Abstract

We report a method of spectral phase measurement for a femtosecond pulse train composed of a discrete Raman spectrum. The method is based on an idea of spectral interference. Making use of a small portion of two Raman pump laser radiations, we produce two sum-frequency spectra that spectrally interfere with each other. Based on this interfering sum-frequency spectra, we successfully derive the spectral phase and reconstruct the temporal profile. The reliability of this method is also confirmed by measuring the spectral phase changes caused by intentionally inserted silica plates of various thicknesses and comparing them to theoretical predictions.

© 2008 Optical Society of America

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References

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2008 (1)

W.-J. Chen, Z.-M. Hsieh, S. W. Huang, H.-Y. Su, C.-J. Lai, T.-T. Tang, C.-H. Lin, C.-K. Lee, R.-P. Pan, and A. H. Kung, Phys. Rev. Lett. 100, 163906 (2008).
[CrossRef] [PubMed]

2005 (4)

2002 (3)

M. Katsuragawa, J. Q. Liang, F. Le Kien, and K. Hakuta, Phys. Rev. A 65, 025801 (2002).
[CrossRef]

D. D. Yavuz, D. R. Walker, G. Y. Yin, and S. E. Harris, Opt. Lett. 27, 769 (2002).
[CrossRef]

S. E. Harris, D. R. Walker, and D. D. Yavuz, Phys. Rev. A 65, 021801(R) (2002).
[CrossRef]

2000 (2)

A. V. Sokolov, D. R. Walker, D. D. Yavuz, G. Y. Yin, and S. E. Harris, Phys. Rev. Lett. 85, 562 (2000).
[CrossRef] [PubMed]

J. Q. Liang, M. Katsuragawa, F. Le Kien, and K. Hakuta, Phys. Rev. Lett. 85, 2474 (2000).
[CrossRef] [PubMed]

1998 (1)

1997 (1)

S. E. Harris and A. V. Sokolov, Phys. Rev. A 55, R4019 (1997).
[CrossRef]

1993 (1)

1965 (1)

Chen, W.-J.

W.-J. Chen, Z.-M. Hsieh, S. W. Huang, H.-Y. Su, C.-J. Lai, T.-T. Tang, C.-H. Lin, C.-K. Lee, R.-P. Pan, and A. H. Kung, Phys. Rev. Lett. 100, 163906 (2008).
[CrossRef] [PubMed]

Goda, S. N.

Hakuta, K.

M. Katsuragawa, J. Q. Liang, F. Le Kien, and K. Hakuta, Phys. Rev. A 65, 025801 (2002).
[CrossRef]

J. Q. Liang, M. Katsuragawa, F. Le Kien, and K. Hakuta, Phys. Rev. Lett. 85, 2474 (2000).
[CrossRef] [PubMed]

Harris, S. E.

M. Y. Shiverdin, D. R. Walker, D. D. Yavuz, G. Y. Yin, and S. E. Harris, Phys. Rev. Lett. 94, 033904 (2005).
[CrossRef]

S. N. Goda, M. Y. Shverdin, D. R. Walker, and S. E. Harris, Opt. Lett. 30, 1222 (2005).
[CrossRef] [PubMed]

D. D. Yavuz, D. R. Walker, G. Y. Yin, and S. E. Harris, Opt. Lett. 27, 769 (2002).
[CrossRef]

S. E. Harris, D. R. Walker, and D. D. Yavuz, Phys. Rev. A 65, 021801(R) (2002).
[CrossRef]

A. V. Sokolov, D. R. Walker, D. D. Yavuz, G. Y. Yin, and S. E. Harris, Phys. Rev. Lett. 85, 562 (2000).
[CrossRef] [PubMed]

S. E. Harris and A. V. Sokolov, Phys. Rev. A 55, R4019 (1997).
[CrossRef]

Hsieh, Z.-M.

W.-J. Chen, Z.-M. Hsieh, S. W. Huang, H.-Y. Su, C.-J. Lai, T.-T. Tang, C.-H. Lin, C.-K. Lee, R.-P. Pan, and A. H. Kung, Phys. Rev. Lett. 100, 163906 (2008).
[CrossRef] [PubMed]

Huang, S. W.

W.-J. Chen, Z.-M. Hsieh, S. W. Huang, H.-Y. Su, C.-J. Lai, T.-T. Tang, C.-H. Lin, C.-K. Lee, R.-P. Pan, and A. H. Kung, Phys. Rev. Lett. 100, 163906 (2008).
[CrossRef] [PubMed]

Iaconic, C.

Kane, D. J.

Katsuragawa, M.

