Abstract

The effects of high-order dispersion on a chirped-pulse oscillator operating in the positive dispersion regime were studied both theoretically and experimentally. It was found that odd and negative even high-order dispersions impair the oscillator stability owing to resonance with the dispersion waves, but can broaden the spectrum as in the case of continuum generation in the fibers. Positive fourth-order dispersion enhances the stability and shifts the stability range into negative dispersion. The destabilization mechanism was found to be a parametrical instability which causes noisy mode locking around zero dispersion.

© 2008 Optical Society of America

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2007 (4)

2006 (2)

J. M. Dudley, G. Genty, and S. Coen, "Supercontinuum generation in photonic crystal fiber," Rev. Mod. Phys. 78, 1135-1184 (2006).
[CrossRef]

V. L. Kalashnikov, E. Podivilov, A. Chernykh, and A. Apolonski, "Chirped-pulse oscillators: theory and experiment," Appl. Phys. B 83, 503-510 (2006).
[CrossRef]

2005 (3)

E. Podivilov and V. L. Kalashnikov, "Heavily-chirped solitary pulses in te normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation," JETP Letters 82, 524-528 (2005).
[CrossRef]

V. L. Kalashnikov, E. Podivilov, A. Chernykh, S. Naumov, A. Fernandez, R. Graf, and A. Apolonski, "Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment," New J. Phys. 7, 217 (2005).
[CrossRef]

S. Naumov, A. Fernandez, R. Graf, P. Dombi, F. Krausz, and A. Apolonski, "Approaching the microjoule frontier with femtosecond laser oscillators," New J. Phys. 7, 216 (2005).
[CrossRef]

2004 (2)

Y. H. Cha, B. Yoo, J. Rhee, and Ch. Kim, "Numerical analysis of sideband generation in femtosecond solid-state lasers with high-order dispersion," J. Korean Phy. Soc. 44, 859-863 (2004).

A. Fernandez, T. Fuji, A. Poppe, A. Fürbach, F. Krausz, and A. Apolonski, "Chirped-pulse oscillators: a route to highpower femtosecond pulses without external amplification," Opt. Lett. 29, 1366-1368 (2004).
[CrossRef] [PubMed]

2003 (3)

2002 (1)

Zh. Li, L. Li, H. Tian, G. Zhou, and K. H. Spatschek, "Chirped femtosecond solitonlike laser pulse form with selffrequency shift," Phys. Rev. Lett. 89, 263901 (2002).
[CrossRef] [PubMed]

2001 (1)

2000 (1)

A. Apolonski, A. Poppe, G. Tempea, C. Spielmann, T. Udem, R. Holzwarth, T. Hänsch, and F. Krausz, "Controlling the phase evolution of few cycle light pulses," Phys. Rev. Lett. 85, 740-743 (2000).
[CrossRef] [PubMed]

1999 (2)

1998 (2)

1997 (5)

J. Fujioka and A. Espinosa, "Soliton-like solution of an extended NLS equation existing in resonance with linear dispersive waves," J. Physical Sociaty of Japan 66, 2601-2607 (1997).
[CrossRef]

A. Rundquist, C. Durfee, Z. Chang, G. Taft, E. Zeek, S. Backus, M. M. Murnane, H. C. Kapteyn, I. Christov, and V. Stoev, "Ultrafast laser and amplifier sources," Appl. Phys. B 65, 161-174 (1997).
[CrossRef]

J. M. Soto-Crespo, N. N. Akhmediev, V. V. Afanasjev, and S. Wabnitz, "Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion," Phys. Rev. E 55, 4783-4796 (1997).
[CrossRef]

M. Santagiustina, "Third-order dispersion radiation in solid-state solitary laser," J. Opt. Soc. Am. B 14, 1484-1495 (1997).
[CrossRef]

J. Herrmann, V. P. Kalosha, and M. Müller, "Highr-order phase dispersions in femtosecond Kerr-lens mode-locked solid-state lasers: sideband generation and pulse splitting," Opt. Lett. 22, 236-238 (1997).
[CrossRef] [PubMed]

1996 (1)

1995 (3)

1994 (6)

Ch. Spielmann, P. F. Curley, T. Brabec, and F. Krausz, "Ultrabroadband femtosecond lasers," IEEE J. Quantum Electron. 30, 1100-1114 (1994).
[CrossRef]

I. P. Christov, M. M. Murnane, H. C. Kapteyn, J. Zhou, and Ch.-P. Huang, "Fourth-order dispersion limited solitary pulses," Opt. Lett. 1465-1467 (1994).
[CrossRef] [PubMed]

V. I. Karpman, "Solitons of the fourth order nonlinear Schrödinger equation," Physics Letters A 193, 355-358 (1994).
[CrossRef]

M. L. Dennis and I. N. Duling III, "Third-order dispersion in femtosecond fiber lasers," Opt. Lett. 19, 1750-1752 (1994).
[CrossRef] [PubMed]

R. J. Deissler and H. R. Brand, "Periodic, quasipereodic, and chaotic localized solutions of the quintic complex Ginzburg-Landau equation," Phys. Rev. Lett. 72, 478-481 (1994).
[CrossRef] [PubMed]

J. Herrmann, "Theory of Kerr-lens mode locking: role of self-focusing and radially varying gain," J. Opt. Soc. Am. B 11, 498-512 (1994).
[CrossRef]

1993 (4)

1992 (1)

1991 (1)

1990 (1)

P. K. A. Wai, H. H. Chen, and Y. C. Lee, "Radiations by "solitons" at the zero group-dispersion wavelength of singlemode optical fibers," Phys. Rev. A 41, 426-439 (1990).
[CrossRef] [PubMed]

1988 (1)

1987 (1)

Afanasjev, V. V.

