfee, Z. Chang, C. Herne, S. Backus, M. Murnane, and H. Kapteyn, “Phase-matched generation of coherent soft x-rays,” Science 280, 1412–1415 (1998).
[CrossRef] [PubMed]

Holzwarth, R.

A. Poppe, R. Holzwarth, A. Apolonski, G. Tempea, Ch. Spielmann, T. W. Hänsch, and F. Krausz, “Few-cycle optical waveform synthesis,” Appl. Phys. B 72, 373–376 (2000).
[CrossRef]

Jundt, D. H.

M. M. Fejer, G. A. Magel, D. H. Jundt, and R. L. Byer, “Quasi-phase-matched second harmonic generation: tuning and tolerances,” IEEE J. Quantum Electron. 28, 2631–2654 (1992).
[CrossRef]

Kan, C.

C. Spielman, N. Burnett, S. Sartania, R. Koppitsch, M. Schnurer, C. Kan, M. Lenzner, P. Wobrauschek, and F. Krausz, “Generation of coherent x-rays in the water window using 5-femtosecond laser pulses,” Science 278, 661–664 (1997).
[CrossRef]

Kaplan, A. E.

Kapteyn, H.

A. Rundquist, C. Durfee, Z. Chang, C. Herne, S. Backus, M. Murnane, and H. Kapteyn, “Phase-matched generation of coherent soft x-rays,” Science 280, 1412–1415 (1998).
[CrossRef] [PubMed]

J. Zhou, J. Peatross, M. Murnane, H. Kapteyn, and I. Christov, “Enhanced high-harmonic generation using 25 fs pulses,” Phys. Rev. Lett. 76, 752–755 (1996).
[CrossRef] [PubMed]

Kapteyn, H. C.

I. P. Christov, H. C. Kapteyn, and M. M. Murnane, “Quasi-phase matching of high-harmonics and attosecond pulses in modulated waveguides,” Opt. Express 7, 362–367 (2000), http://www.opticsexpress.org.
[CrossRef] [PubMed]

R. Bartels, S. Backus, E. Zeek, L. Misoguti, G. Vdovin, I. P. Christov, M. M. Murnane, and H. C. Kapteyn, “Shaped-pulse optimization of coherent emission of high-harmonic soft x-rays,” Nature 406, 164–166 (2000).
[CrossRef] [PubMed]

C. Durfee, A. Rundquist, S. Backus, C. Herne, M. M. Murnane, and H. C. Kapteyn, “Phase matching of high-order harmonics in hollow waveguides,” Phys. Rev. Lett. 83, 2187–2190 (1999).
[CrossRef]

I. P. Christov, H. C. Kapteyn, and M. M. Murnane, “Dispersion-controlled hollow core fiber for phase matched harmonic generation,” Opt. Express 3, 360–364 (1998), http://www.opticsexpress.org.
[CrossRef] [PubMed]

Z. Chang, A. Rundquist, H. Wang, M. M. Murnane, and H. C. Kapteyn, “Generation of coherent soft x rays at 2.7 nm using high harmonics,” Phys. Rev. Lett. 79, 2967–2970 (1997).
[CrossRef]

I. P. Christov, M. M. Murnane, and H. C. Kapteyn, “High-harmonic generation of attosecond pulses in the ‘single-cycle’ regime,” Phys. Rev. Lett. 78, 1251–1254 (1997).
[CrossRef]

Kingston, A. E.

A. Delgarno and A. E. Kingston, “The refractive indices and Verdet constants of inert gases,” Proc. R. Soc. London Ser. A 259, 424–429 (1966).
[CrossRef]

Koppitsch, R.

C. Spielman, N. Burnett, S. Sartania, R. Koppitsch, M. Schnurer, C. Kan, M. Lenzner, P. Wobrauschek, and F. Krausz, “Generation of coherent x-rays in the water window using 5-femtosecond laser pulses,” Science 278, 661–664 (1997).
[CrossRef]

Krausz, F.