M. Katsuragawa and T. Onose, Opt. Lett. 30, 2421 (2005).
[CrossRef] [PubMed]

M. Katsuragawa, K. Yokoyama, and T. Onose, Opt. Express 13, 5628 (2005).
[CrossRef] [PubMed]

M. Katsuragawa, J. Q. Liang, F. Le Kien, and K. Hakuta, Phys. Rev. A 65, 025801 (2002).
[CrossRef]

J. Q. Liang, M. Katsuragawa, F. Le Kien, and K. Hakuta, Phys. Rev. Lett. 85, 2474 (2000).
[CrossRef] [PubMed]

Kung, A. H.

W.-J. Chen, Z.-M. Hsieh, S. W. Huang, H.-Y. Su, C.-J. Lai, T.-T. Tang, C.-H. Lin, C.-K. Lee, R.-P. Pan, and A. H. Kung, Phys. Rev. Lett. 100, 163906 (2008).
[CrossRef] [PubMed]

Lai, C.-J.

W.-J. Chen, Z.-M. Hsieh, S. W. Huang, H.-Y. Su, C.-J. Lai, T.-T. Tang, C.-H. Lin, C.-K. Lee, R.-P. Pan, and A. H. Kung, Phys. Rev. Lett. 100, 163906 (2008).
[CrossRef] [PubMed]

Le Kien, F.

M. Katsuragawa, J. Q. Liang, F. Le Kien, and K. Hakuta, Phys. Rev. A 65, 025801 (2002).
[CrossRef]

J. Q. Liang, M. Katsuragawa, F. Le Kien, and K. Hakuta, Phys. Rev. Lett. 85, 2474 (2000).
[CrossRef] [PubMed]

Lee, C.-K.

W.-J. Chen, Z.-M. Hsieh, S. W. Huang, H.-Y. Su, C.-J. Lai, T.-T. Tang, C.-H. Lin, C.-K. Lee, R.-P. Pan, and A. H. Kung, Phys. Rev. Lett. 100, 163906 (2008).
[CrossRef] [PubMed]

Liang, J. Q.

M. Katsuragawa, J. Q. Liang, F. Le Kien, and K. Hakuta, Phys. Rev. A 65, 025801 (2002).
[CrossRef]

J. Q. Liang, M. Katsuragawa, F. Le Kien, and K. Hakuta, Phys. Rev. Lett. 85, 2474 (2000).
[CrossRef] [PubMed]

Lin, C.-H.

W.-J. Chen, Z.-M. Hsieh, S. W. Huang, H.-Y. Su, C.-J. Lai, T.-T. Tang, C.-H. Lin, C.-K. Lee, R.-P. Pan, and A. H. Kung, Phys. Rev. Lett. 100, 163906 (2008).
[CrossRef] [PubMed]

Malitson, I. H.

Onose, T.

Pan, R.-P.

W.-J. Chen, Z.-M. Hsieh, S. W. Huang, H.-Y. Su, C.-J. Lai, T.-T. Tang, C.-H. Lin, C.-K. Lee, R.-P. Pan, and A. H. Kung, Phys. Rev. Lett. 100, 163906 (2008).
[CrossRef] [PubMed]

Shiverdin, M. Y.

M. Y. Shiverdin, D. R. Walker, D. D. Yavuz, G. Y. Yin, and S. E. Harris, Phys. Rev. Lett. 94, 033904 (2005).
[CrossRef]

Shverdin, M. Y.

Sokolov, A. V.

A. V. Sokolov, D. R. Walker, D. D. Yavuz, G. Y. Yin, and S. E. Harris, Phys. Rev. Lett. 85, 562 (2000).
[CrossRef] [PubMed]

S. E. Harris and A. V. Sokolov, Phys. Rev. A 55, R4019 (1997).
[CrossRef]

Su, H.-Y.

W.-J. Chen, Z.-M. Hsieh, S. W. Huang, H.-Y. Su, C.-J. Lai, T.-T. Tang, C.-H. Lin, C.-K. Lee, R.-P. Pan, and A. H. Kung, Phys. Rev. Lett. 100, 163906 (2008).
[CrossRef] [PubMed]

Tang, T.-T.

W.-J. Chen, Z.-M. Hsieh, S. W. Huang, H.-Y. Su, C.-J. Lai, T.-T. Tang, C.-H. Lin, C.-K. Lee, R.-P. Pan, and A. H. Kung, Phys. Rev. Lett. 100, 163906 (2008).
[CrossRef] [PubMed]

Trebino, R.

Walker, D. R.

