Abstract

We present an experimental study of pulse dynamics in a mode-locked Er:fiber laser. By injecting a continuous wave laser with sinusoidal intensity modulation into the fiber laser, we are able to modulate the gain. Measuring the response of the pulse energy, central frequency, central pulse time, and phase to the gain modulation allows determination of the parameters that describe their coupling. Based on the experimentally derived parameters, we evaluate the free running comb linewidth and frequency uncertainty with feedback included, assuming quantum noise is the limiting factor. Optimization of fiber lasers is also discussed.

© 2014 Optical Society of America

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  5. D. J. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, Science 288, 635 (2000).
    [CrossRef]
  6. C. R. Menyuk, J. K. Wahlstrand, J. Willits, R. P. Smith, T. R. Schibli, and S. T. Cundiff, Opt. Express 15, 6677 (2007).
    [CrossRef]
  7. J. Wahlstrand, J. Willits, T. Schibli, C. Menyuk, and S. Cundiff, Opt. Lett. 32, 3426 (2007).
    [CrossRef]
  8. J. Wahlstrand, J. Willits, C. Menyuk, and S. Cundiff, Opt. Express 16, 18624 (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]
  14. A. Funk, D. Daubendiek, S. T. Cundiff, and C. R. Menyuk, CLEO (OSA, 2011), paper JThB124.
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    [CrossRef]
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  17. L. Nugent-Glandorf, T. A. Johnson, Y. Kobayashi, and S. A. Diddams, Opt. Lett. 36, 1578 (2011).
    [CrossRef]
  18. Y. Song, C. Kim, K. Jung, H. Kim, and J. Kim, Opt. Express 19, 14518 (2011).
    [CrossRef]
  19. S. T. Dawkins, J. J. McFerran, and A. N. Luiten, IEEE Trans. Ultrason. Ferroelectr. Freq. Control 54, 918 (2007).
    [CrossRef]

2011 (2)

2008 (2)

I. Coddington, W. C. Swann, and N. R. Newbury, Phys. Rev. Lett. 100, 013902 (2008).
[CrossRef]

J. Wahlstrand, J. Willits, C. Menyuk, and S. Cundiff, Opt. Express 16, 18624 (2008).
[CrossRef]

2007 (5)

2006 (1)

M. M. Boyd, T. Zelevinsky, A. D. Ludlow, S. M. Foreman, S. Blatt, T. Ido, and J. Ye, Science 314, 1430 (2006).
[CrossRef]

2004 (2)

2002 (1)

T. Udem, R. Holzwarth, and T. W. Hänsch, Nature 416, 233 (2002).
[CrossRef]

2000 (1)

D. J. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, Science 288, 635 (2000).
[CrossRef]

1997 (1)

L. Nelson, D. Jones, K. Tamura, H. Haus, and E. Ippen, Appl. Phys. B 65, 277 (1997).
[CrossRef]

1996 (1)

P. Wai and C. Menyuk, J. Lightwave Technol. 14, 148 (1996).
[CrossRef]

1993 (2)

H. A. Haus and A. Mecozzi, IEEE J. Quantum Electron. 29, 983 (1993).
[CrossRef]

K. Tamura, E. Ippen, H. Haus, and L. Nelson, Opt. Lett. 18, 1080 (1993).
[CrossRef]

Ablowitz, M. J.

Blatt, S.

M. M. Boyd, T. Zelevinsky, A. D. Ludlow, S. M. Foreman, S. Blatt, T. Ido, and J. Ye, Science 314, 1430 (2006).
[CrossRef]

Boyd, M. M.

M. M. Boyd, T. Zelevinsky, A. D. Ludlow, S. M. Foreman, S. Blatt, T. Ido, and J. Ye, Science 314, 1430 (2006).
[CrossRef]

Coddington, I.

I. Coddington, W. C. Swann, and N. R. Newbury, Phys. Rev. Lett. 100, 013902 (2008).
[CrossRef]

Cundiff, S.

Cundiff, S. T.

C. R. Menyuk, J. K. Wahlstrand, J. Willits, R. P. Smith, T. R. Schibli, and S. T. Cundiff, Opt. Express 15, 6677 (2007).
[CrossRef]

M. J. Ablowitz, B. Ilan, and S. T. Cundiff, Opt. Lett. 29, 1808 (2004).
[CrossRef]

D. J. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, Science 288, 635 (2000).
[CrossRef]

A. Funk, D. Daubendiek, S. T. Cundiff, and C. R. Menyuk, CLEO (OSA, 2011), paper JThB124.

Daubendiek, D.

A. Funk, D. Daubendiek, S. T. Cundiff, and C. R. Menyuk, CLEO (OSA, 2011), paper JThB124.

Dawkins, S. T.

S. T. Dawkins, J. J. McFerran, and A. N. Luiten, IEEE Trans. Ultrason. Ferroelectr. Freq. Control 54, 918 (2007).
[CrossRef]

Diddams, S. A.

