Abstract

We studied the effect of pressure variation on intrapulse Raman scattering for a single-cycle and few-cycle pulses in a gas cell of a given length filled with gaseous deuterium, in the framework of a new model equation that goes beyond the slowly varying envelope approximation. We show that, for a single-cycle pulse, pressure variation does not have any influence on the pulse spectrum. On the other hand, for a four-cycle pulse, an increase in pres sure considerably affects the pulse spectrum and leads to substantial broadening and blueshift of the output pulse spectrum. Also, with increasing pressure, more and more energy is transferred from the red to the blue components.

© 2010 Optical Society of America

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  1. P. Corkum, Opt. Photon. News 6, 18 (1995).
    [CrossRef]
  2. F. Krausz, T. Brabec, M. Schnuerer, and C. Spielmann, Opt. Photon. News 9, 46 (1998).
    [CrossRef]
  3. T. Brabec and F. Krausz, Rev. Mod. Phys. 72, 545 (2000).
    [CrossRef]
  4. P. Corkum, Nature 403, 845 (2000).
    [CrossRef] [PubMed]
  5. M. Drescher and Ferenc Krausz, J. Phys. B 38, S727 (2005).
    [CrossRef]
  6. A. Scrinzi, M. Yu Ivanov, R. Kienberger, and D. M. Villeneuve, J. Phys. B 39, R1 (2006).
    [CrossRef]
  7. T. Kobayashi, T. Saito, and H. Ohtani, Nature 414, 531 (2001).
    [CrossRef] [PubMed]
  8. T. Misgeld and M. Kerschensteiner, Nat. Rev. Neurosci. 6, 449 (2006).
  9. D. Meshulach and Y. Silberberg, Nature 396, 239 (1998).
    [CrossRef]
  10. S. Yoshikawa and T. Imasaka, Opt. Commun. 96, 94 (1993).
    [CrossRef]
  11. F. L. Kien, N. H. Shon, and K. Hakuta, Phys. Rev. A 64, 051803 (2001).
    [CrossRef]
  12. A. E. Kaplan, Phys. Rev. Lett. 73, 1243 (1994).
    [CrossRef] [PubMed]
  13. V. Krylov, O. Ollikainen, and U. P. Wild, J. Opt. Soc. Am. B 15, 2910 (1998).
    [CrossRef]
  14. M. Nurhuda, A. Suda, M. Hatayama, K. Nagasaka, and K. Midorikawa, Phys. Rev. A 66, 023811 (2002).
    [CrossRef]
  15. E. Goulielmakis, M. Schultze, M. Hofstetter, V. S. Yakovlev, J. Gagnon, M. Uiberacker, A. L. Aquila, E. M. Gullikson, D. T. Attwood, R. Kienberger, F. Krausz, and U. Kleinberg, Science 320, 1614 (2008).
    [CrossRef] [PubMed]
  16. M. Yamashita, K. Yamane, and R. Morita, IEEE J. Select Topics Quantum Electron. 12, 213 (2006).
    [CrossRef]
  17. A. Kumar, Phys. Rev. A 81, 013807 (2010).
    [CrossRef]
  18. D. P. Shelton and V. Mizrahi, Phys. Rev. A 33, 72 (1986).
    [CrossRef] [PubMed]
  19. V. Mizrahi and D. P. Shelton, Phys. Rev A 32, 3454(1985).
    [CrossRef] [PubMed]

2010 (1)

A. Kumar, Phys. Rev. A 81, 013807 (2010).
[CrossRef]

2008 (1)

E. Goulielmakis, M. Schultze, M. Hofstetter, V. S. Yakovlev, J. Gagnon, M. Uiberacker, A. L. Aquila, E. M. Gullikson, D. T. Attwood, R. Kienberger, F. Krausz, and U. Kleinberg, Science 320, 1614 (2008).
[CrossRef] [PubMed]

2006 (2)

M. Yamashita, K. Yamane, and R. Morita, IEEE J. Select Topics Quantum Electron. 12, 213 (2006).
[CrossRef]

A. Scrinzi, M. Yu Ivanov, R. Kienberger, and D. M. Villeneuve, J. Phys. B 39, R1 (2006).
[CrossRef]

2005 (1)

M. Drescher and Ferenc Krausz, J. Phys. B 38, S727 (2005).
[CrossRef]

2002 (1)

M. Nurhuda, A. Suda, M. Hatayama, K. Nagasaka, and K. Midorikawa, Phys. Rev. A 66, 023811 (2002).
[CrossRef]

2001 (2)

