Abstract

The interference between different harmonics of a few-cycle optical pulse in the region of the spectral overlap is sensitive to the phase of the optical carrier inside the pulse envelope. Near-surface third-harmonic generation from Si(001) combined with second-harmonic generation in a 10µm-thick β-barium borate crystal produces sufficiently strong harmonic emission for single-shot measurement. We propose using this technique to measure the carrier envelope phase of high-energy 5-fs pulses.

© 2000 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] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]

2000 (3)

D. J. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, Science 288, 635 (2000).
[CrossRef] [PubMed]

A. Apolonski, A. Poppe, G. Tempea, Ch. Spielmann, Th. Udem, R. Holzwarth, T. W. Hänsch, and F. Krausz, Phys. Rev. Lett. 85, 740 (2000).
[CrossRef] [PubMed]

P. Dietrich, F. Krausz, and P. B. Corkum, Opt. Lett. 25, 16 (2000).
[CrossRef]

1999 (1)

H. R. Telle, G. Steinmeyer, A. E. Dunlop, J. Stenger, D. H. Sutter, and U. Keller, Appl. Phys. B 69, 327 (1999).
[CrossRef]

1998 (1)

E. Cormier and P. Lambropoulos, Eur. Phys. J. D 2, 15 (1998).
[CrossRef]

1997 (2)

1996 (1)

1992 (1)

P. Brummer and M. Shapiro, Annu. Rev. Phys. Chem. 43, 257 (1992).

1990 (1)

D. J. Moss, E. Graharamani, J. E. Sipe, and H. M. van Driel, Phys. Rev. B 41, 1542 (1990).
[CrossRef]

1987 (1)

J. E. Sipe, D. J. Moss, and H. M. van Driel, Phys. Rev. B 35, 1129 (1987).
[CrossRef]

Anderson, M. H.

Apolonski, A.

A. Apolonski, A. Poppe, G. Tempea, Ch. Spielmann, Th. Udem, R. Holzwarth, T. W. Hänsch, and F. Krausz, Phys. Rev. Lett. 85, 740 (2000).
[CrossRef] [PubMed]

Brabec, T.

Brummer, P.

P. Brummer and M. Shapiro, Annu. Rev. Phys. Chem. 43, 257 (1992).

Corkum, P. B.

Cormier, E.

E. Cormier and P. Lambropoulos, Eur. Phys. J. D 2, 15 (1998).
[CrossRef]

Cundiff, S. T.

D. J. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, Science 288, 635 (2000).
[CrossRef] [PubMed]

De Silvestri, S.

Diddams, S. A.

D. J. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, Science 288, 635 (2000).
[CrossRef] [PubMed]

Dietrich, P.

Downer, M. C.

Dunlop, A. E.

H. R. Telle, G. Steinmeyer, A. E. Dunlop, J. Stenger, D. H. Sutter, and U. Keller, Appl. Phys. B 69, 327 (1999).
[CrossRef]

Ferencz, K.

Graharamani, E.

D. J. Moss, E. Graharamani, J. E. Sipe, and H. M. van Driel, Phys. Rev. B 41, 1542 (1990).
[CrossRef]

Hall, J. L.

D. J. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, Science 288, 635 (2000).
[CrossRef] [PubMed]

Hänsch, T. W.

A. Apolonski, A. Poppe, G. Tempea, Ch. Spielmann, Th. Udem, R. Holzwarth, T. W. Hänsch, and F. Krausz, Phys. Rev. Lett. 85, 740 (2000).
[CrossRef] [PubMed]

L. Xu, Ch. Spielmann, A. Poppe, T. Brabec, F. Krausz, and T. W. Hänsch, Opt. Lett. 21, 2008 (1996).
[CrossRef] [PubMed]

Holzwarth, R.

A. Apolonski, A. Poppe, G. Tempea, Ch. Spielmann, Th. Udem, R. Holzwarth, T. W. Hänsch, and F. Krausz, Phys. Rev. Lett. 85, 740 (2000).
[CrossRef] [PubMed]

Jones, D. J.

D. J. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, Science 288, 635 (2000).
[CrossRef] [PubMed]

Keller, U.

H. R. Telle, G. Steinmeyer, A. E. Dunlop, J. Stenger, D. H. Sutter, and U. Keller, Appl. Phys. B 69, 327 (1999).
[CrossRef]

Krausz, F.

Lambropoulos, P.

E. Cormier and P. Lambropoulos, Eur. Phys. J. D 2, 15 (1998).
[CrossRef]

Lee, Y.-S.

Moss, D. J.

D. J. Moss, E. Graharamani, J. E. Sipe, and H. M. van Driel, Phys. Rev. B 41, 1542 (1990).
[CrossRef]

J. E. Sipe, D. J. Moss, and H. M. van Driel, Phys. Rev. B 35, 1129 (1987).
[CrossRef]

Nisoli, M.

Poppe, A.

A. Apolonski, A. Poppe, G. Tempea, Ch. Spielmann, Th. Udem, R. Holzwarth, T. W. Hänsch, and F. Krausz, Phys. Rev. Lett. 85, 740 (2000).
[CrossRef] [PubMed]

L. Xu, Ch. Spielmann, A. Poppe, T. Brabec, F. Krausz, and T. W. Hänsch, Opt. Lett. 21, 2008 (1996).
[CrossRef] [PubMed]

Ranka, J. K.

