Abstract

The carrier-envelope phase slip of an ultrashort pulse circulating in a mode-locked Ti:sapphire laser is analyzed. The laser cavity is modeled by a dispersion- and nonlinearity-managed nonlinear Schrödinger equation. The combined contributions to the phase slip induced by nonlinear phase and nonlinear dispersion are found to approach zero for strong dispersion maps. The dependence of the slip on third-order dispersion is found as well. The analytical results are verified using numerical simulations.

© 2004 Optical Society of America

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References

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2003

2001

2000

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]

T. Brabec and F. Krausz, Rev. Mod. Phys. 72, 545 (2000).
[CrossRef]

1999

1998

1996

Ablowitz, M. J.

Biondini, G.

Brabec, T.

Chen, Y.

Cho, S. H.

Cundiff, S. T.

K. W. Holman, R. J. Jones, A. Marian, S. T. Cundiff, and J. Ye, Opt. Lett. 28, 851 (2003).
[CrossRef] [PubMed]

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]

Fujimoto, J. G.

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.

Haus, H. A.

Holman, K. W.

Ippen, E. P.

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.

Kärtner, F. X.

Krausz, F.

Marian, A.

Morgner, U.

Poppe, 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]

Spielmann, Ch.

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]

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.

Ye, J.

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Figures (1)

Fig. 1
Fig. 1

(a) Dispersion [Dζ, dotted lines] and nonlinearity maps [gζ, dashed lines] used in (b) and (c). (b) Numerical phase [Eq. (6), solid curve], λ2z/2 (dotted curve) and λG2z/2 (dashed curve). (c) Numerical timing shift [Eq. (6), solid curve], average slope with Eq. (10) (dotted curve), and with Eq. (11), below (dashed curve). (d) Normalized CEPS (12) with λ=2, θ=0.75, for three values of D¯.

Equations (13)

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iAz-k2Aττ+γA2A=-iω-1γA2Aτ,
Az,τ=A0 sechτ/τ0-Texpiϕz, ϕzγA02z/2,
δ˜NLΔ1/vp-Δ1/vgΔ1/vp=1-Tzϕz.
δ˜NL=1-Tzϕz,
iuzz,t+Dζ2utt+gζu2u=-igζu2ut,
iUˆz-D¯2ω2Uˆ+Juˆ=0,
-λ22fˆω-D¯2ω2fˆ+Jfˆexp-iλ2z/2=0.
λ22=2WF-1Jfˆf+tftdt-3D¯2Wft2dt,
ϕz=λ22λG22a21-θqx8πb-3D¯4b,
qxsinh-1x/2x+24+x21/2,  x=2sb.
Tz=-2WlcΔζImu2uutt*dtdz+32Wu4dt,
Tza21-θqx8πb,
δ˜NL11-2a21-θqx/3πD¯11-λ2s/6D¯.

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