A. Poppe, R. Holzwarth, A. Apolonski, G. Tempea, Ch. Spielmann, T. W. Hänsch, and F. Krausz, “Few-cycle optical waveform synthesis,” Appl. Phys. B 72, 373–376 (2000).
[CrossRef]

C. Spielman, N. Burnett, S. Sartania, R. Koppitsch, M. Schnurer, C. Kan, M. Lenzner, P. Wobrauschek, and F. Krausz, “Generation of coherent x-rays in the water window using 5-femtosecond laser pulses,” Science 278, 661–664 (1997).
[CrossRef]

L’Huillier, A.

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

A. L’Huillier, P. Balcou, and L. Lompre, “Coherence and resonance effects in high-order harmonic generation,” Phys. Rev. Lett. 68, 166–169 (1992).
[CrossRef] [PubMed]

Lago, A.

Lange, H. R.

H. R. Lange, A. Chiron, J.-F. Ripoche, A. Mysyrowicz, P. Breger, and P. Agostini, “High-order harmonic generation and quasiphase matching in xenon using self-guided femtosecond pulses,” Phys. Rev. Lett. 81, 1611–1613 (1998).
[CrossRef]

Lenzner, M.

C. Spielman, N. Burnett, S. Sartania, R. Koppitsch, M. Schnurer, C. Kan, M. Lenzner, P. Wobrauschek, and F. Krausz, “Generation of coherent x-rays in the water window using 5-femtosecond laser pulses,” Science 278, 661–664 (1997).
[CrossRef]

Lewenstein, M.

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

Lompre, L.

A. L’Huillier, P. Balcou, and L. Lompre, “Coherence and resonance effects in high-order harmonic generation,” Phys. Rev. Lett. 68, 166–169 (1992).
[CrossRef] [PubMed]

Magel, G. A.

M. M. Fejer, G. A. Magel, D. H. Jundt, and R. L. Byer, “Quasi-phase-matched second harmonic generation: tuning and tolerances,” IEEE J. Quantum Electron. 28, 2631–2654 (1992).
[CrossRef]

Misoguti, L.

R. Bartels, S. Backus, E. Zeek, L. Misoguti, G. Vdovin, I. P. Christov, M. M. Murnane, and H. C. Kapteyn, “Shaped-pulse optimization of coherent emission of high-harmonic soft x-rays,” Nature 406, 164–166 (2000).
[CrossRef] [PubMed]

Mizuuchi, K.

Murnane, M.

A. Rundquist, C. Durfee, Z. Chang, C. Herne, S. Backus, M. Murnane, and H. Kapteyn, “Phase-matched generation of coherent soft x-rays,” Science 280, 1412–1415 (1998).
[CrossRef] [PubMed]

J. Zhou, J. Peatross, M. Murnane, H. Kapteyn, and I. Christov, “Enhanced high-harmonic generation using 25 fs pulses,” Phys. Rev. Lett. 76, 752–755 (1996).
[CrossRef] [PubMed]

Murnane, M. M.

R. Bartels, S. Backus, E. Zeek, L. Misoguti, G. Vdovin, I. P. Christov, M. M. Murnane, and H. C. Kapteyn, “Shaped-pulse optimization of coherent emission of high-harmonic soft x-rays,” Nature 406, 164–166 (2000).
[CrossRef] [PubMed]

I. P. Christov, H. C. Kapteyn, and M. M. Murnane, “Quasi-phase matching of high-harmonics and attosecond pulses in modulated waveguides,” Opt. Express 7, 362–367 (2000), http://www.opticsexpress.org.
[CrossRef] [PubMed]

C. Durfee, A. Rundquist, S. Backus, C. Herne, M. M. Murnane, and H. C. Kapteyn, “Phase matching of high-order harmonics in hollow waveguides,” Phys. Rev. Lett. 83, 2187–2190 (1999).
[CrossRef]

I. P. Christov, H. C. Kapteyn, and M. M. Murnane, “Dispersion-controlled hollow core fiber for phase matched harmonic generation,” Opt. Express 3, 360–364 (1998), http://www.opticsexpress.org.
[CrossRef] [PubMed]

Z. Chang, A. Rundquist, H. Wang, M. M. Murnane, and H. C. Kapteyn, “Generation of coherent soft x rays at 2.7 nm using high harmonics,” Phys. Rev. Lett. 79, 2967–2970 (1997).
[CrossRef]

I. P. Christov, M. M. Murnane, and H. C. Kapteyn, “High-harmonic generation of attosecond pulses in the ‘single-cycle’ regime,” Phys. Rev. Lett. 78, 1251–1254 (1997).
[CrossRef]

Mysyrowicz, A.