S. N. Goda, M. Y. Shverdin, D. R. Walker, and S. E. Harris, Opt. Lett. 30, 1222 (2005).
[CrossRef] [PubMed]

M. Y. Shiverdin, D. R. Walker, D. D. Yavuz, G. Y. Yin, and S. E. Harris, Phys. Rev. Lett. 94, 033904 (2005).
[CrossRef]

S. E. Harris, D. R. Walker, and D. D. Yavuz, Phys. Rev. A 65, 021801(R) (2002).
[CrossRef]

D. D. Yavuz, D. R. Walker, G. Y. Yin, and S. E. Harris, Opt. Lett. 27, 769 (2002).
[CrossRef]

A. V. Sokolov, D. R. Walker, D. D. Yavuz, G. Y. Yin, and S. E. Harris, Phys. Rev. Lett. 85, 562 (2000).
[CrossRef] [PubMed]

Walmsley, I. A.

Yavuz, D. D.

M. Y. Shiverdin, D. R. Walker, D. D. Yavuz, G. Y. Yin, and S. E. Harris, Phys. Rev. Lett. 94, 033904 (2005).
[CrossRef]

S. E. Harris, D. R. Walker, and D. D. Yavuz, Phys. Rev. A 65, 021801(R) (2002).
[CrossRef]

D. D. Yavuz, D. R. Walker, G. Y. Yin, and S. E. Harris, Opt. Lett. 27, 769 (2002).
[CrossRef]

A. V. Sokolov, D. R. Walker, D. D. Yavuz, G. Y. Yin, and S. E. Harris, Phys. Rev. Lett. 85, 562 (2000).
[CrossRef] [PubMed]

Yin, G. Y.

M. Y. Shiverdin, D. R. Walker, D. D. Yavuz, G. Y. Yin, and S. E. Harris, Phys. Rev. Lett. 94, 033904 (2005).
[CrossRef]

D. D. Yavuz, D. R. Walker, G. Y. Yin, and S. E. Harris, Opt. Lett. 27, 769 (2002).
[CrossRef]

A. V. Sokolov, D. R. Walker, D. D. Yavuz, G. Y. Yin, and S. E. Harris, Phys. Rev. Lett. 85, 562 (2000).
[CrossRef] [PubMed]

Yokoyama, K.

J. Opt. Soc. Am. (1)

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

Opt. Express (1)

Opt. Lett. (4)

Phys. Rev. A (3)

S. E. Harris, D. R. Walker, and D. D. Yavuz, Phys. Rev. A 65, 021801(R) (2002).
[CrossRef]

S. E. Harris and A. V. Sokolov, Phys. Rev. A 55, R4019 (1997).
[CrossRef]

M. Katsuragawa, J. Q. Liang, F. Le Kien, and K. Hakuta, Phys. Rev. A 65, 025801 (2002).
[CrossRef]

Phys. Rev. Lett. (4)

A. V. Sokolov, D. R. Walker, D. D. Yavuz, G. Y. Yin, and S. E. Harris, Phys. Rev. Lett. 85, 562 (2000).
[CrossRef] [PubMed]

J. Q. Liang, M. Katsuragawa, F. Le Kien, and K. Hakuta, Phys. Rev. Lett. 85, 2474 (2000).
[CrossRef] [PubMed]

M. Y. Shiverdin, D. R. Walker, D. D. Yavuz, G. Y. Yin, and S. E. Harris, Phys. Rev. Lett. 94, 033904 (2005).
[CrossRef]

W.-J. Chen, Z.-M. Hsieh, S. W. Huang, H.-Y. Su, C.-J. Lai, T.-T. Tang, C.-H. Lin, C.-K. Lee, R.-P. Pan, and A. H. Kung, Phys. Rev. Lett. 100, 163906 (2008).
[CrossRef] [PubMed]

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Figures (4)

Fig. 1
Fig. 1

Schematic of experimental setup for broad Raman sideband generation and its spectral phase measurement system.

Fig. 2
Fig. 2

(a) Sum-frequency spectra with various delays. The intensities of the spectral lines periodically change with different phases reflecting the phase differences Δ ϕ n . The symbols above the spectral lines designate corresponding frequency components of the fundamental. (b) Intensity variations of I n SH with respect to the delay τ (filled circle) and their fitting curves (solid curves).

Fig. 3
Fig. 3

(a) Raman sideband spectrum (solid curve) and its spectral phase (open circles). (b) Reconstructed temporal profile of the Raman sideband.

Fig. 4
Fig. 4

Spectral phases of the Raman sideband spectra (a) without, and with (b) 3, (c) 5, and (d) 10 mm thick silica plates. The open circles and open triangles indicate experimental results, and the open squares indicate results derived with a known refractive index dispersion of silica.

Equations (1)

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I n SH = E n 1 E 0 e i Ω 0 τ + E n E 1 e i Ω 1 τ 2 = E n 1 E 0 2 + E n E 1 2 + 2 E n 1 E n E 0 E 1 cos ( Δ Ω τ Δ ϕ n ) ,

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