F. L. Kien, N. H. Shon, and K. Hakuta, Phys. Rev. A 64, 051803 (2001).
[CrossRef]

T. Kobayashi, T. Saito, and H. Ohtani, Nature 414, 531 (2001).
[CrossRef] [PubMed]

2000 (2)

T. Brabec and F. Krausz, Rev. Mod. Phys. 72, 545 (2000).
[CrossRef]

P. Corkum, Nature 403, 845 (2000).
[CrossRef] [PubMed]

1998 (3)

F. Krausz, T. Brabec, M. Schnuerer, and C. Spielmann, Opt. Photon. News 9, 46 (1998).
[CrossRef]

D. Meshulach and Y. Silberberg, Nature 396, 239 (1998).
[CrossRef]

V. Krylov, O. Ollikainen, and U. P. Wild, J. Opt. Soc. Am. B 15, 2910 (1998).
[CrossRef]

1995 (1)

P. Corkum, Opt. Photon. News 6, 18 (1995).
[CrossRef]

1994 (1)

A. E. Kaplan, Phys. Rev. Lett. 73, 1243 (1994).
[CrossRef] [PubMed]

1993 (1)

S. Yoshikawa and T. Imasaka, Opt. Commun. 96, 94 (1993).
[CrossRef]

1986 (1)

D. P. Shelton and V. Mizrahi, Phys. Rev. A 33, 72 (1986).
[CrossRef] [PubMed]

1985 (1)

V. Mizrahi and D. P. Shelton, Phys. Rev A 32, 3454(1985).
[CrossRef] [PubMed]

Aquila, A. L.

E. Goulielmakis, M. Schultze, M. Hofstetter, V. S. Yakovlev, J. Gagnon, M. Uiberacker, A. L. Aquila, E. M. Gullikson, D. T. Attwood, R. Kienberger, F. Krausz, and U. Kleinberg, Science 320, 1614 (2008).
[CrossRef] [PubMed]

Attwood, D. T.

E. Goulielmakis, M. Schultze, M. Hofstetter, V. S. Yakovlev, J. Gagnon, M. Uiberacker, A. L. Aquila, E. M. Gullikson, D. T. Attwood, R. Kienberger, F. Krausz, and U. Kleinberg, Science 320, 1614 (2008).
[CrossRef] [PubMed]

Brabec, T.

T. Brabec and F. Krausz, Rev. Mod. Phys. 72, 545 (2000).
[CrossRef]

F. Krausz, T. Brabec, M. Schnuerer, and C. Spielmann, Opt. Photon. News 9, 46 (1998).
[CrossRef]

Corkum, P.

P. Corkum, Nature 403, 845 (2000).
[CrossRef] [PubMed]

P. Corkum, Opt. Photon. News 6, 18 (1995).
[CrossRef]

Drescher, M.

M. Drescher and Ferenc Krausz, J. Phys. B 38, S727 (2005).
[CrossRef]

Gagnon, J.

E. Goulielmakis, M. Schultze, M. Hofstetter, V. S. Yakovlev, J. Gagnon, M. Uiberacker, A. L. Aquila, E. M. Gullikson, D. T. Attwood, R. Kienberger, F. Krausz, and U. Kleinberg, Science 320, 1614 (2008).
[CrossRef] [PubMed]

Goulielmakis, E.

E. Goulielmakis, M. Schultze, M. Hofstetter, V. S. Yakovlev, J. Gagnon, M. Uiberacker, A. L. Aquila, E. M. Gullikson, D. T. Attwood, R. Kienberger, F. Krausz, and U. Kleinberg, Science 320, 1614 (2008).
[CrossRef] [PubMed]

Gullikson, E. M.

E. Goulielmakis, M. Schultze, M. Hofstetter, V. S. Yakovlev, J. Gagnon, M. Uiberacker, A. L. Aquila, E. M. Gullikson, D. T. Attwood, R. Kienberger, F. Krausz, and U. Kleinberg, Science 320, 1614 (2008).
[CrossRef] [PubMed]

Hakuta, K.

F. L. Kien, N. H. Shon, and K. Hakuta, Phys. Rev. A 64, 051803 (2001).
[CrossRef]

Hatayama, M.

M. Nurhuda, A. Suda, M. Hatayama, K. Nagasaka, and K. Midorikawa, Phys. Rev. A 66, 023811 (2002).
[CrossRef]

Hofstetter, M.

