Abstract

The effects of variation of the grating separation in a stretcher on the carrier-envelope (CE) phase of amplified pulses are investigated. By translating one of the telescope mirrors in the stretcher with a piezoelectric transducer, it is found that a 1μm change of the distance causes a 3.7±1.2rad shift of the CE phase, which is consistent with theoretical estimations. The results indicate that optical mounts used for gratings and telescope mirrors must be interferometrically stable; otherwise their vibration and thermal drift will cause significant phase error. The CE phase drift was corrected by feedback controlling the grating separation.

© 2006 Optical Society of America

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    [CrossRef]
  2. A. Baltuska, M. Uiberacker, E. Goulielmakis, R. Keinberger, V. S. Yakovlev, T. Udem, T. W. Hänsch, and F. Krausz, IEEE J. Sel. Top. Quantum Electron. 9, 972 (2003).
    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
  6. I. Thomann, E. Gagnon, R. J. Jones, A. Sandhu, A. Lytle, R. Anderson, J. Ye, M. Murnane, and H. Kapteyn, Opt. Express 12, 3493 (2004).
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    [CrossRef] [PubMed]
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  9. O. Martinez, IEEE J. Quantum Electron. 23, 59 (1987).
    [CrossRef]
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    [CrossRef] [PubMed]

2006 (1)

2005 (1)

2004 (1)

2003 (1)

A. Baltuska, M. Uiberacker, E. Goulielmakis, R. Keinberger, V. S. Yakovlev, T. Udem, T. W. Hänsch, and F. Krausz, IEEE J. Sel. Top. Quantum Electron. 9, 972 (2003).
[CrossRef]

2002 (1)

M. Kakehata, Y. Fujihira, H. Takada, Y. Kobayashi, K. Torizuka, T. Homma, and H. Takahashi, Appl. Phys. B 74, S43 (2002).
[CrossRef]

2000 (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]

1987 (1)

O. Martinez, IEEE J. Quantum Electron. 23, 59 (1987).
[CrossRef]

1985 (1)

D. Strickland and G. Mourou, Opt. Commun. 55, 447 (1985).
[CrossRef]

1969 (1)

E. Treacy, IEEE J. Quantum Electron. 5, 454 (1969).
[CrossRef]

Anderson, R.

Apolonski, A.

Backus, S.

Baltuska, A.

A. Baltuska, M. Uiberacker, E. Goulielmakis, R. Keinberger, V. S. Yakovlev, T. Udem, T. W. Hänsch, and F. Krausz, IEEE J. Sel. Top. Quantum Electron. 9, 972 (2003).
[CrossRef]

Chang, Z.

B. Shan, C. Wang, and Z. Chang, "High peak-power kilohertz laser system employing single-stage multi-pass amplification," U.S. patent 7,050,474 (May 23, 2006).

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]

Fuji, T.

Fujihira, Y.

M. Kakehata, Y. Fujihira, H. Takada, Y. Kobayashi, K. Torizuka, T. Homma, and H. Takahashi, Appl. Phys. B 74, S43 (2002).
[CrossRef]

Gagnon, E.

Gohle, C.

Goulielmakis, E.

A. Baltuska, M. Uiberacker, E. Goulielmakis, R. Keinberger, V. S. Yakovlev, T. Udem, T. W. Hänsch, and F. Krausz, IEEE J. Sel. Top. Quantum Electron. 9, 972 (2003).
[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.

C. Gohle, J. Rauschenberger, T. Fuji, T. Udem, A. Apolonski, F. Krausz, and T. W. Hänsch, Opt. Lett. 30, 2487 (2005).
[CrossRef] [PubMed]

A. Baltuska, M. Uiberacker, E. Goulielmakis, R. Keinberger, V. S. Yakovlev, T. Udem, T. W. Hänsch, and F. Krausz, IEEE J. Sel. Top. Quantum Electron. 9, 972 (2003).
[CrossRef]

Homma, T.

