Abstract

The carrier-envelope phase dynamics of few-cycle octave-spanning Ti:sapphire lasers are analyzed based on a numerical one-dimensional dispersion-managed laser model. The dominant contribution to the carrier-envelope phase shift with respect to intracavity energy arises from the asymmetric impact of self-steepening on pulse formation and laser output. We show that this term is larger by a factor of four than the energy-dependent round trip phase and is thus more significant than in the corresponding result for conventional soliton lasers. Frequency shifts due to the Raman effect are studied and found to be of minor impact for octave-spanning lasers.

© 2010 OSA

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  24. I. T. Sorokina, E. Sorokin, E. Wintner, A. Cassanho, and H. P. Jenssen, “Raman induced pulse self-frequency shift in the sub-20 fs Kerr-lens mode-locked Cr:LiSGaF and Cr:LiSAF lasers,” OSA TOPS 19, 359–361 (1998).
  25. V. L. Kalashnikov, E. Sorokin, and I. T. Sorokina, “Mechanisms of spectral shift in ultrashort-pulse laser oscillators,” J. Opt. Soc. Am. B 18(11), 1732–1741 (2001).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]

2009 (1)

2008 (1)

2006 (1)

2005 (1)

2004 (2)

M. J. Ablowitz, B. Ilan, and S. T. Cundiff, “Carrier-envelope phase slip of ultrashort dispersion-managed solitons,” Opt. Lett. 29(15), 1808–1810 (2004).
[CrossRef] [PubMed]

S. Witte, R. T. Zinkstok, W. Hogervorst, and K. S. E. Eikema, “Control and precise measurement of carrier-envelope phase dynamics,” Appl. Phys. B 78(1), 5–12 (2004).
[CrossRef]

2003 (3)

K. W. Holman, R. J. Jones, A. Marian, S. T. Cundiff, and J. Ye, “Detailed studies and control of intensity-related dynamics of femtosecond frequency combs from mode-locked Ti:sapphire lasers,” IEEE J. Sel. Top. Quantum Electron. 9(4), 1018–1024 (2003).
[CrossRef]

T. R. Schibli, O. Kuzucu, J. Kim, E. P. Ippen, J. G. Fujimoto, F. X. Kaertner, V. Scheuer, and G. Angelow, “Toward single-cycle laser systems,” IEEE J. Sel. Top. Quantum Electron. 9(4), 990–1001 (2003).
[CrossRef]

A. Baltuška, Th. Udem, M. Uiberacker, M. Hentschel, E. Goulielmakis, Ch. Gohle, R. Holzwarth, V. S. Yakovlev, A. Scrinzi, T. W. Hänsch, and F. Krausz, “Attosecond control of electronic processes by intense light fields,” Nature 421(6923), 611–615 (2003).
[CrossRef] [PubMed]

2002 (4)

2001 (4)

H. A. Haus and E. P. Ippen, “Group velocity of solitons,” Opt. Lett. 26(21), 1654–1656 (2001).
[CrossRef]

V. L. Kalashnikov, E. Sorokin, and I. T. Sorokina, “Mechanisms of spectral shift in ultrashort-pulse laser oscillators,” J. Opt. Soc. Am. B 18(11), 1732–1741 (2001).
[CrossRef]

M. Kadleikova, J. Breza, and M. Vesely, “Raman spectra of synthetic sapphire,” Microelectron. J. 32(12), 955–958 (2001).
[CrossRef]

A. Poppe, R. Holzwarth, A. Apolonski, G. Tempea, Ch. Spielmann, T. W. Hänsch, and F. Krausz, “Few-cycle optical waveform synthesis,” Appl. Phys. B 72, 373–376 (2001).

2000 (1)

T. Brabec and F. Krausz, “Intense few-cycle laser fields: frontiers of nonlinear optics,” Rev. Mod. Phys. 72(2), 545–591 (2000).
[CrossRef]

1999 (1)

1998 (2)

H. A. Haus, I. Sorokina, and E. Sorokin, “Raman-induced redshift of ultrashort mode-locked laser pulses,” J. Opt. Soc. Am. B 15(1), 223–231 (1998).
[CrossRef]

I. T. Sorokina, E. Sorokin, E. Wintner, A. Cassanho, and H. P. Jenssen, “Raman induced pulse self-frequency shift in the sub-20 fs Kerr-lens mode-locked Cr:LiSGaF and Cr:LiSAF lasers,” OSA TOPS 19, 359–361 (1998).

