Abstract

We extend all-optical quasi-phase matching of high-order harmonic generation into spectral regions where conventional phase matching is not possible. The high laser intensities required to generate harmonics at energy >130eV, coupled with the resulting high level of ionization, preclude conventional phase matching in all nonlinear media. Selective enhancement factors between 40 and 150 in the flux of harmonics at photon energies around 140eV are demonstrated using a train of two counterpropagating pulses.

© 2008 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] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  15. M. V. Ammosov, N. B. Delone, and V. P. Krainov, Zh. Eksp. Teor. Fiz. 91, 2008 (1986).
  16. A. Rundquist, "Phase-matched generation of coherent, ultrafast x-rays using high harmonics," Ph.D. thesis (Washington State University, 1998).

2007 (6)

E. Gagnon, P. Ranitovic, X.-M. Tong, C. L. Cocke, M. M. Murnane, H. C. Kapteyn, and A. S. Sandhu, Science 317, 1374 (2007).
[CrossRef] [PubMed]

R. L. Sandberg, A. Paul, D. A. Raymondson, S. Hadrich, D. M. Gaudiosi, J. Holtsnider, R. I. Tobey, O. Cohen, M. M. Murnane, H. C. Kapteyn, C. Song, J. Miao, Y. Liu, and F. Salmassi, Phys. Rev. Lett. 99, 098103 (2007).
[CrossRef] [PubMed]

H. Kapteyn, O. Cohen, I. Christov, and M. Murnane, Science 371, 775 (2007).
[CrossRef]

X. Zhang, A. L. Lytle, T. Popmintchev, X. Zhou, M. M. Murnane, H. C. Kapteyn, and O. Cohen, Nat. Phys. 3, 270 (2007).
[CrossRef]

A. L. Lytle, X. Zhang, J. Peatross, M. M. Murnane, H. C. Kapteyn, and O. Cohen, Phys. Rev. Lett. 98, 123904 (2007).
[CrossRef] [PubMed]

O. Cohen, A. L. Lytle, X. Zhang, M. M. Murnane, and H. C. Kapteyn, Opt. Lett. 32, 2975 (2007).
[CrossRef] [PubMed]

2006 (1)

N. L. Wagner, A. Wuest, I. P. Christov, T. Popmintchev, X. B. Zhou, M. M. Murnane, and H. C. Kapteyn, Proc. Natl. Acad. Sci. U.S.A. 103, 13279 (2006).
[CrossRef] [PubMed]

2004 (1)

J. Itatani, J. Levesque, D. Zeldler, H. Niikura, H. Pepin, J. C. Kieffer, P. B. Corkum, and D. Villeneuve, Nature 432, 867 (2004).
[CrossRef] [PubMed]

2002 (1)

R. A. Bartels, A. Paul, H. Green, H. C. Kapteyn, M. M. Murnane, S. Backus, I. P. Christov, Y. W. Liu, D. Attwood, and C. Jacobsen, Science 297, 376 (2002).
[PubMed]

2001 (2)

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

S. L. Voronov, I. Kohl, J. B. Madsen, J. Simmons, N. Terry, J. Titensor, Q. Wang, and J. Peatross, Phys. Rev. Lett. 87, 133902 (2001).
[CrossRef] [PubMed]

1998 (1)

A. Rundquist, C. G. Durfee, Z. H. Chang, C. Herne, S. Backus, M. M. Murnane, and H. C. Kapteyn, Science 280, 1412 (1998).
[CrossRef] [PubMed]

1997 (1)

1995 (1)

P. Salieres, A. L'Huillier, and M. Lewenstein, Phys. Rev. Lett. 74, 3776 (1995).
[CrossRef] [PubMed]

1986 (1)

M. V. Ammosov, N. B. Delone, and V. P. Krainov, Zh. Eksp. Teor. Fiz. 91, 2008 (1986).

Nat. Phys. (1)

X. Zhang, A. L. Lytle, T. Popmintchev, X. Zhou, M. M. Murnane, H. C. Kapteyn, and O. Cohen, Nat. Phys. 3, 270 (2007).
[CrossRef]

