Abstract

Two techniques are demonstrated to produce ultrashort pulse trains capable of quasi-phase-matching high-harmonic generation. The first technique makes use of an array of birefringent crystals and is shown to generate high-contrast pulse trains with constant pulse spacing. The second technique employs a grating-pair stretcher, a multiple-order wave plate, and a linear polarizer. Trains of up to 100 pulses are demonstrated with this technique, with almost constant inter-pulse separation. It is shown that arbitrary pulse separation can be achieved by introducing the appropriate dispersion. This principle is demonstrated by using an acousto-optic programmable dispersive filter to introduce third- and fourth-order dispersions leading to a linear and quadratic variation of the separation of pulses through the train. Chirped-pulse trains of this type may be used to quasi-phase-match high-harmonic generation in situations where the coherence length varies through the medium.

© 2010 Optical Society of America

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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
  22. T. Robinson, K. O'Keeffe, M. Landreman, S. M. Hooker, M. Zepf, and B. Dromey, “Simple technique for generating trains of ultrashort pulses,” Opt. Lett. 32, 2203-2205 (2007).
    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]

2010 (1)

K. O'Keeffe, T. Robinson, and S. M. Hooker, “Generation and control of chirped, ultrafast pulse trains,” J. Opt. 12, 015201 (2010).
[CrossRef]

2008 (3)

2007 (8)

O. Cohen, A. L. Lytle, X. Zhang, M. M. Murnane, and H. C. Kapteyn, “Optimizing quasi-phase matching of high harmonic generation using counterpropagating pulse trains,” Opt. Lett. 32, 2975-2977 (2007).
[CrossRef] [PubMed]

A. L. Lytle, X. Zhang, J. Peatross, M. M. Murnane, H. C. Kapteyn, and O. Cohen, “Probe of high-order harmonic generation in a hollow waveguide geometry using counterpropagating light,” Phys. Rev. Lett. 98, 123904 (2007).
[CrossRef] [PubMed]

J. Seres, V. S. Yakovlev, E. Seres, C. Streli, P. Wobrauschek, C. Spielmann, and F. Krausz, “Coherent superposition of laser-driven soft-x-ray harmonics from successive sources,” Nat. Phys. 3, 878-883 (2007).
[CrossRef]

B. Dromey, M. Zepf, M. Landreman, and S. M. Hooker, “Quasi-phasematching of harmonic generation via multimode beating in waveguides,” Opt. Express 15, 7894-7900 (2007).
[CrossRef] [PubMed]

M. Landreman, K. O'Keeffe, T. Robinson, M. Zepf, B. Dromey, and S. M. Hooker, “Comparison of parallel and perpendicular polarized counterpropagating light for suppressing high harmonic generation,” J. Opt. Soc. Am. B 24, 2421-2427 (2007).
[CrossRef]

X. Zhang, A. L. Lytle, T. Popmintchev, X. Zhou, H. C. Kapteyn, M. M. Murnane, and O. Cohen, “Quasi-phase-matching and quantum-path control of high-harmonic generation using counterpropagating light,” Nat. Phys. 3, 270-275 (2007).
[CrossRef]

B. Dromey, M. Zepf, M. Landreman, K. O'Keeffe, T. Robinson, and S. M. Hooker, “Generation of a train of ultrashort pulses from a compact birefringent crystal array,” Appl. Opt. 46, 5142-5146 (2007).
[CrossRef] [PubMed]

T. Robinson, K. O'Keeffe, M. Landreman, S. M. Hooker, M. Zepf, and B. Dromey, “Simple technique for generating trains of ultrashort pulses,” Opt. Lett. 32, 2203-2205 (2007).
[CrossRef] [PubMed]

2005 (2)

R. Yano and H. Gotoh, “Tunable terahertz electromagnetic wave generation using birefringent crystal and grating pair,” Jpn. J. Appl. Phys. 44, 8470-8473 (2005).
[CrossRef]

J. Seres, E. Seres, A. J. Verhoef, G. Tempea, C. Streli, P. Wobrauschek, V. Yakovlev, A. Scrinzi, C. Spielmann, and F. Krausz, “Laser technology: Source of coherent kiloelectronvolt x-rays,” Nature 433, 596 (2005).
[CrossRef] [PubMed]