1997 (1)

P. Christov, M. M. Murnane, and H. C. Kapteyn, “High-Harmonic Generation of Attosecond Pulses in the “Single-Cycle” Regime,” Phys. Rev. Lett. 78(7), 1251–1254 (1997).
[CrossRef]

1996 (1)

1967 (1)

S. P. S. Porto and R. S. Krishnan, “Raman effect of Corundum,” J. Chem. Phys. 47(3), 1009–1012 (1967).
[CrossRef]

Ablowitz, M. J.

Angelow, G.

T. R. Schibli, O. Kuzucu, J. Kim, E. P. Ippen, J. G. Fujimoto, F. X. Kaertner, V. Scheuer, and G. Angelow, “Toward single-cycle laser systems,” IEEE J. Sel. Top. Quantum Electron. 9(4), 990–1001 (2003).
[CrossRef]

Apolonski, A.

A. Poppe, R. Holzwarth, A. Apolonski, G. Tempea, Ch. Spielmann, T. W. Hänsch, and F. Krausz, “Few-cycle optical waveform synthesis,” Appl. Phys. B 72, 373–376 (2001).

Baltuška, A.

A. Baltuška, Th. Udem, M. Uiberacker, M. Hentschel, E. Goulielmakis, Ch. Gohle, R. Holzwarth, V. S. Yakovlev, A. Scrinzi, T. W. Hänsch, and F. Krausz, “Attosecond control of electronic processes by intense light fields,” Nature 421(6923), 611–615 (2003).
[CrossRef] [PubMed]

Benedick, A.

Birge, J.

Birge, J. R.

Brabec, T.

T. Brabec and F. Krausz, “Intense few-cycle laser fields: frontiers of nonlinear optics,” Rev. Mod. Phys. 72(2), 545–591 (2000).
[CrossRef]

L. Xu, Ch. Spielmann, A. Poppe, T. Brabec, F. Krausz, and T. W. Hänsch, “Route to phase control of ultrashort light pulses,” Opt. Lett. 21(24), 2008–2010 (1996).
[CrossRef] [PubMed]

Breza, J.

M. Kadleikova, J. Breza, and M. Vesely, “Raman spectra of synthetic sapphire,” Microelectron. J. 32(12), 955–958 (2001).
[CrossRef]

Cassanho, A.

I. T. Sorokina, E. Sorokin, E. Wintner, A. Cassanho, and H. P. Jenssen, “Raman induced pulse self-frequency shift in the sub-20 fs Kerr-lens mode-locked Cr:LiSGaF and Cr:LiSAF lasers,” OSA TOPS 19, 359–361 (1998).

Chen, J.

Chen, Y.

Cho, S. H.

Christov, P.

P. Christov, M. M. Murnane, and H. C. Kapteyn, “High-Harmonic Generation of Attosecond Pulses in the “Single-Cycle” Regime,” Phys. Rev. Lett. 78(7), 1251–1254 (1997).
[CrossRef]

Crespo, H. M.

Cundiff, S. T.

M. J. Ablowitz, B. Ilan, and S. T. Cundiff, “Carrier-envelope phase slip of ultrashort dispersion-managed solitons,” Opt. Lett. 29(15), 1808–1810 (2004).
[CrossRef] [PubMed]

K. W. Holman, R. J. Jones, A. Marian, S. T. Cundiff, and J. Ye, “Detailed studies and control of intensity-related dynamics of femtosecond frequency combs from mode-locked Ti:sapphire lasers,” IEEE J. Sel. Top. Quantum Electron. 9(4), 1018–1024 (2003).
[CrossRef]

S. T. Cundiff, “Phase stabilization of ultrashort optical pulses,” J. Phys. D Appl. Phys. 35(8), 201 (2002).
[CrossRef]

T. M. Fortier, J. Ye, S. T. Cundiff, and R. S. Windeler, “Nonlinear phase noise generated in air-silica microstructure fiber and its effect on carrier-envelope phase,” Opt. Lett. 27(6), 445–447 (2002).
[CrossRef]

Eikema, K. S. E.

S. Witte, R. T. Zinkstok, W. Hogervorst, and K. S. E. Eikema, “Control and precise measurement of carrier-envelope phase dynamics,” Appl. Phys. B 78(1), 5–12 (2004).
[CrossRef]

Ell, R.

Falcão-Filho, E. L.

Fortier, T. M.

Fujimoto, J. G.

T. R. Schibli, O. Kuzucu, J. Kim, E. P. Ippen, J. G. Fujimoto, F. X. Kaertner, V. Scheuer, and G. Angelow, “Toward single-cycle laser systems,” IEEE J. Sel. Top. Quantum Electron. 9(4), 990–1001 (2003).
[CrossRef]

Y. Chen, F. X. Kärtner, U. Morgner, S. H. Cho, H. A. Haus, E. P. Ippen, and J. G. Fujimoto, “Dispersion-managed mode locking,” J. Opt. Soc. Am. B 16(11), 1999–2004 (1999).
[CrossRef]

Gohle, Ch.

A. Baltuška, Th. Udem, M. Uiberacker, M. Hentschel, E. Goulielmakis, Ch. Gohle, R. Holzwarth, V. S. Yakovlev, A. Scrinzi, T. W. Hänsch, and F. Krausz, “Attosecond control of electronic processes by intense light fields,” Nature 421(6923), 611–615 (2003).
[CrossRef] [PubMed]

Goulielmakis, E.

A. Baltuška, Th. Udem, M. Uiberacker, M. Hentschel, E. Goulielmakis, Ch. Gohle, R. Holzwarth, V. S. Yakovlev, A. Scrinzi, T. W. Hänsch, and F. Krausz, “Attosecond control of electronic processes by intense light fields,” Nature 421(6923), 611–615 (2003).
[CrossRef] [PubMed]

Hänsch, T. W.

A. Baltuška, Th. Udem, M. Uiberacker, M. Hentschel, E. Goulielmakis, Ch. Gohle, R. Holzwarth, V. S. Yakovlev, A. Scrinzi, T. W. Hänsch, and F. Krausz, “Attosecond control of electronic processes by intense light fields,” Nature 421(6923), 611–615 (2003).
[CrossRef] [PubMed]

T. Udem, R. Holzwarth, and T. W. Hänsch, “Optical frequency metrology,” Nature 416(6877), 233–237 (2002).
[CrossRef] [PubMed]

A. Poppe, R. Holzwarth, A. Apolonski, G. Tempea, Ch. Spielmann, T. W. Hänsch, and F. Krausz, “Few-cycle optical waveform synthesis,” Appl. Phys. B 72, 373–376 (2001).

L. Xu, Ch. Spielmann, A. Poppe, T. Brabec, F. Krausz, and T. W. Hänsch, “Route to phase control of ultrashort light pulses,” Opt. Lett. 21(24), 2008–2010 (1996).
[CrossRef] [PubMed]

Haus, H. A.

Helbing, F. W.

Hentschel, M.

A. Baltuška, Th. Udem, M. Uiberacker, M. Hentschel, E. Goulielmakis, Ch. Gohle, R. Holzwarth, V. S. Yakovlev, A. Scrinzi, T. W. Hänsch, and F. Krausz, “Attosecond control of electronic processes by intense light fields,” Nature 421(6923), 611–615 (2003).
[CrossRef] [PubMed]

Hogervorst, W.

S. Witte, R. T. Zinkstok, W. Hogervorst, and K. S. E. Eikema, “Control and precise measurement of carrier-envelope phase dynamics,” Appl. Phys. B 78(1), 5–12 (2004).
[CrossRef]

Holman, K. W.

K. W. Holman, R. J. Jones, A. Marian, S. T. Cundiff, and J. Ye, “Detailed studies and control of intensity-related dynamics of femtosecond frequency combs from mode-locked Ti:sapphire lasers,” IEEE J. Sel. Top. Quantum Electron. 9(4), 1018–1024 (2003).
[CrossRef]

Holzwarth, R.

A. Baltuška, Th. Udem, M. Uiberacker, M. Hentschel, E. Goulielmakis, Ch. Gohle, R. Holzwarth, V. S. Yakovlev, A. Scrinzi, T. W. Hänsch, and F. Krausz, “Attosecond control of electronic processes by intense light fields,” Nature 421(6923), 611–615 (2003).
[CrossRef] [PubMed]

T. Udem, R. Holzwarth, and T. W. Hänsch, “Optical frequency metrology,” Nature 416(6877), 233–237 (2002).
[CrossRef] [PubMed]

A. Poppe, R. Holzwarth, A. Apolonski, G. Tempea, Ch. Spielmann, T. W. Hänsch, and F. Krausz, “Few-cycle optical waveform synthesis,” Appl. Phys. B 72, 373–376 (2001).

Ilan, B.

Ippen, E. P.

T. R. Schibli, O. Kuzucu, J. Kim, E. P. Ippen, J. G. Fujimoto, F. X. Kaertner, V. Scheuer, and G. Angelow, “Toward single-cycle laser systems,” IEEE J. Sel. Top. Quantum Electron. 9(4), 990–1001 (2003).
[CrossRef]

H. A. Haus and E. P. Ippen, “Group velocity of solitons,” Opt. Lett. 26(21), 1654–1656 (2001).
[CrossRef]

Y. Chen, F. X. Kärtner, U. Morgner, S. H. Cho, H. A. Haus, E. P. Ippen, and J. G. Fujimoto, “Dispersion-managed mode locking,” J. Opt. Soc. Am. B 16(11), 1999–2004 (1999).
[CrossRef]

Jenssen, H. P.

I. T. Sorokina, E. Sorokin, E. Wintner, A. Cassanho, and H. P. Jenssen, “Raman induced pulse self-frequency shift in the sub-20 fs Kerr-lens mode-locked Cr:LiSGaF and Cr:LiSAF lasers,” OSA TOPS 19, 359–361 (1998).

Jones, R. J.

K. W. Holman, R. J. Jones, A. Marian, S. T. Cundiff, and J. Ye, “Detailed studies and control of intensity-related dynamics of femtosecond frequency combs from mode-locked Ti:sapphire lasers,” IEEE J. Sel. Top. Quantum Electron. 9(4), 1018–1024 (2003).
[CrossRef]

Kadleikova, M.

M. Kadleikova, J. Breza, and M. Vesely, “Raman spectra of synthetic sapphire,” Microelectron. J. 32(12), 955–958 (2001).
[CrossRef]

Kaertner, F. X.

T. R. Schibli, O. Kuzucu, J. Kim, E. P. Ippen, J. G. Fujimoto, F. X. Kaertner, V. Scheuer, and G. Angelow, “Toward single-cycle laser systems,” IEEE J. Sel. Top. Quantum Electron. 9(4), 990–1001 (2003).
[CrossRef]

Kalashnikov, V. L.

Kapteyn, H. C.

P. Christov, M. M. Murnane, and H. C. Kapteyn, “High-Harmonic Generation of Attosecond Pulses in the “Single-Cycle” Regime,” Phys. Rev. Lett. 78(7), 1251–1254 (1997).
[CrossRef]

Kärtner, F. X.

Keller, U.

Kim, J.

T. R. Schibli, O. Kuzucu, J. Kim, E. P. Ippen, J. G. Fujimoto, F. X. Kaertner, V. Scheuer, and G. Angelow, “Toward single-cycle laser systems,” IEEE J. Sel. Top. Quantum Electron. 9(4), 990–1001 (2003).
[CrossRef]

Kim, J. W.

Krausz, F.

A. Baltuška, Th. Udem, M. Uiberacker, M. Hentschel, E. Goulielmakis, Ch. Gohle, R. Holzwarth, V. S. Yakovlev, A. Scrinzi, T. W. Hänsch, and F. Krausz, “Attosecond control of electronic processes by intense light fields,” Nature 421(6923), 611–615 (2003).
[CrossRef] [PubMed]

A. Poppe, R. Holzwarth, A. Apolonski, G. Tempea, Ch. Spielmann, T. W. Hänsch, and F. Krausz, “Few-cycle optical waveform synthesis,” Appl. Phys. B 72, 373–376 (2001).

T. Brabec and F. Krausz, “Intense few-cycle laser fields: frontiers of nonlinear optics,” Rev. Mod. Phys. 72(2), 545–591 (2000).
[CrossRef]

L. Xu, Ch. Spielmann, A. Poppe, T. Brabec, F. Krausz, and T. W. Hänsch, “Route to phase control of ultrashort light pulses,” Opt. Lett. 21(24), 2008–2010 (1996).
[CrossRef] [PubMed]

Krishnan, R. S.

S. P. S. Porto and R. S. Krishnan, “Raman effect of Corundum,” J. Chem. Phys. 47(3), 1009–1012 (1967).
[CrossRef]

Kuzucu, O.

T. R. Schibli, O. Kuzucu, J. Kim, E. P. Ippen, J. G. Fujimoto, F. X. Kaertner, V. Scheuer, and G. Angelow, “Toward single-cycle laser systems,” IEEE J. Sel. Top. Quantum Electron. 9(4), 990–1001 (2003).
[CrossRef]

Marian, A.

K. W. Holman, R. J. Jones, A. Marian, S. T. Cundiff, and J. Ye, “Detailed studies and control of intensity-related dynamics of femtosecond frequency combs from mode-locked Ti:sapphire lasers,” IEEE J. Sel. Top. Quantum Electron. 9(4), 1018–1024 (2003).
[CrossRef]

Matos, L.

Morgner, U.

Mücke, O. D.

Murnane, M. M.

P. Christov, M. M. Murnane, and H. C. Kapteyn, “High-Harmonic Generation of Attosecond Pulses in the “Single-Cycle” Regime,” Phys. Rev. Lett. 78(7), 1251–1254 (1997).
[CrossRef]

Poppe, A.

A. Poppe, R. Holzwarth, A. Apolonski, G. Tempea, Ch. Spielmann, T. W. Hänsch, and F. Krausz, “Few-cycle optical waveform synthesis,” Appl. Phys. B 72, 373–376 (2001).

L. Xu, Ch. Spielmann, A. Poppe, T. Brabec, F. Krausz, and T. W. Hänsch, “Route to phase control of ultrashort light pulses,” Opt. Lett. 21(24), 2008–2010 (1996).
[CrossRef] [PubMed]

Porto, S. P. S.

S. P. S. Porto and R. S. Krishnan, “Raman effect of Corundum,” J. Chem. Phys. 47(3), 1009–1012 (1967).
[CrossRef]

Sander, M. Y.

Scheuer, V.

T. R. Schibli, O. Kuzucu, J. Kim, E. P. Ippen, J. G. Fujimoto, F. X. Kaertner, V. Scheuer, and G. Angelow, “Toward single-cycle laser systems,” IEEE J. Sel. Top. Quantum Electron. 9(4), 990–1001 (2003).
[CrossRef]

Schibli, T. R.

T. R. Schibli, O. Kuzucu, J. Kim, E. P. Ippen, J. G. Fujimoto, F. X. Kaertner, V. Scheuer, and G. Angelow, “Toward single-cycle laser systems,” IEEE J. Sel. Top. Quantum Electron. 9(4), 990–1001 (2003).
[CrossRef]

Scrinzi, A.

A. Baltuška, Th. Udem, M. Uiberacker, M. Hentschel, E. Goulielmakis, Ch. Gohle, R. Holzwarth, V. S. Yakovlev, A. Scrinzi, T. W. Hänsch, and F. Krausz, “Attosecond control of electronic processes by intense light fields,” Nature 421(6923), 611–615 (2003).
[CrossRef] [PubMed]

Sorokin, E.

Sorokina, I.

Sorokina, I. T.

V. L. Kalashnikov, E. Sorokin, and I. T. Sorokina, “Mechanisms of spectral shift in ultrashort-pulse laser oscillators,” J. Opt. Soc. Am. B 18(11), 1732–1741 (2001).
[CrossRef]

I. T. Sorokina, E. Sorokin, E. Wintner, A. Cassanho, and H. P. Jenssen, “Raman induced pulse self-frequency shift in the sub-20 fs Kerr-lens mode-locked Cr:LiSGaF and Cr:LiSAF lasers,” OSA TOPS 19, 359–361 (1998).

Spielmann, Ch.

A. Poppe, R. Holzwarth, A. Apolonski, G. Tempea, Ch. Spielmann, T. W. Hänsch, and F. Krausz, “Few-cycle optical waveform synthesis,” Appl. Phys. B 72, 373–376 (2001).

L. Xu, Ch. Spielmann, A. Poppe, T. Brabec, F. Krausz, and T. W. Hänsch, “Route to phase control of ultrashort light pulses,” Opt. Lett. 21(24), 2008–2010 (1996).
[CrossRef] [PubMed]

Steinmeyer, G.

Stenger, J.

Telle, H. R.

Tempea, G.

A. Poppe, R. Holzwarth, A. Apolonski, G. Tempea, Ch. Spielmann, T. W. Hänsch, and F. Krausz, “Few-cycle optical waveform synthesis,” Appl. Phys. B 72, 373–376 (2001).

Udem, T.

T. Udem, R. Holzwarth, and T. W. Hänsch, “Optical frequency metrology,” Nature 416(6877), 233–237 (2002).
[CrossRef] [PubMed]

Udem, Th.

A. Baltuška, Th. Udem, M. Uiberacker, M. Hentschel, E. Goulielmakis, Ch. Gohle, R. Holzwarth, V. S. Yakovlev, A. Scrinzi, T. W. Hänsch, and F. Krausz, “Attosecond control of electronic processes by intense light fields,” Nature 421(6923), 611–615 (2003).
[CrossRef] [PubMed]

Uiberacker, M.

A. Baltuška, Th. Udem, M. Uiberacker, M. Hentschel, E. Goulielmakis, Ch. Gohle, R. Holzwarth, V. S. Yakovlev, A. Scrinzi, T. W. Hänsch, and F. Krausz, “Attosecond control of electronic processes by intense light fields,” Nature 421(6923), 611–615 (2003).
[CrossRef] [PubMed]

Vesely, M.

M. Kadleikova, J. Breza, and M. Vesely, “Raman spectra of synthetic sapphire,” Microelectron. J. 32(12), 955–958 (2001).
[CrossRef]

Windeler, R. S.

Winter, A.

Wintner, E.

I. T. Sorokina, E. Sorokin, E. Wintner, A. Cassanho, and H. P. Jenssen, “Raman induced pulse self-frequency shift in the sub-20 fs Kerr-lens mode-locked Cr:LiSGaF and Cr:LiSAF lasers,” OSA TOPS 19, 359–361 (1998).

Witte, S.

S. Witte, R. T. Zinkstok, W. Hogervorst, and K. S. E. Eikema, “Control and precise measurement of carrier-envelope phase dynamics,” Appl. Phys. B 78(1), 5–12 (2004).
[CrossRef]

Xu, L.

Yakovlev, V. S.

A. Baltuška, Th. Udem, M. Uiberacker, M. Hentschel, E. Goulielmakis, Ch. Gohle, R. Holzwarth, V. S. Yakovlev, A. Scrinzi, T. W. Hänsch, and F. Krausz, “Attosecond control of electronic processes by intense light fields,” Nature 421(6923), 611–615 (2003).
[CrossRef] [PubMed]

Ye, J.

K. W. Holman, R. J. Jones, A. Marian, S. T. Cundiff, and J. Ye, “Detailed studies and control of intensity-related dynamics of femtosecond frequency combs from mode-locked Ti:sapphire lasers,” IEEE J. Sel. Top. Quantum Electron. 9(4), 1018–1024 (2003).
[CrossRef]

T. M. Fortier, J. Ye, S. T. Cundiff, and R. S. Windeler, “Nonlinear phase noise generated in air-silica microstructure fiber and its effect on carrier-envelope phase,” Opt. Lett. 27(6), 445–447 (2002).
[CrossRef]

Zinkstok, R. T.

S. Witte, R. T. Zinkstok, W. Hogervorst, and K. S. E. Eikema, “Control and precise measurement of carrier-envelope phase dynamics,” Appl. Phys. B 78(1), 5–12 (2004).
[CrossRef]

Appl. Phys. B (2)

A. Poppe, R. Holzwarth, A. Apolonski, G. Tempea, Ch. Spielmann, T. W. Hänsch, and F. Krausz, “Few-cycle optical waveform synthesis,” Appl. Phys. B 72, 373–376 (2001).

S. Witte, R. T. Zinkstok, W. Hogervorst, and K. S. E. Eikema, “Control and precise measurement of carrier-envelope phase dynamics,” Appl. Phys. B 78(1), 5–12 (2004).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (2)

K. W. Holman, R. J. Jones, A. Marian, S. T. Cundiff, and J. Ye, “Detailed studies and control of intensity-related dynamics of femtosecond frequency combs from mode-locked Ti:sapphire lasers,” IEEE J. Sel. Top. Quantum Electron. 9(4), 1018–1024 (2003).
[CrossRef]

T. R. Schibli, O. Kuzucu, J. Kim, E. P. Ippen, J. G. Fujimoto, F. X. Kaertner, V. Scheuer, and G. Angelow, “Toward single-cycle laser systems,” IEEE J. Sel. Top. Quantum Electron. 9(4), 990–1001 (2003).
[CrossRef]

J. Chem. Phys. (1)

S. P. S. Porto and R. S. Krishnan, “Raman effect of Corundum,” J. Chem. Phys. 47(3), 1009–1012 (1967).
[CrossRef]

J. Opt. Soc. Am. B (5)

J. Phys. D Appl. Phys. (1)

S. T. Cundiff, “Phase stabilization of ultrashort optical pulses,” J. Phys. D Appl. Phys. 35(8), 201 (2002).
[CrossRef]

Microelectron. J. (1)

M. Kadleikova, J. Breza, and M. Vesely, “Raman spectra of synthetic sapphire,” Microelectron. J. 32(12), 955–958 (2001).
[CrossRef]

Nature (2)

A. Baltuška, Th. Udem, M. Uiberacker, M. Hentschel, E. Goulielmakis, Ch. Gohle, R. Holzwarth, V. S. Yakovlev, A. Scrinzi, T. W. Hänsch, and F. Krausz, “Attosecond control of electronic processes by intense light fields,” Nature 421(6923), 611–615 (2003).
[CrossRef] [PubMed]

T. Udem, R. Holzwarth, and T. W. Hänsch, “Optical frequency metrology,” Nature 416(6877), 233–237 (2002).
[CrossRef] [PubMed]

Opt. Express (2)

Opt. Lett. (5)

OSA TOPS (1)

I. T. Sorokina, E. Sorokin, E. Wintner, A. Cassanho, and H. P. Jenssen, “Raman induced pulse self-frequency shift in the sub-20 fs Kerr-lens mode-locked Cr:LiSGaF and Cr:LiSAF lasers,” OSA TOPS 19, 359–361 (1998).

Phys. Rev. Lett. (1)

P. Christov, M. M. Murnane, and H. C. Kapteyn, “High-Harmonic Generation of Attosecond Pulses in the “Single-Cycle” Regime,” Phys. Rev. Lett. 78(7), 1251–1254 (1997).
[CrossRef]

Rev. Mod. Phys. (1)

T. Brabec and F. Krausz, “Intense few-cycle laser fields: frontiers of nonlinear optics,” Rev. Mod. Phys. 72(2), 545–591 (2000).
[CrossRef]

Other (3)

M. Y. Sander, H. M. Crespo, J. R. Birge, and F. X. Kärtner, “Modeling of octave-spanning sub-two-cycle titanium:sapphire lasers: Simulation and Experiment,” Conference on Ultrafast Phenomena, (European Physical Society and Optical Society of America, 2008), THUIIIc.

M. Y. Sander, and F. X. Kärtner, “Carrier-envelope phase dynamics of octave-spanning Titanium:sapphire lasers,” Conference on Lasers and Electro Optics (CLEO), Baltimore, MD, June 1–5, 2009, CMN4.

G. P. Agrawal, Nonlinear Fiber Optics (Academic, 2007).

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Figures (6)

Fig. 1
Fig. 1

Experimental setup of the phase-stabilized 500 MHz ring laser [18]. The 1f-2f output is used for self-referencing in the 1f-2f interferometer to phase-stabilize the laser.

Fig. 2
Fig. 2

Power spectral density (PSD) of simulated spectrum with self-steepening (w ss) and without self-steepening (w/o ss) compared to the measured output spectrum. The wavelengths corresponding to the 1f- and 2f frequencies are marked. Each curve is normalized to its maximum amplitude.

Fig. 3
Fig. 3

Pulse in the geometric middle and at the end of the Ti:sapphire crystal for simulation with and without self-steepening (no ss).

Fig. 4
Fig. 4

(a) Round trip phase shift Φ and (b) nonlinear timing shift τ dependency on intracavity pulse energy W. The linear relationship is described by the respective slopes.

Fig. 5
Fig. 5

Frequency shift Δωfilter due to a rectangular filter with bandwidth Ωf = 1.4 · 1015 rad/s for a spectrum shifted by Δω from the carrier frequency for three values of soliton pulse width τsech .

Fig. 6
Fig. 6

Frequency shifts Δωfilter induced by a rectangular filter of bandwidth of Ωf = 1.4 ·1015 rad/s on a pulse with τsech = 3.5 fs. The linear approximation according to Eq. (15) is plotted as a dashed line.

Tables (2)

Tables Icon

Table 1 Time constants for relaxation behavior from filtering by mirrors and output coupler τFilter and from gain filtering τGain for a given pulse duration τsech .

Tables Icon

Table 2 Raman shift ΔωRaman , value of convolution function G(ωRτsech), resulting frequency shift ΔωTotal and CEPS contribution for each Raman line ωR for different pulse parameters τsech .

Equations (17)

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A ( z , t ) z ​ ​     =     [ g ( z , t ) q ( z , t )   ​   j δ     { | A ( z , t ) | 2 +       j ω C ​ ​ ​     t ( | A ( z , t ) | 2 ) }     j ϕ ( j ​   t ) ​ ​ ]           A ( z , t ) ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​
E ( t )     = ​     n A ( t n ​   T R n τ )   ​ e j ω c ​   ( t     n ​     T R n τ ) e j n Φ C E ​ ​  
Φ C E     =       Φ C E , N L   ​     +             Φ C E ,     L i n                               =       ​ Φ ​     + ​   ω c τ +     Φ C E     =                       =       Φ ​     + ​   ω c τ     +     ω c L ( 1 v g         1 v p )     =     Φ ​     + ​   ω c τ     +     ω c i L i ( k i ω | ω C     k i ω c )
Φ C E W     ​ = ​       Φ W   ​   + ​     ω c τ W     +     τ ω c W         ω c i L i     2 k i ω 2 | ω c ω c W
Φ W =     0.06     rad/nJ       and       τ W =     0.1     fs/nJ
Φ C E W     ​ = ​         Φ W   ​   + ​     ω c τ W     =       0.06     rad/nJ     +     0.23     rad/nJ     =       0.17     rad/nJ
Δ ω R a m a n = i π 16     1 τ s e c h g R δ ω R G ( ω R , i τ s e c h )     L A     W
T Δ ω     =     Δ ω F i l t e r +     Δ ω G a i n     +     Δ ω R a m a n     =     Δ ω τ F i l t e r         Δ ω τ G a i n     + Δ ω R a m a n     with       1 τ G a i n     =     4 3 Ω G 2 τ s e c h 2
Δ ω T o t a l     =     1 1 τ F i l t e r + 1 τ G a i n     Δ ω R a m a n     = i 1 1 τ F i l t e r + 1 τ G a i n     π 16     1 τ s e c h g R δ ω R , i G ( ω R τ s e c h )     L A     W    
Δ f C E Δ P       =     1 2 π Δ Φ C E Δ W       C Δ f C E , S o l i t o n Δ P             with   C     2.6           2.6 L n 2 4 λ A e f f τ s e c h       =         30.3   MHz/W
f ¯ ω ( t )     =     j A 0 τ 2 tanh ( t τ sech )   sech ( t τ sech )
Δ ω f i l t e r = Re f ¯ ω *     Δ a ( t ) d t =     Re f ¯ ω *     g f i l t e r ( t ) A ( t ) d t
f ¯ ω *     Δ a ( t ) d t     =     f ¯ ω *     g f i l t e r ( t ) A ( t ) d t = F { f ¯ ω * }     F { g f i l t e r ( t ) }     F { A ( t ) } d ω
sech ( t )                                             π   sech ( π 2 ω ) tanh ( t )   sech ( t )             j π ω   sech ( π 2 ω )
Δ ω f i l t e r = Re f ¯ ω *     Δ a ( t ) d t     = Re j A 0 τ 2 tanh ( t τ sech )   sech ( t τ sech ) g f i l t e r ( t ) A ( t ) d t     =                               =     Re j A 0 τ sech 2 tanh ( t τ sech )   sech ( t τ sech ) F 1 {   rect ( ω Δ ω Δ ω f Ω f ) } A 0   sech ( t τ sech ) d t                               =     Re F { f ¯ ω * }     F { g f i l t e r ( t ) } F { A ( t ) } d ω       =                               = Re j A 0 τ sech 2 ( j τ sech 2 )     π ω     sech ( π 2 τ sech ω )   rect ( ω Δ ω Δ ω f Ω f ) ... ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​                                                           ... ( A 0 ) π τ sech   sech ( π 2 τ sech ω ) d ω     = ​ ​ ​ ​ ​ ​ ​                             =       Ω f 2 + Δ ω + Δ ω f Ω f 2 + Δ ω + Δ ω f π 2 τ sech ω     sech 2 ( π 2 τ sech ω ) d ω =                                     =     π 2 τ sech [ 4 π 2 τ sech 2     log [ cosh ( π 2 τ sech ω ) ] +     2 ω π τ sech   tanh ( π 2 τ sech ω ) ] | Ω f 2 + Δ ω + Δ ω f Ω f 2 + Δ ω + Δ ω f =                             =     4 τ sech {  log [ cosh ( π 2 τ sech ( Ω f 2 + Δ ω + Δ ω f ) ) ]     +     log  [ cosh ( π 2 τ sech ( Ω f 2 + Δ ω + Δ ω f ) ) ] } + ...                                                                         + 2 π [     ( Ω f 2 + Δ ω + Δ ω f )   tanh ( π 2 τ sech ( Ω f 2 + Δ ω + Δ ω f ) )       ]         ...                                                                         2 π     [ ( Ω f 2 + Δ ω + Δ ω f )   tanh ( π 2 τ sech ( Ω f 2 + Δ ω + Δ ω f ) ) ]
Δ ω f i l t e r     Δ ω f     ( Ω f 2 + Δ ω f + Δ ω Ω f 2 + Δ ω f + Δ ω π 2 τ sech ω     sech 2 ( π 2 τ sech ω ) d ω | Δ ω = 0 ) Δ ω         =     π 2 τ sech ( Ω f 2 + Δ ω f + Δ ω )     sech 2 ( π 2 τ sech     ( Ω f 2 + Δ ω f + Δ ω ) ) | Δ ω = 0 Δ ω     +     ...           ... +     π 2 τ sech     ( Ω f 2 + Δ ω f + Δ ω )     sech 2 ( π 2 τ sech     ( Ω f 2 + Δ ω f + Δ ω ) ) | Δ ω = 0     Δ ω         =     π 2 τ sech [     ( Ω f 2 + Δ ω f )     sech 2 ( π 2 τ sech     ( Ω f 2 + Δ ω f ) ) ( Ω f 2 + Δ ω f )     sech 2 ( π 2 τ sech     ( Ω f 2 + Δ ω f ) ) ] Δ ω
Δ ω f i l t e r     = f o r Δ ω f = 0           π 2 τ sech     Ω f sech 2 ( τ sech π 2     Ω f 2 ) Δ ω             =               1 τ f i l t e r Δ ω      

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