Nature (2)

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

J. Itatani, J. Levesque, D. Zeldler, H. Niikura, H. Pepin, J. C. Kieffer, P. B. Corkum, and D. Villeneuve, Nature 432, 867 (2004).
[CrossRef] [PubMed]

Opt. Express (1)

Opt. Lett. (1)

Phys. Rev. Lett. (4)

A. L. Lytle, X. Zhang, J. Peatross, M. M. Murnane, H. C. Kapteyn, and O. Cohen, Phys. Rev. Lett. 98, 123904 (2007).
[CrossRef] [PubMed]

S. L. Voronov, I. Kohl, J. B. Madsen, J. Simmons, N. Terry, J. Titensor, Q. Wang, and J. Peatross, Phys. Rev. Lett. 87, 133902 (2001).
[CrossRef] [PubMed]

R. L. Sandberg, A. Paul, D. A. Raymondson, S. Hadrich, D. M. Gaudiosi, J. Holtsnider, R. I. Tobey, O. Cohen, M. M. Murnane, H. C. Kapteyn, C. Song, J. Miao, Y. Liu, and F. Salmassi, Phys. Rev. Lett. 99, 098103 (2007).
[CrossRef] [PubMed]

P. Salieres, A. L'Huillier, and M. Lewenstein, Phys. Rev. Lett. 74, 3776 (1995).
[CrossRef] [PubMed]

Proc. Natl. Acad. Sci. U.S.A. (1)

N. L. Wagner, A. Wuest, I. P. Christov, T. Popmintchev, X. B. Zhou, M. M. Murnane, and H. C. Kapteyn, Proc. Natl. Acad. Sci. U.S.A. 103, 13279 (2006).
[CrossRef] [PubMed]

Science (4)

E. Gagnon, P. Ranitovic, X.-M. Tong, C. L. Cocke, M. M. Murnane, H. C. Kapteyn, and A. S. Sandhu, Science 317, 1374 (2007).
[CrossRef] [PubMed]

H. Kapteyn, O. Cohen, I. Christov, and M. Murnane, Science 371, 775 (2007).
[CrossRef]

A. Rundquist, C. G. Durfee, Z. H. Chang, C. Herne, S. Backus, M. M. Murnane, and H. C. Kapteyn, Science 280, 1412 (1998).
[CrossRef] [PubMed]

R. A. Bartels, A. Paul, H. Green, H. C. Kapteyn, M. M. Murnane, S. Backus, I. P. Christov, Y. W. Liu, D. Attwood, and C. Jacobsen, Science 297, 376 (2002).
[PubMed]

Zh. Eksp. Teor. Fiz. (1)

M. V. Ammosov, N. B. Delone, and V. P. Krainov, Zh. Eksp. Teor. Fiz. 91, 2008 (1986).

Other (1)

A. Rundquist, "Phase-matched generation of coherent, ultrafast x-rays using high harmonics," Ph.D. thesis (Washington State University, 1998).

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Figures (2)

Fig. 1
Fig. 1

Experimental setup for all-optical QPM in He.

Fig. 2
Fig. 2

(a) HHG spectra from 110   torr He with with zero (light gray), one (medium gray), and two (black) counterpropagating pulses. The dotted black curve shows HHG spectra under similar laser conditions, but at a pressure of 500   torr , which is optimal for conventional phase matching of lower-order harmonics up to q 77 ( 120 eV ) , at ionization levels below critical. (b) Enhancement factors for harmonic orders 79–95. The circles show the ratio of QPM emission using two counterpropagating pulses to that without using counterpropagating pulses at a pressure of 110   torr . The squares show the ratio of QPM emission at 110   torr to that without counterpropagating pulses at a pressure of 500   torr .

Equations (2)

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Δ k = q { ( u 11 2 λ 0 4 π a 2 ) P ( ( 1 η ) 2 π λ 0 δ n η [ N atm r e λ 0 ] ) } ,
η cr = [ ( λ 0 N atm 2 π δ n ) ( 1 1 q 2 ) + 1 ] 1 .

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