D. J. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, Science 288, 635 (2000).
[CrossRef] [PubMed]

Sartania, S.

Shapiro, M.

P. Brummer and M. Shapiro, Annu. Rev. Phys. Chem. 43, 257 (1992).

Sipe, J. E.

D. J. Moss, E. Graharamani, J. E. Sipe, and H. M. van Driel, Phys. Rev. B 41, 1542 (1990).
[CrossRef]

J. E. Sipe, D. J. Moss, and H. M. van Driel, Phys. Rev. B 35, 1129 (1987).
[CrossRef]

Spielmann, Ch.

Steinmeyer, G.

H. R. Telle, G. Steinmeyer, A. E. Dunlop, J. Stenger, D. H. Sutter, and U. Keller, Appl. Phys. B 69, 327 (1999).
[CrossRef]

Stenger, J.

H. R. Telle, G. Steinmeyer, A. E. Dunlop, J. Stenger, D. H. Sutter, and U. Keller, Appl. Phys. B 69, 327 (1999).
[CrossRef]

Stentz, A.

D. J. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, Science 288, 635 (2000).
[CrossRef] [PubMed]

Sutter, D. H.

H. R. Telle, G. Steinmeyer, A. E. Dunlop, J. Stenger, D. H. Sutter, and U. Keller, Appl. Phys. B 69, 327 (1999).
[CrossRef]

Svelto, O.

Szipocs, R.

Telle, H. R.

H. R. Telle, G. Steinmeyer, A. E. Dunlop, J. Stenger, D. H. Sutter, and U. Keller, Appl. Phys. B 69, 327 (1999).
[CrossRef]

Tempea, G.

A. Apolonski, A. Poppe, G. Tempea, Ch. Spielmann, Th. Udem, R. Holzwarth, T. W. Hänsch, and F. Krausz, Phys. Rev. Lett. 85, 740 (2000).
[CrossRef] [PubMed]

Udem, Th.

A. Apolonski, A. Poppe, G. Tempea, Ch. Spielmann, Th. Udem, R. Holzwarth, T. W. Hänsch, and F. Krausz, Phys. Rev. Lett. 85, 740 (2000).
[CrossRef] [PubMed]

van Driel, H. M.

D. J. Moss, E. Graharamani, J. E. Sipe, and H. M. van Driel, Phys. Rev. B 41, 1542 (1990).
[CrossRef]

J. E. Sipe, D. J. Moss, and H. M. van Driel, Phys. Rev. B 35, 1129 (1987).
[CrossRef]

Windeler, R. S.

D. J. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, Science 288, 635 (2000).
[CrossRef] [PubMed]

Xu, L.

Annu. Rev. Phys. Chem. (1)

P. Brummer and M. Shapiro, Annu. Rev. Phys. Chem. 43, 257 (1992).

Appl. Phys. B (1)

H. R. Telle, G. Steinmeyer, A. E. Dunlop, J. Stenger, D. H. Sutter, and U. Keller, Appl. Phys. B 69, 327 (1999).
[CrossRef]

Eur. Phys. J. D (1)

E. Cormier and P. Lambropoulos, Eur. Phys. J. D 2, 15 (1998).
[CrossRef]

Opt. Lett. (4)

Phys. Rev. B (2)

J. E. Sipe, D. J. Moss, and H. M. van Driel, Phys. Rev. B 35, 1129 (1987).
[CrossRef]

D. J. Moss, E. Graharamani, J. E. Sipe, and H. M. van Driel, Phys. Rev. B 41, 1542 (1990).
[CrossRef]

Phys. Rev. Lett. (1)

A. Apolonski, A. Poppe, G. Tempea, Ch. Spielmann, Th. Udem, R. Holzwarth, T. W. Hänsch, and F. Krausz, Phys. Rev. Lett. 85, 740 (2000).
[CrossRef] [PubMed]

Science (1)

D. J. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, Science 288, 635 (2000).
[CrossRef] [PubMed]

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Figures (3)

Fig. 1
Fig. 1

Calculated second- and third-harmonic power spectra of a 4.5-fs transform-limited Gaussian pulse for carrier phases of 0 (solid curves), π/2 (dotted curves), and π (dashed curves).

Fig. 2
Fig. 2

(a) Experimental and (b) theoretical power spectra of second and third harmonics of a pulse with a bandwidth corresponding to a 4.5-fs Gaussian pulse and with third- and fourth-order dispersion.

Fig. 3
Fig. 3

Calculated second- and third-harmonic power spectra in the overlap region of the 4.5 fs-pulse used in Fig. 1 but with linear dispersion of 35 fs2 for carrier phases of 0 (dashed curve) and π (solid curve).

Equations (6)

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

E=E0 cosω1t+ϕ+E0 cosω2t+ϕ=2E0cosω1+ω2t/2+ϕcosω1-ω2t/2.
Et=E0 expiω0t+ϕexp-t/2τ2,
Eω=-Etexp-iωtdt=-E0exp-iωt×expiω0t+ϕexp-t/2τ2dt=expiϕEω.
P2ω=χ2-Eω1Eω-ω1dω1=exp2iϕχ2-Eω1Eω-ω1dω1,
P3ω=χ3--Eω1Eω2×Eω-ω1-ω2dω1dω2=exp3iϕχ3--Eω1Eω2×Eω-ω1-ω2dω1dω2.
IωP2ω+P3ω2.

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