Abstract

We propose and demonstrate a novel linear procedure for measurement of the carrier-envelope offset (CEO) phase of femtosecond oscillators. The technique is based on a Mach–Zehnder interferometer, a ring resonator, and a spectrograph. In this scheme, interference between subsequent pulses from a pulse train may frustrate the interference between identical pulses in the Mach–Zehnder, resulting in a modification of interference contrast depending on the CEO phase. We suggest spectrally and spatially resolved interferometry for robust detection of the fringe visibility. It is shown by numerical simulations and experimentally demonstrated that the visibility of such fringes uniquely depends on the CEO phase of the pulse train. Since the method relies only on linear interactions and does not require any nonlinear conversion, it allows characterizing the CEO frequency of mode-locked oscillators with virtually arbitrarily low bandwidth and power levels.

© 2007 Optical Society of America

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  1. A. Baltuska, Th. Udem, M. Uiberacker, M. Hentschel, E. Goulielmakis, C. Gohle, R. Holzwarth, V. S. Yakovlev, A. Scrinzi, T. W. Hänsch, and F. Krausz, Nature 421, 611 (2003).
    [CrossRef] [PubMed]
  2. G. G. Paulus, F. Grasbon, H. Walther, P. Villoresi, M. Nisoli, S. Stagira, E. Priori, and S. De Silvestri, Nature 414, 182 (2001).
    [CrossRef] [PubMed]
  3. T. Udem, R. Holzwarth, and T. W. Hänsch, Nature 416, 233 (2002).
    [CrossRef] [PubMed]
  4. D. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, Science 288, 635 (2001).
    [CrossRef]
  5. A. Apolonski, A. Poppe, G. Tempea, C. Spielmann, T. Udem, R. Holzwarth, T. W. Hänsch, and F. Krausz, Phys. Rev. Lett. 85, 740 (2000).
    [CrossRef] [PubMed]
  6. M. Mehendale, S. A. Mitchell, J.-P. Likforman, D. M. Villeneuve, and P. B. Corkum, Opt. Lett. 25, 1672 (2000).
    [CrossRef]
  7. M. Kakehata, H. Takada, Y. Kobayashi, K. Torizuka, Y. Fujihira, T. Homma, and H. Takahashi, Opt. Lett. 26, 1436 (2001).
    [CrossRef]
  8. H. R. Telle, G. Steinmeyer, A. E. Dunlop, J. Stenger, D. H. Sutter, and U. Keller, Appl. Phys. B: Photophys. Laser Chem. 69, 327 (1999).
    [CrossRef]
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    [CrossRef] [PubMed]
  10. R. J. Jones, I. Thomann, and J. Ye, Phys. Rev. A 69, 051803 (2004).
    [CrossRef]
  11. L. Xu, C. Spielmann, A. Poppe, T. Brabec, F. Krausz, and T. W. Hänsch, Opt. Lett. 21, 2008 (1996).
    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]

2004 (1)

R. J. Jones, I. Thomann, and J. Ye, Phys. Rev. A 69, 051803 (2004).
[CrossRef]

2003 (1)

A. Baltuska, Th. Udem, M. Uiberacker, M. Hentschel, E. Goulielmakis, C. Gohle, R. Holzwarth, V. S. Yakovlev, A. Scrinzi, T. W. Hänsch, and F. Krausz, Nature 421, 611 (2003).
[CrossRef] [PubMed]

2002 (1)

T. Udem, R. Holzwarth, and T. W. Hänsch, Nature 416, 233 (2002).
[CrossRef] [PubMed]

2001 (3)

D. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, Science 288, 635 (2001).
[CrossRef]

G. G. Paulus, F. Grasbon, H. Walther, P. Villoresi, M. Nisoli, S. Stagira, E. Priori, and S. De Silvestri, Nature 414, 182 (2001).
[CrossRef] [PubMed]

M. Kakehata, H. Takada, Y. Kobayashi, K. Torizuka, Y. Fujihira, T. Homma, and H. Takahashi, Opt. Lett. 26, 1436 (2001).
[CrossRef]