2003 (1)

E. A. Gibson, A. Paul, N. Wagner, R. Tobey, D. Gaudiosi, S. Backus, I. P. Christov, A. Aquila, E. M. Gullikson, D. T. Attwood, M. M. Murnane, and H. C. Kapteyn, “Coherent soft x-ray generation in the water window with quasi-phase matching,” Science 302, 95-98 (2003).
[CrossRef] [PubMed]

2000 (1)

A. H. Zewail, “Femtochemistry: Atomic-scale dynamics of the chemical bond,” J. Phys. Chem. A 104, 5660-5694 (2000).
[CrossRef]

1998 (1)

1997 (2)

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

P. Tournois, “Acousto-optic programmable dispersive filter for adaptive compensation of group delay time dispersion in laser systems,” Opt. Commun. 140, 245-249 (1997).
[CrossRef]

1996 (1)

1994 (1)

A. S. Weling, B. B. Hu, N. M. Froberg, and D. H. Auston, “Generation of tunable narrow-band THz radiation from large aperture photoconducting antennas,” Appl. Phys. Lett. 64, 137-139 (1994).
[CrossRef]

1993 (1)

1990 (2)

A. M. Weiner, D. E. Leaird, G. P. Wiederrecht, and K. A. Nelson, “Femtosecond pulse sequences used for optical manipulation of molecular motion,” Science 247, 1317-1319 (1990).
[CrossRef] [PubMed]

A. M. Weiner, D. E. Leaird, J. S. Patel, and J. R. Wullert, “Programmable femtosecond pulse shaping by use of a multielement liquid-crystal phase modulator,” Opt. Lett. 15, 326-328 (1990).
[CrossRef] [PubMed]

1988 (1)

Aquila, A.

E. A. Gibson, A. Paul, N. Wagner, R. Tobey, D. Gaudiosi, S. Backus, I. P. Christov, A. Aquila, E. M. Gullikson, D. T. Attwood, M. M. Murnane, and H. C. Kapteyn, “Coherent soft x-ray generation in the water window with quasi-phase matching,” Science 302, 95-98 (2003).
[CrossRef] [PubMed]

Arpin, P.

Attwood, D. T.

E. A. Gibson, A. Paul, N. Wagner, R. Tobey, D. Gaudiosi, S. Backus, I. P. Christov, A. Aquila, E. M. Gullikson, D. T. Attwood, M. M. Murnane, and H. C. Kapteyn, “Coherent soft x-ray generation in the water window with quasi-phase matching,” Science 302, 95-98 (2003).
[CrossRef] [PubMed]

Auston, D. H.

A. S. Weling, B. B. Hu, N. M. Froberg, and D. H. Auston, “Generation of tunable narrow-band THz radiation from large aperture photoconducting antennas,” Appl. Phys. Lett. 64, 137-139 (1994).
[CrossRef]

Backus, S.

E. A. Gibson, A. Paul, N. Wagner, R. Tobey, D. Gaudiosi, S. Backus, I. P. Christov, A. Aquila, E. M. Gullikson, D. T. Attwood, M. M. Murnane, and H. C. Kapteyn, “Coherent soft x-ray generation in the water window with quasi-phase matching,” Science 302, 95-98 (2003).
[CrossRef] [PubMed]

Bahabad, A.

Christov, I. P.

E. A. Gibson, A. Paul, N. Wagner, R. Tobey, D. Gaudiosi, S. Backus, I. P. Christov, A. Aquila, E. M. Gullikson, D. T. Attwood, M. M. Murnane, and H. C. Kapteyn, “Coherent soft x-ray generation in the water window with quasi-phase matching,” Science 302, 95-98 (2003).
[CrossRef] [PubMed]

Cohen, O.

Dromey, B.

Froberg, N. M.

A. S. Weling, B. B. Hu, N. M. Froberg, and D. H. Auston, “Generation of tunable narrow-band THz radiation from large aperture photoconducting antennas,” Appl. Phys. Lett. 64, 137-139 (1994).
[CrossRef]

Gaudiosi, D.

E. A. Gibson, A. Paul, N. Wagner, R. Tobey, D. Gaudiosi, S. Backus, I. P. Christov, A. Aquila, E. M. Gullikson, D. T. Attwood, M. M. Murnane, and H. C. Kapteyn, “Coherent soft x-ray generation in the water window with quasi-phase matching,” Science 302, 95-98 (2003).
[CrossRef] [PubMed]

Gibson, E. A.

