Abstract

We perform what we believe is the first computational study of phase jitter and comb linewidths in a nonsolitonic fiber laser with large changes in the pulse on each round trip. For fiber lasers operating in or near the similariton regime, we investigate how the pulse parameters and noise performance depend on the system parameters. Across a large dispersion range, the dechirped pulse width, timing jitter, phase jitter, and comb linewidths are smaller when the gain in the optical amplifier is larger. Over a narrow range of negative dispersion values near zero, the timing jitter and comb linewidths are smaller with a wider optical filter. However, with the wider optical filter, the pulse width increases significantly, and the noise performance deteriorates rapidly as the dispersion increases above zero. These trends are in general agreement with experimental studies of timing jitter and the linewidth of the carrier-envelope offset frequency in Yb-fiber lasers and are consistent with the Namiki–Haus theory of timing jitter in a stretched-pulse laser.

© 2018 Optical Society of America

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References

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    [Crossref]
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    [Crossref]
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    [Crossref]
  6. C. R. Menyuk and S. Wang, “Spectral methods for determining the stability and noise performance of passively modelocked lasers,” Nanophotonics 5, 332–350 (2016).
    [Crossref]
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    [Crossref]
  8. R. Paschotta, “Noise of mode-locked lasers (Part II): timing jitter and other fluctuations,” Appl. Phys. B 79, 163–173 (2004).
    [Crossref]
  9. N. R. Newbury and W. C. Swann, “Low-noise fiber-laser frequency combs,” J. Opt. Soc. Am. B 24, 1756–1770 (2007).
    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
  13. J. Wahlstrand, J. Willits, C. Menyuk, and S. Cundiff, “The quantum-limited comb lineshape of a mode-locked laser: fundamental limits on frequency uncertainty,” Opt. Express 16, 18624–18630 (2008).
    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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  29. W. Chen, Y. Song, K. Jung, M. Hu, C. Wang, and J. Kim, “Few-femtosecond timing jitter from a picosecond all-polarization-maintaining Yb-fiber laser,” Opt. Express 24, 1347–1357 (2016).
    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
  38. D. Jones, S. Diddams, J. Ranka, A. Stentz, R. Windeler, J. Hall, and S. Cundiff, “Carrier-envelope phase control of femtosecond mode-locked lasers and direct optical frequency synthesis,” Science 288, 635–639 (2000).
    [Crossref]
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    [Crossref]

2016 (3)

C. R. Menyuk and S. Wang, “Spectral methods for determining the stability and noise performance of passively modelocked lasers,” Nanophotonics 5, 332–350 (2016).
[Crossref]

Y. Shen, J. Zweck, S. Wang, and C. Menyuk, “Spectra of short pulse solutions of the cubic-quintic complex Ginzburg Landau equation near zero dispersion,” Stud. Appl. Math. 137, 238–255 (2016).
[Crossref]

W. Chen, Y. Song, K. Jung, M. Hu, C. Wang, and J. Kim, “Few-femtosecond timing jitter from a picosecond all-polarization-maintaining Yb-fiber laser,” Opt. Express 24, 1347–1357 (2016).
[Crossref]

2015 (1)

A. Chong, L. G. Wright, and F. W. Wise, “Ultrafast fiber lasers based on self-similar pulse evolution: a review of current progress,” Rep. Prog. Phys. 78, 113901 (2015).
[Crossref]

2014 (2)

H. Kim, P. Qin, Y. Song, H. Yang, J. Shin, C. Kim, K. Jung, C. Wang, and J. Kim, “Sub-20-attosecond timing jitter mode-locked fiber lasers,” IEEE J. Sel. Top. Quantum Electron. 20, 260–267 (2014).
[Crossref]

P. Qin, Y. Song, H. Kim, J. Shin, D. Kwon, M. Hu, C. Wang, and J. Kim, “Reduction of timing jitter and intensity noise in normal-dispersion passively mode-locked fiber lasers by narrow band-pass filtering,” Opt. Express 22, 28276–28283 (2014).
[Crossref]

2013 (1)

2011 (5)

2010 (3)

2008 (4)

T. Schibli, I. Hartl, D. Yost, M. Martin, A. Marcinkevičius, M. Fermann, and J. Ye, “Optical frequency comb with submillihertz linewidth and more than 10 W average power,” Nat. Photonics 2, 355–359 (2008).
[Crossref]

R. O. Moore, G. Biondini, and W. L. Kath, “A method to compute statistics of large, noise-induced perturbations of nonlinear Schrödinger solitons,” SIAM Rev. 50, 523–549 (2008).
[Crossref]

A. Chong, W. H. Renninger, and F. W. Wise, “Properties of normal-dispersion femtosecond fiber lasers,” J. Opt. Soc. Am. B 25, 140–148 (2008).
[Crossref]

J. Wahlstrand, J. Willits, C. Menyuk, and S. Cundiff, “The quantum-limited comb lineshape of a mode-locked laser: fundamental limits on frequency uncertainty,” Opt. Express 16, 18624–18630 (2008).
[Crossref]