2000 (2)

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

M. Mehendale, S. A. Mitchell, J.-P. Likforman, D. M. Villeneuve, and P. B. Corkum, Opt. Lett. 25, 1672 (2000).
[CrossRef]

1999 (1)

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

1997 (1)

1996 (1)

1995 (2)

1990 (2)

C. Sainz, J. E. Calatroni, and G. Tribillon, Meas. Sci. Technol. 1, 356 (1990).
[CrossRef]

H. R. Telle, D. Meschede, and T. W. Hänsch, Opt. Lett. 15, 532 (1990).
[CrossRef] [PubMed]

Apolonski, A.

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

Baltuska, A.

A. Baltuska, Th. Udem, M. Uiberacker, M. Hentschel, E. Goulielmakis, C. Gohle, R. Holzwarth, V. S. Yakovlev, A. Scrinzi, T. W. Hänsch, and F. Krausz, Nature 421, 611 (2003).
[CrossRef] [PubMed]

Bor, Z.

Brabec, T.

Calatroni, J. E.

C. Sainz, J. E. Calatroni, and G. Tribillon, Meas. Sci. Technol. 1, 356 (1990).
[CrossRef]

Corkum, P. B.

Cundiff, S. T.

D. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, Science 288, 635 (2001).
[CrossRef]

De Silvestri, S.

G. G. Paulus, F. Grasbon, H. Walther, P. Villoresi, M. Nisoli, S. Stagira, E. Priori, and S. De Silvestri, Nature 414, 182 (2001).
[CrossRef] [PubMed]

Diddams, S. A.

D. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, Science 288, 635 (2001).
[CrossRef]

Dunlop, A. E.

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

Fujihira, Y.

Gohle, C.

A. Baltuska, Th. Udem, M. Uiberacker, M. Hentschel, E. Goulielmakis, C. Gohle, R. Holzwarth, V. S. Yakovlev, A. Scrinzi, T. W. Hänsch, and F. Krausz, Nature 421, 611 (2003).
[CrossRef] [PubMed]

Goulielmakis, E.

A. Baltuska, Th. Udem, M. Uiberacker, M. Hentschel, E. Goulielmakis, C. Gohle, R. Holzwarth, V. S. Yakovlev, A. Scrinzi, T. W. Hänsch, and F. Krausz, Nature 421, 611 (2003).
[CrossRef] [PubMed]

Grasbon, F.

G. G. Paulus, F. Grasbon, H. Walther, P. Villoresi, M. Nisoli, S. Stagira, E. Priori, and S. De Silvestri, Nature 414, 182 (2001).
[CrossRef] [PubMed]

Hall, J. L.

D. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, Science 288, 635 (2001).
[CrossRef]

Hänsch, T. W.

A. Baltuska, Th. Udem, M. Uiberacker, M. Hentschel, E. Goulielmakis, C. Gohle, R. Holzwarth, V. S. Yakovlev, A. Scrinzi, T. W. Hänsch, and F. Krausz, Nature 421, 611 (2003).
[CrossRef] [PubMed]

T. Udem, R. Holzwarth, and T. W. Hänsch, Nature 416, 233 (2002).
[CrossRef] [PubMed]

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

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

H. R. Telle, D. Meschede, and T. W. Hänsch, Opt. Lett. 15, 532 (1990).
[CrossRef] [PubMed]

Hentschel, M.

A. Baltuska, Th. Udem, M. Uiberacker, M. Hentschel, E. Goulielmakis, C. Gohle, R. Holzwarth, V. S. Yakovlev, A. Scrinzi, T. W. Hänsch, and F. Krausz, Nature 421, 611 (2003).
[CrossRef] [PubMed]

Holzwarth, R.

A. Baltuska, Th. Udem, M. Uiberacker, M. Hentschel, E. Goulielmakis, C. Gohle, R. Holzwarth, V. S. Yakovlev, A. Scrinzi, T. W. Hänsch, and F. Krausz, Nature 421, 611 (2003).
[CrossRef] [PubMed]

T. Udem, R. Holzwarth, and T. W. Hänsch, Nature 416, 233 (2002).
[CrossRef] [PubMed]

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

Homma, T.

Jones, D.

D. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, Science 288, 635 (2001).
[CrossRef]

Jones, R. J.

R. J. Jones, I. Thomann, and J. Ye, Phys. Rev. A 69, 051803 (2004).
[CrossRef]

Kakehata, M.

Keller, U.

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

Kobayashi, T.

Kobayashi, Y.

Kovács, A. P.

Krausz, F.

A. Baltuska, Th. Udem, M. Uiberacker, M. Hentschel, E. Goulielmakis, C. Gohle, R. Holzwarth, V. S. Yakovlev, A. Scrinzi, T. W. Hänsch, and F. Krausz, Nature 421, 611 (2003).
[CrossRef] [PubMed]

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

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

Likforman, J.-P.

Mehendale, M.

Meschede, D.

Meshulach, D.

Misawa, K.

Mitchell, S. A.

Nisoli, M.

G. G. Paulus, F. Grasbon, H. Walther, P. Villoresi, M. Nisoli, S. Stagira, E. Priori, and S. De Silvestri, Nature 414, 182 (2001).
[CrossRef] [PubMed]

Osvay, K.

Paulus, G. G.

G. G. Paulus, F. Grasbon, H. Walther, P. Villoresi, M. Nisoli, S. Stagira, E. Priori, and S. De Silvestri, Nature 414, 182 (2001).
[CrossRef] [PubMed]

Poppe, A.

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

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

Priori, E.

G. G. Paulus, F. Grasbon, H. Walther, P. Villoresi, M. Nisoli, S. Stagira, E. Priori, and S. De Silvestri, Nature 414, 182 (2001).
[CrossRef] [PubMed]

Ranka, J. K.

D. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, Science 288, 635 (2001).
[CrossRef]

Sainz, C.

C. Sainz, J. E. Calatroni, and G. Tribillon, Meas. Sci. Technol. 1, 356 (1990).
[CrossRef]

Scrinzi, A.

A. Baltuska, Th. Udem, M. Uiberacker, M. Hentschel, E. Goulielmakis, C. Gohle, R. Holzwarth, V. S. Yakovlev, A. Scrinzi, T. W. Hänsch, and F. Krausz, Nature 421, 611 (2003).
[CrossRef] [PubMed]

Silberberg, Y.

Spielmann, C.

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

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

Stagira, S.

G. G. Paulus, F. Grasbon, H. Walther, P. Villoresi, M. Nisoli, S. Stagira, E. Priori, and S. De Silvestri, Nature 414, 182 (2001).
[CrossRef] [PubMed]

Steinmeyer, G.

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

Stentz, A.

D. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, Science 288, 635 (2001).
[CrossRef]

Sutter, D. H.

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

Szipöcs, R.

Takada, H.

Takahashi, H.

Telle, H. R.

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

H. R. Telle, D. Meschede, and T. W. Hänsch, Opt. Lett. 15, 532 (1990).
[CrossRef] [PubMed]

Tempea, G.

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

Thomann, I.

R. J. Jones, I. Thomann, and J. Ye, Phys. Rev. A 69, 051803 (2004).
[CrossRef]

Torizuka, K.

Tribillon, G.

C. Sainz, J. E. Calatroni, and G. Tribillon, Meas. Sci. Technol. 1, 356 (1990).
[CrossRef]

Udem, T.

T. Udem, R. Holzwarth, and T. W. Hänsch, Nature 416, 233 (2002).
[CrossRef] [PubMed]

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

Udem, Th.

A. Baltuska, Th. Udem, M. Uiberacker, M. Hentschel, E. Goulielmakis, C. Gohle, R. Holzwarth, V. S. Yakovlev, A. Scrinzi, T. W. Hänsch, and F. Krausz, Nature 421, 611 (2003).
[CrossRef] [PubMed]

Uiberacker, M.

A. Baltuska, Th. Udem, M. Uiberacker, M. Hentschel, E. Goulielmakis, C. Gohle, R. Holzwarth, V. S. Yakovlev, A. Scrinzi, T. W. Hänsch, and F. Krausz, Nature 421, 611 (2003).
[CrossRef] [PubMed]

Villeneuve, D. M.

Villoresi, P.

G. G. Paulus, F. Grasbon, H. Walther, P. Villoresi, M. Nisoli, S. Stagira, E. Priori, and S. De Silvestri, Nature 414, 182 (2001).
[CrossRef] [PubMed]

Walther, H.

G. G. Paulus, F. Grasbon, H. Walther, P. Villoresi, M. Nisoli, S. Stagira, E. Priori, and S. De Silvestri, Nature 414, 182 (2001).
[CrossRef] [PubMed]

Windeler, R. S.

D. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, Science 288, 635 (2001).
[CrossRef]

Xu, L.

Yakovlev, V. S.

A. Baltuska, Th. Udem, M. Uiberacker, M. Hentschel, E. Goulielmakis, C. Gohle, R. Holzwarth, V. S. Yakovlev, A. Scrinzi, T. W. Hänsch, and F. Krausz, Nature 421, 611 (2003).
[CrossRef] [PubMed]

Ye, J.

R. J. Jones, I. Thomann, and J. Ye, Phys. Rev. A 69, 051803 (2004).
[CrossRef]

Yelin, D.

Appl. Phys. B: Photophys. Laser Chem. (1)

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

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

Meas. Sci. Technol. (1)

C. Sainz, J. E. Calatroni, and G. Tribillon, Meas. Sci. Technol. 1, 356 (1990).
[CrossRef]

Nature (3)

A. Baltuska, Th. Udem, M. Uiberacker, M. Hentschel, E. Goulielmakis, C. Gohle, R. Holzwarth, V. S. Yakovlev, A. Scrinzi, T. W. Hänsch, and F. Krausz, Nature 421, 611 (2003).
[CrossRef] [PubMed]

G. G. Paulus, F. Grasbon, H. Walther, P. Villoresi, M. Nisoli, S. Stagira, E. Priori, and S. De Silvestri, Nature 414, 182 (2001).
[CrossRef] [PubMed]

T. Udem, R. Holzwarth, and T. W. Hänsch, Nature 416, 233 (2002).
[CrossRef] [PubMed]

Opt. Lett. (6)

Phys. Rev. A (1)

R. J. Jones, I. Thomann, and J. Ye, Phys. Rev. A 69, 051803 (2004).
[CrossRef]

Phys. Rev. Lett. (1)

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

Science (1)

D. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, Science 288, 635 (2001).
[CrossRef]

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Figures (3)

Fig. 1
Fig. 1

(A) Principle of measurement. A Mach–Zehnder interferometer (beam splitters BS1 and BS4) is combined with a multiple beam interferometer (resonant ring). An interference pattern is formed by subsequent pulses ( 1 S , 2 S , 3 S ) of a pulse train accumulated in the resonant ring in the sample arm of the interferometer with one reference pulse ( 3 R ) . (B) Blur of the superimposed spectrally resolved interference pattern when the pulse-to-pulse CEO phase change Δ φ CEO is π 2 .

Fig. 2
Fig. 2

(A) Visibility of SSRI fringes of a pulse train versus CEO phase change between subsequent pulses. (B) Visibility for a mismatched resonator ring ( Δ = 12 μ m ) versus wavelength.

Fig. 3
Fig. 3

(A), (B) Captured SSRI fringes for different mismatch values of the resonant ring. (C), (D) Visibility of SSRI fringes in function of CEO phase change for different finesse values. (E), (F) Measured spectral visibility of the SSRI fringes when the resonant ring is detuned to Δ = 46 μ m along with the corresponding first principle simulation.

Equations (1)

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I ( ω , y ) = I ref ( ω , y ) + I sam ( ω , y ) + 2 I ref ( ω , y ) I sam ( ω , y ) cos [ Δ φ ( ω ) + ϑ ω c ( y y 0 ) ] .

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