E. Goulielmakis, M. Schultze, M. Hofstetter, V. S. Yakovlev, J. Gagnon, M. Uiberacker, A. L. Aquila, E. M. Gullikson, D. T. Attwood, R. Kienberger, F. Krausz, and U. Kleinberg, Science 320, 1614 (2008).
[CrossRef] [PubMed]

Imasaka, T.

S. Yoshikawa and T. Imasaka, Opt. Commun. 96, 94 (1993).
[CrossRef]

Kaplan, A. E.

A. E. Kaplan, Phys. Rev. Lett. 73, 1243 (1994).
[CrossRef] [PubMed]

Kerschensteiner, M.

T. Misgeld and M. Kerschensteiner, Nat. Rev. Neurosci. 6, 449 (2006).

Kien, F. L.

F. L. Kien, N. H. Shon, and K. Hakuta, Phys. Rev. A 64, 051803 (2001).
[CrossRef]

Kienberger, R.

E. Goulielmakis, M. Schultze, M. Hofstetter, V. S. Yakovlev, J. Gagnon, M. Uiberacker, A. L. Aquila, E. M. Gullikson, D. T. Attwood, R. Kienberger, F. Krausz, and U. Kleinberg, Science 320, 1614 (2008).
[CrossRef] [PubMed]

A. Scrinzi, M. Yu Ivanov, R. Kienberger, and D. M. Villeneuve, J. Phys. B 39, R1 (2006).
[CrossRef]

Kleinberg, U.

E. Goulielmakis, M. Schultze, M. Hofstetter, V. S. Yakovlev, J. Gagnon, M. Uiberacker, A. L. Aquila, E. M. Gullikson, D. T. Attwood, R. Kienberger, F. Krausz, and U. Kleinberg, Science 320, 1614 (2008).
[CrossRef] [PubMed]

Kobayashi, T.

T. Kobayashi, T. Saito, and H. Ohtani, Nature 414, 531 (2001).
[CrossRef] [PubMed]

Krausz, F.

E. Goulielmakis, M. Schultze, M. Hofstetter, V. S. Yakovlev, J. Gagnon, M. Uiberacker, A. L. Aquila, E. M. Gullikson, D. T. Attwood, R. Kienberger, F. Krausz, and U. Kleinberg, Science 320, 1614 (2008).
[CrossRef] [PubMed]

T. Brabec and F. Krausz, Rev. Mod. Phys. 72, 545 (2000).
[CrossRef]

F. Krausz, T. Brabec, M. Schnuerer, and C. Spielmann, Opt. Photon. News 9, 46 (1998).
[CrossRef]

Krausz, Ferenc

M. Drescher and Ferenc Krausz, J. Phys. B 38, S727 (2005).
[CrossRef]

Krylov, V.

Kumar, A.

A. Kumar, Phys. Rev. A 81, 013807 (2010).
[CrossRef]

Meshulach, D.

D. Meshulach and Y. Silberberg, Nature 396, 239 (1998).
[CrossRef]

Midorikawa, K.

M. Nurhuda, A. Suda, M. Hatayama, K. Nagasaka, and K. Midorikawa, Phys. Rev. A 66, 023811 (2002).
[CrossRef]

Misgeld, T.

T. Misgeld and M. Kerschensteiner, Nat. Rev. Neurosci. 6, 449 (2006).

Mizrahi, V.

D. P. Shelton and V. Mizrahi, Phys. Rev. A 33, 72 (1986).
[CrossRef] [PubMed]

V. Mizrahi and D. P. Shelton, Phys. Rev A 32, 3454(1985).
[CrossRef] [PubMed]

Morita, R.

M. Yamashita, K. Yamane, and R. Morita, IEEE J. Select Topics Quantum Electron. 12, 213 (2006).
[CrossRef]

Nagasaka, K.

M. Nurhuda, A. Suda, M. Hatayama, K. Nagasaka, and K. Midorikawa, Phys. Rev. A 66, 023811 (2002).
[CrossRef]

Nurhuda, M.

M. Nurhuda, A. Suda, M. Hatayama, K. Nagasaka, and K. Midorikawa, Phys. Rev. A 66, 023811 (2002).
[CrossRef]

Ohtani, H.

T. Kobayashi, T. Saito, and H. Ohtani, Nature 414, 531 (2001).
[CrossRef] [PubMed]

Ollikainen, O.

Saito, T.

T. Kobayashi, T. Saito, and H. Ohtani, Nature 414, 531 (2001).
[CrossRef] [PubMed]

Schnuerer, M.