E. A. Gibson, A. Paul, N. Wagner, R. Tobey, D. Gaudiosi, S. Backus, I. P. Christov, A. Aquila, E. M. Gullikson, D. T. Attwood, M. M. Murnane, and H. C. Kapteyn, “Coherent soft x-ray generation in the water window with quasi-phase matching,” Science 302, 95-98 (2003).
[CrossRef] [PubMed]

Gotoh, H.

R. Yano and H. Gotoh, “Tunable terahertz electromagnetic wave generation using birefringent crystal and grating pair,” Jpn. J. Appl. Phys. 44, 8470-8473 (2005).
[CrossRef]

Gullikson, E. M.

E. A. Gibson, A. Paul, N. Wagner, R. Tobey, D. Gaudiosi, S. Backus, I. P. Christov, A. Aquila, E. M. Gullikson, D. T. Attwood, M. M. Murnane, and H. C. Kapteyn, “Coherent soft x-ray generation in the water window with quasi-phase matching,” Science 302, 95-98 (2003).
[CrossRef] [PubMed]

Heritage, J. P.

Hooker, S. M.

Hu, B. B.

A. S. Weling, B. B. Hu, N. M. Froberg, and D. H. Auston, “Generation of tunable narrow-band THz radiation from large aperture photoconducting antennas,” Appl. Phys. Lett. 64, 137-139 (1994).
[CrossRef]

Kapteyn, H. C.

A. L. Lytle, X. Zhang, R. L. Sandberg, O. Cohen, H. C. Kapteyn, and M. M. Murnane, “Quasi-phase matching and characterization of high-order harmonic generation in hollow waveguides using counterpropagating light,” Opt. Express 16, 6544-6566 (2008).
[CrossRef] [PubMed]

A. L. Lytle, X. Zhang, P. Arpin, O. Cohen, M. M. Murnane, and H. C. Kapteyn, “Quasi-phase matching of high-order harmonic generation at high photon energies using counterpropagating pulses,” Opt. Lett. 33, 174-176 (2008).
[CrossRef] [PubMed]

A. Bahabad, O. Cohen, M. M. Murnane, and H. C. Kapteyn, “Quasi-periodic and random quasi-phase matching of high harmonic generation,” Opt. Lett. 33, 1936-1938 (2008).
[CrossRef] [PubMed]

O. Cohen, A. L. Lytle, X. Zhang, M. M. Murnane, and H. C. Kapteyn, “Optimizing quasi-phase matching of high harmonic generation using counterpropagating pulse trains,” Opt. Lett. 32, 2975-2977 (2007).
[CrossRef] [PubMed]

X. Zhang, A. L. Lytle, T. Popmintchev, X. Zhou, H. C. Kapteyn, M. M. Murnane, and O. Cohen, “Quasi-phase-matching and quantum-path control of high-harmonic generation using counterpropagating light,” Nat. Phys. 3, 270-275 (2007).
[CrossRef]

A. L. Lytle, X. Zhang, J. Peatross, M. M. Murnane, H. C. Kapteyn, and O. Cohen, “Probe of high-order harmonic generation in a hollow waveguide geometry using counterpropagating light,” Phys. Rev. Lett. 98, 123904 (2007).
[CrossRef] [PubMed]

E. A. Gibson, A. Paul, N. Wagner, R. Tobey, D. Gaudiosi, S. Backus, I. P. Christov, A. Aquila, E. M. Gullikson, D. T. Attwood, M. M. Murnane, and H. C. Kapteyn, “Coherent soft x-ray generation in the water window with quasi-phase matching,” Science 302, 95-98 (2003).
[CrossRef] [PubMed]

Kirschner, E. M.

Krausz, F.

J. Seres, V. S. Yakovlev, E. Seres, C. Streli, P. Wobrauschek, C. Spielmann, and F. Krausz, “Coherent superposition of laser-driven soft-x-ray harmonics from successive sources,” Nat. Phys. 3, 878-883 (2007).
[CrossRef]

J. Seres, E. Seres, A. J. Verhoef, G. Tempea, C. Streli, P. Wobrauschek, V. Yakovlev, A. Scrinzi, C. Spielmann, and F. Krausz, “Laser technology: Source of coherent kiloelectronvolt x-rays,” Nature 433, 596 (2005).
[CrossRef] [PubMed]

Landreman, M.