J. M. Soto-Crespo, N. N. Akhmediev, V. V. Afanasjev, and S. Wabnitz, "Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion," Phys. Rev. E 55, 4783-4796 (1997).
[CrossRef]

Akhmediev, N.

N. Akhmediev and M. Karlsson, "Cherenkov radiation emitted in optical fibers" Phys. Rev. E 51, 2602-2607 (1995).

Akhmediev, N. N.

J. M. Soto-Crespo, N. N. Akhmediev, V. V. Afanasjev, and S. Wabnitz, "Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion," Phys. Rev. E 55, 4783-4796 (1997).
[CrossRef]

Angelow, G.

Anis, H.

Apolonski, A.

V. L. Kalashnikov, E. Podivilov, A. Chernykh, and A. Apolonski, "Chirped-pulse oscillators: theory and experiment," Appl. Phys. B 83, 503-510 (2006).
[CrossRef]

S. Naumov, A. Fernandez, R. Graf, P. Dombi, F. Krausz, and A. Apolonski, "Approaching the microjoule frontier with femtosecond laser oscillators," New J. Phys. 7, 216 (2005).
[CrossRef]

V. L. Kalashnikov, E. Podivilov, A. Chernykh, S. Naumov, A. Fernandez, R. Graf, and A. Apolonski, "Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment," New J. Phys. 7, 217 (2005).
[CrossRef]

A. Fernandez, T. Fuji, A. Poppe, A. Fürbach, F. Krausz, and A. Apolonski, "Chirped-pulse oscillators: a route to highpower femtosecond pulses without external amplification," Opt. Lett. 29, 1366-1368 (2004).
[CrossRef] [PubMed]

A. Apolonski, A. Poppe, G. Tempea, C. Spielmann, T. Udem, R. Holzwarth, T. Hänsch, and F. Krausz, "Controlling the phase evolution of few cycle light pulses," Phys. Rev. Lett. 85, 740-743 (2000).
[CrossRef] [PubMed]

Backus, S.

A. Rundquist, C. Durfee, Z. Chang, G. Taft, E. Zeek, S. Backus, M. M. Murnane, H. C. Kapteyn, I. Christov, and V. Stoev, "Ultrafast laser and amplifier sources," Appl. Phys. B 65, 161-174 (1997).
[CrossRef]

Bouma, B. E.

Boussen, S. M.

Brabec, T.

Ch. Spielmann, P. F. Curley, T. Brabec, and F. Krausz, "Ultrabroadband femtosecond lasers," IEEE J. Quantum Electron. 30, 1100-1114 (1994).
[CrossRef]

T. Brabec and S. M. J. Kelly, "Third-order dispersion as limiting factor to mode locking in femtosecond solitary lasers," Opt. Lett. 18, 2002-2004 (1993).
[CrossRef] [PubMed]

Brand, H. R.

R. J. Deissler and H. R. Brand, "Periodic, quasipereodic, and chaotic localized solutions of the quintic complex Ginzburg-Landau equation," Phys. Rev. Lett. 72, 478-481 (1994).
[CrossRef] [PubMed]

Cameron, D. M. J.

Cha, Y. H.

Y. H. Cha, B. Yoo, J. Rhee, and Ch. Kim, "Numerical analysis of sideband generation in femtosecond solid-state lasers with high-order dispersion," J. Korean Phy. Soc. 44, 859-863 (2004).

Chang, Z.

A. Rundquist, C. Durfee, Z. Chang, G. Taft, E. Zeek, S. Backus, M. M. Murnane, H. C. Kapteyn, I. Christov, and V. Stoev, "Ultrafast laser and amplifier sources," Appl. Phys. B 65, 161-174 (1997).
[CrossRef]

Chen, H. H.

P. K. A. Wai, H. H. Chen, and Y. C. Lee, "Radiations by "solitons" at the zero group-dispersion wavelength of singlemode optical fibers," Phys. Rev. A 41, 426-439 (1990).
[CrossRef] [PubMed]

P. K. A. Wai, C. R. Menyuk, H. H. Chen, and Y. C. Lee, "Soliton at the zero-group-dispersion wavelength of a singlemodel fiber," Opt. Lett. 12, 628-630 (1987).
[CrossRef] [PubMed]

Chernykh, A.

V. L. Kalashnikov and A. Chernykh, "Spectral anomalies and stability of chirped-pulse oscillators," Phys. Rev. A 75, 033820 (2007).
[CrossRef]

V. L. Kalashnikov, E. Podivilov, A. Chernykh, and A. Apolonski, "Chirped-pulse oscillators: theory and experiment," Appl. Phys. B 83, 503-510 (2006).
[CrossRef]

V. L. Kalashnikov, E. Podivilov, A. Chernykh, S. Naumov, A. Fernandez, R. Graf, and A. Apolonski, "Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment," New J. Phys. 7, 217 (2005).
[CrossRef]

A. Chernykh and S. K. Turitsyn, "Soliton and collapse regimes of pulse generation in passively mode-locking laser systems," Opt. Lett. 20, 398-400 (1995).
[CrossRef] [PubMed]

Cho, S. H.