L. Nugent-Glandorf, T. A. Johnson, Y. Kobayashi, and S. A. Diddams, Opt. Lett. 36, 1578 (2011).
[CrossRef]

S. A. Diddams, L. Hollberg, and V. Mbele, Nature 445, 627 (2007).
[CrossRef]

B. R. Washburn, S. A. Diddams, N. R. Newbury, J. W. Nicholson, M. F. Yan, and C. G. Jrgensen, Opt. Lett. 29, 250 (2004).
[CrossRef]

D. J. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, Science 288, 635 (2000).
[CrossRef]

Foreman, S. M.

M. M. Boyd, T. Zelevinsky, A. D. Ludlow, S. M. Foreman, S. Blatt, T. Ido, and J. Ye, Science 314, 1430 (2006).
[CrossRef]

Funk, A.

A. Funk, D. Daubendiek, S. T. Cundiff, and C. R. Menyuk, CLEO (OSA, 2011), paper JThB124.

Hall, J. L.

D. J. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, Science 288, 635 (2000).
[CrossRef]

Hänsch, T. W.

T. Udem, R. Holzwarth, and T. W. Hänsch, Nature 416, 233 (2002).
[CrossRef]

Haus, H.

L. Nelson, D. Jones, K. Tamura, H. Haus, and E. Ippen, Appl. Phys. B 65, 277 (1997).
[CrossRef]

K. Tamura, E. Ippen, H. Haus, and L. Nelson, Opt. Lett. 18, 1080 (1993).
[CrossRef]

Haus, H. A.

H. A. Haus and A. Mecozzi, IEEE J. Quantum Electron. 29, 983 (1993).
[CrossRef]

Hollberg, L.

S. A. Diddams, L. Hollberg, and V. Mbele, Nature 445, 627 (2007).
[CrossRef]

Holzwarth, R.

T. Udem, R. Holzwarth, and T. W. Hänsch, Nature 416, 233 (2002).
[CrossRef]

Ido, T.

M. M. Boyd, T. Zelevinsky, A. D. Ludlow, S. M. Foreman, S. Blatt, T. Ido, and J. Ye, Science 314, 1430 (2006).
[CrossRef]

Ilan, B.

Ippen, E.

L. Nelson, D. Jones, K. Tamura, H. Haus, and E. Ippen, Appl. Phys. B 65, 277 (1997).
[CrossRef]

K. Tamura, E. Ippen, H. Haus, and L. Nelson, Opt. Lett. 18, 1080 (1993).
[CrossRef]

Johnson, T. A.

Jones, D.

L. Nelson, D. Jones, K. Tamura, H. Haus, and E. Ippen, Appl. Phys. B 65, 277 (1997).
[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, Science 288, 635 (2000).
[CrossRef]

Jrgensen, C. G.

Jung, K.

Kim, C.

Kim, H.

Kim, J.

Kobayashi, Y.

Ludlow, A. D.

M. M. Boyd, T. Zelevinsky, A. D. Ludlow, S. M. Foreman, S. Blatt, T. Ido, and J. Ye, Science 314, 1430 (2006).
[CrossRef]

Luiten, A. N.

S. T. Dawkins, J. J. McFerran, and A. N. Luiten, IEEE Trans. Ultrason. Ferroelectr. Freq. Control 54, 918 (2007).
[CrossRef]

Mbele, V.

S. A. Diddams, L. Hollberg, and V. Mbele, Nature 445, 627 (2007).
[CrossRef]

McFerran, J. J.

S. T. Dawkins, J. J. McFerran, and A. N. Luiten, IEEE Trans. Ultrason. Ferroelectr. Freq. Control 54, 918 (2007).
[CrossRef]

Mecozzi, A.

H. A. Haus and A. Mecozzi, IEEE J. Quantum Electron. 29, 983 (1993).
[CrossRef]

Menyuk, C.

Menyuk, C. R.

C. R. Menyuk, J. K. Wahlstrand, J. Willits, R. P. Smith, T. R. Schibli, and S. T. Cundiff, Opt. Express 15, 6677 (2007).
[CrossRef]

A. Funk, D. Daubendiek, S. T. Cundiff, and C. R. Menyuk, CLEO (OSA, 2011), paper JThB124.

Nelson, L.

L. Nelson, D. Jones, K. Tamura, H. Haus, and E. Ippen, Appl. Phys. B 65, 277 (1997).
[CrossRef]

K. Tamura, E. Ippen, H. Haus, and L. Nelson, Opt. Lett. 18, 1080 (1993).
[CrossRef]

Newbury, N. R.

Nicholson, J. W.

Nugent-Glandorf, L.

Ranka, J. K.

D. J. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, Science 288, 635 (2000).
[CrossRef]

Schibli, T.

Schibli, T. R.

Smith, R. P.

Song, Y.

Stentz, A.

D. J. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, Science 288, 635 (2000).
[CrossRef]

Swann, W. C.

I. Coddington, W. C. Swann, and N. R. Newbury, Phys. Rev. Lett. 100, 013902 (2008).
[CrossRef]

N. R. Newbury and W. C. Swann, J. Opt. Soc. Am. B 24, 1756 (2007).
[CrossRef]

Tamura, K.