H. R. Lange, A. Chiron, J.-F. Ripoche, A. Mysyrowicz, P. Breger, and P. Agostini, “High-order harmonic generation and quasiphase matching in xenon using self-guided femtosecond pulses,” Phys. Rev. Lett. 81, 1611–1613 (1998).
[CrossRef]

Peatross, J.

J. Peatross, S. Voronov, and I. Prokopovich, “Selective zoning of high harmonic emission using counter-propagating light,” Opt. Express 1, 114–125 (1997), http://www.opticsexpress.org.
[CrossRef] [PubMed]

J. Zhou, J. Peatross, M. Murnane, H. Kapteyn, and I. Christov, “Enhanced high-harmonic generation using 25 fs pulses,” Phys. Rev. Lett. 76, 752–755 (1996).
[CrossRef] [PubMed]

Poppe, A.

A. Poppe, R. Holzwarth, A. Apolonski, G. Tempea, Ch. Spielmann, T. W. Hänsch, and F. Krausz, “Few-cycle optical waveform synthesis,” Appl. Phys. B 72, 373–376 (2000).
[CrossRef]

Prokopovich, I.

Ripoche, J.-F.

H. R. Lange, A. Chiron, J.-F. Ripoche, A. Mysyrowicz, P. Breger, and P. Agostini, “High-order harmonic generation and quasiphase matching in xenon using self-guided femtosecond pulses,” Phys. Rev. Lett. 81, 1611–1613 (1998).
[CrossRef]

Rundquist, A.

C. Durfee, A. Rundquist, S. Backus, C. Herne, M. M. Murnane, and H. C. Kapteyn, “Phase matching of high-order harmonics in hollow waveguides,” Phys. Rev. Lett. 83, 2187–2190 (1999).
[CrossRef]

A. Rundquist, C. Durfee, Z. Chang, C. Herne, S. Backus, M. Murnane, and H. Kapteyn, “Phase-matched generation of coherent soft x-rays,” Science 280, 1412–1415 (1998).
[CrossRef] [PubMed]

Z. Chang, A. Rundquist, H. Wang, M. M. Murnane, and H. C. Kapteyn, “Generation of coherent soft x rays at 2.7 nm using high harmonics,” Phys. Rev. Lett. 79, 2967–2970 (1997).
[CrossRef]

Salieres, P.

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

Sartania, S.

C. Spielman, N. Burnett, S. Sartania, R. Koppitsch, M. Schnurer, C. Kan, M. Lenzner, P. Wobrauschek, and F. Krausz, “Generation of coherent x-rays in the water window using 5-femtosecond laser pulses,” Science 278, 661–664 (1997).
[CrossRef]

Schnurer, M.

C. Spielman, N. Burnett, S. Sartania, R. Koppitsch, M. Schnurer, C. Kan, M. Lenzner, P. Wobrauschek, and F. Krausz, “Generation of coherent x-rays in the water window using 5-femtosecond laser pulses,” Science 278, 661–664 (1997).
[CrossRef]

Schnürer, M.

G. Tempea, M. Geissler, M. Schnürer, and T. Brabec, “Self-phase-matched high harmonic generation,” Phys. Rev. Lett. 84, 4329–4332 (2000).
[CrossRef] [PubMed]

Shkolnikov, P. L.

Spielman, C.

C. Spielman, N. Burnett, S. Sartania, R. Koppitsch, M. Schnurer, C. Kan, M. Lenzner, P. Wobrauschek, and F. Krausz, “Generation of coherent x-rays in the water window using 5-femtosecond laser pulses,” Science 278, 661–664 (1997).
[CrossRef]

Spielmann, Ch.