Christov, I.

A. Rundquist, C. Durfee, Z. Chang, G. Taft, E. Zeek, S. Backus, M. M. Murnane, H. C. Kapteyn, I. Christov, and V. Stoev, "Ultrafast laser and amplifier sources," Appl. Phys. B 65, 161-174 (1997).
[CrossRef]

Christov, I. P.

I. P. Christov, M. M. Murnane, H. C. Kapteyn, J. Zhou, and Ch.-P. Huang, "Fourth-order dispersion limited solitary pulses," Opt. Lett. 1465-1467 (1994).
[CrossRef] [PubMed]

Coen, S.

J. M. Dudley, G. Genty, and S. Coen, "Supercontinuum generation in photonic crystal fiber," Rev. Mod. Phys. 78, 1135-1184 (2006).
[CrossRef]

Cormier, J.-F.

Cunnighan, J. E.

Curley, P. F.

Ch. Spielmann, P. F. Curley, T. Brabec, and F. Krausz, "Ultrabroadband femtosecond lasers," IEEE J. Quantum Electron. 30, 1100-1114 (1994).
[CrossRef]

Deissler, R. J.

R. J. Deissler and H. R. Brand, "Periodic, quasipereodic, and chaotic localized solutions of the quintic complex Ginzburg-Landau equation," Phys. Rev. Lett. 72, 478-481 (1994).
[CrossRef] [PubMed]

Dennis, M. L.

Dewald, S.

Dombi, P.

S. Naumov, A. Fernandez, R. Graf, P. Dombi, F. Krausz, and A. Apolonski, "Approaching the microjoule frontier with femtosecond laser oscillators," New J. Phys. 7, 216 (2005).
[CrossRef]

Dudley, J. M.

J. M. Dudley, Ch. Finot, D. J. Richardson, and G. Millot, "Self-similarity in ultrafast nonlinear optics", Nature Phy. 3, 597 (2007).
[CrossRef]

J. M. Dudley, G. Genty, and S. Coen, "Supercontinuum generation in photonic crystal fiber," Rev. Mod. Phys. 78, 1135-1184 (2006).
[CrossRef]

J. M. Dudley, S. M. Boussen, D. M. J. Cameron, and J. D. Harvey, "Complete characterization of a self-mode-locked Ti:sapphire laser in the vicinity of zero group-delay dispersion by frequency-resolved optical gating," Appl. Opt. 38, 3308-3315 (1999).
[CrossRef]

Duling, I. N.

Durfee, C.

A. Rundquist, C. Durfee, Z. Chang, G. Taft, E. Zeek, S. Backus, M. M. Murnane, H. C. Kapteyn, I. Christov, and V. Stoev, "Ultrafast laser and amplifier sources," Appl. Phys. B 65, 161-174 (1997).
[CrossRef]

Elgin, J. N.

Espinosa, A.

J. Fujioka and A. Espinosa, "Soliton-like solution of an extended NLS equation existing in resonance with linear dispersive waves," J. Physical Sociaty of Japan 66, 2601-2607 (1997).
[CrossRef]

Fernandez, A.

S. Naumov, A. Fernandez, R. Graf, P. Dombi, F. Krausz, and A. Apolonski, "Approaching the microjoule frontier with femtosecond laser oscillators," New J. Phys. 7, 216 (2005).
[CrossRef]

V. L. Kalashnikov, E. Podivilov, A. Chernykh, S. Naumov, A. Fernandez, R. Graf, and A. Apolonski, "Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment," New J. Phys. 7, 217 (2005).
[CrossRef]

A. Fernandez, T. Fuji, A. Poppe, A. Fürbach, F. Krausz, and A. Apolonski, "Chirped-pulse oscillators: a route to highpower femtosecond pulses without external amplification," Opt. Lett. 29, 1366-1368 (2004).
[CrossRef] [PubMed]

Finot, Ch.

J. M. Dudley, Ch. Finot, D. J. Richardson, and G. Millot, "Self-similarity in ultrafast nonlinear optics", Nature Phy. 3, 597 (2007).
[CrossRef]

Fuji, T.

Fujimoto, J. G.

Fujioka, J.

J. Fujioka and A. Espinosa, "Soliton-like solution of an extended NLS equation existing in resonance with linear dispersive waves," J. Physical Sociaty of Japan 66, 2601-2607 (1997).
[CrossRef]

Fürbach, A.

Gatz, S.

Genty, G.

J. M. Dudley, G. Genty, and S. Coen, "Supercontinuum generation in photonic crystal fiber," Rev. Mod. Phys. 78, 1135-1184 (2006).
[CrossRef]

Graf, R.

V. L. Kalashnikov, E. Podivilov, A. Chernykh, S. Naumov, A. Fernandez, R. Graf, and A. Apolonski, "Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment," New J. Phys. 7, 217 (2005).
[CrossRef]

S. Naumov, A. Fernandez, R. Graf, P. Dombi, F. Krausz, and A. Apolonski, "Approaching the microjoule frontier with femtosecond laser oscillators," New J. Phys. 7, 216 (2005).
[CrossRef]

Hänsch, T.