L. Nelson, D. Jones, K. Tamura, H. Haus, and E. Ippen, Appl. Phys. B 65, 277 (1997).
[CrossRef]

K. Tamura, E. Ippen, H. Haus, and L. Nelson, Opt. Lett. 18, 1080 (1993).
[CrossRef]

Udem, T.

T. Udem, R. Holzwarth, and T. W. Hänsch, Nature 416, 233 (2002).
[CrossRef]

Wahlstrand, J.

Wahlstrand, J. K.

Wai, P.

P. Wai and C. Menyuk, J. Lightwave Technol. 14, 148 (1996).
[CrossRef]

Washburn, B. R.

Willits, J.

Windeler, R. S.

D. J. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, Science 288, 635 (2000).
[CrossRef]

Yan, M. F.

Ye, J.

M. M. Boyd, T. Zelevinsky, A. D. Ludlow, S. M. Foreman, S. Blatt, T. Ido, and J. Ye, Science 314, 1430 (2006).
[CrossRef]

Zelevinsky, T.

M. M. Boyd, T. Zelevinsky, A. D. Ludlow, S. M. Foreman, S. Blatt, T. Ido, and J. Ye, Science 314, 1430 (2006).
[CrossRef]

Appl. Phys. B (1)

L. Nelson, D. Jones, K. Tamura, H. Haus, and E. Ippen, Appl. Phys. B 65, 277 (1997).
[CrossRef]

IEEE J. Quantum Electron. (1)

H. A. Haus and A. Mecozzi, IEEE J. Quantum Electron. 29, 983 (1993).
[CrossRef]

IEEE Trans. Ultrason. Ferroelectr. Freq. Control (1)

S. T. Dawkins, J. J. McFerran, and A. N. Luiten, IEEE Trans. Ultrason. Ferroelectr. Freq. Control 54, 918 (2007).
[CrossRef]

J. Lightwave Technol. (1)

P. Wai and C. Menyuk, J. Lightwave Technol. 14, 148 (1996).
[CrossRef]

J. Opt. Soc. Am. B (1)

Nature (2)

T. Udem, R. Holzwarth, and T. W. Hänsch, Nature 416, 233 (2002).
[CrossRef]

S. A. Diddams, L. Hollberg, and V. Mbele, Nature 445, 627 (2007).
[CrossRef]

Opt. Express (3)

Opt. Lett. (5)

Phys. Rev. Lett. (1)

I. Coddington, W. C. Swann, and N. R. Newbury, Phys. Rev. Lett. 100, 013902 (2008).
[CrossRef]

Science (2)

D. J. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, Science 288, 635 (2000).
[CrossRef]

M. M. Boyd, T. Zelevinsky, A. D. Ludlow, S. M. Foreman, S. Blatt, T. Ido, and J. Ye, Science 314, 1430 (2006).
[CrossRef]

Other (1)

A. Funk, D. Daubendiek, S. T. Cundiff, and C. R. Menyuk, CLEO (OSA, 2011), paper JThB124.

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Figures (5)

Fig. 1.
Fig. 1.

Experimental setup. The test laser has a repetition rate of 96 MHz, while the reference laser is 24 MHz. PS, phase shifter; mono, monochromator; F to V, frequency to voltage convertor.

Fig. 2.
Fig. 2.

Experimental measurements of pulse parameter changes for (a) pulse energy Δw, (b) central frequency Δϖ, (c) central pulse timing Δτ, and (d) pulse phase Δθ, and their corresponding fitting. The points are the experimental results and the blue curves are their fitting.

Fig. 3.
Fig. 3.

Free running linewidth of comb lines as a function of frequency offset from the central frequency. The red line is the result with full matrix A elements. The black line is the result when timing jitter caused by dispersion, gain, and intensity fluctuation is neglected (Aτw=Aτg=Aτϖ=0. The blue line is the result when in addition phase jitter induced by dispersion, gain and intensity fluctuation is neglected (Aθw=Aθg=Aθϖ=0).

Fig. 4.
Fig. 4.

Free running comb lines linewidth with different laser parameters for (a) dispersion term, (b) Kerr shock term, (c) Kerr phase term, and (d) cavity lifetime. Different values are labeled in the legend. The insets in (b) and (c) are the zoom in for comb lines near 50 THz away.

Fig. 5.
Fig. 5.

Calculated phase noise spectrum with a simple feedback for comb line at the central frequency (black), 50 THz away (red), and 100 THz away (blue).

Equations (4)

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

dVdt=AV+S,
dΔViΔVjdT=k,l(Aik+Ajl)ΔVi(T)ΔVj(T)+Dij,
In(ω)0dTcos(ωT)exp{12Ωn2[Δτ(T)]2+Ωn2Δτ(T)Δθ(T)12[Δθ(T)]2}.
Snϕ(ω)=12Ωn2[Δτ(ω)]2Ωn2Δτ(ω)Δθ(ω)+12[Δθ(ω)]2,

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