F. Krausz, T. Brabec, M. Schnuerer, and C. Spielmann, Opt. Photon. News 9, 46 (1998).
[CrossRef]

Schultze, M.

E. Goulielmakis, M. Schultze, M. Hofstetter, V. S. Yakovlev, J. Gagnon, M. Uiberacker, A. L. Aquila, E. M. Gullikson, D. T. Attwood, R. Kienberger, F. Krausz, and U. Kleinberg, Science 320, 1614 (2008).
[CrossRef] [PubMed]

Scrinzi, A.

A. Scrinzi, M. Yu Ivanov, R. Kienberger, and D. M. Villeneuve, J. Phys. B 39, R1 (2006).
[CrossRef]

Shelton, D. P.

D. P. Shelton and V. Mizrahi, Phys. Rev. A 33, 72 (1986).
[CrossRef] [PubMed]

V. Mizrahi and D. P. Shelton, Phys. Rev A 32, 3454(1985).
[CrossRef] [PubMed]

Shon, N. H.

F. L. Kien, N. H. Shon, and K. Hakuta, Phys. Rev. A 64, 051803 (2001).
[CrossRef]

Silberberg, Y.

D. Meshulach and Y. Silberberg, Nature 396, 239 (1998).
[CrossRef]

Spielmann, C.

F. Krausz, T. Brabec, M. Schnuerer, and C. Spielmann, Opt. Photon. News 9, 46 (1998).
[CrossRef]

Suda, A.

M. Nurhuda, A. Suda, M. Hatayama, K. Nagasaka, and K. Midorikawa, Phys. Rev. A 66, 023811 (2002).
[CrossRef]

Uiberacker, M.

E. Goulielmakis, M. Schultze, M. Hofstetter, V. S. Yakovlev, J. Gagnon, M. Uiberacker, A. L. Aquila, E. M. Gullikson, D. T. Attwood, R. Kienberger, F. Krausz, and U. Kleinberg, Science 320, 1614 (2008).
[CrossRef] [PubMed]

Villeneuve, D. M.

A. Scrinzi, M. Yu Ivanov, R. Kienberger, and D. M. Villeneuve, J. Phys. B 39, R1 (2006).
[CrossRef]

Wild, U. P.

Yakovlev, V. S.

E. Goulielmakis, M. Schultze, M. Hofstetter, V. S. Yakovlev, J. Gagnon, M. Uiberacker, A. L. Aquila, E. M. Gullikson, D. T. Attwood, R. Kienberger, F. Krausz, and U. Kleinberg, Science 320, 1614 (2008).
[CrossRef] [PubMed]

Yamane, K.

M. Yamashita, K. Yamane, and R. Morita, IEEE J. Select Topics Quantum Electron. 12, 213 (2006).
[CrossRef]

Yamashita, M.

M. Yamashita, K. Yamane, and R. Morita, IEEE J. Select Topics Quantum Electron. 12, 213 (2006).
[CrossRef]

Yoshikawa, S.

S. Yoshikawa and T. Imasaka, Opt. Commun. 96, 94 (1993).
[CrossRef]

Yu Ivanov, M.

A. Scrinzi, M. Yu Ivanov, R. Kienberger, and D. M. Villeneuve, J. Phys. B 39, R1 (2006).
[CrossRef]

IEEE J. Select Topics Quantum Electron. (1)

M. Yamashita, K. Yamane, and R. Morita, IEEE J. Select Topics Quantum Electron. 12, 213 (2006).
[CrossRef]

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

J. Phys. B (2)

M. Drescher and Ferenc Krausz, J. Phys. B 38, S727 (2005).
[CrossRef]

A. Scrinzi, M. Yu Ivanov, R. Kienberger, and D. M. Villeneuve, J. Phys. B 39, R1 (2006).
[CrossRef]

Nature (3)

T. Kobayashi, T. Saito, and H. Ohtani, Nature 414, 531 (2001).
[CrossRef] [PubMed]

D. Meshulach and Y. Silberberg, Nature 396, 239 (1998).
[CrossRef]

P. Corkum, Nature 403, 845 (2000).
[CrossRef] [PubMed]

Opt. Commun. (1)

S. Yoshikawa and T. Imasaka, Opt. Commun. 96, 94 (1993).
[CrossRef]

Opt. Photon. News (2)

P. Corkum, Opt. Photon. News 6, 18 (1995).
[CrossRef]

F. Krausz, T. Brabec, M. Schnuerer, and C. Spielmann, Opt. Photon. News 9, 46 (1998).
[CrossRef]

Phys. Rev A (1)

