Abstract

We investigate the dynamics of the carrier-envelope-offset (CEO) frequency, fCEO, controlled by a pump current on the self-referencing of an optical frequency comb generated from a diode-pumped solid-state laser at 1.56 μm. We observe a reversal point in the tuning of fCEO with the pump current. Between the low- and high-frequency region in the dynamic response of fCEO to pump current modulation, we observe a significant phase shift of 180deg in the transfer function. As a result, it is impossible to stabilize fCEO at a pump current above the reversal point, although the free-running CEO beat at this point has a higher signal-to-noise ratio than underneath the reversal point at which the locking is straightforward. Our results indicate that a high signal-to-noise ratio and a low-noise CEO beat are not sufficient indicators for the feasibility of comb self-referencing in cases for which CEO dynamics play a dominant role.

© 2012 Optical Society of America

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References

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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, Science 288, 635 (2000).
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    [CrossRef]
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    [CrossRef]
  4. N. Newbury and B. Washburn, IEEE J. Quantum Electron. 41, 1388 (2005).
    [CrossRef]
  5. K. W. Holman, R. J. Jones, A. Marian, S. T. Cundiff, and Y. Je, IEEE J. Sel. Top. Quantum Electron. 9, 1018 (2003).
    [CrossRef]
  6. M. C. Stumpf, S. Pekarek, A. E. H. Oehler, T. Südmeyer, J. M. Dudley, and U. Keller, Appl. Phys. B 99, 401 (2010).
    [CrossRef]
  7. S. Schilt, N. Bucalovic, V. Dolgovskiy, C. Schori, M. Stumpf, G. Di Domenico, S. Pekarek, A. Oehler, T. Südmeyer, U. Keller, and P. Thomann, Opt. Express 19, 24171 (2011).
    [CrossRef]
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    [CrossRef]
  9. S. Schilt, N. Bucalovic, L. Tombez, V. Dolgovskiy, C. Schori, G. Di Domenico, M. Zaffalon, and P. Thomann, Rev. Sci. Instrum. 82, 123116 (2011).
    [CrossRef]
  10. M. C. Stumpf, “Diode-pumped solid state lasers for optical frequency combs,” Dissertation ETH Nr. 18799 (University of Neuchatel, 2009).
  11. R. W. Fox, C. W. Oates, and L. Hollberg, “Cavity-enhanced spectroscopies,” in Experimental Methods in the Physical Sciences (Academic, 2003), Vol. 40, Chap. 1, pp. 1–323.

2012 (1)

2011 (2)

S. Schilt, N. Bucalovic, L. Tombez, V. Dolgovskiy, C. Schori, G. Di Domenico, M. Zaffalon, and P. Thomann, Rev. Sci. Instrum. 82, 123116 (2011).
[CrossRef]

S. Schilt, N. Bucalovic, V. Dolgovskiy, C. Schori, M. Stumpf, G. Di Domenico, S. Pekarek, A. Oehler, T. Südmeyer, U. Keller, and P. Thomann, Opt. Express 19, 24171 (2011).
[CrossRef]

2010 (1)

M. C. Stumpf, S. Pekarek, A. E. H. Oehler, T. Südmeyer, J. M. Dudley, and U. Keller, Appl. Phys. B 99, 401 (2010).
[CrossRef]

2005 (1)

N. Newbury and B. Washburn, IEEE J. Quantum Electron. 41, 1388 (2005).
[CrossRef]

2003 (1)

K. W. Holman, R. J. Jones, A. Marian, S. T. Cundiff, and Y. Je, IEEE J. Sel. Top. Quantum Electron. 9, 1018 (2003).
[CrossRef]

2001 (1)

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]

1999 (1)

H. R. Telle, G. Steinmeyer, A. E. Dunlop, J. Stenger, D. H. Sutter, and U. Keller, Appl. Phys. B 69, 327 (1999).
[CrossRef]

Angelow, G.

Boiko, A.

Bucalovic, N.

Cundiff, S. T.

K. W. Holman, R. J. Jones, A. Marian, S. T. Cundiff, and Y. Je, IEEE J. Sel. Top. Quantum Electron. 9, 1018 (2003).
[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]

Di Domenico, G.

Diddams, S. 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]

Dolgovskiy, V.

Dudley, J. M.

M. C. Stumpf, S. Pekarek, A. E. H. Oehler, T. Südmeyer, J. M. Dudley, and U. Keller, Appl. Phys. B 99, 401 (2010).
[CrossRef]

Dunlop, A. E.

H. R. Telle, G. Steinmeyer, A. E. Dunlop, J. Stenger, D. H. Sutter, and U. Keller, Appl. Phys. B 69, 327 (1999).
[CrossRef]

Ell, R.

Fox, R. W.

R. W. Fox, C. W. Oates, and L. Hollberg, “Cavity-enhanced spectroscopies,” in Experimental Methods in the Physical Sciences (Academic, 2003), Vol. 40, Chap. 1, pp. 1–323.

Fujimoto, J. G.

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]

Hollberg, L.

R. W. Fox, C. W. Oates, and L. Hollberg, “Cavity-enhanced spectroscopies,” in Experimental Methods in the Physical Sciences (Academic, 2003), Vol. 40, Chap. 1, pp. 1–323.

Holman, K. W.

K. W. Holman, R. J. Jones, A. Marian, S. T. Cundiff, and Y. Je, IEEE J. Sel. Top. Quantum Electron. 9, 1018 (2003).
[CrossRef]

Ippen, E. P.

Je, Y.

K. W. Holman, R. J. Jones, A. Marian, S. T. Cundiff, and Y. Je, IEEE J. Sel. Top. Quantum Electron. 9, 1018 (2003).
[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]

Jones, R. J.

K. W. Holman, R. J. Jones, A. Marian, S. T. Cundiff, and Y. Je, IEEE J. Sel. Top. Quantum Electron. 9, 1018 (2003).
[CrossRef]

Kärtner, F. X.

Keller, U.

S. Schilt, N. Bucalovic, V. Dolgovskiy, C. Schori, M. Stumpf, G. Di Domenico, S. Pekarek, A. Oehler, T. Südmeyer, U. Keller, and P. Thomann, Opt. Express 19, 24171 (2011).
[CrossRef]

M. C. Stumpf, S. Pekarek, A. E. H. Oehler, T. Südmeyer, J. M. Dudley, and U. Keller, Appl. Phys. B 99, 401 (2010).
[CrossRef]

H. R. Telle, G. Steinmeyer, A. E. Dunlop, J. Stenger, D. H. Sutter, and U. Keller, Appl. Phys. B 69, 327 (1999).
[CrossRef]

Lederer, M. J.

Luther-Davies, B.

Marian, A.

K. W. Holman, R. J. Jones, A. Marian, S. T. Cundiff, and Y. Je, IEEE J. Sel. Top. Quantum Electron. 9, 1018 (2003).
[CrossRef]

Morgner, U.

Newbury, N.

N. Newbury and B. Washburn, IEEE J. Quantum Electron. 41, 1388 (2005).
[CrossRef]

Oates, C. W.

R. W. Fox, C. W. Oates, and L. Hollberg, “Cavity-enhanced spectroscopies,” in Experimental Methods in the Physical Sciences (Academic, 2003), Vol. 40, Chap. 1, pp. 1–323.

Oehler, A.

Oehler, A. E. H.

M. C. Stumpf, S. Pekarek, A. E. H. Oehler, T. Südmeyer, J. M. Dudley, and U. Keller, Appl. Phys. B 99, 401 (2010).
[CrossRef]

Pekarek, S.

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]

Scheuer, V.

Schilt, S.

Schori, C.

Steinmeyer, G.

H. R. Telle, G. Steinmeyer, A. E. Dunlop, J. Stenger, D. H. Sutter, and U. Keller, Appl. Phys. B 69, 327 (1999).
[CrossRef]

Stenger, J.

H. R. Telle, G. Steinmeyer, A. E. Dunlop, J. Stenger, D. H. Sutter, and U. Keller, Appl. Phys. B 69, 327 (1999).
[CrossRef]

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]

Stumpf, M.

Stumpf, M. C.

M. C. Stumpf, S. Pekarek, A. E. H. Oehler, T. Südmeyer, J. M. Dudley, and U. Keller, Appl. Phys. B 99, 401 (2010).
[CrossRef]

M. C. Stumpf, “Diode-pumped solid state lasers for optical frequency combs,” Dissertation ETH Nr. 18799 (University of Neuchatel, 2009).

Südmeyer, T.

Sutter, D. H.

H. R. Telle, G. Steinmeyer, A. E. Dunlop, J. Stenger, D. H. Sutter, and U. Keller, Appl. Phys. B 69, 327 (1999).
[CrossRef]

Telle, H. R.

H. R. Telle, G. Steinmeyer, A. E. Dunlop, J. Stenger, D. H. Sutter, and U. Keller, Appl. Phys. B 69, 327 (1999).
[CrossRef]

Thomann, P.

Tombez, L.

S. Schilt, N. Bucalovic, L. Tombez, V. Dolgovskiy, C. Schori, G. Di Domenico, M. Zaffalon, and P. Thomann, Rev. Sci. Instrum. 82, 123116 (2011).
[CrossRef]

Tschudi, T.

Washburn, B.

N. Newbury and B. Washburn, IEEE J. Quantum Electron. 41, 1388 (2005).
[CrossRef]

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]

Zaffalon, M.

S. Schilt, N. Bucalovic, L. Tombez, V. Dolgovskiy, C. Schori, G. Di Domenico, M. Zaffalon, and P. Thomann, Rev. Sci. Instrum. 82, 123116 (2011).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. B (2)

H. R. Telle, G. Steinmeyer, A. E. Dunlop, J. Stenger, D. H. Sutter, and U. Keller, Appl. Phys. B 69, 327 (1999).
[CrossRef]

M. C. Stumpf, S. Pekarek, A. E. H. Oehler, T. Südmeyer, J. M. Dudley, and U. Keller, Appl. Phys. B 99, 401 (2010).
[CrossRef]

IEEE J. Quantum Electron. (1)

N. Newbury and B. Washburn, IEEE J. Quantum Electron. 41, 1388 (2005).
[CrossRef]

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

K. W. Holman, R. J. Jones, A. Marian, S. T. Cundiff, and Y. Je, IEEE J. Sel. Top. Quantum Electron. 9, 1018 (2003).
[CrossRef]

Opt. Express (1)

Opt. Lett. (1)

Rev. Sci. Instrum. (1)

S. Schilt, N. Bucalovic, L. Tombez, V. Dolgovskiy, C. Schori, G. Di Domenico, M. Zaffalon, and P. Thomann, Rev. Sci. Instrum. 82, 123116 (2011).
[CrossRef]

Science (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]

Other (2)

M. C. Stumpf, “Diode-pumped solid state lasers for optical frequency combs,” Dissertation ETH Nr. 18799 (University of Neuchatel, 2009).

R. W. Fox, C. W. Oates, and L. Hollberg, “Cavity-enhanced spectroscopies,” in Experimental Methods in the Physical Sciences (Academic, 2003), Vol. 40, Chap. 1, pp. 1–323.

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Figures (4)

Fig. 1.
Fig. 1.

Static tuning curve of the CEO frequency f CEO with respect to the pump current showing a reversal point at I p 860 mA : f CEO vs I p (left scale, black circles) and static tuning coefficient (right scale, grey squares) f CEO is stabilized to 20 MHz in the ERGO comb, which can be realized in principle at two current values I low and I high .

Fig. 2.
Fig. 2.

Frequency noise power spectral density (PSD) of the CEO beat measured at two different pump currents I low and I high at which f CEO = 20 MHz , located on each side of the reversal point. Only the noise that exceeds the β -separation line S δ ν ( f ) = ( 8 l n 2 / π 2 ) f (dashed line) contributes to the linewidth of the CEO beat [8]. Inset: corresponding CEO-beat showing a higher signal-to-noise ratio at I high than at I low .

Fig. 3.
Fig. 3.

Amplitude (a) and phase (b) of the dynamic response of f CEO to pump current modulation measured at different pump currents: I p = I low below the reversal point (green curves), I p = I high above the reversal point (red curves) and I p = I reversal at the reversal point (orange curves).

Fig. 4.
Fig. 4.

Gain (a) and phase (b) of the overall CEO stabilization loop transfer function at the two different pump currents I p = I low (top curves) and I p = I high (bottom curves). At I p = I low , the phase margin is sufficient to achieve a feedback bandwidth (labeled as f 0 dB ) of several kHz. At I p = I high , the phase is < 180 degrees already at 1 Hz Fourier frequency, which prevents the CEO stabilization.

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