A. Poppe, R. Holzwarth, A. Apolonski, G. Tempea, Ch. Spielmann, T. W. Hänsch, and F. Krausz, “Few-cycle optical waveform synthesis,” Appl. Phys. B 72, 373–376 (2000).
[CrossRef]

Tempea, G.

A. Poppe, R. Holzwarth, A. Apolonski, G. Tempea, Ch. Spielmann, T. W. Hänsch, and F. Krausz, “Few-cycle optical waveform synthesis,” Appl. Phys. B 72, 373–376 (2000).
[CrossRef]

G. Tempea, M. Geissler, M. Schnürer, and T. Brabec, “Self-phase-matched high harmonic generation,” Phys. Rev. Lett. 84, 4329–4332 (2000).
[CrossRef] [PubMed]

Vdovin, G.

R. Bartels, S. Backus, E. Zeek, L. Misoguti, G. Vdovin, I. P. Christov, M. M. Murnane, and H. C. Kapteyn, “Shaped-pulse optimization of coherent emission of high-harmonic soft x-rays,” Nature 406, 164–166 (2000).
[CrossRef] [PubMed]

Voronov, S.

Wang, H.

Z. Chang, A. Rundquist, H. Wang, M. M. Murnane, and H. C. Kapteyn, “Generation of coherent soft x rays at 2.7 nm using high harmonics,” Phys. Rev. Lett. 79, 2967–2970 (1997).
[CrossRef]

Wobrauschek, P.

C. Spielman, N. Burnett, S. Sartania, R. Koppitsch, M. Schnurer, C. Kan, M. Lenzner, P. Wobrauschek, and F. Krausz, “Generation of coherent x-rays in the water window using 5-femtosecond laser pulses,” Science 278, 661–664 (1997).
[CrossRef]

Yamamoto, K. Y.

Zeek, E.

R. Bartels, S. Backus, E. Zeek, L. Misoguti, G. Vdovin, I. P. Christov, M. M. Murnane, and H. C. Kapteyn, “Shaped-pulse optimization of coherent emission of high-harmonic soft x-rays,” Nature 406, 164–166 (2000).
[CrossRef] [PubMed]

Zhou, J.

J. Zhou, J. Peatross, M. Murnane, H. Kapteyn, and I. Christov, “Enhanced high-harmonic generation using 25 fs pulses,” Phys. Rev. Lett. 76, 752–755 (1996).
[CrossRef] [PubMed]

Appl. Phys. B (1)

A. Poppe, R. Holzwarth, A. Apolonski, G. Tempea, Ch. Spielmann, T. W. Hänsch, and F. Krausz, “Few-cycle optical waveform synthesis,” Appl. Phys. B 72, 373–376 (2000).
[CrossRef]

IEEE J. Quantum Electron. (1)

M. M. Fejer, G. A. Magel, D. H. Jundt, and R. L. Byer, “Quasi-phase-matched second harmonic generation: tuning and tolerances,” IEEE J. Quantum Electron. 28, 2631–2654 (1992).
[CrossRef]

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

Nature (1)

R. Bartels, S. Backus, E. Zeek, L. Misoguti, G. Vdovin, I. P. Christov, M. M. Murnane, and H. C. Kapteyn, “Shaped-pulse optimization of coherent emission of high-harmonic soft x-rays,” Nature 406, 164–166 (2000).
[CrossRef] [PubMed]

Opt. Express (4)

Opt. Lett. (1)

Phys. Rev. A (2)

I. P. Christov, “Enhanced generation of attosecond pulses in dispersion-controlled hollow-core fiber,” Phys. Rev. A 60, 3244–3250 (1999).
[CrossRef]

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

Phys. Rev. Lett. (7)

C. Durfee, A. Rundquist, S. Backus, C. Herne, M. M. Murnane, and H. C. Kapteyn, “Phase matching of high-order harmonics in hollow waveguides,” Phys. Rev. Lett. 83, 2187–2190 (1999).
[CrossRef]

