Abstract

A concept for orthogonal control of phase and group delay inside a laser cavity by a specially designed compensator assembly is discussed. Similar to the construction of variable polarization retarder, this assembly consists of two thin wedge prisms made from appropriately chosen optical materials. Being shifted as a whole, the assembly allows changing the phase delay with no influence on the cavity round-trip time, whereas relative shifting of the prisms enables adjustment of the latter. This scheme is discussed theoretically and verified experimentally, indicating a factor 30 reduction of the influence on the repetition rate compared to the commonly used silica wedge pair. For a 2π adjustment of the carrier-envelope phase shift, single-pass timing differences are reduced to the single-femtosecond regime. With negligible distortions of timing and dispersion, the described compensator device greatly simplifies carrier-envelope phase control and experiments in extreme nonlinear optics. © 2008 Optical Society of America

© 2008 Optical Society of America

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  1. A. Baltuška, T. Fuji, and T. Kobayashi, Phys. Rev. Lett. 88, 133901 (2002).
    [CrossRef] [PubMed]
  2. 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]
  3. 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]
  4. A. Poppe, R. Holzwarth, A. Apolonski, G. Tempea, C. Spielmann, T. W. Hänsch, and F. Krausz, Appl. Phys. B 72, 373 (2001).
  5. F. Lindner, G. G. Paulus, H. Walther, A. Baltuška, E. Goulielmakis, M. Lezius, and F. Krausz, Phys. Rev. Lett. 92, 113001 (2004).
    [CrossRef] [PubMed]
  6. R. Ell, J. R. Birge, M. Araghchini, and F. X. Kärtner, Opt. Express 14, 5829 (2006).
    [CrossRef] [PubMed]
  7. J. Babinet, C. R. Hebd. Seances Acad. Sci. 29, 514 (1849).
  8. M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, 1999), pp. 821-823.
  9. Optical glass data sheets, Schott AG, Mainz, Germany, revision 10/10/2007, available online at http://www.schott.com/.
  10. K. Osvay, A. P. Kovács, Zs. Heiner, G. Kurdi, J. Klebniczki, and M. Csatári, IEEE J. Sel. Top. Quantum Electron. 10, 213 (2004).
    [CrossRef]
  11. H. R. Telle, G. Steinmeyer, A. E. Dunlop, J. Stenger, D. H. Sutter, and U. Keller, Appl. Phys. B 69, 327 (1999).
    [CrossRef]

2006 (1)

2004 (2)

K. Osvay, A. P. Kovács, Zs. Heiner, G. Kurdi, J. Klebniczki, and M. Csatári, IEEE J. Sel. Top. Quantum Electron. 10, 213 (2004).
[CrossRef]

F. Lindner, G. G. Paulus, H. Walther, A. Baltuška, E. Goulielmakis, M. Lezius, and F. Krausz, Phys. Rev. Lett. 92, 113001 (2004).
[CrossRef] [PubMed]

2002 (1)

A. Baltuška, T. Fuji, and T. Kobayashi, Phys. Rev. Lett. 88, 133901 (2002).
[CrossRef] [PubMed]

2001 (1)

A. Poppe, R. Holzwarth, A. Apolonski, G. Tempea, C. Spielmann, T. W. Hänsch, and F. Krausz, Appl. Phys. B 72, 373 (2001).

2000 (2)

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

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]

1849 (1)

J. Babinet, C. R. Hebd. Seances Acad. Sci. 29, 514 (1849).

Apolonski, A.

A. Poppe, R. Holzwarth, A. Apolonski, G. Tempea, C. Spielmann, T. W. Hänsch, and F. Krausz, Appl. Phys. B 72, 373 (2001).

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]

Araghchini, M.

Babinet, J.

J. Babinet, C. R. Hebd. Seances Acad. Sci. 29, 514 (1849).

Baltuška, A.