Leaird, D. E.

A. M. Weiner, D. E. Leaird, J. S. Patel, and J. R. Wullert, “Programmable femtosecond pulse shaping by use of a multielement liquid-crystal phase modulator,” Opt. Lett. 15, 326-328 (1990).
[CrossRef] [PubMed]

A. M. Weiner, D. E. Leaird, G. P. Wiederrecht, and K. A. Nelson, “Femtosecond pulse sequences used for optical manipulation of molecular motion,” Science 247, 1317-1319 (1990).
[CrossRef] [PubMed]

Liu, Y.

Lytle, A. L.

Murnane, M. M.

A. L. Lytle, X. Zhang, P. Arpin, O. Cohen, M. M. Murnane, and H. C. Kapteyn, “Quasi-phase matching of high-order harmonic generation at high photon energies using counterpropagating pulses,” Opt. Lett. 33, 174-176 (2008).
[CrossRef] [PubMed]

A. L. Lytle, X. Zhang, R. L. Sandberg, O. Cohen, H. C. Kapteyn, and M. M. Murnane, “Quasi-phase matching and characterization of high-order harmonic generation in hollow waveguides using counterpropagating light,” Opt. Express 16, 6544-6566 (2008).
[CrossRef] [PubMed]

A. Bahabad, O. Cohen, M. M. Murnane, and H. C. Kapteyn, “Quasi-periodic and random quasi-phase matching of high harmonic generation,” Opt. Lett. 33, 1936-1938 (2008).
[CrossRef] [PubMed]

O. Cohen, A. L. Lytle, X. Zhang, M. M. Murnane, and H. C. Kapteyn, “Optimizing quasi-phase matching of high harmonic generation using counterpropagating pulse trains,” Opt. Lett. 32, 2975-2977 (2007).
[CrossRef] [PubMed]

X. Zhang, A. L. Lytle, T. Popmintchev, X. Zhou, H. C. Kapteyn, M. M. Murnane, and O. Cohen, “Quasi-phase-matching and quantum-path control of high-harmonic generation using counterpropagating light,” Nat. Phys. 3, 270-275 (2007).
[CrossRef]

A. L. Lytle, X. Zhang, J. Peatross, M. M. Murnane, H. C. Kapteyn, and O. Cohen, “Probe of high-order harmonic generation in a hollow waveguide geometry using counterpropagating light,” Phys. Rev. Lett. 98, 123904 (2007).
[CrossRef] [PubMed]

E. A. Gibson, A. Paul, N. Wagner, R. Tobey, D. Gaudiosi, S. Backus, I. P. Christov, A. Aquila, E. M. Gullikson, D. T. Attwood, M. M. Murnane, and H. C. Kapteyn, “Coherent soft x-ray generation in the water window with quasi-phase matching,” Science 302, 95-98 (2003).
[CrossRef] [PubMed]

Nelson, K. A.

M. M. Wefers and K. A. Nelson, “Programmable phase and amplitude femtosecond pulse shaping,” Opt. Lett. 18, 2032-2034 (1993).
[CrossRef] [PubMed]

A. M. Weiner, D. E. Leaird, G. P. Wiederrecht, and K. A. Nelson, “Femtosecond pulse sequences used for optical manipulation of molecular motion,” Science 247, 1317-1319 (1990).
[CrossRef] [PubMed]

O'Keeffe, K.

Park, S.

Patel, J. S.

Paul, A.

E. A. Gibson, A. Paul, N. Wagner, R. Tobey, D. Gaudiosi, S. Backus, I. P. Christov, A. Aquila, E. M. Gullikson, D. T. Attwood, M. M. Murnane, and H. C. Kapteyn, “Coherent soft x-ray generation in the water window with quasi-phase matching,” Science 302, 95-98 (2003).
[CrossRef] [PubMed]

Peatross, J.

A. L. Lytle, X. Zhang, J. Peatross, M. M. Murnane, H. C. Kapteyn, and O. Cohen, “Probe of high-order harmonic generation in a hollow waveguide geometry using counterpropagating light,” Phys. Rev. Lett. 98, 123904 (2007).
[CrossRef] [PubMed]

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

Popmintchev, T.

X. Zhang, A. L. Lytle, T. Popmintchev, X. Zhou, H. C. Kapteyn, M. M. Murnane, and O. Cohen, “Quasi-phase-matching and quantum-path control of high-harmonic generation using counterpropagating light,” Nat. Phys. 3, 270-275 (2007).
[CrossRef]

Prokopovich, I.

Robinson, T.

Sandberg, R. L.

Scrinzi, A.

J. Seres, E. Seres, A. J. Verhoef, G. Tempea, C. Streli, P. Wobrauschek, V. Yakovlev, A. Scrinzi, C. Spielmann, and F. Krausz, “Laser technology: Source of coherent kiloelectronvolt x-rays,” Nature 433, 596 (2005).
[CrossRef] [PubMed]

Seres, E.

J. Seres, V. S. Yakovlev, E. Seres, C. Streli, P. Wobrauschek, C. Spielmann, and F. Krausz, “Coherent superposition of laser-driven soft-x-ray harmonics from successive sources,” Nat. Phys. 3, 878-883 (2007).
[CrossRef]

J. Seres, E. Seres, A. J. Verhoef, G. Tempea, C. Streli, P. Wobrauschek, V. Yakovlev, A. Scrinzi, C. Spielmann, and F. Krausz, “Laser technology: Source of coherent kiloelectronvolt x-rays,” Nature 433, 596 (2005).
[CrossRef] [PubMed]

Seres, J.

J. Seres, V. S. Yakovlev, E. Seres, C. Streli, P. Wobrauschek, C. Spielmann, and F. Krausz, “Coherent superposition of laser-driven soft-x-ray harmonics from successive sources,” Nat. Phys. 3, 878-883 (2007).
[CrossRef]

J. Seres, E. Seres, A. J. Verhoef, G. Tempea, C. Streli, P. Wobrauschek, V. Yakovlev, A. Scrinzi, C. Spielmann, and F. Krausz, “Laser technology: Source of coherent kiloelectronvolt x-rays,” Nature 433, 596 (2005).
[CrossRef] [PubMed]

Siders, C. W.

Siders, J. L.

Siegman, A. E.

A. E. Siegman, Lasers (University Science Books, 1990).

Spielmann, C.

J. Seres, V. S. Yakovlev, E. Seres, C. Streli, P. Wobrauschek, C. Spielmann, and F. Krausz, “Coherent superposition of laser-driven soft-x-ray harmonics from successive sources,” Nat. Phys. 3, 878-883 (2007).
[CrossRef]

J. Seres, E. Seres, A. J. Verhoef, G. Tempea, C. Streli, P. Wobrauschek, V. Yakovlev, A. Scrinzi, C. Spielmann, and F. Krausz, “Laser technology: Source of coherent kiloelectronvolt x-rays,” Nature 433, 596 (2005).
[CrossRef] [PubMed]

Streli, C.

J. Seres, V. S. Yakovlev, E. Seres, C. Streli, P. Wobrauschek, C. Spielmann, and F. Krausz, “Coherent superposition of laser-driven soft-x-ray harmonics from successive sources,” Nat. Phys. 3, 878-883 (2007).
[CrossRef]

J. Seres, E. Seres, A. J. Verhoef, G. Tempea, C. Streli, P. Wobrauschek, V. Yakovlev, A. Scrinzi, C. Spielmann, and F. Krausz, “Laser technology: Source of coherent kiloelectronvolt x-rays,” Nature 433, 596 (2005).
[CrossRef] [PubMed]

Taylor, A. J.

Tempea, G.

J. Seres, E. Seres, A. J. Verhoef, G. Tempea, C. Streli, P. Wobrauschek, V. Yakovlev, A. Scrinzi, C. Spielmann, and F. Krausz, “Laser technology: Source of coherent kiloelectronvolt x-rays,” Nature 433, 596 (2005).
[CrossRef] [PubMed]

Tobey, R.

E. A. Gibson, A. Paul, N. Wagner, R. Tobey, D. Gaudiosi, S. Backus, I. P. Christov, A. Aquila, E. M. Gullikson, D. T. Attwood, M. M. Murnane, and H. C. Kapteyn, “Coherent soft x-ray generation in the water window with quasi-phase matching,” Science 302, 95-98 (2003).
[CrossRef] [PubMed]

Tournois, P.

P. Tournois, “Acousto-optic programmable dispersive filter for adaptive compensation of group delay time dispersion in laser systems,” Opt. Commun. 140, 245-249 (1997).
[CrossRef]

Verhoef, A. J.

J. Seres, E. Seres, A. J. Verhoef, G. Tempea, C. Streli, P. Wobrauschek, V. Yakovlev, A. Scrinzi, C. Spielmann, and F. Krausz, “Laser technology: Source of coherent kiloelectronvolt x-rays,” Nature 433, 596 (2005).
[CrossRef] [PubMed]

Voronov, S.

Wagner, N.

E. A. Gibson, A. Paul, N. Wagner, R. Tobey, D. Gaudiosi, S. Backus, I. P. Christov, A. Aquila, E. M. Gullikson, D. T. Attwood, M. M. Murnane, and H. C. Kapteyn, “Coherent soft x-ray generation in the water window with quasi-phase matching,” Science 302, 95-98 (2003).
[CrossRef] [PubMed]

Wefers, M. M.

Weiner, A. M.

Weling, A. S.

A. S. Weling, B. B. Hu, N. M. Froberg, and D. H. Auston, “Generation of tunable narrow-band THz radiation from large aperture photoconducting antennas,” Appl. Phys. Lett. 64, 137-139 (1994).
[CrossRef]

Wiederrecht, G. P.

A. M. Weiner, D. E. Leaird, G. P. Wiederrecht, and K. A. Nelson, “Femtosecond pulse sequences used for optical manipulation of molecular motion,” Science 247, 1317-1319 (1990).
[CrossRef] [PubMed]

Wobrauschek, P.

J. Seres, V. S. Yakovlev, E. Seres, C. Streli, P. Wobrauschek, C. Spielmann, and F. Krausz, “Coherent superposition of laser-driven soft-x-ray harmonics from successive sources,” Nat. Phys. 3, 878-883 (2007).
[CrossRef]

J. Seres, E. Seres, A. J. Verhoef, G. Tempea, C. Streli, P. Wobrauschek, V. Yakovlev, A. Scrinzi, C. Spielmann, and F. Krausz, “Laser technology: Source of coherent kiloelectronvolt x-rays,” Nature 433, 596 (2005).
[CrossRef] [PubMed]

Wullert, J. R.

Yakovlev, V.

J. Seres, E. Seres, A. J. Verhoef, G. Tempea, C. Streli, P. Wobrauschek, V. Yakovlev, A. Scrinzi, C. Spielmann, and F. Krausz, “Laser technology: Source of coherent kiloelectronvolt x-rays,” Nature 433, 596 (2005).
[CrossRef] [PubMed]

Yakovlev, V. S.

J. Seres, V. S. Yakovlev, E. Seres, C. Streli, P. Wobrauschek, C. Spielmann, and F. Krausz, “Coherent superposition of laser-driven soft-x-ray harmonics from successive sources,” Nat. Phys. 3, 878-883 (2007).
[CrossRef]

Yano, R.

R. Yano and H. Gotoh, “Tunable terahertz electromagnetic wave generation using birefringent crystal and grating pair,” Jpn. J. Appl. Phys. 44, 8470-8473 (2005).
[CrossRef]

Zepf, M.

Zewail, A. H.

A. H. Zewail, “Femtochemistry: Atomic-scale dynamics of the chemical bond,” J. Phys. Chem. A 104, 5660-5694 (2000).
[CrossRef]

Zhang, X.

Zhou, X.

X. Zhang, A. L. Lytle, T. Popmintchev, X. Zhou, H. C. Kapteyn, M. M. Murnane, and O. Cohen, “Quasi-phase-matching and quantum-path control of high-harmonic generation using counterpropagating light,” Nat. Phys. 3, 270-275 (2007).
[CrossRef]

Appl. Opt. (2)

Appl. Phys. Lett. (1)

A. S. Weling, B. B. Hu, N. M. Froberg, and D. H. Auston, “Generation of tunable narrow-band THz radiation from large aperture photoconducting antennas,” Appl. Phys. Lett. 64, 137-139 (1994).
[CrossRef]

J. Opt. (1)

K. O'Keeffe, T. Robinson, and S. M. Hooker, “Generation and control of chirped, ultrafast pulse trains,” J. Opt. 12, 015201 (2010).
[CrossRef]

J. Opt. Soc. Am. B (2)

J. Phys. Chem. A (1)

A. H. Zewail, “Femtochemistry: Atomic-scale dynamics of the chemical bond,” J. Phys. Chem. A 104, 5660-5694 (2000).
[CrossRef]

Jpn. J. Appl. Phys. (1)

R. Yano and H. Gotoh, “Tunable terahertz electromagnetic wave generation using birefringent crystal and grating pair,” Jpn. J. Appl. Phys. 44, 8470-8473 (2005).
[CrossRef]

Nat. Phys. (2)

X. Zhang, A. L. Lytle, T. Popmintchev, X. Zhou, H. C. Kapteyn, M. M. Murnane, and O. Cohen, “Quasi-phase-matching and quantum-path control of high-harmonic generation using counterpropagating light,” Nat. Phys. 3, 270-275 (2007).
[CrossRef]

J. Seres, V. S. Yakovlev, E. Seres, C. Streli, P. Wobrauschek, C. Spielmann, and F. Krausz, “Coherent superposition of laser-driven soft-x-ray harmonics from successive sources,” Nat. Phys. 3, 878-883 (2007).
[CrossRef]

Nature (1)

J. Seres, E. Seres, A. J. Verhoef, G. Tempea, C. Streli, P. Wobrauschek, V. Yakovlev, A. Scrinzi, C. Spielmann, and F. Krausz, “Laser technology: Source of coherent kiloelectronvolt x-rays,” Nature 433, 596 (2005).
[CrossRef] [PubMed]

Opt. Commun. (1)

P. Tournois, “Acousto-optic programmable dispersive filter for adaptive compensation of group delay time dispersion in laser systems,” Opt. Commun. 140, 245-249 (1997).
[CrossRef]

Opt. Express (3)

Opt. Lett. (7)

Phys. Rev. Lett. (1)

A. L. Lytle, X. Zhang, J. Peatross, M. M. Murnane, H. C. Kapteyn, and O. Cohen, “Probe of high-order harmonic generation in a hollow waveguide geometry using counterpropagating light,” Phys. Rev. Lett. 98, 123904 (2007).
[CrossRef] [PubMed]

Science (2)

E. A. Gibson, A. Paul, N. Wagner, R. Tobey, D. Gaudiosi, S. Backus, I. P. Christov, A. Aquila, E. M. Gullikson, D. T. Attwood, M. M. Murnane, and H. C. Kapteyn, “Coherent soft x-ray generation in the water window with quasi-phase matching,” Science 302, 95-98 (2003).
[CrossRef] [PubMed]

A. M. Weiner, D. E. Leaird, G. P. Wiederrecht, and K. A. Nelson, “Femtosecond pulse sequences used for optical manipulation of molecular motion,” Science 247, 1317-1319 (1990).
[CrossRef] [PubMed]

Other (1)

A. E. Siegman, Lasers (University Science Books, 1990).

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Figures (13)

Fig. 1
Fig. 1

Crystal arrangements and cross-correlations for (a) a train of eight equally spaced pulses and (b) a train of eight macropulses, each macropulse consisting of four pulses. Calcite crystals were used with L = 0.42   mm .

Fig. 2
Fig. 2

The pulse trains used for the QPM experiment. Cross-correlations of (a) one and (b) two macropulses, each consisting of eight individual pulses, are shown.

Fig. 3
Fig. 3

Intensity of the 27th harmonic recorded as a function of the position of the point of overlap of a single macropulse and the driving pulse in the capillary. The inset shows the measured longitudinal variation of L c .

Fig. 4
Fig. 4

Intensity of the 27th harmonic recorded as a function of the position of the point of overlap of a single macropulse and two macropulses with the driving pulse in the capillary. The energy per macropulse is 0.06 mJ on target in both cases.

Fig. 5
Fig. 5

Normalized cross-correlation traces obtained with stretched pulses of FWHM durations of (a) 5 ps, (b) 10 ps, (c) 15 ps, and (d) 33 ps passed through multiple-order calcite wave plates of various thicknesses.

Fig. 6
Fig. 6

Plot of 1 / Δ τ as a function of the thickness of the calcite crystal for stretched pulses of durations 5, 10, 15, and 33 ps showing the expected linear dependence of Eq. (12).

Fig. 7
Fig. 7

Variation in the pulse separation, Δ τ , across the pulse train generated when a 30 ps stretched pulse passes through crystals of varying thicknesses. Linear fits to the data are also shown.

Fig. 8
Fig. 8

Experimental setup used to generate and control trains of ultrashort pulses with (a) constant spacing and (b) variable spacing using an AOPDF. G, grating stretcher; W, multiple-order wave plate; P, polarizer.

Fig. 9
Fig. 9

Cross-correlation signal recorded for a 1.4 ps stretched pulse passed through a 0.8 mm crystal and ϕ ( 3 ) = ± 1 × 10 6 fs 3 applied by the AOPDF. The lower plot shows Δ τ p , p 1 as a function of p for the two sets of data along with linear fits.

Fig. 10
Fig. 10

Cross-correlation signals recorded for a 1.4 ps stretched pulse passed through a 1.6 mm crystal and with various third-order dispersions applied by the AOPDF. The signals have been displaced vertically for clarity.

Fig. 11
Fig. 11

The rate of change of pulse separation with pulse number, Δ τ p , p 1 , is plotted as a function of ϕ ( 3 ) for calcite crystals of thicknesses 0.8 and 1.6 mm.

Fig. 12
Fig. 12

Cross-correlation signal recorded for a 1.4 ps stretched pulse passed through a 0.8 mm crystal and ϕ ( 4 ) = ± 1 × 10 8 fs 4 applied by the AOPDF. The lower plot shows the pulse spacing, Δ τ p , p 1 , as a function of p for the two sets of data along with quadratic fits.

Fig. 13
Fig. 13

Simulation of QPM in a medium where L c varies linearly with position. The upper plot shows the pulse trains used (an intensity of 1 corresponds to complete suppression of the harmonic generation), while the lower plot shows the simulated harmonic intensity as these pulse trains are scanned through the medium.

Equations (16)

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ν = ( cos   δ + sin   δ cos   δ sin   δ ) 2 n ( 1 + δ 1 δ ) 2 n .
E ( z = 0 , t ) = A   exp ( a 0 t 2 ) exp [ i ( ω 0 t + b 0 t 2 ) ]
= A   exp ( Γ 0 t 2 ) exp ( i ω 0 t ) ,
E ( , t ) = A Γ ( ) Γ 0   exp [ i ( β 0 ω 0 t ) ] exp [ Γ ( ) ( t β 0 ) 2 ] ,
E ( , t ) = f ( , t ) exp ( i ω 0 t ) exp [ i ϕ ( , t ) ] ,
f ( , t ) = A Γ ( ) Γ 0   exp { R [ Γ ( ) ] ( t β 0 ) 2 } ,
ϕ ( , t ) = β 0 γ ( t β 0 ) 2 ,
γ = b + 2 β 0 ( a 2 + b 2 ) ( 1 + 2 β 0 b ) 2 + ( 2 β 0 a ) 2 .
E pol 2 f ¯ ( , t ) exp [ i ϕ ¯ ( , t ) ] cos [ ϕ o ( , t ) ϕ e ( , t ) 2 ] ,
β 0 o β 0 e + γ e ( t β 0 e ) 2 γ o ( t β 0 o ) 2 = 2 m π .
Δ τ = π ( β 0 e γ e β 0 o γ o ) + ( γ o γ e ) t
π b 1 β 0 e β 0 o ,
E = a ( ω ) exp [ i Φ ( ω , t ) ] ,
ϕ ( ω ) = n = 0 1 n ! ϕ ( n ) ( ω ω 0 ) n ,
τ ( p ) = L d k d ω = d ϕ d ω = n = 1 1 ( n 1 ) ! ϕ ( n ) ( p Δ ω ) n 1 .
Δ τ ( p ) = d τ d p = n = 2 1 ( n 2 ) ! ϕ ( n ) p n 2 ( Δ ω ) n 1 .

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