2007 (2)

2006 (1)

R. Paschotta, A. Schlatter, S. Zeller, H. Telle, and U. Keller, “Optical phase noise and carrier-envelope offset noise of mode-locked lasers,” Appl. Phys. B 82, 265–273 (2006).
[Crossref]

2005 (1)

N. R. Newbury and B. R. Washburn, “Theory of the frequency comb output from a femtosecond fiber laser,” IEEE J. Quantum Electron. 41, 1388–1402 (2005).
[Crossref]

2004 (3)

F. Ilday, J. Buckley, W. Clark, and F. Wise, “Self-similar evolution of parabolic pulses in a laser,” Phys. Rev. Lett. 92, 213902 (2004).
[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]

2002 (2)

H. R. Telle, B. Lipphardt, and J. Stenger, “Kerr-lens, mode-locked lasers as transfer oscillators for optical frequency measurements,” Appl. Phys. B 74, 1–6 (2002).
[Crossref]

C. McKinstrie and C. Xie, “Phase jitter in single-channel soliton systems with constant dispersion,” IEEE J. Sel. Top. Quantum Electron. 8, 616–625 (2002).
[Crossref]

2000 (2)

D. Jones, S. Diddams, J. Ranka, A. Stentz, R. Windeler, J. Hall, and S. Cundiff, “Carrier-envelope phase control of femtosecond mode-locked lasers and direct optical frequency synthesis,” Science 288, 635–639 (2000).
[Crossref]

M. Fermann, V. Kruglov, B. Thomsen, J. Dudley, and J. Harvey, “Self-similar propagation and amplification of parabolic pulses in optical fibers,” Phys. Rev. Lett. 84, 6010–6013 (2000).
[Crossref]

1997 (1)

S. Namiki and H. A. Haus, “Noise of the stretched pulse fiber laser. I. Theory,” IEEE J. Quantum Electron. 33, 649–659 (1997).
[Crossref]

1993 (1)

H. A. Haus and A. Mecozzi, “Noise of mode-locked lasers,” IEEE J. Quantum Electron. 29, 983–996 (1993).
[Crossref]

1991 (1)

Agrawal, G. P.

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

Bale, B. G.

Biondini, G.

R. O. Moore, G. Biondini, and W. L. Kath, “A method to compute statistics of large, noise-induced perturbations of nonlinear Schrödinger solitons,” SIAM Rev. 50, 523–549 (2008).
[Crossref]

Buckley, J.

F. Ilday, J. Buckley, W. Clark, and F. Wise, “Self-similar evolution of parabolic pulses in a laser,” Phys. Rev. Lett. 92, 213902 (2004).
[Crossref]

Chen, W.

Chong, A.

A. Chong, L. G. Wright, and F. W. Wise, “Ultrafast fiber lasers based on self-similar pulse evolution: a review of current progress,” Rep. Prog. Phys. 78, 113901 (2015).
[Crossref]

W. H. Renninger, A. Chong, and F. W. Wise, “Amplifier similaritons in a dispersion-mapped fiber laser [invited],” Opt. Express 19, 22496–22501 (2011).
[Crossref]

W. H. Renninger, A. Chong, and F. W. Wise, “Self-similar pulse evolution in an all-normal-dispersion laser,” Phys. Rev. A 82, 021805 (2010).
[Crossref]

A. Chong, W. H. Renninger, and F. W. Wise, “Properties of normal-dispersion femtosecond fiber lasers,” J. Opt. Soc. Am. B 25, 140–148 (2008).
[Crossref]

Clark, W.

F. Ilday, J. Buckley, W. Clark, and F. Wise, “Self-similar evolution of parabolic pulses in a laser,” Phys. Rev. Lett. 92, 213902 (2004).
[Crossref]

Cundiff, S.

J. Wahlstrand, J. Willits, C. Menyuk, and S. Cundiff, “The quantum-limited comb lineshape of a mode-locked laser: fundamental limits on frequency uncertainty,” Opt. Express 16, 18624–18630 (2008).
[Crossref]

D. Jones, S. Diddams, J. Ranka, A. Stentz, R. Windeler, J. Hall, and S. Cundiff, “Carrier-envelope phase control of femtosecond mode-locked lasers and direct optical frequency synthesis,” Science 288, 635–639 (2000).
[Crossref]

Diddams, S.

D. Jones, S. Diddams, J. Ranka, A. Stentz, R. Windeler, J. Hall, and S. Cundiff, “Carrier-envelope phase control of femtosecond mode-locked lasers and direct optical frequency synthesis,” Science 288, 635–639 (2000).
[Crossref]

Diddmans, S. A.

Docherty, A.

Dudley, J.

M. Fermann, V. Kruglov, B. Thomsen, J. Dudley, and J. Harvey, “Self-similar propagation and amplification of parabolic pulses in optical fibers,” Phys. Rev. Lett. 84, 6010–6013 (2000).
[Crossref]

Ell, R.