F. Lindner, G. G. Paulus, H. Walther, A. Baltuška, E. Goulielmakis, M. Lezius, and F. Krausz, Phys. Rev. Lett. 92, 113001 (2004).
[CrossRef] [PubMed]

A. Baltuška, T. Fuji, and T. Kobayashi, Phys. Rev. Lett. 88, 133901 (2002).
[CrossRef] [PubMed]

Birge, J. R.

Born, M.

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, 1999), pp. 821-823.

Csatári, M.

K. Osvay, A. P. Kovács, Zs. Heiner, G. Kurdi, J. Klebniczki, and M. Csatári, IEEE J. Sel. Top. Quantum Electron. 10, 213 (2004).
[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]

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]

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]

Ell, R.

Fuji, T.

A. Baltuška, T. Fuji, and T. Kobayashi, Phys. Rev. Lett. 88, 133901 (2002).
[CrossRef] [PubMed]

Goulielmakis, E.

F. Lindner, G. G. Paulus, H. Walther, A. Baltuška, E. Goulielmakis, M. Lezius, and F. Krausz, Phys. Rev. Lett. 92, 113001 (2004).
[CrossRef] [PubMed]

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. Poppe, R. Holzwarth, A. Apolonski, G. Tempea, C. Spielmann, T. W. Hänsch, and F. Krausz, Appl. Phys. B 72, 373 (2001).

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]

Heiner, Zs.

K. Osvay, A. P. Kovács, Zs. Heiner, G. Kurdi, J. Klebniczki, and M. Csatári, IEEE J. Sel. Top. Quantum Electron. 10, 213 (2004).
[CrossRef]

Holzwarth, R.

A. Poppe, R. Holzwarth, A. Apolonski, G. Tempea, C. Spielmann, T. W. Hänsch, and F. Krausz, Appl. Phys. B 72, 373 (2001).

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]

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]

Kärtner, F. X.

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]

Klebniczki, J.

K. Osvay, A. P. Kovács, Zs. Heiner, G. Kurdi, J. Klebniczki, and M. Csatári, IEEE J. Sel. Top. Quantum Electron. 10, 213 (2004).
[CrossRef]

Kobayashi, T.

A. Baltuška, T. Fuji, and T. Kobayashi, Phys. Rev. Lett. 88, 133901 (2002).
[CrossRef] [PubMed]

Kovács, A. P.

K. Osvay, A. P. Kovács, Zs. Heiner, G. Kurdi, J. Klebniczki, and M. Csatári, IEEE J. Sel. Top. Quantum Electron. 10, 213 (2004).
[CrossRef]

Krausz, F.

F. Lindner, G. G. Paulus, H. Walther, A. Baltuška, E. Goulielmakis, M. Lezius, and F. Krausz, Phys. Rev. Lett. 92, 113001 (2004).
[CrossRef] [PubMed]

A. Poppe, R. Holzwarth, A. Apolonski, G. Tempea, C. Spielmann, T. W. Hänsch, and F. Krausz, Appl. Phys. B 72, 373 (2001).

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]

Kurdi, G.

K. Osvay, A. P. Kovács, Zs. Heiner, G. Kurdi, J. Klebniczki, and M. Csatári, IEEE J. Sel. Top. Quantum Electron. 10, 213 (2004).
[CrossRef]

Lezius, M.

F. Lindner, G. G. Paulus, H. Walther, A. Baltuška, E. Goulielmakis, M. Lezius, and F. Krausz, Phys. Rev. Lett. 92, 113001 (2004).
[CrossRef] [PubMed]

Lindner, F.

F. Lindner, G. G. Paulus, H. Walther, A. Baltuška, E. Goulielmakis, M. Lezius, and F. Krausz, Phys. Rev. Lett. 92, 113001 (2004).
[CrossRef] [PubMed]

Osvay, K.

K. Osvay, A. P. Kovács, Zs. Heiner, G. Kurdi, J. Klebniczki, and M. Csatári, IEEE J. Sel. Top. Quantum Electron. 10, 213 (2004).
[CrossRef]

Paulus, G. G.

F. Lindner, G. G. Paulus, H. Walther, A. Baltuška, E. Goulielmakis, M. Lezius, and F. Krausz, Phys. Rev. Lett. 92, 113001 (2004).
[CrossRef] [PubMed]

Poppe, A.

A. Poppe, R. Holzwarth, A. Apolonski, G. Tempea, C. Spielmann, T. W. Hänsch, and F. Krausz, Appl. Phys. B 72, 373 (2001).

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]

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]

Spielmann, C.

A. Poppe, R. Holzwarth, A. Apolonski, G. Tempea, C. Spielmann, T. W. Hänsch, and F. Krausz, Appl. Phys. B 72, 373 (2001).

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]

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]

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. Poppe, R. Holzwarth, A. Apolonski, G. Tempea, C. Spielmann, T. W. Hänsch, and F. Krausz, Appl. Phys. B 72, 373 (2001).

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, T.

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]

Walther, H.

F. Lindner, G. G. Paulus, H. Walther, A. Baltuška, E. Goulielmakis, M. Lezius, and F. Krausz, Phys. Rev. Lett. 92, 113001 (2004).
[CrossRef] [PubMed]

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]

Wolf, E.

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, 1999), pp. 821-823.

Appl. Phys. B (2)

A. Poppe, R. Holzwarth, A. Apolonski, G. Tempea, C. Spielmann, T. W. Hänsch, and F. Krausz, Appl. Phys. B 72, 373 (2001).

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

C. R. Hebd. Seances Acad. Sci. (1)

J. Babinet, C. R. Hebd. Seances Acad. Sci. 29, 514 (1849).

IEEE J. Sel. Top. Quantum Electron. (1)

K. Osvay, A. P. Kovács, Zs. Heiner, G. Kurdi, J. Klebniczki, and M. Csatári, IEEE J. Sel. Top. Quantum Electron. 10, 213 (2004).
[CrossRef]

Opt. Express (1)

Phys. Rev. Lett. (3)

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]

F. Lindner, G. G. Paulus, H. Walther, A. Baltuška, E. Goulielmakis, M. Lezius, and F. Krausz, Phys. Rev. Lett. 92, 113001 (2004).
[CrossRef] [PubMed]

A. Baltuška, T. Fuji, and T. Kobayashi, Phys. Rev. Lett. 88, 133901 (2002).
[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]

Other (2)

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, 1999), pp. 821-823.

Optical glass data sheets, Schott AG, Mainz, Germany, revision 10/10/2007, available online at http://www.schott.com/.

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Figures (5)

Fig. 1
Fig. 1

(a) Traditional carrier-envelope offset (CEO) frequency, tuning intracavity setup with two identical wedges; (b) isochronic setup of reduced repetition rate detuning consisting of two wedges of different materials and apex angles being tuned as a whole.

Fig. 2
Fig. 2

Output spectrum of the laser oscillator in the case of the traditional setup (solid curve) and using the isochronic compensator (dashed curve).

Fig. 3
Fig. 3

Change of (a) CEO frequency and (b) repetition rate as a function of mutual translation of two identical intracavity silica wedges.

Fig. 4
Fig. 4

Change of (a) CEO frequency and (b) repetition rate as a function of translation of the isochronic (mixed material) wedge pair. The diagonal line has been calculated for the measured apex angles, the horizontal line for the designed ones.

Fig. 5
Fig. 5

Change of spectral group delay of a laser pulse passing through a CEP adjustment device when varying the CE phase by 2 π . The dashed and dashed–dotted curves have been calculated for the fused-silica wedge pair and the composite plate, respectively, while the solid curve refers to the novel assembly with mixed glasses.

Equations (4)

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GD = ( n g , 2 1 ) d 2 ( n g , 1 1 ) d 1 c ,
Δ φ CE = ω c [ ( n g , 2 n 2 ) d 2 ( n g , 2 n 2 ) d 1 ] ,
GDD = 1 c 2 ω 2 [ ω ( n 1 d 1 n 2 d 2 ) ] .
Γ ( n g , 1 1 ) ( n g , 2 1 )

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