M. Kakehata, Y. Fujihira, H. Takada, Y. Kobayashi, K. Torizuka, T. Homma, and H. Takahashi, Appl. Phys. B 74, S43 (2002).
[CrossRef]

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]

Jones, R. J.

Kakehata, M.

M. Kakehata, Y. Fujihira, H. Takada, Y. Kobayashi, K. Torizuka, T. Homma, and H. Takahashi, Appl. Phys. B 74, S43 (2002).
[CrossRef]

Kapteyn, H.

Kapteyn, H. C.

Keinberger, R.

A. Baltuska, M. Uiberacker, E. Goulielmakis, R. Keinberger, V. S. Yakovlev, T. Udem, T. W. Hänsch, and F. Krausz, IEEE J. Sel. Top. Quantum Electron. 9, 972 (2003).
[CrossRef]

Kobayashi, Y.

M. Kakehata, Y. Fujihira, H. Takada, Y. Kobayashi, K. Torizuka, T. Homma, and H. Takahashi, Appl. Phys. B 74, S43 (2002).
[CrossRef]

Krausz, F.

C. Gohle, J. Rauschenberger, T. Fuji, T. Udem, A. Apolonski, F. Krausz, and T. W. Hänsch, Opt. Lett. 30, 2487 (2005).
[CrossRef] [PubMed]

A. Baltuska, M. Uiberacker, E. Goulielmakis, R. Keinberger, V. S. Yakovlev, T. Udem, T. W. Hänsch, and F. Krausz, IEEE J. Sel. Top. Quantum Electron. 9, 972 (2003).
[CrossRef]

Lytle, A.

Lytle, A. L.

Martinez, O.

O. Martinez, IEEE J. Quantum Electron. 23, 59 (1987).
[CrossRef]

Mourou, G.

D. Strickland and G. Mourou, Opt. Commun. 55, 447 (1985).
[CrossRef]

Murnane, M.

Murnane, M. M.

Paul, A.

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]

Rauschenberger, J.

Sandhu, A.

Sandhu, A. S.

Shan, B.

B. Shan, C. Wang, and Z. Chang, "High peak-power kilohertz laser system employing single-stage multi-pass amplification," U.S. patent 7,050,474 (May 23, 2006).

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]

Strickland, D.

D. Strickland and G. Mourou, Opt. Commun. 55, 447 (1985).
[CrossRef]

Takada, H.

M. Kakehata, Y. Fujihira, H. Takada, Y. Kobayashi, K. Torizuka, T. Homma, and H. Takahashi, Appl. Phys. B 74, S43 (2002).
[CrossRef]

Takahashi, H.

M. Kakehata, Y. Fujihira, H. Takada, Y. Kobayashi, K. Torizuka, T. Homma, and H. Takahashi, Appl. Phys. B 74, S43 (2002).
[CrossRef]

Thomann, I.

Torizuka, K.

M. Kakehata, Y. Fujihira, H. Takada, Y. Kobayashi, K. Torizuka, T. Homma, and H. Takahashi, Appl. Phys. B 74, S43 (2002).
[CrossRef]

Treacy, E.

E. Treacy, IEEE J. Quantum Electron. 5, 454 (1969).
[CrossRef]

Udem, T.

C. Gohle, J. Rauschenberger, T. Fuji, T. Udem, A. Apolonski, F. Krausz, and T. W. Hänsch, Opt. Lett. 30, 2487 (2005).
[CrossRef] [PubMed]

A. Baltuska, M. Uiberacker, E. Goulielmakis, R. Keinberger, V. S. Yakovlev, T. Udem, T. W. Hänsch, and F. Krausz, IEEE J. Sel. Top. Quantum Electron. 9, 972 (2003).
[CrossRef]

Uiberacker, M.

A. Baltuska, M. Uiberacker, E. Goulielmakis, R. Keinberger, V. S. Yakovlev, T. Udem, T. W. Hänsch, and F. Krausz, IEEE J. Sel. Top. Quantum Electron. 9, 972 (2003).
[CrossRef]

Wang, C.

B. Shan, C. Wang, and Z. Chang, "High peak-power kilohertz laser system employing single-stage multi-pass amplification," U.S. patent 7,050,474 (May 23, 2006).

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]

Yakovlev, V. S.

A. Baltuska, M. Uiberacker, E. Goulielmakis, R. Keinberger, V. S. Yakovlev, T. Udem, T. W. Hänsch, and F. Krausz, IEEE J. Sel. Top. Quantum Electron. 9, 972 (2003).
[CrossRef]

Ye, J.

Appl. Phys. B (1)

M. Kakehata, Y. Fujihira, H. Takada, Y. Kobayashi, K. Torizuka, T. Homma, and H. Takahashi, Appl. Phys. B 74, S43 (2002).
[CrossRef]

IEEE J. Quantum Electron. (2)

E. Treacy, IEEE J. Quantum Electron. 5, 454 (1969).
[CrossRef]

O. Martinez, IEEE J. Quantum Electron. 23, 59 (1987).
[CrossRef]

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

A. Baltuska, M. Uiberacker, E. Goulielmakis, R. Keinberger, V. S. Yakovlev, T. Udem, T. W. Hänsch, and F. Krausz, IEEE J. Sel. Top. Quantum Electron. 9, 972 (2003).
[CrossRef]

Opt. Commun. (1)

D. Strickland and G. Mourou, Opt. Commun. 55, 447 (1985).
[CrossRef]

Opt. Express (1)

Opt. Lett. (2)

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 (1)

B. Shan, C. Wang, and Z. Chang, "High peak-power kilohertz laser system employing single-stage multi-pass amplification," U.S. patent 7,050,474 (May 23, 2006).

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Figures (4)

Fig. 1
Fig. 1

Kansas Light Source laser system for testing the effects of the grating separation of the stretcher on the CE phase stability. G1 and G2 are the gratings. M1 is one of the telescope mirrors driven by a piezoelectric transducer (PZT). The oscillator CE offset frequency f 0 is stabilized by feedback controlling the acousto-optic modulator (AOM). Pulses with the same CE phase are selected by the Pockels cell (PC) and are sent to the chirped pulse amplifier.

Fig. 2
Fig. 2

Parameters of the grating stretcher. Mirrors are used in (a) to form the telescope. G1 and G2 are the gratings; γ s is the incidence angle on the first grating; θ s is the angle between the diffracted beam and the incident beam; M1 and M2 are mirrors for the telescope; l eff is the effective distance. (b) Conventional stretcher with a lens-based telescope. G 1 is the image of the G1 formed by the telescope. G s is the effective perpendicular distance between the gratings.

Fig. 3
Fig. 3

Dependence of the CE phase of the amplified pulses on the grating separation. (a), (c) Fringe pattern of the collinear f-to- 2 f interferometer and the corresponding relative CE phase obtained when a 60 V sinusoidal voltage is applied to the PZT, which caused the PZT to move 3.6 μ m ; (b), (d) with a 30 V dc voltage applied to the PZT.

Fig. 4
Fig. 4

CE phase of the amplified pulses stabilized by feedback controlling the grating separation. The rms phase error in 200 s is 179 mrad . The CE phase drift without the stabilization is shown in Fig. 3d.

Equations (6)

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ϕ ( ω ) = ω τ ( ω ) 4 π ( G s d s ) tan [ γ s θ s ( ω ) ] ,
φ CE φ CE = ω 0 τ ( ω 0 ) ϕ ( ω 0 ) = 4 π ( G s d s ) tan [ γ s θ s ( ω ) ] .
Δ φ CE Δ l eff = 2 π λ d s 2 2 π λ .
( τ p ) 2 = τ p 2 + ( τ s l eff Δ l eff ) 2 ,
Δ l eff = Δ ( l eff 2 f ) 2 Δ .
Δ φ CE Δ Δ φ CE Δ l eff = 4 π sin ( γ s θ s ) 1 d s .

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