A. L’Huillier, P. Balcou, and L. Lompre, “Coherence and resonance effects in high-order harmonic generation,” Phys. Rev. Lett. 68, 166–169 (1992).
[CrossRef] [PubMed]

J. Zhou, J. Peatross, M. Murnane, H. Kapteyn, and I. Christov, “Enhanced high-harmonic generation using 25 fs pulses,” Phys. Rev. Lett. 76, 752–755 (1996).
[CrossRef] [PubMed]

Z. Chang, A. Rundquist, H. Wang, M. M. Murnane, and H. C. Kapteyn, “Generation of coherent soft x rays at 2.7 nm using high harmonics,” Phys. Rev. Lett. 79, 2967–2970 (1997).
[CrossRef]

H. R. Lange, A. Chiron, J.-F. Ripoche, A. Mysyrowicz, P. Breger, and P. Agostini, “High-order harmonic generation and quasiphase matching in xenon using self-guided femtosecond pulses,” Phys. Rev. Lett. 81, 1611–1613 (1998).
[CrossRef]

G. Tempea, M. Geissler, M. Schnürer, and T. Brabec, “Self-phase-matched high harmonic generation,” Phys. Rev. Lett. 84, 4329–4332 (2000).
[CrossRef] [PubMed]

I. P. Christov, M. M. Murnane, and H. C. Kapteyn, “High-harmonic generation of attosecond pulses in the ‘single-cycle’ regime,” Phys. Rev. Lett. 78, 1251–1254 (1997).
[CrossRef]

Proc. R. Soc. London Ser. A (1)

A. Delgarno and A. E. Kingston, “The refractive indices and Verdet constants of inert gases,” Proc. R. Soc. London Ser. A 259, 424–429 (1966).
[CrossRef]

Science (2)

C. Spielman, N. Burnett, S. Sartania, R. Koppitsch, M. Schnurer, C. Kan, M. Lenzner, P. Wobrauschek, and F. Krausz, “Generation of coherent x-rays in the water window using 5-femtosecond laser pulses,” Science 278, 661–664 (1997).
[CrossRef]

A. Rundquist, C. Durfee, Z. Chang, C. Herne, S. Backus, M. Murnane, and H. Kapteyn, “Phase-matched generation of coherent soft x-rays,” Science 280, 1412–1415 (1998).
[CrossRef] [PubMed]

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Figures (6)

Fig. 1
Fig. 1

Period of modulation of the walls of a corrugated hollow waveguide as a function propagation distance: (a) for quasi-phase-matched generation of attosecond pulses and (b) for generation of isolated harmonics.

Fig. 2
Fig. 2

(a) Dependence of the normalized intensity of the laser pulse as a function of propagation distance and (b) energy of the attosecond pulse (harmonics from 89 to 105). Solid curves, aperiodic corrugation; dashed curve, periodic corrugation.

Fig. 3
Fig. 3

Harmonic spectra for quasi-phase-matched generation of an attosecond pulse in a chirped waveguide: 1, at the input and 2, at the output. Dashed curve, the case with no chirp of the corrugation (periodic corrugation).

Fig. 4
Fig. 4

(a) Time profile of the laser pulse at the input of the waveguide (dashed curve) and at the output (solid curve). (b) Attosecond x-ray pulse at the input (dashed curve) and at the output (solid curve).

Fig. 5
Fig. 5

Energy of the 95th harmonic versus propagation distance: (a) Noncorrugated waveguide and (b) periodic (sine) corrugation of the waveguide (curve 1) and aperiodic corrugation (curve 2).

Fig. 6
Fig. 6

Generation of an isolated harmonic in a hollow waveguide: (a) No corrugation, (b) aperiodic corrugation, (c) same as in (b) but on a linear scale.

Equations (2)

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-2c 2Ezt+ΔE=4πc2Ne2mP(E)E+Ipt1E P(E)t-1c2[1-n2(p)]2Et2,
-2c 2Ehzt+ΔEh=4πc2Ne2mP(E)Eh+a,

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