Abstract

We formulate a theory of quasi-phase matching of high harmonic generation using weak counterpropagating pulse trains. We predict the optimal laser intensities and pulse shapes for the counterpropagating field and find that the conversion efficiency is better than the efficiency obtained by simply suppressing harmonic emission from out-of-phase regions.

© 2007 Optical Society of America

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References

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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
  16. D. M. Gaudiosi, B. Reagan, T. Popmintchev, M. Grisham, M. Berrill, O. Cohen, B. Walker, M. M. Murnane, H. C. Kapteyn, and J. J. Rocca, Phys. Rev. Lett. 96, 203001 (2006).
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    [CrossRef] [PubMed]

2007 (5)

H. C. Kapteyn, O. Cohen, I. P. Christov, and M. M. Murnane, Science 317, 775 (2007).
[CrossRef] [PubMed]

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

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

O. Cohen, X. Zhang, A. Lytle, T. Popmintchev, M. M. Murnane, and H. C. Kapteyn, Phys. Rev. Lett. 99, 053902 (2007).
[CrossRef] [PubMed]

O. Cohen, T. Popmintchev, D. M. Gaudiosi, M. M. Murnane, and H. C. Kapteyn, Phys. Rev. Lett. 98, 043903 (2007).
[CrossRef] [PubMed]

2006 (1)

D. M. Gaudiosi, B. Reagan, T. Popmintchev, M. Grisham, M. Berrill, O. Cohen, B. Walker, M. M. Murnane, H. C. Kapteyn, and J. J. Rocca, Phys. Rev. Lett. 96, 203001 (2006).
[CrossRef] [PubMed]

2003 (2)

A. Paul, R. A. Bartels, R. Tobey, H. Green, S. Weiman, I. P. Christov, M. M. Murnane, H. C. Kapteyn, and S. Backus, Nature 421, 51 (2003).
[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, Science 302, 95 (2003).
[CrossRef] [PubMed]

2001 (1)

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]

2000 (2)

1998 (2)

Z. Chang, A. Rundquist, H. Wang, I. Christov, H. C. Kapteyn, and M. M. Murnane, Phys. Rev. A 58, R30 (1998).
[CrossRef]

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

1997 (1)

1995 (2)

C. Kan, C. E. Capjack, R. Rankin, and N. H. Burnett, Phys. Rev. A 52, 4336 (1995).
[CrossRef]

M. Lewenstein, P. Salieres, and A. L'huillier, Phys. Rev. A 52, 4747 (1995).
[CrossRef] [PubMed]

1993 (1)

1992 (1)

M. M. Fejer, G. A. Magel, H. J. Dieter, and R. L. Byer, IEEE J. Quantum Electron. 28, 2631 (1992).
[CrossRef]

IEEE J. Quantum Electron. (1)

M. M. Fejer, G. A. Magel, H. J. Dieter, and R. L. Byer, IEEE J. Quantum Electron. 28, 2631 (1992).
[CrossRef]

Nat. Phys. (1)

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

Nature (1)

A. Paul, R. A. Bartels, R. Tobey, H. Green, S. Weiman, I. P. Christov, M. M. Murnane, H. C. Kapteyn, and S. Backus, Nature 421, 51 (2003).
[CrossRef] [PubMed]

Opt. Express (2)

Opt. Lett. (1)

Phys. Rev. A (4)

M. Geissler, G. Tempea, and T. Brabec, Phys. Rev. A 62, 033817 (2000).
[CrossRef]

C. Kan, C. E. Capjack, R. Rankin, and N. H. Burnett, Phys. Rev. A 52, 4336 (1995).
[CrossRef]

M. Lewenstein, P. Salieres, and A. L'huillier, Phys. Rev. A 52, 4747 (1995).
[CrossRef] [PubMed]

Z. Chang, A. Rundquist, H. Wang, I. Christov, H. C. Kapteyn, and M. M. Murnane, Phys. Rev. A 58, R30 (1998).
[CrossRef]

Phys. Rev. Lett. (5)

O. Cohen, X. Zhang, A. Lytle, T. Popmintchev, M. M. Murnane, and H. C. Kapteyn, Phys. Rev. Lett. 99, 053902 (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]

D. M. Gaudiosi, B. Reagan, T. Popmintchev, M. Grisham, M. Berrill, O. Cohen, B. Walker, M. M. Murnane, H. C. Kapteyn, and J. J. Rocca, Phys. Rev. Lett. 96, 203001 (2006).
[CrossRef] [PubMed]

O. Cohen, T. Popmintchev, D. M. Gaudiosi, M. M. Murnane, and H. C. Kapteyn, Phys. Rev. Lett. 98, 043903 (2007).
[CrossRef] [PubMed]

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

Science (3)

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, Science 302, 95 (2003).
[CrossRef] [PubMed]

H. C. Kapteyn, O. Cohen, I. P. Christov, and M. M. Murnane, Science 317, 775 (2007).
[CrossRef] [PubMed]

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

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Figures (2)

Fig. 1
Fig. 1

Influence of a weak counterpropagating field on the phase of the emitted harmonics. (a) Phase modulation of both the “short” and the “long” quantum paths for the 131st harmonic order (solid curves) by a counterpropagating beam for a driving laser intensity of 10 15 W cm 2 and a counterpropagating laser intensity of 10 11 W cm 2 in He. Fits to a cosine function (dotted curves) are also shown. (b) Calculated amplitude of the phase oscillations as a function of the ratio r between the peak fields of the backward- and forward-propagating beams. (c) Calculated amplitude of the phase oscillations of the long trajectory of harmonic order 101 as a function of the emission time with field ratio r = 0.01 . (d) Microscopic effective emission factor as a function of the phase modulation amplitude A.

Fig. 2
Fig. 2

QPM efficiency factor for (a) a secant hyperbolic and (b) a square counterpropagating pulse train as a function of the pulse width and peak phase modulation amplitude. Note the different color scales in the two plots.

Equations (4)

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Δ Φ ( z ) Δ I ( z ) E 0 2 r cos ( 2 π z Λ ) .
ξ = 1 Λ 0 Λ exp [ i Δ Φ ( z ) ] d z = 1 Λ 0 Λ exp [ i A cos ( 2 π Λ z ) ] d z = J 0 ( A ) .
E H H G = 0 L E H H G 0 ( z ) exp [ i π L C ( z ) z + A ( z ) cos ( 2 π Λ z ) ] d z ,
E H H G 0 L E H H G 0 ( z ) ξ [ A ( z ) ] exp [ i π L C ( z ) z ] d z .

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