Abstract

We present a study of the impact of the cross-coupling between the two servo loops used to stabilize the repetition rate frep and the carrier-envelope offset (CEO) frequency fCEO in a commercial Er:fiber frequency comb, based on the combination of experimental measurements and a model of the coupled loops. The developed theoretical model enables us to quantify the influence of the servo-loop coupling on an optical comb line, by simulating the hypothetic case where no coupling would be present. Numerical values for the model were obtained from an extensive characterization of the comb, in terms of frequency noise and dynamic response to a modulation applied to each actuator, for both frep and fCEO. To validate the model, the frequency noise of an optical comb line at 1.56 μm was experimentally measured from the heterodyne beat between the comb and a cavity-stabilized ultranarrow-linewidth laser and showed good agreement with the calculated noise spectrum. The coupling between the two stabilization loops results in a more than 10-fold reduction of the comb mode frequency noise power spectral density in a wide Fourier frequency range.

© 2012 Optical Society of America

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  3. M. C. Stowe, M. J. Thorpe, A. Pe’er, J. Ye, J. E. Stalnaker, V. Gerginov, and S. A. Diddams, “Direct frequency comb spectroscopy,” Adv. At. Mol.Opt. Phys. 55, 1–60 (2008).
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  5. B. Bernhardt, A. Ozawa, P. Jacquet, M. Jacquey, Y. Kobayashi, T. Udem, R. Holzwarth, G. Guelachvili, T. W. Hänsch, and N. Picqué, “Cavity-enhanced dual-comb spectroscopy,” Nat. Photonics 4, 55–57 (2010).
  6. R. Paschotta, A. Schlatter, S. C. Zeller, H. R. Telle, and U. Keller, “Optical phase noise and carrier-envelope offset of mode-locked lasers,” Appl. Phys. B 82, 265–273 (2006).
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  7. E. Benkler, H. R. Telle, A. Zach, and F. Tauser, “Circumvention of noise contributions in fiber laser baser frequency combs,” Opt. Express 13, 5662–5668 (2005).
    [CrossRef]
  8. 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).
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    [CrossRef]
  13. J. Rauschenberger, T. Fortier, D. Jones, J. Ye, and S. Cundiff, “Control of the frequency comb from a modelocked Erbium-doped fiber laser,” Opt. Express 10, 1404–1410 (2002).
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    [CrossRef]
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    [CrossRef]
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  25. J. Bechhoefer, “Feedback for physicists: a tutorial essay on control,” Rev. Mod. Phys. 77, 783–836 (2005).
    [CrossRef]
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    [CrossRef]
  28. S. Schilt, N. Bucalovic, V. Dolgovskiy, C. Schori, M. C. Stumpf, G. Di Domenico, S. Pekarek, A. E. H. Oehler, T. Südmeyer, U. Keller, and P. Thomann, “Fully stabilized optical frequency comb with sub-radian CEO phase noise from a SESAM-modelocked 1.5 μm solid-state laser,” Opt. Express 19, 24171–24181 (2011).
    [CrossRef]
  29. J. J. McFerran, W. C. Swann, B. R. Washburn, and N. R. Newbury, “Suppression of pump-induced frequency noise in fiber-laser frequency combs leading to sub-radion fceo phase excursion,” Appl. Phys. B 86, 219–227 (2007).
    [CrossRef]
  30. J. Millo, M. Abgrall, M. Lours, E. M. L. English, H. Jiang, J. Guéna, A. Clairon, S. Bize, Y. Le Coq, G. Santarelli, and M. E. Tobar, “Ultra-low noise microwave generation with fiber-based optical frequency comb and application to atomic fountain clock,” Appl. Phys. Lett. 94, 141105 (2009).
    [CrossRef]

2012

W. Zhang, M. Lours, M. Fischer, R. Holzwarth, G. Santarelli, and Y. Le Coq, “Characterizing a fiber-based frequency comb with electro-optic modulator,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 59, 432–438 (2012).
[CrossRef]

2011

W. Zhang, Z. Xu, M. Lours, R. Boudot, Y. Kersalé, A. N. Luiten, Y. Le Coq, and G. Santarelli, “Advanced noise reduction techniques for ultra-low phase noise optical-to-microwave division with femtosecond fiber combs,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 58, 900–908 (2011).
[CrossRef]

S. Schilt, N. Bucalovic, L. Tombez, V. Dolgovskiy, C. Schori, G. Di Domenico, M. Zaffalon, and P. Thomann, “Frequency discriminators for the characterization of narrow-spectrum heterodyne beat signals: application to the measurement of a sub-hertz carrier-envelope-offset beat in an optical frequency comb,” Rev. Sci. Instrum. 82, 123116(2011).
[CrossRef]

D. C. Heinecke, A. Bartels, and S. A. Diddams, “Offset frequency dynamics and phase noise properties of a self-referenced 10 GHz Ti-sapphire frequency comb,” Opt. Express 19, 18440–18451 (2011).
[CrossRef]

S. Schilt, N. Bucalovic, V. Dolgovskiy, C. Schori, M. C. Stumpf, G. Di Domenico, S. Pekarek, A. E. H. Oehler, T. Südmeyer, U. Keller, and P. Thomann, “Fully stabilized optical frequency comb with sub-radian CEO phase noise from a SESAM-modelocked 1.5 μm solid-state laser,” Opt. Express 19, 24171–24181 (2011).
[CrossRef]

2010

B. Bernhardt, A. Ozawa, P. Jacquet, M. Jacquey, Y. Kobayashi, T. Udem, R. Holzwarth, G. Guelachvili, T. W. Hänsch, and N. Picqué, “Cavity-enhanced dual-comb spectroscopy,” Nat. Photonics 4, 55–57 (2010).

2009

J. Millo, M. Abgrall, M. Lours, E. M. L. English, H. Jiang, J. Guéna, A. Clairon, S. Bize, Y. Le Coq, G. Santarelli, and M. E. Tobar, “Ultra-low noise microwave generation with fiber-based optical frequency comb and application to atomic fountain clock,” Appl. Phys. Lett. 94, 141105 (2009).
[CrossRef]

2008

M. C. Stowe, M. J. Thorpe, A. Pe’er, J. Ye, J. E. Stalnaker, V. Gerginov, and S. A. Diddams, “Direct frequency comb spectroscopy,” Adv. At. Mol.Opt. Phys. 55, 1–60 (2008).
[CrossRef]

2007

D. R. Walker, T. Udem, C. Gohle, B. Stein, and T. W. Hänsch, “Frequency dependence of the fixed point in a fluctuating frequency comb,” Appl. Phys. B 89, 535–538 (2007).
[CrossRef]

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

K. Kim, J. W. Nicholson, M. Yan, J. C. Knight, N. R. Newbury, and S. A. Diddams, “Characterization of frequency noise on a broadband infrared frequency comb using optical heterodyne techniques,” Opt. Express 15, 17715–17723 (2007).
[CrossRef]

J. J. McFerran, W. C. Swann, B. R. Washburn, and N. R. Newbury, “Suppression of pump-induced frequency noise in fiber-laser frequency combs leading to sub-radion fceo phase excursion,” Appl. Phys. B 86, 219–227 (2007).
[CrossRef]

2006

M. J. Thorpe, K. D. Moll, R. J. Jones, B. Safdi, and J. Ye, “Broadband cavity ringdown spectroscopy for sensitive and rapid molecular detection,” Science 311, 1595–1599 (2006).
[CrossRef]

T. W. Hänsch, “Nobel lecture: passion for precision,” Rev. Mod. Phys. 78, 1297–1309 (2006).
[CrossRef]

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

2005

L. Hollberg, S. Diddams, A. Bartels, T. Fortier, and K. Kim, “The measurement of optical frequencies,” Metrologia 42, S105–S124 (2005).
[CrossRef]

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

J. Bechhoefer, “Feedback for physicists: a tutorial essay on control,” Rev. Mod. Phys. 77, 783–836 (2005).
[CrossRef]

E. Benkler, H. R. Telle, A. Zach, and F. Tauser, “Circumvention of noise contributions in fiber laser baser frequency combs,” Opt. Express 13, 5662–5668 (2005).
[CrossRef]

B. R. Washburn, W. C. Swann, and N. R. Newbury, “Response dynamics of the frequency comb output from a femtosecond laser,” Opt. Express 13, 10622–10633 (2005).
[CrossRef]

2004

N. Haverkamp, H. Hundertmark, C. Fallnich, and H. R. Telle, “Frequency stabilization of mode-locked Erbium fiber lasers using pump power control,” Appl. Phys. B 78, 321–324 (2004).
[CrossRef]

2003

J. Ye, H. Schnatz, and L. W. Hollberg, “Optical frequency combs: from frequency metrology to optical phase control,” IEEE J. Sel. Top. Quantum Electron. 9, 1041–1058 (2003).
[CrossRef]

2002

F. W. Helbing, G. Steinmeyer, J. Stenger, H. R. Telle, and U. Keller, “Carrier–envelope-offset dynamics and stabilization of femtosecond pulses,” Appl. Phys. B. 74, S35–S42 (2002).
[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]

J. Rauschenberger, T. Fortier, D. Jones, J. Ye, and S. Cundiff, “Control of the frequency comb from a modelocked Erbium-doped fiber laser,” Opt. Express 10, 1404–1410 (2002).

1999

H. R. Telle, G. Steinmeyer, A. E. Dunlop, J. Stenger, D. H. Sutter, and U. Keller, “Carrier-envelope offset phase control: a novel concept for absolute optical frequency measurement and ultrashort pulse generation,” Appl. Phys. B 69, 327–332 (1999).
[CrossRef]

Abgrall, M.

J. Millo, M. Abgrall, M. Lours, E. M. L. English, H. Jiang, J. Guéna, A. Clairon, S. Bize, Y. Le Coq, G. Santarelli, and M. E. Tobar, “Ultra-low noise microwave generation with fiber-based optical frequency comb and application to atomic fountain clock,” Appl. Phys. Lett. 94, 141105 (2009).
[CrossRef]

Bartels, A.

Bechhoefer, J.

J. Bechhoefer, “Feedback for physicists: a tutorial essay on control,” Rev. Mod. Phys. 77, 783–836 (2005).
[CrossRef]

Benkler, E.

Bernhardt, B.

B. Bernhardt, A. Ozawa, P. Jacquet, M. Jacquey, Y. Kobayashi, T. Udem, R. Holzwarth, G. Guelachvili, T. W. Hänsch, and N. Picqué, “Cavity-enhanced dual-comb spectroscopy,” Nat. Photonics 4, 55–57 (2010).

Bize, S.

J. Millo, M. Abgrall, M. Lours, E. M. L. English, H. Jiang, J. Guéna, A. Clairon, S. Bize, Y. Le Coq, G. Santarelli, and M. E. Tobar, “Ultra-low noise microwave generation with fiber-based optical frequency comb and application to atomic fountain clock,” Appl. Phys. Lett. 94, 141105 (2009).
[CrossRef]

Borsutzky, A.

O. Svelto, S. Longhi, G. Della Valle, S. Kück, G. Huber, M. Pollnau, H. Hillmer, S. Hansmann, R. Engelbrecht, H. Brand, J. Kaiser, A. B. Peterson, R. Malz, S. Steinberg, G. Marowsky, U. Brinkmann, D. Lo, A. Borsutzky, H. Wächter, M. W. Sigrist, E. Saldin, E. Schneidmiller, M. Yurkov, K. Midorikawa, J. Hein, R. Sauerbrey, and J. Helmcke, “Lasers and coherent light sources,” in Springer Handbook of Lasers and Optics, F. Träger, ed. (Springer, 2007), pp. 583–936.

Boudot, R.

W. Zhang, Z. Xu, M. Lours, R. Boudot, Y. Kersalé, A. N. Luiten, Y. Le Coq, and G. Santarelli, “Advanced noise reduction techniques for ultra-low phase noise optical-to-microwave division with femtosecond fiber combs,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 58, 900–908 (2011).
[CrossRef]

Brand, H.

O. Svelto, S. Longhi, G. Della Valle, S. Kück, G. Huber, M. Pollnau, H. Hillmer, S. Hansmann, R. Engelbrecht, H. Brand, J. Kaiser, A. B. Peterson, R. Malz, S. Steinberg, G. Marowsky, U. Brinkmann, D. Lo, A. Borsutzky, H. Wächter, M. W. Sigrist, E. Saldin, E. Schneidmiller, M. Yurkov, K. Midorikawa, J. Hein, R. Sauerbrey, and J. Helmcke, “Lasers and coherent light sources,” in Springer Handbook of Lasers and Optics, F. Träger, ed. (Springer, 2007), pp. 583–936.

Brinkmann, U.

O. Svelto, S. Longhi, G. Della Valle, S. Kück, G. Huber, M. Pollnau, H. Hillmer, S. Hansmann, R. Engelbrecht, H. Brand, J. Kaiser, A. B. Peterson, R. Malz, S. Steinberg, G. Marowsky, U. Brinkmann, D. Lo, A. Borsutzky, H. Wächter, M. W. Sigrist, E. Saldin, E. Schneidmiller, M. Yurkov, K. Midorikawa, J. Hein, R. Sauerbrey, and J. Helmcke, “Lasers and coherent light sources,” in Springer Handbook of Lasers and Optics, F. Träger, ed. (Springer, 2007), pp. 583–936.

Bucalovic, N.

S. Schilt, N. Bucalovic, V. Dolgovskiy, C. Schori, M. C. Stumpf, G. Di Domenico, S. Pekarek, A. E. H. Oehler, T. Südmeyer, U. Keller, and P. Thomann, “Fully stabilized optical frequency comb with sub-radian CEO phase noise from a SESAM-modelocked 1.5 μm solid-state laser,” Opt. Express 19, 24171–24181 (2011).
[CrossRef]

S. Schilt, N. Bucalovic, L. Tombez, V. Dolgovskiy, C. Schori, G. Di Domenico, M. Zaffalon, and P. Thomann, “Frequency discriminators for the characterization of narrow-spectrum heterodyne beat signals: application to the measurement of a sub-hertz carrier-envelope-offset beat in an optical frequency comb,” Rev. Sci. Instrum. 82, 123116(2011).
[CrossRef]

V. Dolgovskiy, S. Schilt, G. Di Domenico, N. Bucalovic, C. Schori, and P. Thomann, “1.5 μm cavity-stabilized laser for ultra-stable microwave generation,” in Proceedings of 2011 Joint Conference of the IEEE International Frequency Control and the European Frequency and Time Forum (FCS), San Francisco, USA, May 2–5, 2011 (IEEE, 2011), pp. 1–3.

Clairon, A.

J. Millo, M. Abgrall, M. Lours, E. M. L. English, H. Jiang, J. Guéna, A. Clairon, S. Bize, Y. Le Coq, G. Santarelli, and M. E. Tobar, “Ultra-low noise microwave generation with fiber-based optical frequency comb and application to atomic fountain clock,” Appl. Phys. Lett. 94, 141105 (2009).
[CrossRef]

Cundiff, S.

Della Valle, G.

O. Svelto, S. Longhi, G. Della Valle, S. Kück, G. Huber, M. Pollnau, H. Hillmer, S. Hansmann, R. Engelbrecht, H. Brand, J. Kaiser, A. B. Peterson, R. Malz, S. Steinberg, G. Marowsky, U. Brinkmann, D. Lo, A. Borsutzky, H. Wächter, M. W. Sigrist, E. Saldin, E. Schneidmiller, M. Yurkov, K. Midorikawa, J. Hein, R. Sauerbrey, and J. Helmcke, “Lasers and coherent light sources,” in Springer Handbook of Lasers and Optics, F. Träger, ed. (Springer, 2007), pp. 583–936.

Di Domenico, G.

S. Schilt, N. Bucalovic, V. Dolgovskiy, C. Schori, M. C. Stumpf, G. Di Domenico, S. Pekarek, A. E. H. Oehler, T. Südmeyer, U. Keller, and P. Thomann, “Fully stabilized optical frequency comb with sub-radian CEO phase noise from a SESAM-modelocked 1.5 μm solid-state laser,” Opt. Express 19, 24171–24181 (2011).
[CrossRef]

S. Schilt, N. Bucalovic, L. Tombez, V. Dolgovskiy, C. Schori, G. Di Domenico, M. Zaffalon, and P. Thomann, “Frequency discriminators for the characterization of narrow-spectrum heterodyne beat signals: application to the measurement of a sub-hertz carrier-envelope-offset beat in an optical frequency comb,” Rev. Sci. Instrum. 82, 123116(2011).
[CrossRef]

V. Dolgovskiy, S. Schilt, G. Di Domenico, N. Bucalovic, C. Schori, and P. Thomann, “1.5 μm cavity-stabilized laser for ultra-stable microwave generation,” in Proceedings of 2011 Joint Conference of the IEEE International Frequency Control and the European Frequency and Time Forum (FCS), San Francisco, USA, May 2–5, 2011 (IEEE, 2011), pp. 1–3.

Diddams, S.

L. Hollberg, S. Diddams, A. Bartels, T. Fortier, and K. Kim, “The measurement of optical frequencies,” Metrologia 42, S105–S124 (2005).
[CrossRef]

Diddams, S. A.

Dolgovskiy, V.

S. Schilt, N. Bucalovic, V. Dolgovskiy, C. Schori, M. C. Stumpf, G. Di Domenico, S. Pekarek, A. E. H. Oehler, T. Südmeyer, U. Keller, and P. Thomann, “Fully stabilized optical frequency comb with sub-radian CEO phase noise from a SESAM-modelocked 1.5 μm solid-state laser,” Opt. Express 19, 24171–24181 (2011).
[CrossRef]

S. Schilt, N. Bucalovic, L. Tombez, V. Dolgovskiy, C. Schori, G. Di Domenico, M. Zaffalon, and P. Thomann, “Frequency discriminators for the characterization of narrow-spectrum heterodyne beat signals: application to the measurement of a sub-hertz carrier-envelope-offset beat in an optical frequency comb,” Rev. Sci. Instrum. 82, 123116(2011).
[CrossRef]

V. Dolgovskiy, S. Schilt, G. Di Domenico, N. Bucalovic, C. Schori, and P. Thomann, “1.5 μm cavity-stabilized laser for ultra-stable microwave generation,” in Proceedings of 2011 Joint Conference of the IEEE International Frequency Control and the European Frequency and Time Forum (FCS), San Francisco, USA, May 2–5, 2011 (IEEE, 2011), pp. 1–3.

Dunlop, A. E.

H. R. Telle, G. Steinmeyer, A. E. Dunlop, J. Stenger, D. H. Sutter, and U. Keller, “Carrier-envelope offset phase control: a novel concept for absolute optical frequency measurement and ultrashort pulse generation,” Appl. Phys. B 69, 327–332 (1999).
[CrossRef]

Engelbrecht, R.

O. Svelto, S. Longhi, G. Della Valle, S. Kück, G. Huber, M. Pollnau, H. Hillmer, S. Hansmann, R. Engelbrecht, H. Brand, J. Kaiser, A. B. Peterson, R. Malz, S. Steinberg, G. Marowsky, U. Brinkmann, D. Lo, A. Borsutzky, H. Wächter, M. W. Sigrist, E. Saldin, E. Schneidmiller, M. Yurkov, K. Midorikawa, J. Hein, R. Sauerbrey, and J. Helmcke, “Lasers and coherent light sources,” in Springer Handbook of Lasers and Optics, F. Träger, ed. (Springer, 2007), pp. 583–936.

English, E. M. L.

J. Millo, M. Abgrall, M. Lours, E. M. L. English, H. Jiang, J. Guéna, A. Clairon, S. Bize, Y. Le Coq, G. Santarelli, and M. E. Tobar, “Ultra-low noise microwave generation with fiber-based optical frequency comb and application to atomic fountain clock,” Appl. Phys. Lett. 94, 141105 (2009).
[CrossRef]

Fallnich, C.

N. Haverkamp, H. Hundertmark, C. Fallnich, and H. R. Telle, “Frequency stabilization of mode-locked Erbium fiber lasers using pump power control,” Appl. Phys. B 78, 321–324 (2004).
[CrossRef]

Fischer, M.

W. Zhang, M. Lours, M. Fischer, R. Holzwarth, G. Santarelli, and Y. Le Coq, “Characterizing a fiber-based frequency comb with electro-optic modulator,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 59, 432–438 (2012).
[CrossRef]

Fortier, T.

L. Hollberg, S. Diddams, A. Bartels, T. Fortier, and K. Kim, “The measurement of optical frequencies,” Metrologia 42, S105–S124 (2005).
[CrossRef]

J. Rauschenberger, T. Fortier, D. Jones, J. Ye, and S. Cundiff, “Control of the frequency comb from a modelocked Erbium-doped fiber laser,” Opt. Express 10, 1404–1410 (2002).

Gerginov, V.

M. C. Stowe, M. J. Thorpe, A. Pe’er, J. Ye, J. E. Stalnaker, V. Gerginov, and S. A. Diddams, “Direct frequency comb spectroscopy,” Adv. At. Mol.Opt. Phys. 55, 1–60 (2008).
[CrossRef]

Gohle, C.

D. R. Walker, T. Udem, C. Gohle, B. Stein, and T. W. Hänsch, “Frequency dependence of the fixed point in a fluctuating frequency comb,” Appl. Phys. B 89, 535–538 (2007).
[CrossRef]

Guelachvili, G.

B. Bernhardt, A. Ozawa, P. Jacquet, M. Jacquey, Y. Kobayashi, T. Udem, R. Holzwarth, G. Guelachvili, T. W. Hänsch, and N. Picqué, “Cavity-enhanced dual-comb spectroscopy,” Nat. Photonics 4, 55–57 (2010).

Guéna, J.

J. Millo, M. Abgrall, M. Lours, E. M. L. English, H. Jiang, J. Guéna, A. Clairon, S. Bize, Y. Le Coq, G. Santarelli, and M. E. Tobar, “Ultra-low noise microwave generation with fiber-based optical frequency comb and application to atomic fountain clock,” Appl. Phys. Lett. 94, 141105 (2009).
[CrossRef]

Hänsch, T. W.

B. Bernhardt, A. Ozawa, P. Jacquet, M. Jacquey, Y. Kobayashi, T. Udem, R. Holzwarth, G. Guelachvili, T. W. Hänsch, and N. Picqué, “Cavity-enhanced dual-comb spectroscopy,” Nat. Photonics 4, 55–57 (2010).

D. R. Walker, T. Udem, C. Gohle, B. Stein, and T. W. Hänsch, “Frequency dependence of the fixed point in a fluctuating frequency comb,” Appl. Phys. B 89, 535–538 (2007).
[CrossRef]

T. W. Hänsch, “Nobel lecture: passion for precision,” Rev. Mod. Phys. 78, 1297–1309 (2006).
[CrossRef]

Hansmann, S.

O. Svelto, S. Longhi, G. Della Valle, S. Kück, G. Huber, M. Pollnau, H. Hillmer, S. Hansmann, R. Engelbrecht, H. Brand, J. Kaiser, A. B. Peterson, R. Malz, S. Steinberg, G. Marowsky, U. Brinkmann, D. Lo, A. Borsutzky, H. Wächter, M. W. Sigrist, E. Saldin, E. Schneidmiller, M. Yurkov, K. Midorikawa, J. Hein, R. Sauerbrey, and J. Helmcke, “Lasers and coherent light sources,” in Springer Handbook of Lasers and Optics, F. Träger, ed. (Springer, 2007), pp. 583–936.

Haverkamp, N.

N. Haverkamp, H. Hundertmark, C. Fallnich, and H. R. Telle, “Frequency stabilization of mode-locked Erbium fiber lasers using pump power control,” Appl. Phys. B 78, 321–324 (2004).
[CrossRef]

Hein, J.

O. Svelto, S. Longhi, G. Della Valle, S. Kück, G. Huber, M. Pollnau, H. Hillmer, S. Hansmann, R. Engelbrecht, H. Brand, J. Kaiser, A. B. Peterson, R. Malz, S. Steinberg, G. Marowsky, U. Brinkmann, D. Lo, A. Borsutzky, H. Wächter, M. W. Sigrist, E. Saldin, E. Schneidmiller, M. Yurkov, K. Midorikawa, J. Hein, R. Sauerbrey, and J. Helmcke, “Lasers and coherent light sources,” in Springer Handbook of Lasers and Optics, F. Träger, ed. (Springer, 2007), pp. 583–936.

Heinecke, D. C.

Helbing, F. W.

F. W. Helbing, G. Steinmeyer, J. Stenger, H. R. Telle, and U. Keller, “Carrier–envelope-offset dynamics and stabilization of femtosecond pulses,” Appl. Phys. B. 74, S35–S42 (2002).
[CrossRef]

Helmcke, J.

O. Svelto, S. Longhi, G. Della Valle, S. Kück, G. Huber, M. Pollnau, H. Hillmer, S. Hansmann, R. Engelbrecht, H. Brand, J. Kaiser, A. B. Peterson, R. Malz, S. Steinberg, G. Marowsky, U. Brinkmann, D. Lo, A. Borsutzky, H. Wächter, M. W. Sigrist, E. Saldin, E. Schneidmiller, M. Yurkov, K. Midorikawa, J. Hein, R. Sauerbrey, and J. Helmcke, “Lasers and coherent light sources,” in Springer Handbook of Lasers and Optics, F. Träger, ed. (Springer, 2007), pp. 583–936.

Hillmer, H.

O. Svelto, S. Longhi, G. Della Valle, S. Kück, G. Huber, M. Pollnau, H. Hillmer, S. Hansmann, R. Engelbrecht, H. Brand, J. Kaiser, A. B. Peterson, R. Malz, S. Steinberg, G. Marowsky, U. Brinkmann, D. Lo, A. Borsutzky, H. Wächter, M. W. Sigrist, E. Saldin, E. Schneidmiller, M. Yurkov, K. Midorikawa, J. Hein, R. Sauerbrey, and J. Helmcke, “Lasers and coherent light sources,” in Springer Handbook of Lasers and Optics, F. Träger, ed. (Springer, 2007), pp. 583–936.

Hollberg, L.

L. Hollberg, S. Diddams, A. Bartels, T. Fortier, and K. Kim, “The measurement of optical frequencies,” Metrologia 42, S105–S124 (2005).
[CrossRef]

Hollberg, L. W.

J. Ye, H. Schnatz, and L. W. Hollberg, “Optical frequency combs: from frequency metrology to optical phase control,” IEEE J. Sel. Top. Quantum Electron. 9, 1041–1058 (2003).
[CrossRef]

Holzwarth, R.

W. Zhang, M. Lours, M. Fischer, R. Holzwarth, G. Santarelli, and Y. Le Coq, “Characterizing a fiber-based frequency comb with electro-optic modulator,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 59, 432–438 (2012).
[CrossRef]

B. Bernhardt, A. Ozawa, P. Jacquet, M. Jacquey, Y. Kobayashi, T. Udem, R. Holzwarth, G. Guelachvili, T. W. Hänsch, and N. Picqué, “Cavity-enhanced dual-comb spectroscopy,” Nat. Photonics 4, 55–57 (2010).

Huber, G.

O. Svelto, S. Longhi, G. Della Valle, S. Kück, G. Huber, M. Pollnau, H. Hillmer, S. Hansmann, R. Engelbrecht, H. Brand, J. Kaiser, A. B. Peterson, R. Malz, S. Steinberg, G. Marowsky, U. Brinkmann, D. Lo, A. Borsutzky, H. Wächter, M. W. Sigrist, E. Saldin, E. Schneidmiller, M. Yurkov, K. Midorikawa, J. Hein, R. Sauerbrey, and J. Helmcke, “Lasers and coherent light sources,” in Springer Handbook of Lasers and Optics, F. Träger, ed. (Springer, 2007), pp. 583–936.

Hundertmark, H.

N. Haverkamp, H. Hundertmark, C. Fallnich, and H. R. Telle, “Frequency stabilization of mode-locked Erbium fiber lasers using pump power control,” Appl. Phys. B 78, 321–324 (2004).
[CrossRef]

Jacquet, P.

B. Bernhardt, A. Ozawa, P. Jacquet, M. Jacquey, Y. Kobayashi, T. Udem, R. Holzwarth, G. Guelachvili, T. W. Hänsch, and N. Picqué, “Cavity-enhanced dual-comb spectroscopy,” Nat. Photonics 4, 55–57 (2010).

Jacquey, M.

B. Bernhardt, A. Ozawa, P. Jacquet, M. Jacquey, Y. Kobayashi, T. Udem, R. Holzwarth, G. Guelachvili, T. W. Hänsch, and N. Picqué, “Cavity-enhanced dual-comb spectroscopy,” Nat. Photonics 4, 55–57 (2010).

Jiang, H.

J. Millo, M. Abgrall, M. Lours, E. M. L. English, H. Jiang, J. Guéna, A. Clairon, S. Bize, Y. Le Coq, G. Santarelli, and M. E. Tobar, “Ultra-low noise microwave generation with fiber-based optical frequency comb and application to atomic fountain clock,” Appl. Phys. Lett. 94, 141105 (2009).
[CrossRef]

Jones, D.

Jones, R. J.

M. J. Thorpe, K. D. Moll, R. J. Jones, B. Safdi, and J. Ye, “Broadband cavity ringdown spectroscopy for sensitive and rapid molecular detection,” Science 311, 1595–1599 (2006).
[CrossRef]

Kaiser, J.

O. Svelto, S. Longhi, G. Della Valle, S. Kück, G. Huber, M. Pollnau, H. Hillmer, S. Hansmann, R. Engelbrecht, H. Brand, J. Kaiser, A. B. Peterson, R. Malz, S. Steinberg, G. Marowsky, U. Brinkmann, D. Lo, A. Borsutzky, H. Wächter, M. W. Sigrist, E. Saldin, E. Schneidmiller, M. Yurkov, K. Midorikawa, J. Hein, R. Sauerbrey, and J. Helmcke, “Lasers and coherent light sources,” in Springer Handbook of Lasers and Optics, F. Träger, ed. (Springer, 2007), pp. 583–936.

Keller, U.

S. Schilt, N. Bucalovic, V. Dolgovskiy, C. Schori, M. C. Stumpf, G. Di Domenico, S. Pekarek, A. E. H. Oehler, T. Südmeyer, U. Keller, and P. Thomann, “Fully stabilized optical frequency comb with sub-radian CEO phase noise from a SESAM-modelocked 1.5 μm solid-state laser,” Opt. Express 19, 24171–24181 (2011).
[CrossRef]

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

F. W. Helbing, G. Steinmeyer, J. Stenger, H. R. Telle, and U. Keller, “Carrier–envelope-offset dynamics and stabilization of femtosecond pulses,” Appl. Phys. B. 74, S35–S42 (2002).
[CrossRef]

H. R. Telle, G. Steinmeyer, A. E. Dunlop, J. Stenger, D. H. Sutter, and U. Keller, “Carrier-envelope offset phase control: a novel concept for absolute optical frequency measurement and ultrashort pulse generation,” Appl. Phys. B 69, 327–332 (1999).
[CrossRef]

Kersalé, Y.

W. Zhang, Z. Xu, M. Lours, R. Boudot, Y. Kersalé, A. N. Luiten, Y. Le Coq, and G. Santarelli, “Advanced noise reduction techniques for ultra-low phase noise optical-to-microwave division with femtosecond fiber combs,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 58, 900–908 (2011).
[CrossRef]

Kim, K.

Knight, J. C.

Kobayashi, Y.

B. Bernhardt, A. Ozawa, P. Jacquet, M. Jacquey, Y. Kobayashi, T. Udem, R. Holzwarth, G. Guelachvili, T. W. Hänsch, and N. Picqué, “Cavity-enhanced dual-comb spectroscopy,” Nat. Photonics 4, 55–57 (2010).

Kück, S.

O. Svelto, S. Longhi, G. Della Valle, S. Kück, G. Huber, M. Pollnau, H. Hillmer, S. Hansmann, R. Engelbrecht, H. Brand, J. Kaiser, A. B. Peterson, R. Malz, S. Steinberg, G. