Abstract

A theoretical description of the pulse dynamics in a mode-locked laser including gain dynamics is developed. Relaxation oscillations and frequency pulling are predicted that influence the pulse parameters. Experimental observations of the response of a mode-locked Ti:sapphire laser to an abrupt change in the pump power confirm that the predicted behavior occurs. These results provide a framework for understanding the effects of noise on the spectrum of the laser.

© 2007 Optical Society of America

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  1. D. J. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, "Carrier-envelope control of femtosecond mode-locked lasers and direct optical frequency synthesis," Science 288, 635-639 (2000).
    [CrossRef] [PubMed]
  2. Th. Udem, R. Holzwarth, and T. W.  Hänsch, "Optical frequency metrology," Nature (London) 416, 233-237 (2002).
    [CrossRef]
  3. S. A. Diddams, A. Bartels, T. M. Ramond, C. W. Oates, E. A. Curtis, and J. C. Bergquist, "Design and control of femtosecond lasers for optical clocks and synthesis of low-noise optical and microwave signals," J. Sel. Top. Quantum Electron. 9, 1072-1080 (2003).
    [CrossRef]
  4. M. M. Boyd, T. Zelevinsky, A. D. Ludlow, S. M. Foreman, S. Blatt, T. Ido, and J. Ye, "Optical atomic coherence at the one second time scale," Science 314, 1430-1433 (2006).
    [CrossRef] [PubMed]
  5. E. Goulielmakis, M. Uiberacker, R. Kienberger, A. Baltuska, V. Yakovlev, A. Scrinzi, Th. Westerwalbesloh, U. Kleineberg, U. Heinzmann, M. Drescher, and F. Krausz, "Direct measurement of light waves," Science 305, 1267-1269 (2004).
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    [CrossRef]
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  26. R. Paschotta, "Noise of mode-locked lasers (Part II): Timing jitter and other fluctuations," Appl. Phys. B 79, 163-173 (2004).
    [CrossRef]
  27. M. E. Grein, H. A. Haus, Y. Chen, and E. P. Ippen, "Quantum-limited timing jitter in actively mode-locked lasers," IEEE J. Quantum Electron. 40, 1458-1470 (2004).
    [CrossRef]
  28. H. A. Haus, K. Tamura, L. E. Nelson, and E. P. Ippen, "Stretched-pulse additive pulse mode-locking in fiber ring lasers: Theory and experiment," IEEE J. Quantum Electron. 31, 591-598 (1995).
    [CrossRef]
  29. N. J. Smith, N. J. Doran, W. Forysiak, and F. M. Knox, "Soliton transmission using periodic dispersion compensation," J. Lightwave Technol. 15, 1808-1822 (1997).
    [CrossRef]
  30. M. J. Ablowitz and G. Biondini, "Multiscale pulse dynamics in communication systems with strong dispersion management," Opt. Lett. 23, 1668-1670 (1998).
    [CrossRef]
  31. I. Gabitov and S. K. Turitsyn, "Breathing solitons in optical fiber links," JETP Lett. 63, 861-866 (1996) [Pis’ma Zh. Eksp. Teor. Fiz. 63, 814-819 (1996)].
    [CrossRef]
  32. H. A. Haus and M. N. Islam, "Theory of the soliton laser," IEEE J. Quantum Electron. 21, 1172-1188 (1985).
    [CrossRef]
  33. N. J. Smith, N. J. Doran, F. M. Knox, and W. Forysiak, "Energy-scaling characteristics of solitons in strongly dispersion-managed fibers," Opt. Lett. 21, 1981-1983 (1996).
    [CrossRef] [PubMed]
  34. T. Yu, E. A. Golovchenko, A. N. Pilipetskii, and C. R. Menyuk, "Dispersion-managed soliton interactions in optical fibers," Opt. Lett. 22, 793-795 (1997).
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    [CrossRef]

2006 (3)

2005 (1)

Q. Quraishi, S. T. Cundiff, B. Ilan, andM. J. Ablowitz, "Dynamics of nonlinear and dispersion managed solitons," Phys. Rev. Lett. 94, 243904 (2005).
[CrossRef]

2004 (6)

R. Paschotta, "Noise of mode-locked lasers (Part I): Numerical model," Appl. Phys. B 79, 153-162 (2004).
[CrossRef]

R. Paschotta, "Noise of mode-locked lasers (Part II): Timing jitter and other fluctuations," Appl. Phys. B 79, 163-173 (2004).
[CrossRef]

M. E. Grein, H. A. Haus, Y. Chen, and E. P. Ippen, "Quantum-limited timing jitter in actively mode-locked lasers," IEEE J. Quantum Electron. 40, 1458-1470 (2004).
[CrossRef]

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

Y. Takushima, H. Sotobayashi, M. E. Grein, E. P. Ippen, and H. A. Haus, "Linewidth of mode combs of passively and actively mode-locked semiconductor laser diodes," Proc. SPIE 5595, 213-227 (2004).
[CrossRef]

E. Goulielmakis, M. Uiberacker, R. Kienberger, A. Baltuska, V. Yakovlev, A. Scrinzi, Th. Westerwalbesloh, U. Kleineberg, U. Heinzmann, M. Drescher, and F. Krausz, "Direct measurement of light waves," Science 305, 1267-1269 (2004).
[CrossRef] [PubMed]

2003 (2)

S. A. Diddams, A. Bartels, T. M. Ramond, C. W. Oates, E. A. Curtis, and J. C. Bergquist, "Design and control of femtosecond lasers for optical clocks and synthesis of low-noise optical and microwave signals," J. Sel. Top. Quantum Electron. 9, 1072-1080 (2003).
[CrossRef]

K. W. Holman, R. J. Jones, A. Marian, S. T. Cundiff, and J. Ye, "Detailed studies and control of intensityrelated dynamics of femtosecond frequency combs from mode-Locked Ti:sapphire lasers," J. Sel. Top. Quantum Electron. 9, 1018-1024 (2003).
[CrossRef]

2002 (2)

Th. Udem, R. Holzwarth, and T. W.  Hänsch, "Optical frequency metrology," Nature (London) 416, 233-237 (2002).
[CrossRef]

S. T. Cundiff, J. M. Soto-Crespo, and N. Akhmediev, "Experimental evidence for soliton explosions," Phys. Rev. Lett. 88, 073903 (2002).
[CrossRef] [PubMed]

2001 (3)

L. A. Jiang, M. E. Grein, H. A. Haus, and E. P. Ippen, "Noise of mode-locked semiconductor lasers," IEEE J. Sel. Top. Quantum Electron. 7, 159-167 (2001).
[CrossRef]

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

A. Poppe, R. Holzwarth, A. Apolonski, G. Tempea, Ch. Spielmann, T.W. H¨ansch, and F. Krausz, "Few-cycle optical waveform synthesis," Appl. Phys. B 72, 373-376 (2001).
[CrossRef]

2000 (1)

D. J. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, "Carrier-envelope control of femtosecond mode-locked lasers and direct optical frequency synthesis," Science 288, 635-639 (2000).
[CrossRef] [PubMed]

1999 (1)

C. R. Menyuk, "Application of multiple-scale-length methods to the study of optical fiber transmission," J. Eng. Math. 36, 113-136 (1999).
[CrossRef]

1998 (1)

1997 (3)

1996 (3)

1995 (2)

H. A. Haus, K. Tamura, L. E. Nelson, and E. P. Ippen, "Stretched-pulse additive pulse mode-locking in fiber ring lasers: Theory and experiment," IEEE J. Quantum Electron. 31, 591-598 (1995).
[CrossRef]

T. Georges, "Perturbation theory for the assessment of soliton transmission control," J. Opt. Fiber Technol. 1, 97-116 (1995).
[CrossRef]

1993 (1)

H. A. Haus and A. Mecozzi, "Noise of mode-locked lasers," IEEE J. Quantum Electron. 29, 983-995 (1993).
[CrossRef]

1991 (1)

1986 (1)

D. von der Linde, "Characterization of the noise in continuously operating mode-locked lasers," Appl. Phys. B 39, 201-217 (1986).
[CrossRef]

1958 (1)

A. L. Schawlow and C. H. Townes, "Infrared and optical masers," Phys. Rev. 112, 1940-1949 (1958).
[CrossRef]

Ablowitz, M. J.

Akhmediev, N.

S. T. Cundiff, J. M. Soto-Crespo, and N. Akhmediev, "Experimental evidence for soliton explosions," Phys. Rev. Lett. 88, 073903 (2002).
[CrossRef] [PubMed]

Apolonski, A.

A. Poppe, R. Holzwarth, A. Apolonski, G. Tempea, Ch. Spielmann, T.W. H¨ansch, and F. Krausz, "Few-cycle optical waveform synthesis," Appl. Phys. B 72, 373-376 (2001).
[CrossRef]

Baltuska, A.

E. Goulielmakis, M. Uiberacker, R. Kienberger, A. Baltuska, V. Yakovlev, A. Scrinzi, Th. Westerwalbesloh, U. Kleineberg, U. Heinzmann, M. Drescher, and F. Krausz, "Direct measurement of light waves," Science 305, 1267-1269 (2004).
[CrossRef] [PubMed]

Bartels, A.

S. A. Diddams, A. Bartels, T. M. Ramond, C. W. Oates, E. A. Curtis, and J. C. Bergquist, "Design and control of femtosecond lasers for optical clocks and synthesis of low-noise optical and microwave signals," J. Sel. Top. Quantum Electron. 9, 1072-1080 (2003).
[CrossRef]

Bergquist, J. C.

S. A. Diddams, A. Bartels, T. M. Ramond, C. W. Oates, E. A. Curtis, and J. C. Bergquist, "Design and control of femtosecond lasers for optical clocks and synthesis of low-noise optical and microwave signals," J. Sel. Top. Quantum Electron. 9, 1072-1080 (2003).
[CrossRef]

Biondini, G.

Blatt, S.

M. M. Boyd, T. Zelevinsky, A. D. Ludlow, S. M. Foreman, S. Blatt, T. Ido, and J. Ye, "Optical atomic coherence at the one second time scale," Science 314, 1430-1433 (2006).
[CrossRef] [PubMed]

Boyd, M. M.

M. M. Boyd, T. Zelevinsky, A. D. Ludlow, S. M. Foreman, S. Blatt, T. Ido, and J. Ye, "Optical atomic coherence at the one second time scale," Science 314, 1430-1433 (2006).
[CrossRef] [PubMed]

Brabec, T.

Chen, Y.

M. E. Grein, H. A. Haus, Y. Chen, and E. P. Ippen, "Quantum-limited timing jitter in actively mode-locked lasers," IEEE J. Quantum Electron. 40, 1458-1470 (2004).
[CrossRef]

Chen, Y.-C.

Cundiff, S. T.

Q. Quraishi, S. T. Cundiff, B. Ilan, andM. J. Ablowitz, "Dynamics of nonlinear and dispersion managed solitons," Phys. Rev. Lett. 94, 243904 (2005).
[CrossRef]

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

K. W. Holman, R. J. Jones, A. Marian, S. T. Cundiff, and J. Ye, "Detailed studies and control of intensityrelated dynamics of femtosecond frequency combs from mode-Locked Ti:sapphire lasers," J. Sel. Top. Quantum Electron. 9, 1018-1024 (2003).
[CrossRef]

S. T. Cundiff, J. M. Soto-Crespo, and N. Akhmediev, "Experimental evidence for soliton explosions," Phys. Rev. Lett. 88, 073903 (2002).
[CrossRef] [PubMed]

D. J. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, "Carrier-envelope control of femtosecond mode-locked lasers and direct optical frequency synthesis," Science 288, 635-639 (2000).
[CrossRef] [PubMed]

Curtis, E. A.

S. A. Diddams, A. Bartels, T. M. Ramond, C. W. Oates, E. A. Curtis, and J. C. Bergquist, "Design and control of femtosecond lasers for optical clocks and synthesis of low-noise optical and microwave signals," J. Sel. Top. Quantum Electron. 9, 1072-1080 (2003).
[CrossRef]

Diddams, S. A.

S. A. Diddams, A. Bartels, T. M. Ramond, C. W. Oates, E. A. Curtis, and J. C. Bergquist, "Design and control of femtosecond lasers for optical clocks and synthesis of low-noise optical and microwave signals," J. Sel. Top. Quantum Electron. 9, 1072-1080 (2003).
[CrossRef]

D. J. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, "Carrier-envelope control of femtosecond mode-locked lasers and direct optical frequency synthesis," Science 288, 635-639 (2000).
[CrossRef] [PubMed]

Doran, N. J.

N. J. Smith, N. J. Doran, W. Forysiak, and F. M. Knox, "Soliton transmission using periodic dispersion compensation," J. Lightwave Technol. 15, 1808-1822 (1997).
[CrossRef]

N. J. Smith, N. J. Doran, F. M. Knox, and W. Forysiak, "Energy-scaling characteristics of solitons in strongly dispersion-managed fibers," Opt. Lett. 21, 1981-1983 (1996).
[CrossRef] [PubMed]

Drescher, M.

E. Goulielmakis, M. Uiberacker, R. Kienberger, A. Baltuska, V. Yakovlev, A. Scrinzi, Th. Westerwalbesloh, U. Kleineberg, U. Heinzmann, M. Drescher, and F. Krausz, "Direct measurement of light waves," Science 305, 1267-1269 (2004).
[CrossRef] [PubMed]

Foreman, S. M.

M. M. Boyd, T. Zelevinsky, A. D. Ludlow, S. M. Foreman, S. Blatt, T. Ido, and J. Ye, "Optical atomic coherence at the one second time scale," Science 314, 1430-1433 (2006).
[CrossRef] [PubMed]

Forysiak, W.

N. J. Smith, N. J. Doran, W. Forysiak, and F. M. Knox, "Soliton transmission using periodic dispersion compensation," J. Lightwave Technol. 15, 1808-1822 (1997).
[CrossRef]

N. J. Smith, N. J. Doran, F. M. Knox, and W. Forysiak, "Energy-scaling characteristics of solitons in strongly dispersion-managed fibers," Opt. Lett. 21, 1981-1983 (1996).
[CrossRef] [PubMed]

Gabitov, I.

I. Gabitov and S. K. Turitsyn, "Breathing solitons in optical fiber links," JETP Lett. 63, 861-866 (1996) [Pis’ma Zh. Eksp. Teor. Fiz. 63, 814-819 (1996)].
[CrossRef]

Georges, T.

T. Georges, "Perturbation theory for the assessment of soliton transmission control," J. Opt. Fiber Technol. 1, 97-116 (1995).
[CrossRef]

Golovchenko, E. A.

Goulielmakis, E.

E. Goulielmakis, M. Uiberacker, R. Kienberger, A. Baltuska, V. Yakovlev, A. Scrinzi, Th. Westerwalbesloh, U. Kleineberg, U. Heinzmann, M. Drescher, and F. Krausz, "Direct measurement of light waves," Science 305, 1267-1269 (2004).
[CrossRef] [PubMed]

Grein, M. E.

Y. Takushima, H. Sotobayashi, M. E. Grein, E. P. Ippen, and H. A. Haus, "Linewidth of mode combs of passively and actively mode-locked semiconductor laser diodes," Proc. SPIE 5595, 213-227 (2004).
[CrossRef]

M. E. Grein, H. A. Haus, Y. Chen, and E. P. Ippen, "Quantum-limited timing jitter in actively mode-locked lasers," IEEE J. Quantum Electron. 40, 1458-1470 (2004).
[CrossRef]

L. A. Jiang, M. E. Grein, H. A. Haus, and E. P. Ippen, "Noise of mode-locked semiconductor lasers," IEEE J. Sel. Top. Quantum Electron. 7, 159-167 (2001).
[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, "Carrier-envelope control of femtosecond mode-locked lasers and direct optical frequency synthesis," Science 288, 635-639 (2000).
[CrossRef] [PubMed]

Hänsch, T. W.

Th. Udem, R. Holzwarth, and T. W.  Hänsch, "Optical frequency metrology," Nature (London) 416, 233-237 (2002).
[CrossRef]

Hänsch, T.W.

Haus, H. A.

M. E. Grein, H. A. Haus, Y. Chen, and E. P. Ippen, "Quantum-limited timing jitter in actively mode-locked lasers," IEEE J. Quantum Electron. 40, 1458-1470 (2004).
[CrossRef]

Y. Takushima, H. Sotobayashi, M. E. Grein, E. P. Ippen, and H. A. Haus, "Linewidth of mode combs of passively and actively mode-locked semiconductor laser diodes," Proc. SPIE 5595, 213-227 (2004).
[CrossRef]

L. A. Jiang, M. E. Grein, H. A. Haus, and E. P. Ippen, "Noise of mode-locked semiconductor lasers," IEEE J. Sel. Top. Quantum Electron. 7, 159-167 (2001).
[CrossRef]

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

H. A. Haus, K. Tamura, L. E. Nelson, and E. P. Ippen, "Stretched-pulse additive pulse mode-locking in fiber ring lasers: Theory and experiment," IEEE J. Quantum Electron. 31, 591-598 (1995).
[CrossRef]

H. A. Haus and A. Mecozzi, "Noise of mode-locked lasers," IEEE J. Quantum Electron. 29, 983-995 (1993).
[CrossRef]

H. A. Haus, "Quantum noise in a solitonlike repeater," J. Opt. Soc. Am. B 8, 1122-1126 (1991).
[CrossRef]

Heinzmann, U.

E. Goulielmakis, M. Uiberacker, R. Kienberger, A. Baltuska, V. Yakovlev, A. Scrinzi, Th. Westerwalbesloh, U. Kleineberg, U. Heinzmann, M. Drescher, and F. Krausz, "Direct measurement of light waves," Science 305, 1267-1269 (2004).
[CrossRef] [PubMed]

Holman, K. W.

K. W. Holman, R. J. Jones, A. Marian, S. T. Cundiff, and J. Ye, "Detailed studies and control of intensityrelated dynamics of femtosecond frequency combs from mode-Locked Ti:sapphire lasers," J. Sel. Top. Quantum Electron. 9, 1018-1024 (2003).
[CrossRef]

Holzwarth, R.

Th. Udem, R. Holzwarth, and T. W.  Hänsch, "Optical frequency metrology," Nature (London) 416, 233-237 (2002).
[CrossRef]

A. Poppe, R. Holzwarth, A. Apolonski, G. Tempea, Ch. Spielmann, T.W. H¨ansch, and F. Krausz, "Few-cycle optical waveform synthesis," Appl. Phys. B 72, 373-376 (2001).
[CrossRef]

Hsu, S.-H.

Ido, T.

M. M. Boyd, T. Zelevinsky, A. D. Ludlow, S. M. Foreman, S. Blatt, T. Ido, and J. Ye, "Optical atomic coherence at the one second time scale," Science 314, 1430-1433 (2006).
[CrossRef] [PubMed]

Ilan, B.

Q. Quraishi, S. T. Cundiff, B. Ilan, andM. J. Ablowitz, "Dynamics of nonlinear and dispersion managed solitons," Phys. Rev. Lett. 94, 243904 (2005).
[CrossRef]

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

Ippen, E. P.

Y. Takushima, H. Sotobayashi, M. E. Grein, E. P. Ippen, and H. A. Haus, "Linewidth of mode combs of passively and actively mode-locked semiconductor laser diodes," Proc. SPIE 5595, 213-227 (2004).
[CrossRef]

M. E. Grein, H. A. Haus, Y. Chen, and E. P. Ippen, "Quantum-limited timing jitter in actively mode-locked lasers," IEEE J. Quantum Electron. 40, 1458-1470 (2004).
[CrossRef]

L. A. Jiang, M. E. Grein, H. A. Haus, and E. P. Ippen, "Noise of mode-locked semiconductor lasers," IEEE J. Sel. Top. Quantum Electron. 7, 159-167 (2001).
[CrossRef]

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

H. A. Haus, K. Tamura, L. E. Nelson, and E. P. Ippen, "Stretched-pulse additive pulse mode-locking in fiber ring lasers: Theory and experiment," IEEE J. Quantum Electron. 31, 591-598 (1995).
[CrossRef]

Jiang, L. A.

L. A. Jiang, M. E. Grein, H. A. Haus, and E. P. Ippen, "Noise of mode-locked semiconductor lasers," IEEE J. Sel. Top. Quantum Electron. 7, 159-167 (2001).
[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, "Carrier-envelope control of femtosecond mode-locked lasers and direct optical frequency synthesis," Science 288, 635-639 (2000).
[CrossRef] [PubMed]

Jones, R. J.

K. W. Holman, R. J. Jones, A. Marian, S. T. Cundiff, and J. Ye, "Detailed studies and control of intensityrelated dynamics of femtosecond frequency combs from mode-Locked Ti:sapphire lasers," J. Sel. Top. Quantum Electron. 9, 1018-1024 (2003).
[CrossRef]

Juang, D.-G.

Kienberger, R.

E. Goulielmakis, M. Uiberacker, R. Kienberger, A. Baltuska, V. Yakovlev, A. Scrinzi, Th. Westerwalbesloh, U. Kleineberg, U. Heinzmann, M. Drescher, and F. Krausz, "Direct measurement of light waves," Science 305, 1267-1269 (2004).
[CrossRef] [PubMed]

Kleineberg, U.

E. Goulielmakis, M. Uiberacker, R. Kienberger, A. Baltuska, V. Yakovlev, A. Scrinzi, Th. Westerwalbesloh, U. Kleineberg, U. Heinzmann, M. Drescher, and F. Krausz, "Direct measurement of light waves," Science 305, 1267-1269 (2004).
[CrossRef] [PubMed]

Knox, F. M.

N. J. Smith, N. J. Doran, W. Forysiak, and F. M. Knox, "Soliton transmission using periodic dispersion compensation," J. Lightwave Technol. 15, 1808-1822 (1997).
[CrossRef]

N. J. Smith, N. J. Doran, F. M. Knox, and W. Forysiak, "Energy-scaling characteristics of solitons in strongly dispersion-managed fibers," Opt. Lett. 21, 1981-1983 (1996).
[CrossRef] [PubMed]

Krausz, F.

E. Goulielmakis, M. Uiberacker, R. Kienberger, A. Baltuska, V. Yakovlev, A. Scrinzi, Th. Westerwalbesloh, U. Kleineberg, U. Heinzmann, M. Drescher, and F. Krausz, "Direct measurement of light waves," Science 305, 1267-1269 (2004).
[CrossRef] [PubMed]

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, 2008-2010 (1996).
[CrossRef] [PubMed]

Lin, K.-H.

Ludlow, A. D.

M. M. Boyd, T. Zelevinsky, A. D. Ludlow, S. M. Foreman, S. Blatt, T. Ido, and J. Ye, "Optical atomic coherence at the one second time scale," Science 314, 1430-1433 (2006).
[CrossRef] [PubMed]

Marian, A.

K. W. Holman, R. J. Jones, A. Marian, S. T. Cundiff, and J. Ye, "Detailed studies and control of intensityrelated dynamics of femtosecond frequency combs from mode-Locked Ti:sapphire lasers," J. Sel. Top. Quantum Electron. 9, 1018-1024 (2003).
[CrossRef]

Marks, B. S.

Matos, L.

Mecozzi, A.

H. A. Haus and A. Mecozzi, "Noise of mode-locked lasers," IEEE J. Quantum Electron. 29, 983-995 (1993).
[CrossRef]

Menyuk, C. R.

Nelson, L. E.

H. A. Haus, K. Tamura, L. E. Nelson, and E. P. Ippen, "Stretched-pulse additive pulse mode-locking in fiber ring lasers: Theory and experiment," IEEE J. Quantum Electron. 31, 591-598 (1995).
[CrossRef]

Oates, C. W.

S. A. Diddams, A. Bartels, T. M. Ramond, C. W. Oates, E. A. Curtis, and J. C. Bergquist, "Design and control of femtosecond lasers for optical clocks and synthesis of low-noise optical and microwave signals," J. Sel. Top. Quantum Electron. 9, 1072-1080 (2003).
[CrossRef]

Paschotta, R.

R. Paschotta, "Noise of mode-locked lasers (Part I): Numerical model," Appl. Phys. B 79, 153-162 (2004).
[CrossRef]

R. Paschotta, "Noise of mode-locked lasers (Part II): Timing jitter and other fluctuations," Appl. Phys. B 79, 163-173 (2004).
[CrossRef]

Pilipetskii, A. N.

Poppe, A.

A. Poppe, R. Holzwarth, A. Apolonski, G. Tempea, Ch. Spielmann, T.W. H¨ansch, and F. Krausz, "Few-cycle optical waveform synthesis," Appl. Phys. B 72, 373-376 (2001).
[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, 2008-2010 (1996).
[CrossRef] [PubMed]

Quraishi, Q.

Q. Quraishi, S. T. Cundiff, B. Ilan, andM. J. Ablowitz, "Dynamics of nonlinear and dispersion managed solitons," Phys. Rev. Lett. 94, 243904 (2005).
[CrossRef]

Ramond, T. M.

S. A. Diddams, A. Bartels, T. M. Ramond, C. W. Oates, E. A. Curtis, and J. C. Bergquist, "Design and control of femtosecond lasers for optical clocks and synthesis of low-noise optical and microwave signals," J. Sel. Top. Quantum Electron. 9, 1072-1080 (2003).
[CrossRef]

Ranka, J. K.

D. J. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, "Carrier-envelope control of femtosecond mode-locked lasers and direct optical frequency synthesis," Science 288, 635-639 (2000).
[CrossRef] [PubMed]

Schawlow, A. L.

A. L. Schawlow and C. H. Townes, "Infrared and optical masers," Phys. Rev. 112, 1940-1949 (1958).
[CrossRef]

Scrinzi, A.

E. Goulielmakis, M. Uiberacker, R. Kienberger, A. Baltuska, V. Yakovlev, A. Scrinzi, Th. Westerwalbesloh, U. Kleineberg, U. Heinzmann, M. Drescher, and F. Krausz, "Direct measurement of light waves," Science 305, 1267-1269 (2004).
[CrossRef] [PubMed]

Smith, N. J.

N. J. Smith, N. J. Doran, W. Forysiak, and F. M. Knox, "Soliton transmission using periodic dispersion compensation," J. Lightwave Technol. 15, 1808-1822 (1997).
[CrossRef]

N. J. Smith, N. J. Doran, F. M. Knox, and W. Forysiak, "Energy-scaling characteristics of solitons in strongly dispersion-managed fibers," Opt. Lett. 21, 1981-1983 (1996).
[CrossRef] [PubMed]

Sotobayashi, H.

Y. Takushima, H. Sotobayashi, M. E. Grein, E. P. Ippen, and H. A. Haus, "Linewidth of mode combs of passively and actively mode-locked semiconductor laser diodes," Proc. SPIE 5595, 213-227 (2004).
[CrossRef]

Soto-Crespo, J. M.

S. T. Cundiff, J. M. Soto-Crespo, and N. Akhmediev, "Experimental evidence for soliton explosions," Phys. Rev. Lett. 88, 073903 (2002).
[CrossRef] [PubMed]

Spielmann, Ch.

A. Poppe, R. Holzwarth, A. Apolonski, G. Tempea, Ch. Spielmann, T.W. H¨ansch, and F. Krausz, "Few-cycle optical waveform synthesis," Appl. Phys. B 72, 373-376 (2001).
[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, 2008-2010 (1996).
[CrossRef] [PubMed]

Stentz, A.

D. J. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, "Carrier-envelope control of femtosecond mode-locked lasers and direct optical frequency synthesis," Science 288, 635-639 (2000).
[CrossRef] [PubMed]

Takushima, Y.

Y. Takushima, H. Sotobayashi, M. E. Grein, E. P. Ippen, and H. A. Haus, "Linewidth of mode combs of passively and actively mode-locked semiconductor laser diodes," Proc. SPIE 5595, 213-227 (2004).
[CrossRef]

Tamura, K.

H. A. Haus, K. Tamura, L. E. Nelson, and E. P. Ippen, "Stretched-pulse additive pulse mode-locking in fiber ring lasers: Theory and experiment," IEEE J. Quantum Electron. 31, 591-598 (1995).
[CrossRef]

Tempea, G.

A. Poppe, R. Holzwarth, A. Apolonski, G. Tempea, Ch. Spielmann, T.W. H¨ansch, and F. Krausz, "Few-cycle optical waveform synthesis," Appl. Phys. B 72, 373-376 (2001).
[CrossRef]

Townes, C. H.

A. L. Schawlow and C. H. Townes, "Infrared and optical masers," Phys. Rev. 112, 1940-1949 (1958).
[CrossRef]

Turitsyn, S. K.

I. Gabitov and S. K. Turitsyn, "Breathing solitons in optical fiber links," JETP Lett. 63, 861-866 (1996) [Pis’ma Zh. Eksp. Teor. Fiz. 63, 814-819 (1996)].
[CrossRef]

Udem, Th.

Th. Udem, R. Holzwarth, and T. W.  Hänsch, "Optical frequency metrology," Nature (London) 416, 233-237 (2002).
[CrossRef]

Uiberacker, M.

E. Goulielmakis, M. Uiberacker, R. Kienberger, A. Baltuska, V. Yakovlev, A. Scrinzi, Th. Westerwalbesloh, U. Kleineberg, U. Heinzmann, M. Drescher, and F. Krausz, "Direct measurement of light waves," Science 305, 1267-1269 (2004).
[CrossRef] [PubMed]

von der Linde, D.

D. von der Linde, "Characterization of the noise in continuously operating mode-locked lasers," Appl. Phys. B 39, 201-217 (1986).
[CrossRef]

Westerwalbesloh, Th.

E. Goulielmakis, M. Uiberacker, R. Kienberger, A. Baltuska, V. Yakovlev, A. Scrinzi, Th. Westerwalbesloh, U. Kleineberg, U. Heinzmann, M. Drescher, and F. Krausz, "Direct measurement of light waves," Science 305, 1267-1269 (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, "Carrier-envelope control of femtosecond mode-locked lasers and direct optical frequency synthesis," Science 288, 635-639 (2000).
[CrossRef] [PubMed]

Xu, L.

Yakovlev, V.

E. Goulielmakis, M. Uiberacker, R. Kienberger, A. Baltuska, V. Yakovlev, A. Scrinzi, Th. Westerwalbesloh, U. Kleineberg, U. Heinzmann, M. Drescher, and F. Krausz, "Direct measurement of light waves," Science 305, 1267-1269 (2004).
[CrossRef] [PubMed]

Ye, J.

M. M. Boyd, T. Zelevinsky, A. D. Ludlow, S. M. Foreman, S. Blatt, T. Ido, and J. Ye, "Optical atomic coherence at the one second time scale," Science 314, 1430-1433 (2006).
[CrossRef] [PubMed]

K. W. Holman, R. J. Jones, A. Marian, S. T. Cundiff, and J. Ye, "Detailed studies and control of intensityrelated dynamics of femtosecond frequency combs from mode-Locked Ti:sapphire lasers," J. Sel. Top. Quantum Electron. 9, 1018-1024 (2003).
[CrossRef]

Yu, T.

Zelevinsky, T.

M. M. Boyd, T. Zelevinsky, A. D. Ludlow, S. M. Foreman, S. Blatt, T. Ido, and J. Ye, "Optical atomic coherence at the one second time scale," Science 314, 1430-1433 (2006).
[CrossRef] [PubMed]

Appl. Phys. B (4)

A. Poppe, R. Holzwarth, A. Apolonski, G. Tempea, Ch. Spielmann, T.W. H¨ansch, and F. Krausz, "Few-cycle optical waveform synthesis," Appl. Phys. B 72, 373-376 (2001).
[CrossRef]

D. von der Linde, "Characterization of the noise in continuously operating mode-locked lasers," Appl. Phys. B 39, 201-217 (1986).
[CrossRef]

R. Paschotta, "Noise of mode-locked lasers (Part I): Numerical model," Appl. Phys. B 79, 153-162 (2004).
[CrossRef]

R. Paschotta, "Noise of mode-locked lasers (Part II): Timing jitter and other fluctuations," Appl. Phys. B 79, 163-173 (2004).
[CrossRef]

IEEE J. Quantum Electron. (3)

M. E. Grein, H. A. Haus, Y. Chen, and E. P. Ippen, "Quantum-limited timing jitter in actively mode-locked lasers," IEEE J. Quantum Electron. 40, 1458-1470 (2004).
[CrossRef]

H. A. Haus, K. Tamura, L. E. Nelson, and E. P. Ippen, "Stretched-pulse additive pulse mode-locking in fiber ring lasers: Theory and experiment," IEEE J. Quantum Electron. 31, 591-598 (1995).
[CrossRef]