A. Apolonski, A. Poppe, G. Tempea, C. Spielmann, T. Udem, R. Holzwarth, T. Hänsch, and F. Krausz, "Controlling the phase evolution of few cycle light pulses," Phys. Rev. Lett. 85, 740-743 (2000).
[CrossRef] [PubMed]

Harvey, J. D.

Haus, H. A.

Herrmann, J.

Holzwarth, R.

A. Apolonski, A. Poppe, G. Tempea, C. Spielmann, T. Udem, R. Holzwarth, T. Hänsch, and F. Krausz, "Controlling the phase evolution of few cycle light pulses," Phys. Rev. Lett. 85, 740-743 (2000).
[CrossRef] [PubMed]

Höök, A.

Huang, Ch.-P.

I. P. Christov, M. M. Murnane, H. C. Kapteyn, J. Zhou, and Ch.-P. Huang, "Fourth-order dispersion limited solitary pulses," Opt. Lett. 1465-1467 (1994).
[CrossRef] [PubMed]

Ippen, E. P.

Kalashnikov, V. L.

V. L. Kalashnikov and A. Chernykh, "Spectral anomalies and stability of chirped-pulse oscillators," Phys. Rev. A 75, 033820 (2007).
[CrossRef]

V. L. Kalashnikov, E. Podivilov, A. Chernykh, and A. Apolonski, "Chirped-pulse oscillators: theory and experiment," Appl. Phys. B 83, 503-510 (2006).
[CrossRef]

E. Podivilov and V. L. Kalashnikov, "Heavily-chirped solitary pulses in te normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation," JETP Letters 82, 524-528 (2005).
[CrossRef]

V. L. Kalashnikov, E. Podivilov, A. Chernykh, S. Naumov, A. Fernandez, R. Graf, and A. Apolonski, "Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment," New J. Phys. 7, 217 (2005).
[CrossRef]

V. L. Kalashnikov, E. Sorokin, and I. T. Sorokina, "Multipulse operation and limits of the Kerr-lens mode locking stability," IEEE J. Quantum Electron. 39, 323-336 (2003).
[CrossRef]

V. L. Kalashnikov, E. Sorokin, S. Naumov, and I. T. Sorokina, "Spectral poperties of the Kerr-lens mode-locked Cr4+:YAG laser," J. Opt. Soc. Am. B 20, 2084-2092 (2003).
[CrossRef]

Kalosha, V. P.

Kapteyn, H. C.

A. Rundquist, C. Durfee, Z. Chang, G. Taft, E. Zeek, S. Backus, M. M. Murnane, H. C. Kapteyn, I. Christov, and V. Stoev, "Ultrafast laser and amplifier sources," Appl. Phys. B 65, 161-174 (1997).
[CrossRef]

I. P. Christov, M. M. Murnane, H. C. Kapteyn, J. Zhou, and Ch.-P. Huang, "Fourth-order dispersion limited solitary pulses," Opt. Lett. 1465-1467 (1994).
[CrossRef] [PubMed]

Karlsson, M.

N. Akhmediev and M. Karlsson, "Cherenkov radiation emitted in optical fibers" Phys. Rev. E 51, 2602-2607 (1995).

Karlssson, M.

Karpman, V. I.

V. I. Karpman, "Solitons of the fourth order nonlinear Schrödinger equation," Physics Letters A 193, 355-358 (1994).
[CrossRef]

Kärtner, F. X.

Kelly, S. M. J.

Kim, Ch.

Y. H. Cha, B. Yoo, J. Rhee, and Ch. Kim, "Numerical analysis of sideband generation in femtosecond solid-state lasers with high-order dispersion," J. Korean Phy. Soc. 44, 859-863 (2004).

Knox, W. H.

Kowalevicz, A. M.

Krausz, F.

S. Naumov, A. Fernandez, R. Graf, P. Dombi, F. Krausz, and A. Apolonski, "Approaching the microjoule frontier with femtosecond laser oscillators," New J. Phys. 7, 216 (2005).
[CrossRef]

A. Fernandez, T. Fuji, A. Poppe, A. Fürbach, F. Krausz, and A. Apolonski, "Chirped-pulse oscillators: a route to highpower femtosecond pulses without external amplification," Opt. Lett. 29, 1366-1368 (2004).
[CrossRef] [PubMed]

A. Apolonski, A. Poppe, G. Tempea, C. Spielmann, T. Udem, R. Holzwarth, T. Hänsch, and F. Krausz, "Controlling the phase evolution of few cycle light pulses," Phys. Rev. Lett. 85, 740-743 (2000).
[CrossRef] [PubMed]

Ch. Spielmann, P. F. Curley, T. Brabec, and F. Krausz, "Ultrabroadband femtosecond lasers," IEEE J. Quantum Electron. 30, 1100-1114 (1994).
[CrossRef]

Kuznetsov, E. A.

V. E. Zakharov and E. A. Kuznetsov, "Optical solitons and quasisolitons," J. Exp. Theor. Phys. 86, 1035-1046 (1998).
[CrossRef]

Lee, Y. C.

P. K. A. Wai, H. H. Chen, and Y. C. Lee, "Radiations by "solitons" at the zero group-dispersion wavelength of singlemode optical fibers," Phys. Rev. A 41, 426-439 (1990).
[CrossRef] [PubMed]

P. K. A. Wai, C. R. Menyuk, H. H. Chen, and Y. C. Lee, "Soliton at the zero-group-dispersion wavelength of a singlemodel fiber," Opt. Lett. 12, 628-630 (1987).
[CrossRef] [PubMed]

Li, L.

Zh. Li, L. Li, H. Tian, G. Zhou, and K. H. Spatschek, "Chirped femtosecond solitonlike laser pulse form with selffrequency shift," Phys. Rev. Lett. 89, 263901 (2002).
[CrossRef] [PubMed]

Li, Zh.

Zh. Li, L. Li, H. Tian, G. Zhou, and K. H. Spatschek, "Chirped femtosecond solitonlike laser pulse form with selffrequency shift," Phys. Rev. Lett. 89, 263901 (2002).
[CrossRef] [PubMed]

Logvin, Y.

Menyuk, C. R.

Millot, G.

J. M. Dudley, Ch. Finot, D. J. Richardson, and G. Millot, "Self-similarity in ultrafast nonlinear optics", Nature Phy. 3, 597 (2007).
[CrossRef]

Moores, J. D.

Morgner, U.

Müller, M.

Murnane, M. M.

A. Rundquist, C. Durfee, Z. Chang, G. Taft, E. Zeek, S. Backus, M. M. Murnane, H. C. Kapteyn, I. Christov, and V. Stoev, "Ultrafast laser and amplifier sources," Appl. Phys. B 65, 161-174 (1997).
[CrossRef]

I. P. Christov, M. M. Murnane, H. C. Kapteyn, J. Zhou, and Ch.-P. Huang, "Fourth-order dispersion limited solitary pulses," Opt. Lett. 1465-1467 (1994).
[CrossRef] [PubMed]

Naumov, S.

V. L. Kalashnikov, E. Podivilov, A. Chernykh, S. Naumov, A. Fernandez, R. Graf, and A. Apolonski, "Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment," New J. Phys. 7, 217 (2005).
[CrossRef]

S. Naumov, A. Fernandez, R. Graf, P. Dombi, F. Krausz, and A. Apolonski, "Approaching the microjoule frontier with femtosecond laser oscillators," New J. Phys. 7, 216 (2005).
[CrossRef]

V. L. Kalashnikov, E. Sorokin, S. Naumov, and I. T. Sorokina, "Spectral poperties of the Kerr-lens mode-locked Cr4+:YAG laser," J. Opt. Soc. Am. B 20, 2084-2092 (2003).
[CrossRef]

Nelson, L. E.

Piché, M.

Podivilov, E.

V. L. Kalashnikov, E. Podivilov, A. Chernykh, and A. Apolonski, "Chirped-pulse oscillators: theory and experiment," Appl. Phys. B 83, 503-510 (2006).
[CrossRef]

E. Podivilov and V. L. Kalashnikov, "Heavily-chirped solitary pulses in te normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation," JETP Letters 82, 524-528 (2005).
[CrossRef]

V. L. Kalashnikov, E. Podivilov, A. Chernykh, S. Naumov, A. Fernandez, R. Graf, and A. Apolonski, "Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment," New J. Phys. 7, 217 (2005).
[CrossRef]

Poppe, A.

A. Fernandez, T. Fuji, A. Poppe, A. Fürbach, F. Krausz, and A. Apolonski, "Chirped-pulse oscillators: a route to highpower femtosecond pulses without external amplification," Opt. Lett. 29, 1366-1368 (2004).
[CrossRef] [PubMed]

A. Apolonski, A. Poppe, G. Tempea, C. Spielmann, T. Udem, R. Holzwarth, T. Hänsch, and F. Krausz, "Controlling the phase evolution of few cycle light pulses," Phys. Rev. Lett. 85, 740-743 (2000).
[CrossRef] [PubMed]

Proctor, B.

Rhee, J.

Y. H. Cha, B. Yoo, J. Rhee, and Ch. Kim, "Numerical analysis of sideband generation in femtosecond solid-state lasers with high-order dispersion," J. Korean Phy. Soc. 44, 859-863 (2004).

Richardson, D. J.

J. M. Dudley, Ch. Finot, D. J. Richardson, and G. Millot, "Self-similarity in ultrafast nonlinear optics", Nature Phy. 3, 597 (2007).
[CrossRef]

Rundquist, A.

A. Rundquist, C. Durfee, Z. Chang, G. Taft, E. Zeek, S. Backus, M. M. Murnane, H. C. Kapteyn, I. Christov, and V. Stoev, "Ultrafast laser and amplifier sources," Appl. Phys. B 65, 161-174 (1997).
[CrossRef]

Santagiustina, M.

Scheuer, V.

Sorokin, E.

V. L. Kalashnikov, E. Sorokin, S. Naumov, and I. T. Sorokina, "Spectral poperties of the Kerr-lens mode-locked Cr4+:YAG laser," J. Opt. Soc. Am. B 20, 2084-2092 (2003).
[CrossRef]

V. L. Kalashnikov, E. Sorokin, and I. T. Sorokina, "Multipulse operation and limits of the Kerr-lens mode locking stability," IEEE J. Quantum Electron. 39, 323-336 (2003).
[CrossRef]

Sorokina, I. T.

V. L. Kalashnikov, E. Sorokin, and I. T. Sorokina, "Multipulse operation and limits of the Kerr-lens mode locking stability," IEEE J. Quantum Electron. 39, 323-336 (2003).
[CrossRef]

V. L. Kalashnikov, E. Sorokin, S. Naumov, and I. T. Sorokina, "Spectral poperties of the Kerr-lens mode-locked Cr4+:YAG laser," J. Opt. Soc. Am. B 20, 2084-2092 (2003).
[CrossRef]

Soto-Crespo, J. M.

J. M. Soto-Crespo, N. N. Akhmediev, V. V. Afanasjev, and S. Wabnitz, "Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion," Phys. Rev. E 55, 4783-4796 (1997).
[CrossRef]

Spatschek, K. H.

Zh. Li, L. Li, H. Tian, G. Zhou, and K. H. Spatschek, "Chirped femtosecond solitonlike laser pulse form with selffrequency shift," Phys. Rev. Lett. 89, 263901 (2002).
[CrossRef] [PubMed]

Spielmann, C.

A. Apolonski, A. Poppe, G. Tempea, C. Spielmann, T. Udem, R. Holzwarth, T. Hänsch, and F. Krausz, "Controlling the phase evolution of few cycle light pulses," Phys. Rev. Lett. 85, 740-743 (2000).
[CrossRef] [PubMed]

Spielmann, Ch.

Ch. Spielmann, P. F. Curley, T. Brabec, and F. Krausz, "Ultrabroadband femtosecond lasers," IEEE J. Quantum Electron. 30, 1100-1114 (1994).
[CrossRef]

Stoev, V.

A. Rundquist, C. Durfee, Z. Chang, G. Taft, E. Zeek, S. Backus, M. M. Murnane, H. C. Kapteyn, I. Christov, and V. Stoev, "Ultrafast laser and amplifier sources," Appl. Phys. B 65, 161-174 (1997).
[CrossRef]

Taft, G.

A. Rundquist, C. Durfee, Z. Chang, G. Taft, E. Zeek, S. Backus, M. M. Murnane, H. C. Kapteyn, I. Christov, and V. Stoev, "Ultrafast laser and amplifier sources," Appl. Phys. B 65, 161-174 (1997).
[CrossRef]

Tang, C. L.

Tempea, G.

A. Apolonski, A. Poppe, G. Tempea, C. Spielmann, T. Udem, R. Holzwarth, T. Hänsch, and F. Krausz, "Controlling the phase evolution of few cycle light pulses," Phys. Rev. Lett. 85, 740-743 (2000).
[CrossRef] [PubMed]

Tian, H.

Zh. Li, L. Li, H. Tian, G. Zhou, and K. H. Spatschek, "Chirped femtosecond solitonlike laser pulse form with selffrequency shift," Phys. Rev. Lett. 89, 263901 (2002).
[CrossRef] [PubMed]

Tucay Zare, A.

Turitsyn, S. K.

Udem, T.

A. Apolonski, A. Poppe, G. Tempea, C. Spielmann, T. Udem, R. Holzwarth, T. Hänsch, and F. Krausz, "Controlling the phase evolution of few cycle light pulses," Phys. Rev. Lett. 85, 740-743 (2000).
[CrossRef] [PubMed]

Wabnitz, S.

J. M. Soto-Crespo, N. N. Akhmediev, V. V. Afanasjev, and S. Wabnitz, "Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion," Phys. Rev. E 55, 4783-4796 (1997).
[CrossRef]

Wai, P. K. A.

P. K. A. Wai, H. H. Chen, and Y. C. Lee, "Radiations by "solitons" at the zero group-dispersion wavelength of singlemode optical fibers," Phys. Rev. A 41, 426-439 (1990).
[CrossRef] [PubMed]

P. K. A. Wai, C. R. Menyuk, H. H. Chen, and Y. C. Lee, "Soliton at the zero-group-dispersion wavelength of a singlemodel fiber," Opt. Lett. 12, 628-630 (1987).
[CrossRef] [PubMed]

Walmsley, I. A.

Westwig, E.

Wise, F.

Wise, F. W.

Wright, E. M.

Yoo, B.

Y. H. Cha, B. Yoo, J. Rhee, and Ch. Kim, "Numerical analysis of sideband generation in femtosecond solid-state lasers with high-order dispersion," J. Korean Phy. Soc. 44, 859-863 (2004).

Zakharov, V. E.

V. E. Zakharov and E. A. Kuznetsov, "Optical solitons and quasisolitons," J. Exp. Theor. Phys. 86, 1035-1046 (1998).
[CrossRef]

Zeek, E.

A. Rundquist, C. Durfee, Z. Chang, G. Taft, E. Zeek, S. Backus, M. M. Murnane, H. C. Kapteyn, I. Christov, and V. Stoev, "Ultrafast laser and amplifier sources," Appl. Phys. B 65, 161-174 (1997).
[CrossRef]

Zhou, G.

Zh. Li, L. Li, H. Tian, G. Zhou, and K. H. Spatschek, "Chirped femtosecond solitonlike laser pulse form with selffrequency shift," Phys. Rev. Lett. 89, 263901 (2002).
[CrossRef] [PubMed]

Zhou, J.

I. P. Christov, M. M. Murnane, H. C. Kapteyn, J. Zhou, and Ch.-P. Huang, "Fourth-order dispersion limited solitary pulses," Opt. Lett. 1465-1467 (1994).
[CrossRef] [PubMed]

Zhu, X.

Appl. Opt. (1)

Appl. Phys. B (2)

A. Rundquist, C. Durfee, Z. Chang, G. Taft, E. Zeek, S. Backus, M. M. Murnane, H. C. Kapteyn, I. Christov, and V. Stoev, "Ultrafast laser and amplifier sources," Appl. Phys. B 65, 161-174 (1997).
[CrossRef]

V. L. Kalashnikov, E. Podivilov, A. Chernykh, and A. Apolonski, "Chirped-pulse oscillators: theory and experiment," Appl. Phys. B 83, 503-510 (2006).
[CrossRef]

IEEE J. Quantum Electron. (2)

V. L. Kalashnikov, E. Sorokin, and I. T. Sorokina, "Multipulse operation and limits of the Kerr-lens mode locking stability," IEEE J. Quantum Electron. 39, 323-336 (2003).
[CrossRef]

Ch. Spielmann, P. F. Curley, T. Brabec, and F. Krausz, "Ultrabroadband femtosecond lasers," IEEE J. Quantum Electron. 30, 1100-1114 (1994).
[CrossRef]

J. Exp. Theor. Phys. (1)

V. E. Zakharov and E. A. Kuznetsov, "Optical solitons and quasisolitons," J. Exp. Theor. Phys. 86, 1035-1046 (1998).
[CrossRef]

J. Korean Phy. Soc. (1)

Y. H. Cha, B. Yoo, J. Rhee, and Ch. Kim, "Numerical analysis of sideband generation in femtosecond solid-state lasers with high-order dispersion," J. Korean Phy. Soc. 44, 859-863 (2004).

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

J. Physical Sociaty of Japan (1)

J. Fujioka and A. Espinosa, "Soliton-like solution of an extended NLS equation existing in resonance with linear dispersive waves," J. Physical Sociaty of Japan 66, 2601-2607 (1997).
[CrossRef]

JETP Letters (1)

E. Podivilov and V. L. Kalashnikov, "Heavily-chirped solitary pulses in te normal dispersion region: new solutions of the cubic-quintic complex Ginzburg-Landau equation," JETP Letters 82, 524-528 (2005).
[CrossRef]

Nature Phy. (1)

J. M. Dudley, Ch. Finot, D. J. Richardson, and G. Millot, "Self-similarity in ultrafast nonlinear optics", Nature Phy. 3, 597 (2007).
[CrossRef]

New J. Phys. (2)

V. L. Kalashnikov, E. Podivilov, A. Chernykh, S. Naumov, A. Fernandez, R. Graf, and A. Apolonski, "Approaching the microjoule frontier with femtosecond laser oscillators: theory and comparison with experiment," New J. Phys. 7, 217 (2005).
[CrossRef]

S. Naumov, A. Fernandez, R. Graf, P. Dombi, F. Krausz, and A. Apolonski, "Approaching the microjoule frontier with femtosecond laser oscillators," New J. Phys. 7, 216 (2005).
[CrossRef]

Opt. Express (2)

Opt. Lett. (17)

A. Fernandez, T. Fuji, A. Poppe, A. Fürbach, F. Krausz, and A. Apolonski, "Chirped-pulse oscillators: a route to highpower femtosecond pulses without external amplification," Opt. Lett. 29, 1366-1368 (2004).
[CrossRef] [PubMed]

M. Piché, J.-F. Cormier, and X. Zhu, "Bright optical soliton in the presence of fourth-order dispersion," Opt. Lett. 21, 845-847 (1996).
[CrossRef] [PubMed]

A. Höök and M. Karlssson, "Ultrashort solitons at the minimum-dispersion wavelength: effect of fourth-order dispersion," Opt. Lett. 18, 1388-1390 (1993).
[CrossRef] [PubMed]

S. H. Cho, F. X. Kärtner, U. Morgner, E. P. Ippen, J. G. Fujimoto, J. E. Cunnighan, and W. H. Knox, "Generation of 90-nJ pulses with a 4-MHz repetition-rate Kerr-lens mode-locked Ti:Al2O3 laser operating with net positive and negative intracavity dispersion," Opt. Lett. 26, 560-562 (2001).
[CrossRef]

A. M. Kowalevicz, A. Tucay Zare, F. X. Kärtner, J. G. Fujimoto, S. Dewald, U. Morgner, V. Scheuer, and G. Angelow, "Generation of 150-nJ pulses from a multiple-pass cavity Kerr-lens mode-locked Ti:Al2O3 oscillator," Opt. Lett. 28, 1597-1599 (2003).
[CrossRef] [PubMed]

I. P. Christov, M. M. Murnane, H. C. Kapteyn, J. Zhou, and Ch.-P. Huang, "Fourth-order dispersion limited solitary pulses," Opt. Lett. 1465-1467 (1994).
[CrossRef] [PubMed]