F. Kärtner, U. Morgner, T. Schibli, R. Ell, H. Haus, J. Fujimoto, and E. Ippen, “Few-cycle pulses directly from a laser,” in Few-Cycle Laser Pulse Generation and Its Applications (Springer, 2004), pp. 73–136.

Fermann, M.

T. Schibli, I. Hartl, D. Yost, M. Martin, A. Marcinkevičius, M. Fermann, and J. Ye, “Optical frequency comb with submillihertz linewidth and more than 10 W average power,” Nat. Photonics 2, 355–359 (2008).
[Crossref]

I. Hartl, T. Schibli, A. Marcinkevicius, D. Yost, D. Hudson, M. Fermann, and J. Ye, “Cavity-enhanced similariton Yb-fiber laser frequency comb: 3 × 1014 W/cm2 peak intensity at 136  MHz,” Opt. Lett. 32, 2870–2872 (2007).
[Crossref]

M. Fermann, V. Kruglov, B. Thomsen, J. Dudley, and J. Harvey, “Self-similar propagation and amplification of parabolic pulses in optical fibers,” Phys. Rev. Lett. 84, 6010–6013 (2000).
[Crossref]

Fujimoto, J.

F. Kärtner, U. Morgner, T. Schibli, R. Ell, H. Haus, J. Fujimoto, and E. Ippen, “Few-cycle pulses directly from a laser,” in Few-Cycle Laser Pulse Generation and Its Applications (Springer, 2004), pp. 73–136.

Hall, J.

D. Jones, S. Diddams, J. Ranka, A. Stentz, R. Windeler, J. Hall, and S. Cundiff, “Carrier-envelope phase control of femtosecond mode-locked lasers and direct optical frequency synthesis,” Science 288, 635–639 (2000).
[Crossref]

Hartl, I.

T. Schibli, I. Hartl, D. Yost, M. Martin, A. Marcinkevičius, M. Fermann, and J. Ye, “Optical frequency comb with submillihertz linewidth and more than 10 W average power,” Nat. Photonics 2, 355–359 (2008).
[Crossref]

I. Hartl, T. Schibli, A. Marcinkevicius, D. Yost, D. Hudson, M. Fermann, and J. Ye, “Cavity-enhanced similariton Yb-fiber laser frequency comb: 3 × 1014 W/cm2 peak intensity at 136  MHz,” Opt. Lett. 32, 2870–2872 (2007).
[Crossref]

Harvey, J.

M. Fermann, V. Kruglov, B. Thomsen, J. Dudley, and J. Harvey, “Self-similar propagation and amplification of parabolic pulses in optical fibers,” Phys. Rev. Lett. 84, 6010–6013 (2000).
[Crossref]

Haus, H.

F. Kärtner, U. Morgner, T. Schibli, R. Ell, H. Haus, J. Fujimoto, and E. Ippen, “Few-cycle pulses directly from a laser,” in Few-Cycle Laser Pulse Generation and Its Applications (Springer, 2004), pp. 73–136.

Haus, H. A.

S. Namiki and H. A. Haus, “Noise of the stretched pulse fiber laser. I. Theory,” IEEE J. Quantum Electron. 33, 649–659 (1997).
[Crossref]

H. A. Haus and A. Mecozzi, “Noise of mode-locked lasers,” IEEE J. Quantum Electron. 29, 983–996 (1993).
[Crossref]

H. A. Haus, “Quantum noise in a solitonlike repeater system,” J. Opt. Soc. Am. B 8, 1122–1126 (1991).
[Crossref]

Hu, M.

Hudson, D.

Iannone, E.

E. Iannone, F. Matera, A. Mecozzi, and M. Settembre, Nonlinear Optical Communication Networks (Wiley, 1998).

Ilday, F.

F. Ilday, J. Buckley, W. Clark, and F. Wise, “Self-similar evolution of parabolic pulses in a laser,” Phys. Rev. Lett. 92, 213902 (2004).
[Crossref]

Ippen, E.

F. Kärtner, U. Morgner, T. Schibli, R. Ell, H. Haus, J. Fujimoto, and E. Ippen, “Few-cycle pulses directly from a laser,” in Few-Cycle Laser Pulse Generation and Its Applications (Springer, 2004), pp. 73–136.

Johnson, T. A.

Jones, D.

D. Jones, S. Diddams, J. Ranka, A. Stentz, R. Windeler, J. Hall, and S. Cundiff, “Carrier-envelope phase control of femtosecond mode-locked lasers and direct optical frequency synthesis,” Science 288, 635–639 (2000).
[Crossref]

Jung, K.

Kärtner, F.

F. Kärtner, U. Morgner, T. Schibli, R. Ell, H. Haus, J. Fujimoto, and E. Ippen, “Few-cycle pulses directly from a laser,” in Few-Cycle Laser Pulse Generation and Its Applications (Springer, 2004), pp. 73–136.

Kath, W. L.

R. O. Moore, G. Biondini, and W. L. Kath, “A method to compute statistics of large, noise-induced perturbations of nonlinear Schrödinger solitons,” SIAM Rev. 50, 523–549 (2008).
[Crossref]

Keller, U.