H. A. Haus and A. Mecozzi, "Noise of mode-locked lasers," IEEE J. Quantum Electron. 29, 983-995 (1993).
[CrossRef]

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

L. A. Jiang, M. E. Grein, H. A. Haus, and E. P. Ippen, "Noise of mode-locked semiconductor lasers," IEEE J. Sel. Top. Quantum Electron. 7, 159-167 (2001).
[CrossRef]

J. Eng. Math. (1)

C. R. Menyuk, "Application of multiple-scale-length methods to the study of optical fiber transmission," J. Eng. Math. 36, 113-136 (1999).
[CrossRef]

J. Lightwave Technol. (2)

C. R. Menyuk and B. S. Marks, "Interaction of polarization mode dispersion and nonlinearity in optical fiber transmission systems," J. Lightwave Technol. 24, 2806-2826 (2006).
[CrossRef]

N. J. Smith, N. J. Doran, W. Forysiak, and F. M. Knox, "Soliton transmission using periodic dispersion compensation," J. Lightwave Technol. 15, 1808-1822 (1997).
[CrossRef]

J. Opt. Fiber Technol. (1)

T. Georges, "Perturbation theory for the assessment of soliton transmission control," J. Opt. Fiber Technol. 1, 97-116 (1995).
[CrossRef]

J. Opt. Soc. Am. B (2)

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 intensityrelated dynamics of femtosecond frequency combs from mode-Locked Ti:sapphire lasers," J. Sel. Top. Quantum Electron. 9, 1018-1024 (2003).
[CrossRef]

S. A. Diddams, A. Bartels, T. M. Ramond, C. W. Oates, E. A. Curtis, and J. C. Bergquist, "Design and control of femtosecond lasers for optical clocks and synthesis of low-noise optical and microwave signals," J. Sel. Top. Quantum Electron. 9, 1072-1080 (2003).
[CrossRef]

JETP Lett. (1)

I. Gabitov and S. K. Turitsyn, "Breathing solitons in optical fiber links," JETP Lett. 63, 861-866 (1996) [Pis’ma Zh. Eksp. Teor. Fiz. 63, 814-819 (1996)].
[CrossRef]

Nature (London) (1)

Th. Udem, R. Holzwarth, and T. W.  Hänsch, "Optical frequency metrology," Nature (London) 416, 233-237 (2002).
[CrossRef]

Opt. Express (1)

Opt. Lett. (6)

Phys. Rev. (1)

A. L. Schawlow and C. H. Townes, "Infrared and optical masers," Phys. Rev. 112, 1940-1949 (1958).
[CrossRef]

Phys. Rev. Lett. (2)

Q. Quraishi, S. T. Cundiff, B. Ilan, andM. J. Ablowitz, "Dynamics of nonlinear and dispersion managed solitons," Phys. Rev. Lett. 94, 243904 (2005).
[CrossRef]

S. T. Cundiff, J. M. Soto-Crespo, and N. Akhmediev, "Experimental evidence for soliton explosions," Phys. Rev. Lett. 88, 073903 (2002).
[CrossRef] [PubMed]

Proc. SPIE (1)

Y. Takushima, H. Sotobayashi, M. E. Grein, E. P. Ippen, and H. A. Haus, "Linewidth of mode combs of passively and actively mode-locked semiconductor laser diodes," Proc. SPIE 5595, 213-227 (2004).
[CrossRef]

Science (3)

D. J. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, "Carrier-envelope control of femtosecond mode-locked lasers and direct optical frequency synthesis," Science 288, 635-639 (2000).
[CrossRef] [PubMed]

M. M. Boyd, T. Zelevinsky, A. D. Ludlow, S. M. Foreman, S. Blatt, T. Ido, and J. Ye, "Optical atomic coherence at the one second time scale," Science 314, 1430-1433 (2006).
[CrossRef] [PubMed]

E. Goulielmakis, M. Uiberacker, R. Kienberger, A. Baltuska, V. Yakovlev, A. Scrinzi, Th. Westerwalbesloh, U. Kleineberg, U. Heinzmann, M. Drescher, and F. Krausz, "Direct measurement of light waves," Science 305, 1267-1269 (2004).
[CrossRef] [PubMed]

Other (3)

F. X. K¨artner, U. Morgner, T. Schibli, R. Ell, H. A. Haus, J. G. Fujimoto, and E. P. Ippen, "Few-cycle pulses directly from a laser," in Few-cycle Laser Pulse Generation and its Applications, F. X. K¨artner, ed., Topics in Applied Physics, vol. 95 (Springer, Berlin, Germany, 2004), pp. 73-135.

W. Koechner and M. Bass, Solid-state lasers (Springer, New York, NY, 2003), pp. 72-75.

H. A. Haus and M. N. Islam, "Theory of the soliton laser," IEEE J. Quantum Electron. 21, 1172-1188 (1985).
[CrossRef]

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Figures (2)

Fig. 1.
Fig. 1.

Experimental data showing the (a) laser intensity and fluorescence and (b) central frequency as a function of time following a sudden drop in the pump power. Curves are for pump powers of 5.1 W (black), 5.3 W (red) and 5.5 W (blue). The curves (a) are normalized to the value prior to the step in pump power. In (a) the pump intensity is also shown (dashed line).

Fig. 2.
Fig. 2.

Measured oscillation frequency (filled circles, left axis) and damping rate (open circles, right axis) as function of pump power for mode-locked (red) and cw (black) operation of the laser.

Equations (38)

Equations on this page are rendered with MathJax. Learn more.

T R u T t T = [ i θ sl + i D 2 2 t 2 l + g ( 1 + 1 Ω g 2 2 t 2 ) + ( i γ + δ ) u T t 2 ] u T t ,
g = g 0 1 + w P s T R ,
d v d T = A v + S ,
d g d T = g 0 g τ f 1 τ f g w P s T R ,
d w d T = w τ ph ( w ) + 2 g w T R .
w d T + A ww Δ w + A wg Δ g = 0 ,
g d T + A gw Δ w + A gg Δ g = Δ g 0 τ f ,
N 2 d T = ( 1 τ f + 1 τ ph N ph , eq N 2 , eq ) ( Δ N 2 Δ N 20 ) + 1 τ ph Δ N ph ,
N ph d T = d τ ph 1 d N ph Δ N ph 1 τ ph N ph , eq N 2 , eq Δ N 2 ,
N 2 , eq N ph , eq = 1 A w g A g w τ ph 2 = 13 ,
d Δ ϖ d T + A ϖ w Δ w + A ϖ g Δ g + A ϖ ϖ Δϖ = 0 ,
g ˜ ( ω ) = g ( 0 ) + g ( 1 ) ω + 1 2 g ( 2 ) ω 2 + 1 6 g ( 3 ) ω 3 ,
l ˜ ( ω ) = l ( 0 ) + l ( 1 ) ω + 1 2 l ( 2 ) ω 2 + 1 6 l ( 3 ) ω 3 ,
A ϖ w = 3.23 T R [ g ( 3 ) l ( 3 ) ] 1 t FWHM 4 w eq , A ϖ g = 2.77 T R g ( 1 ) g ( 0 ) 1 t FWHM 2 ,
Δ w = A w g ω osc 2 + α 2 Δ g 0 τ f { 1 e α T [ cos ( ω osc T ) + α ω osc sin ( ω osc T ) ] } ,
Δ g = A w w ω osc 2 + α 2 Δ g 0 τ f { 1 e α T [ cos ( ω osc T ) + α ω osc sin ( ω osc T ) ] }
+ 1 ω osc Δ g 0 τ f e α T sin ( ω osc T ) ,
dΔϖ exp ( A ϖϖ T ) d T = ( A ϖ w A w g A ϖ g A w w ) ω osc 2 + α 2 Δ g 0 τ f
× { exp ( A ϖϖ T ) exp [ ( α A ϖϖ ) T ] cos ( ω osc T )
α ω osc exp [ ( α A ϖϖ ) T ] sin ( ω osc T ) }
A ϖ g 1 ω osc Δ g 0 τ f exp [ ( α A ϖϖ ) T ] sin ( ω osc T ) .
Δϖ = ( A ϖ w A w g A ϖ g A w w ) ω osc 2 + α 2 Δ g 0 τ f { 1 A ϖϖ [ 1 exp ( A ϖϖ T ) ]
1 ω osc ω osc 2 α α ¯ ω osc 2 + α ¯ 2 exp ( α T ) sin ( ω osc T )
α + α ¯ ω osc 2 + α ¯ 2 [ exp ( A ϖϖ T ) exp ( α T ) cos ( ω osc T ) ] }
+ A ϖ g 1 ω osc Δ g 0 τ f { α ¯ ω osc 2 + α ¯ 2 exp ( α T ) sin ( ω osc T )
ω osc ω osc 2 + α ¯ 2 [ exp ( A ϖϖ T ) exp ( α T ) cos ( ω osc T ) ] } .
Δ u T = i [ u 0 ] Δ u + i N [ u 0 ] Δ u * ,
d t 1 d t 2 v * ( t 1 ) ( t 1 , t 2 ) u ( t 2 ) = d t 1 d t 2 u ( t 2 ) * ( t 2 , t 1 ) v * ( t 1 ) ,
d t 1 d t 2 v * ( t 1 ) 𝒩 ( t 1 , t 2 ) u * ( t 2 ) = d t 1 d t 2 u * ( t 2 ) 𝒩 ( t 2 , t 1 ) v * ( t 1 ) .
v T = i [ u 0 ] v i 𝒩 [ u 0 ] v * .
P [ u ] = i [ g ( 1 ) l ( 3 ) ] u t i 6 [ g ( 3 ) l ( 3 ) ] 3 u t 3 + i Δ g ( 1 ) u t .
u w = 1 w [ C 1 ( t p ) C 2 ( t p ) ( t τ ) 2 t p 2 ] u 0 ( t ) , u ϖ = i ( t τ ) u 0 ( t ) , u τ = t τ t p 2 u 0 ( t ) , u θ = i u 0 ( t ) ,
v w = 2 u 0 ( t ) , v ϖ = 2 i w t τ t p 2 u 0 ( t ) , v τ = 2 w ( t τ ) u 0 ( t ) , v θ = 2 i w [ C 1 ( t p ) C 2 ( t p ) ( t τ ) 2 t p 2 ] u 0 ( t ) ,
C 1 ( t p ) = 1 + 3 s t p 4 1 + 5 s t p 4 , C 2 ( t p ) = 1 + s t p 4 1 + 5 s t p 4 .
T R dΔϖ d T = [ g ( 1 ) l ( 1 ) ] 1 t p 2 + 1 4 [ g ( 3 ) l ( 3 ) ] 1 t p 4 + Δ g ( 1 ) t p 2 .
T R dΔϖ d T = 1 4 t p 2 [ g ( 3 ) l ( 3 ) ] ( 1 t p , eq 2 1 t p 2 ) + Δ g ( 1 ) t p 2
= 1 2 t p 5 [ g ( 3 ) l ( 3 ) ] Δ t p + Δ g ( 1 ) t p 2 .
A ϖ w = 1 2 T R t p 4 [ g ( 3 ) l ( 3 ) ] 1 + s t p 4 1 + 5 s t p 4 , A ϖ g = 1 T R t p 2 g ( 1 ) g ( 0 ) .

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