V. Mizrahi and D. P. Shelton, Phys. Rev A 32, 3454(1985).
[CrossRef] [PubMed]

Phys. Rev. A (4)

A. Kumar, Phys. Rev. A 81, 013807 (2010).
[CrossRef]

D. P. Shelton and V. Mizrahi, Phys. Rev. A 33, 72 (1986).
[CrossRef] [PubMed]

M. Nurhuda, A. Suda, M. Hatayama, K. Nagasaka, and K. Midorikawa, Phys. Rev. A 66, 023811 (2002).
[CrossRef]

F. L. Kien, N. H. Shon, and K. Hakuta, Phys. Rev. A 64, 051803 (2001).
[CrossRef]

Phys. Rev. Lett. (1)

A. E. Kaplan, Phys. Rev. Lett. 73, 1243 (1994).
[CrossRef] [PubMed]

Rev. Mod. Phys. (1)

T. Brabec and F. Krausz, Rev. Mod. Phys. 72, 545 (2000).
[CrossRef]

Science (1)

E. Goulielmakis, M. Schultze, M. Hofstetter, V. S. Yakovlev, J. Gagnon, M. Uiberacker, A. L. Aquila, E. M. Gullikson, D. T. Attwood, R. Kienberger, F. Krausz, and U. Kleinberg, Science 320, 1614 (2008).
[CrossRef] [PubMed]

Other (1)

T. Misgeld and M. Kerschensteiner, Nat. Rev. Neurosci. 6, 449 (2006).

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Figures (3)

Fig. 1
Fig. 1

Normalized dimensionless spectral intensity of a single-cycle Gaussian pulse (at 0.8 μm ) has been plotted as a function of the wavelength λ, after 60 cm of propagation in a gas cell filled with D 2 gas at pressures of 500 mbar (dotted curve), 1 bar (dashed–dotted curve), and 1.5 bar (solid curve).

Fig. 2
Fig. 2

Plot of the normalized dimensionless spectral intensity of a four-cycle pulse (at 0.8 μm ), as a function of the wavelength λ, after 60 cm of propagation in a gas cell filled with D 2 gas at pressures p = 0.5 bar (dotted curve), p = 1 bar (dashed–dotted curve), and p = 1.5 bar (solid curve).

Fig. 3
Fig. 3

Unwrapped spectral phase of the output pulse for p = 1.5 bar after 60 cm of propagation.

Equations (7)

Equations on this page are rendered with MathJax. Learn more.

¯ 2 E ¯ 2 β ¯ 0 ( 1 ) ( 2 E ¯ τ ξ β ¯ 0 ( 3 ) 6 4 E ¯ τ 4 α ¯ 0 ( 2 ) 4 3 E ¯ τ 3 ) = χ ¯ ( 3 ) c ¯ 2 2 τ 2 ( E ¯ 2 E ¯ ) + ( R ¯ ( 3 ) c ¯ 2 ) 2 τ 2 ( E ¯ ( τ ) 0 g ¯ R ( τ 1 ) [ E ¯ ( τ τ 1 ) · E ¯ ( τ τ 1 ) ] d τ 1 ) ,
r ¯ = r l 0 = ( x l 0 , y l 0 , z l 0 ) , t ¯ = t t 0 , E ¯ = E E 0 ,
¯ 2 = 2 x ¯ 2 + 2 y ¯ 2 ,
c ¯ = t 0 c l 0 , g R ( t ) = 1 t 0 g ¯ R ( t ¯ ) , χ ¯ ( 3 ) = E 0 2 χ ( 3 ) , R ¯ ( 3 ) = E 0 2 χ R ( 3 ) ,
g R ( t ) = τ 1 2 + τ 2 2 τ 1 τ 2 2 e t / τ 2 sin ( t τ 1 ) ( t > 0 ) .
β ¯ 0 ( 1 ) ( β ¯ ω ¯ ) ω ¯ = ω ¯ 0 , β ¯ 0 ( 3 ) ( 3 β ¯ ω ¯ 3 ) ω ¯ = ω ¯ 0 , α ¯ 0 ( 2 ) ( 2 α ¯ ω ¯ 2 ) ω ¯ = ω ¯ 0 ,
E ¯ = e 1 2 ( t ¯ / T ¯ 0 ) 2 e K r 2 / 2 cos ( ω ¯ 0 t ¯ ) ,

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