R. Paschotta, A. Schlatter, S. Zeller, H. Telle, and U. Keller, “Optical phase noise and carrier-envelope offset noise of mode-locked lasers,” Appl. Phys. B 82, 265–273 (2006).
[Crossref]

Kim, C.

Kim, H.

Kim, J.

Kim, T. K.

Kobayashi, Y.

Kruglov, V.

M. Fermann, V. Kruglov, B. Thomsen, J. Dudley, and J. Harvey, “Self-similar propagation and amplification of parabolic pulses in optical fibers,” Phys. Rev. Lett. 84, 6010–6013 (2000).
[Crossref]

Kwon, D.

Li, P.

P. Li, W. H. Renninger, Z. Zhao, Z. Zhang, and F. W. Wise, “Frequency noise of amplifier-similariton laser combs,” in CLEO: Science and Innovations (Optical Society of America, 2013), paper CTu1I.6.

Lipphardt, B.

H. R. Telle, B. Lipphardt, and J. Stenger, “Kerr-lens, mode-locked lasers as transfer oscillators for optical frequency measurements,” Appl. Phys. B 74, 1–6 (2002).
[Crossref]

Marcinkevicius, A.

T. Schibli, I. Hartl, D. Yost, M. Martin, A. Marcinkevičius, M. Fermann, and J. Ye, “Optical frequency comb with submillihertz linewidth and more than 10 W average power,” Nat. Photonics 2, 355–359 (2008).
[Crossref]

I. Hartl, T. Schibli, A. Marcinkevicius, D. Yost, D. Hudson, M. Fermann, and J. Ye, “Cavity-enhanced similariton Yb-fiber laser frequency comb: 3 × 1014 W/cm2 peak intensity at 136  MHz,” Opt. Lett. 32, 2870–2872 (2007).
[Crossref]

Marks, B.

Martin, M.

T. Schibli, I. Hartl, D. Yost, M. Martin, A. Marcinkevičius, M. Fermann, and J. Ye, “Optical frequency comb with submillihertz linewidth and more than 10 W average power,” Nat. Photonics 2, 355–359 (2008).
[Crossref]

Matera, F.

E. Iannone, F. Matera, A. Mecozzi, and M. Settembre, Nonlinear Optical Communication Networks (Wiley, 1998).

McKinstrie, C.

C. McKinstrie and C. Xie, “Phase jitter in single-channel soliton systems with constant dispersion,” IEEE J. Sel. Top. Quantum Electron. 8, 616–625 (2002).
[Crossref]

Mecozzi, A.

H. A. Haus and A. Mecozzi, “Noise of mode-locked lasers,” IEEE J. Quantum Electron. 29, 983–996 (1993).
[Crossref]

E. Iannone, F. Matera, A. Mecozzi, and M. Settembre, Nonlinear Optical Communication Networks (Wiley, 1998).

Menyuk, C.

Menyuk, C. R.

C. R. Menyuk and S. Wang, “Spectral methods for determining the stability and noise performance of passively modelocked lasers,” Nanophotonics 5, 332–350 (2016).
[Crossref]

Moore, R. O.

R. O. Moore, G. Biondini, and W. L. Kath, “A method to compute statistics of large, noise-induced perturbations of nonlinear Schrödinger solitons,” SIAM Rev. 50, 523–549 (2008).
[Crossref]

Morgner, U.

F. Kärtner, U. Morgner, T. Schibli, R. Ell, H. Haus, J. Fujimoto, and E. Ippen, “Few-cycle pulses directly from a laser,” in Few-Cycle Laser Pulse Generation and Its Applications (Springer, 2004), pp. 73–136.

Nam, C. H.

Namiki, S.

S. Namiki and H. A. Haus, “Noise of the stretched pulse fiber laser. I. Theory,” IEEE J. Quantum Electron. 33, 649–659 (1997).
[Crossref]

Newbury, N. R.

N. R. Newbury and W. C. Swann, “Low-noise fiber-laser frequency combs,” J. Opt. Soc. Am. B 24, 1756–1770 (2007).
[Crossref]

N. R. Newbury and B. R. Washburn, “Theory of the frequency comb output from a femtosecond fiber laser,” IEEE J. Quantum Electron. 41, 1388–1402 (2005).
[Crossref]

Nugent-Glandorf, L.

Papoulis, A.

A. Papoulis and S. U. Pillai, Probability, Random Variables, and Stochastic Processes (McGraw-Hill, 2002).

Paschotta, R.

R. Paschotta, “Timing jitter and phase noise of mode-locked fiber lasers,” Opt. Express 18, 5041–5054 (2010).
[Crossref]

R. Paschotta, A. Schlatter, S. Zeller, H. Telle, and U. Keller, “Optical phase noise and carrier-envelope offset noise of mode-locked lasers,” Appl. Phys. B 82, 265–273 (2006).
[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]

Pillai, S. U.

A. Papoulis and S. U. Pillai, Probability, Random Variables, and Stochastic Processes (McGraw-Hill, 2002).

Qin, P.

H. Kim, P. Qin, Y. Song, H. Yang, J. Shin, C. Kim, K. Jung, C. Wang, and J. Kim, “Sub-20-attosecond timing jitter mode-locked fiber lasers,” IEEE J. Sel. Top. Quantum Electron. 20, 260–267 (2014).
[Crossref]

P. Qin, Y. Song, H. Kim, J. Shin, D. Kwon, M. Hu, C. Wang, and J. Kim, “Reduction of timing jitter and intensity noise in normal-dispersion passively mode-locked fiber lasers by narrow band-pass filtering,” Opt. Express 22, 28276–28283 (2014).
[Crossref]

Ranka, J.

D. Jones, S. Diddams, J. Ranka, A. Stentz, R. Windeler, J. Hall, and S. Cundiff, “Carrier-envelope phase control of femtosecond mode-locked lasers and direct optical frequency synthesis,” Science 288, 635–639 (2000).
[Crossref]

Renninger, W. H.

W. H. Renninger, A. Chong, and F. W. Wise, “Amplifier similaritons in a dispersion-mapped fiber laser [invited],” Opt. Express 19, 22496–22501 (2011).
[Crossref]

W. H. Renninger, A. Chong, and F. W. Wise, “Self-similar pulse evolution in an all-normal-dispersion laser,” Phys. Rev. A 82, 021805 (2010).
[Crossref]

A. Chong, W. H. Renninger, and F. W. Wise, “Properties of normal-dispersion femtosecond fiber lasers,” J. Opt. Soc. Am. B 25, 140–148 (2008).
[Crossref]

P. Li, W. H. Renninger, Z. Zhao, Z. Zhang, and F. W. Wise, “Frequency noise of amplifier-similariton laser combs,” in CLEO: Science and Innovations (Optical Society of America, 2013), paper CTu1I.6.

Schibli, T.

T. Schibli, I. Hartl, D. Yost, M. Martin, A. Marcinkevičius, M. Fermann, and J. Ye, “Optical frequency comb with submillihertz linewidth and more than 10 W average power,” Nat. Photonics 2, 355–359 (2008).
[Crossref]

I. Hartl, T. Schibli, A. Marcinkevicius, D. Yost, D. Hudson, M. Fermann, and J. Ye, “Cavity-enhanced similariton Yb-fiber laser frequency comb: 3 × 1014 W/cm2 peak intensity at 136  MHz,” Opt. Lett. 32, 2870–2872 (2007).
[Crossref]

F. Kärtner, U. Morgner, T. Schibli, R. Ell, H. Haus, J. Fujimoto, and E. Ippen, “Few-cycle pulses directly from a laser,” in Few-Cycle Laser Pulse Generation and Its Applications (Springer, 2004), pp. 73–136.

Schlatter, A.

R. Paschotta, A. Schlatter, S. Zeller, H. Telle, and U. Keller, “Optical phase noise and carrier-envelope offset noise of mode-locked lasers,” Appl. Phys. B 82, 265–273 (2006).
[Crossref]

Settembre, M.

E. Iannone, F. Matera, A. Mecozzi, and M. Settembre, Nonlinear Optical Communication Networks (Wiley, 1998).

Shen, Y.

Y. Shen, J. Zweck, S. Wang, and C. Menyuk, “Spectra of short pulse solutions of the cubic-quintic complex Ginzburg Landau equation near zero dispersion,” Stud. Appl. Math. 137, 238–255 (2016).
[Crossref]

Shin, J.

P. Qin, Y. Song, H. Kim, J. Shin, D. Kwon, M. Hu, C. Wang, and J. Kim, “Reduction of timing jitter and intensity noise in normal-dispersion passively mode-locked fiber lasers by narrow band-pass filtering,” Opt. Express 22, 28276–28283 (2014).
[Crossref]

H. Kim, P. Qin, Y. Song, H. Yang, J. Shin, C. Kim, K. Jung, C. Wang, and J. Kim, “Sub-20-attosecond timing jitter mode-locked fiber lasers,” IEEE J. Sel. Top. Quantum Electron. 20, 260–267 (2014).
[Crossref]

Song, Y.

Stenger, J.

H. R. Telle, B. Lipphardt, and J. Stenger, “Kerr-lens, mode-locked lasers as transfer oscillators for optical frequency measurements,” Appl. Phys. B 74, 1–6 (2002).
[Crossref]

Stentz, A.

D. Jones, S. Diddams, J. Ranka, A. Stentz, R. Windeler, J. Hall, and S. Cundiff, “Carrier-envelope phase control of femtosecond mode-locked lasers and direct optical frequency synthesis,” Science 288, 635–639 (2000).
[Crossref]

Swann, W. C.

Telle, H.

R. Paschotta, A. Schlatter, S. Zeller, H. Telle, and U. Keller, “Optical phase noise and carrier-envelope offset noise of mode-locked lasers,” Appl. Phys. B 82, 265–273 (2006).
[Crossref]

Telle, H. R.