P. K. A. Wai, C. R. Menyuk, H. H. Chen, and Y. C. Lee, "Soliton at the zero-group-dispersion wavelength of a singlemodel fiber," Opt. Lett. 12, 628-630 (1987).
[CrossRef] [PubMed]

F. W. Wise, I. A. Walmsley, and C. L. Tang, "Simultaneous formation of solitons and diespersive waves in a femtosecond ring dye laser" Opt. Lett. 13, 129-131 (1988).
[CrossRef] [PubMed]

J. N. Elgin, "Soliton propagation in an optical fiber with third-order dispersion," Opt. Lett. 15, 1409-1410 (1992).
[CrossRef]

H. A. Haus, J. D. Moores and L. E. Nelson, "Effect of third-order dispersion on passive mode locking," Opt. Lett. 18, 51-53 (1993).
[CrossRef] [PubMed]

B. Proctor, E. Westwig, and F. Wise, "Characterization of a Kerr-lens mode-locked Ti:sapphire laser with positive group-velocity dispersion," Opt. Lett. 18, 1654-1656 (1993).
[CrossRef] [PubMed]

T. Brabec and S. M. J. Kelly, "Third-order dispersion as limiting factor to mode locking in femtosecond solitary lasers," Opt. Lett. 18, 2002-2004 (1993).
[CrossRef] [PubMed]

M. L. Dennis and I. N. Duling III, "Third-order dispersion in femtosecond fiber lasers," Opt. Lett. 19, 1750-1752 (1994).
[CrossRef] [PubMed]

A. Chernykh and S. K. Turitsyn, "Soliton and collapse regimes of pulse generation in passively mode-locking laser systems," Opt. Lett. 20, 398-400 (1995).
[CrossRef] [PubMed]

M. Santagiustina and E. M. Wright, "Supression of third-order dispersion radiation in solid-state soliton lasers" Opt. Lett. 20, 2267-2269 (1995).
[CrossRef] [PubMed]

J. Herrmann, V. P. Kalosha, and M. Müller, "Highr-order phase dispersions in femtosecond Kerr-lens mode-locked solid-state lasers: sideband generation and pulse splitting," Opt. Lett. 22, 236-238 (1997).
[CrossRef] [PubMed]

S. H. Cho, B. E. Bouma, E. P. Ippen, and J. G. Fujimoto, "Low-repetition-rate high-peak-power Kerr-lens mode-locked TiAl2O3 laser with a multiple-pass cavity," Opt. Lett. 24, 417-419 (1999).
[CrossRef]

Phys. Rev. A (2)

V. L. Kalashnikov and A. Chernykh, "Spectral anomalies and stability of chirped-pulse oscillators," Phys. Rev. A 75, 033820 (2007).
[CrossRef]

P. K. A. Wai, H. H. Chen, and Y. C. Lee, "Radiations by "solitons" at the zero group-dispersion wavelength of singlemode optical fibers," Phys. Rev. A 41, 426-439 (1990).
[CrossRef] [PubMed]

Phys. Rev. E (2)

J. M. Soto-Crespo, N. N. Akhmediev, V. V. Afanasjev, and S. Wabnitz, "Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion," Phys. Rev. E 55, 4783-4796 (1997).
[CrossRef]

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Figures (9)

Fig. 1.
Fig. 1.

Dependence of the stability threshold on the energy and higher-order dispersion.

Fig. 2.
Fig. 2.

The pulse peak power evolution (a), spectral (b) and temporal (c) profiles (at z=104 Lcav ) of the strongly perturbed pulse, E*=288 nJ, β 2=90 fs2, β 3=-300 fs2.

Fig. 3.
Fig. 3.

Pulse spectrum (a), temporal profile (b) and enlarged temporal profile (c) at the stability border (z=104 Lcav ). E=144 nJ, β 4=4000 fs4. The red curve is the GDD profile β 2+6β 4 ω 2 [7].

Fig. 4.
Fig. 4.

Broadest experimental spectrum for the 10.7 MHz Ti:sapphire oscillator (blue curve) and net GDD (black curve). β 2≈55 fs2, β 3≈126 fs3, β 4≈4500 fs4.

Fig. 5.
Fig. 5.

Dependence of the spectral Δ (black curve) and temporal T (red curve) widths on β 4 at the stability threshold. E=144 nJ, z=104 Lcav .

Fig. 6.
Fig. 6.

Spectrum at z=104 Lcav for E=144 nJ, β 2=31 fs2, β 5 =-103 fs5 (black) and 0 fs5 (red). The blue curve is the GDD profile.

Fig. 7.
Fig. 7.

The pulse train (a), generated spectrum (b), and autocorrelation trace (c) realized in the Ti:sapphire chaotic mode-locked oscillator.

Fig. 8.
Fig. 8.

Relative standard deviation of the peak power evolution in dependence on β 4 at the stability threshold. E=144 nJ.

Fig. 9.
Fig. 9.

Relative standard deviation of the peak power evolution as a function of β 2. E=144 nJ, β 4=4000 fs4.

Equations (1)

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A z = [ σ A + α 2 A t 2 k = 2 N i k + 1 β k k A t k ] + [ ( κ i γ ) P κ ζ P 2 ] A .

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