Abstract

Following the experiments of Shverdin and colleagues [Phys. Rev. Lett. 94, 033904 (2005)] , we describe a technique for determining the temporal envelope of an optical beam whose spectrum consists of n discrete, equally spaced frequency components. Four-wave mixing is employed to generate n1 higher-frequency sidebands. The relative intensities of these sidebands, together with the intensities of the incident sidebands, determine the unknown relative phases of the incident beam.

© 2005 Optical Society of America

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References

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  1. A. V. Sokolov, D. R. Walker, D. D. Yavuz, G. Y. Yin, and S. E. Harris, Phys. Rev. Lett. 85, 562 (2000).
    [CrossRef] [PubMed]
  2. A. V. Sokolov, M. Y. Shverdin, D. R. Walker, D. D. Yavuz, A. M. Burzo, G. Y. Yin, and S. E. Harris, J. Mod. Opt. 52, 285 (2005).
    [CrossRef]
  3. A. Nazarkin, G. Korn, M. Wittmann, and T. Elsaesser, Phys. Rev. Lett. 83, 2560 (1999).
    [CrossRef]
  4. J. Q. Liang, M. Katsuragawa, Fam Le Kien, and K. Hakuta, Phys. Rev. Lett. 85, 2474 (2000).
    [CrossRef] [PubMed]
  5. A. V. Sokolov, D. R. Walker, G. Y. Yin, and S. E. Harris, Phys. Rev. Lett. 87, 033402 (2001).
    [CrossRef]
  6. M. Y. Shverdin, D. R. Walker, D. D. Yavuz, G. Y. Yin, and S. E. Harris, Phys. Rev. Lett. 94, 033904 (2005).
    [CrossRef]
  7. R. Trebino, Frequency-Resolved Optical Gating: the Measurement of Ultrashort Laser Pulses (Kluwer Academic, Norwell, Mass., 2000).
    [CrossRef]
  8. G. C. Bjorklund, IEEE J. Quantum Electron. 11, 287 (1975).
    [CrossRef]
  9. S. T. Cundiff and J. Ye, Rev. Mod. Phys. 75, 325 (2003).
    [CrossRef]

2005 (2)

A. V. Sokolov, M. Y. Shverdin, D. R. Walker, D. D. Yavuz, A. M. Burzo, G. Y. Yin, and S. E. Harris, J. Mod. Opt. 52, 285 (2005).
[CrossRef]

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

2003 (1)

S. T. Cundiff and J. Ye, Rev. Mod. Phys. 75, 325 (2003).
[CrossRef]

2001 (1)

A. V. Sokolov, D. R. Walker, G. Y. Yin, and S. E. Harris, Phys. Rev. Lett. 87, 033402 (2001).
[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, Fam Le Kien, and K. Hakuta, Phys. Rev. Lett. 85, 2474 (2000).
[CrossRef] [PubMed]

1999 (1)

A. Nazarkin, G. Korn, M. Wittmann, and T. Elsaesser, Phys. Rev. Lett. 83, 2560 (1999).
[CrossRef]

1975 (1)

G. C. Bjorklund, IEEE J. Quantum Electron. 11, 287 (1975).
[CrossRef]

Bjorklund, G. C.

G. C. Bjorklund, IEEE J. Quantum Electron. 11, 287 (1975).
[CrossRef]

Burzo, A. M.

A. V. Sokolov, M. Y. Shverdin, D. R. Walker, D. D. Yavuz, A. M. Burzo, G. Y. Yin, and S. E. Harris, J. Mod. Opt. 52, 285 (2005).
[CrossRef]

Cundiff, S. T.

S. T. Cundiff and J. Ye, Rev. Mod. Phys. 75, 325 (2003).
[CrossRef]

Elsaesser, T.

A. Nazarkin, G. Korn, M. Wittmann, and T. Elsaesser, Phys. Rev. Lett. 83, 2560 (1999).
[CrossRef]

Hakuta, K.

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

Harris, S. E.

A. V. Sokolov, M. Y. Shverdin, D. R. Walker, D. D. Yavuz, A. M. Burzo, G. Y. Yin, and S. E. Harris, J. Mod. Opt. 52, 285 (2005).
[CrossRef]

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

A. V. Sokolov, D. R. Walker, G. Y. Yin, and S. E. Harris, Phys. Rev. Lett. 87, 033402 (2001).
[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]

Katsuragawa, M.

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

Korn, G.

A. Nazarkin, G. Korn, M. Wittmann, and T. Elsaesser, Phys. Rev. Lett. 83, 2560 (1999).
[CrossRef]

Le Kien, Fam

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

Liang, J. Q.

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

Nazarkin, A.

A. Nazarkin, G. Korn, M. Wittmann, and T. Elsaesser, Phys. Rev. Lett. 83, 2560 (1999).
[CrossRef]

Shverdin, M. Y.

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

A. V. Sokolov, M. Y. Shverdin, D. R. Walker, D. D. Yavuz, A. M. Burzo, G. Y. Yin, and S. E. Harris, J. Mod. Opt. 52, 285 (2005).
[CrossRef]

Sokolov, A. V.

A. V. Sokolov, M. Y. Shverdin, D. R. Walker, D. D. Yavuz, A. M. Burzo, G. Y. Yin, and S. E. Harris, J. Mod. Opt. 52, 285 (2005).
[CrossRef]

A. V. Sokolov, D. R. Walker, G. Y. Yin, and S. E. Harris, Phys. Rev. Lett. 87, 033402 (2001).
[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]

Trebino, R.

R. Trebino, Frequency-Resolved Optical Gating: the Measurement of Ultrashort Laser Pulses (Kluwer Academic, Norwell, Mass., 2000).
[CrossRef]

Walker, D. R.

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

A. V. Sokolov, M. Y. Shverdin, D. R. Walker, D. D. Yavuz, A. M. Burzo, G. Y. Yin, and S. E. Harris, J. Mod. Opt. 52, 285 (2005).
[CrossRef]

A. V. Sokolov, D. R. Walker, G. Y. Yin, and S. E. Harris, Phys. Rev. Lett. 87, 033402 (2001).
[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]

Wittmann, M.

A. Nazarkin, G. Korn, M. Wittmann, and T. Elsaesser, Phys. Rev. Lett. 83, 2560 (1999).
[CrossRef]

Yavuz, D. D.

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

A. V. Sokolov, M. Y. Shverdin, D. R. Walker, D. D. Yavuz, A. M. Burzo, G. Y. Yin, and S. E. Harris, J. Mod. Opt. 52, 285 (2005).
[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]

Ye, J.

S. T. Cundiff and J. Ye, Rev. Mod. Phys. 75, 325 (2003).
[CrossRef]

Yin, G. Y.

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

A. V. Sokolov, M. Y. Shverdin, D. R. Walker, D. D. Yavuz, A. M. Burzo, G. Y. Yin, and S. E. Harris, J. Mod. Opt. 52, 285 (2005).
[CrossRef]

A. V. Sokolov, D. R. Walker, G. Y. Yin, and S. E. Harris, Phys. Rev. Lett. 87, 033402 (2001).
[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]

IEEE J. Quantum Electron. (1)

G. C. Bjorklund, IEEE J. Quantum Electron. 11, 287 (1975).
[CrossRef]

J. Mod. Opt. (1)

A. V. Sokolov, M. Y. Shverdin, D. R. Walker, D. D. Yavuz, A. M. Burzo, G. Y. Yin, and S. E. Harris, J. Mod. Opt. 52, 285 (2005).
[CrossRef]

Phys. Rev. Lett. (5)

A. Nazarkin, G. Korn, M. Wittmann, and T. Elsaesser, Phys. Rev. Lett. 83, 2560 (1999).
[CrossRef]

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

A. V. Sokolov, D. R. Walker, G. Y. Yin, and S. E. Harris, Phys. Rev. Lett. 87, 033402 (2001).
[CrossRef]

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

Rev. Mod. Phys. (1)

S. T. Cundiff and J. Ye, Rev. Mod. Phys. 75, 325 (2003).
[CrossRef]

Other (1)

R. Trebino, Frequency-Resolved Optical Gating: the Measurement of Ultrashort Laser Pulses (Kluwer Academic, Norwell, Mass., 2000).
[CrossRef]

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Figures (3)

Fig. 1
Fig. 1

Experimental setup for synthesis and characterization of a set of sidebands. Through molecular modulation, optical sidebands are produced in a D 2 cell. The sidebands are dispersed through a prism, individually phase modulated, recombined, and focused into a Xe cell. A detector measures the power spectral density of the sidebands generated through difference-frequency conversion.

Fig. 2
Fig. 2

Three waveforms of equal power are depicted (left-hand panels) along with the spectral amplitudes (middle panels) and the spectral amplitudes generated by difference frequency conversion (right-hand panels). From top to bottom, the waveforms are (a) single-cycle, (b) FM, and (c) sawtooth waveforms. The waveforms consist of nine Fourier sidebands spanning 3.2 octaves. Amplitude comparisons between rows are meaningful, but comparisons between columns are not.

Fig. 3
Fig. 3

(a) Nine-Fourier-component sawtooth waveform (solid) and its envelope amplitude (dotted). The waveform is significantly altered as the carrier-envelope phase is changed by (b) π 3 rad , (c) 2 π 3 rad , and (d) π rad while the envelope amplitude remains unchanged.

Equations (3)

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P ( ω q ) = K i = q n + 1 n j = q i + 1 n E i E j E k * exp [ ι ( ϕ i + ϕ j ϕ k ) ] 2 ,
P ( ω 5 ) = K z 3 2 z 1 * + 2 z 4 z 2 z 1 * + 2 z 4 z 3 z 2 * + z 4 2 z 3 * 2 ,
P ( ω 6 ) = K 2 z 4 z 3 z 1 * + z 4 2 z 2 * 2 ,

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