H. R. Telle, B. Lipphardt, and J. Stenger, “Kerr-lens, mode-locked lasers as transfer oscillators for optical frequency measurements,” Appl. Phys. B 74, 1–6 (2002).
[Crossref]

Thomsen, B.

M. Fermann, V. Kruglov, B. Thomsen, J. Dudley, and J. Harvey, “Self-similar propagation and amplification of parabolic pulses in optical fibers,” Phys. Rev. Lett. 84, 6010–6013 (2000).
[Crossref]

Wabnitz, S.

Wahlstrand, J.

Wang, C.

Wang, S.

C. R. Menyuk and S. Wang, “Spectral methods for determining the stability and noise performance of passively modelocked lasers,” Nanophotonics 5, 332–350 (2016).
[Crossref]

Y. Shen, J. Zweck, S. Wang, and C. Menyuk, “Spectra of short pulse solutions of the cubic-quintic complex Ginzburg Landau equation near zero dispersion,” Stud. Appl. Math. 137, 238–255 (2016).
[Crossref]

S. Wang, A. Docherty, B. Marks, and C. Menyuk, “Comparison of numerical methods for modeling laser mode locking with saturable gain,” J. Opt. Soc. Am. B 30, 3064–3074 (2013).
[Crossref]

Washburn, B. R.

N. R. Newbury and B. R. Washburn, “Theory of the frequency comb output from a femtosecond fiber laser,” IEEE J. Quantum Electron. 41, 1388–1402 (2005).
[Crossref]

Willits, J.

Windeler, R.

D. Jones, S. Diddams, J. Ranka, A. Stentz, R. Windeler, J. Hall, and S. Cundiff, “Carrier-envelope phase control of femtosecond mode-locked lasers and direct optical frequency synthesis,” Science 288, 635–639 (2000).
[Crossref]

Wise, F.

F. Ilday, J. Buckley, W. Clark, and F. Wise, “Self-similar evolution of parabolic pulses in a laser,” Phys. Rev. Lett. 92, 213902 (2004).
[Crossref]

F. Wise, personal communication (Cornell University, 2016).

Wise, F. W.

A. Chong, L. G. Wright, and F. W. Wise, “Ultrafast fiber lasers based on self-similar pulse evolution: a review of current progress,” Rep. Prog. Phys. 78, 113901 (2015).
[Crossref]

W. H. Renninger, A. Chong, and F. W. Wise, “Amplifier similaritons in a dispersion-mapped fiber laser [invited],” Opt. Express 19, 22496–22501 (2011).
[Crossref]

W. H. Renninger, A. Chong, and F. W. Wise, “Self-similar pulse evolution in an all-normal-dispersion laser,” Phys. Rev. A 82, 021805 (2010).
[Crossref]

A. Chong, W. H. Renninger, and F. W. Wise, “Properties of normal-dispersion femtosecond fiber lasers,” J. Opt. Soc. Am. B 25, 140–148 (2008).
[Crossref]

P. Li, W. H. Renninger, Z. Zhao, Z. Zhang, and F. W. Wise, “Frequency noise of amplifier-similariton laser combs,” in CLEO: Science and Innovations (Optical Society of America, 2013), paper CTu1I.6.

Wright, L. G.

A. Chong, L. G. Wright, and F. W. Wise, “Ultrafast fiber lasers based on self-similar pulse evolution: a review of current progress,” Rep. Prog. Phys. 78, 113901 (2015).
[Crossref]

Xie, C.

C. McKinstrie and C. Xie, “Phase jitter in single-channel soliton systems with constant dispersion,” IEEE J. Sel. Top. Quantum Electron. 8, 616–625 (2002).
[Crossref]

Yang, H.

H. Kim, P. Qin, Y. Song, H. Yang, J. Shin, C. Kim, K. Jung, C. Wang, and J. Kim, “Sub-20-attosecond timing jitter mode-locked fiber lasers,” IEEE J. Sel. Top. Quantum Electron. 20, 260–267 (2014).
[Crossref]

Ye, J.

T. Schibli, I. Hartl, D. Yost, M. Martin, A. Marcinkevičius, M. Fermann, and J. Ye, “Optical frequency comb with submillihertz linewidth and more than 10 W average power,” Nat. Photonics 2, 355–359 (2008).
[Crossref]

I. Hartl, T. Schibli, A. Marcinkevicius, D. Yost, D. Hudson, M. Fermann, and J. Ye, “Cavity-enhanced similariton Yb-fiber laser frequency comb: 3 × 1014 W/cm2 peak intensity at 136  MHz,” Opt. Lett. 32, 2870–2872 (2007).
[Crossref]

Yost, D.

T. Schibli, I. Hartl, D. Yost, M. Martin, A. Marcinkevičius, M. Fermann, and J. Ye, “Optical frequency comb with submillihertz linewidth and more than 10 W average power,” Nat. Photonics 2, 355–359 (2008).
[Crossref]

I. Hartl, T. Schibli, A. Marcinkevicius, D. Yost, D. Hudson, M. Fermann, and J. Ye, “Cavity-enhanced similariton Yb-fiber laser frequency comb: 3 × 1014 W/cm2 peak intensity at 136  MHz,” Opt. Lett. 32, 2870–2872 (2007).
[Crossref]

Zeller, S.

R. Paschotta, A. Schlatter, S. Zeller, H. Telle, and U. Keller, “Optical phase noise and carrier-envelope offset noise of mode-locked lasers,” Appl. Phys. B 82, 265–273 (2006).
[Crossref]

Zhang, Z.

P. Li, W. H. Renninger, Z. Zhao, Z. Zhang, and F. W. Wise, “Frequency noise of amplifier-similariton laser combs,” in CLEO: Science and Innovations (Optical Society of America, 2013), paper CTu1I.6.

Zhao, Z.

P. Li, W. H. Renninger, Z. Zhao, Z. Zhang, and F. W. Wise, “Frequency noise of amplifier-similariton laser combs,” in CLEO: Science and Innovations (Optical Society of America, 2013), paper CTu1I.6.

Zweck, J.

Y. Shen, J. Zweck, S. Wang, and C. Menyuk, “Spectra of short pulse solutions of the cubic-quintic complex Ginzburg Landau equation near zero dispersion,” Stud. Appl. Math. 137, 238–255 (2016).
[Crossref]

Appl. Phys. B (4)

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]

R. Paschotta, A. Schlatter, S. Zeller, H. Telle, and U. Keller, “Optical phase noise and carrier-envelope offset noise of mode-locked lasers,” Appl. Phys. B 82, 265–273 (2006).
[Crossref]

H. R. Telle, B. Lipphardt, and J. Stenger, “Kerr-lens, mode-locked lasers as transfer oscillators for optical frequency measurements,” Appl. Phys. B 74, 1–6 (2002).
[Crossref]

IEEE J. Quantum Electron. (3)

N. R. Newbury and B. R. Washburn, “Theory of the frequency comb output from a femtosecond fiber laser,” IEEE J. Quantum Electron. 41, 1388–1402 (2005).
[Crossref]

H. A. Haus and A. Mecozzi, “Noise of mode-locked lasers,” IEEE J. Quantum Electron. 29, 983–996 (1993).
[Crossref]

S. Namiki and H. A. Haus, “Noise of the stretched pulse fiber laser. I. Theory,” IEEE J. Quantum Electron. 33, 649–659 (1997).
[Crossref]

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

C. McKinstrie and C. Xie, “Phase jitter in single-channel soliton systems with constant dispersion,” IEEE J. Sel. Top. Quantum Electron. 8, 616–625 (2002).
[Crossref]

H. Kim, P. Qin, Y. Song, H. Yang, J. Shin, C. Kim, K. Jung, C. Wang, and J. Kim, “Sub-20-attosecond timing jitter mode-locked fiber lasers,” IEEE J. Sel. Top. Quantum Electron. 20, 260–267 (2014).
[Crossref]

J. Opt. Soc. Am. B (4)

Nanophotonics (1)

C. R. Menyuk and S. Wang, “Spectral methods for determining the stability and noise performance of passively modelocked lasers,” Nanophotonics 5, 332–350 (2016).
[Crossref]

Nat. Photonics (1)

T. Schibli, I. Hartl, D. Yost, M. Martin, A. Marcinkevičius, M. Fermann, and J. Ye, “Optical frequency comb with submillihertz linewidth and more than 10 W average power,” Nat. Photonics 2, 355–359 (2008).
[Crossref]

Opt. Express (6)

Opt. Lett. (5)

Phys. Rev. A (1)

W. H. Renninger, A. Chong, and F. W. Wise, “Self-similar pulse evolution in an all-normal-dispersion laser,” Phys. Rev. A 82, 021805 (2010).
[Crossref]

Phys. Rev. Lett. (2)

M. Fermann, V. Kruglov, B. Thomsen, J. Dudley, and J. Harvey, “Self-similar propagation and amplification of parabolic pulses in optical fibers,” Phys. Rev. Lett. 84, 6010–6013 (2000).
[Crossref]

F. Ilday, J. Buckley, W. Clark, and F. Wise, “Self-similar evolution of parabolic pulses in a laser,” Phys. Rev. Lett. 92, 213902 (2004).
[Crossref]

Rep. Prog. Phys. (1)

A. Chong, L. G. Wright, and F. W. Wise, “Ultrafast fiber lasers based on self-similar pulse evolution: a review of current progress,” Rep. Prog. Phys. 78, 113901 (2015).
[Crossref]

Science (1)

D. Jones, S. Diddams, J. Ranka, A. Stentz, R. Windeler, J. Hall, and S. Cundiff, “Carrier-envelope phase control of femtosecond mode-locked lasers and direct optical frequency synthesis,” Science 288, 635–639 (2000).
[Crossref]

SIAM Rev. (1)

R. O. Moore, G. Biondini, and W. L. Kath, “A method to compute statistics of large, noise-induced perturbations of nonlinear Schrödinger solitons,” SIAM Rev. 50, 523–549 (2008).
[Crossref]

Stud. Appl. Math. (1)

Y. Shen, J. Zweck, S. Wang, and C. Menyuk, “Spectra of short pulse solutions of the cubic-quintic complex Ginzburg Landau equation near zero dispersion,” Stud. Appl. Math. 137, 238–255 (2016).
[Crossref]

Other (6)

F. Wise, personal communication (Cornell University, 2016).

A. Papoulis and S. U. Pillai, Probability, Random Variables, and Stochastic Processes (McGraw-Hill, 2002).

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

E. Iannone, F. Matera, A. Mecozzi, and M. Settembre, Nonlinear Optical Communication Networks (Wiley, 1998).

P. Li, W. H. Renninger, Z. Zhao, Z. Zhang, and F. W. Wise, “Frequency noise of amplifier-similariton laser combs,” in CLEO: Science and Innovations (Optical Society of America, 2013), paper CTu1I.6.

F. Kärtner, U. Morgner, T. Schibli, R. Ell, H. Haus, J. Fujimoto, and E. Ippen, “Few-cycle pulses directly from a laser,” in Few-Cycle Laser Pulse Generation and Its Applications (Springer, 2004), pp. 73–136.

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Figures (4)

Fig. 1.
Fig. 1. Optical pulse at the exit to the fiber amplifier. In the top row, we show the pulse power, and in the bottom row we show the local frequency, both as functions of time. (In the bottom row, the time window is one-third of that in the top row.) In the different columns, we show the results for different values of the round-trip dispersion: βRT=50  kfs2 (left), βRT=10  kfs2 (middle), and βRT=50  kfs2 (right). The results for Systems A, B, and C are shown in red, blue, and black, respectively. The dotted curves in the top row show parabolic fits to the pulse power with the same energy and pulse width.
Fig. 2.
Fig. 2. Left, relative error between the pulse at the exit to the fiber amplifier and the best-fit parabolic pulse as a function of βRT; middle, minimum pulse width after pulse compression at the exit to the laser system as a function of βRT; right, chirp at entrance to fiber amplifier. The results for Systems A, B, and C are shown with red crosses, blue circles, and black squares, respectively.
Fig. 3.
Fig. 3. Pulse parameters as functions of round-trip dispersion, βRT, at the entrance (top row) and exit (bottom row) of the fiber amplifier. Left to right: RMS pulse width, peak power, and RMS spectral width.
Fig. 4.
Fig. 4. Jitter and comb linewidths as functions of the round-trip dispersion, βRT. Left column, frequency jitter (top) and timing jitter per round trip (bottom); middle column, energy jitter (top) and phase jitter per round trip (bottom); right column, optical linewidth as a function of the round-trip dispersion, βRT, for the comb lines at the frequency for which the power is 50% (top) and 10% (bottom) of the maximum spectral power for System A at zero dispersion.

Equations (21)

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

uz=[g2(1+1Ωg22t2)iβ22t2+iγ|u|2]u.
g(z)=g01+E(z)/Esat,
uout=[1l01+|uin|2/Psat]uin,
tC=t|u(t)|2dt|u(t)|2dt,
un(t)=U(tnTR)exp(inϕsl),whereU(t)=ER(t)exp[iϕ(t)].
ϕ(t)=ϕc+ωct+Ct2.
un(t)=(1+ΔEn/E)1/2U(tnTRΔtn)×exp[i(nϕsl+Δθn+Δωn(tnTR))],
u(t)=(1+ΔE/E)1/2U(tΔt)exp[i(ψsl+Δθ+Δωt)],
v(t)=u(t+Δt)exp[iΔω(t+Δt)]=(1+ΔE/E)1/2U(t)exp[i(ψsl+Δθ)].
X=R(v)|v|2dtandY=I(v)|v|2dt,
Δθ=ψarg(CU+iSU)ψsl,
CU=R(U)|U|2dtandSU=I(U)|U|2dt.
u(t)=n=AnU(tnTRΔtn)exp[iΔϕn(tnTR)],
S(ω)=limTE[|u^T(ω)|2],
u^T(ω)=12TTTu(t)exp(iωt)dt.
S(ω)=1TRn=E[AoAnexp{i(Δθ0Δθn+ω(ΔtnΔt0))}×exp{in(TRωϕsl)}U^(ωΔω0)U^*(ωΔωn)].
S(ω)=ETR|U^(ω)|2n=E[exp{i(Δθ0Δθn+ω(ΔtnΔt0)}]×exp[in(TRωϕsl)].
E[(Δθn)2]=Cθθ|n|TR,E[(Δtn)2]=Ctt|n|TR,
S(ω)=ETR|U^(ω)|2n=exp[L(ω)|n|TR/2+in(TRωϕsl)],
L(ω)=Cθθ2Ctθω+Cttω2.
S(ω)=ETR|U^(ω)|2×1exp[L(ω)TR]12exp[L(ω)TR/2]cos(TRωϕsl)+exp[L(ω)TR].

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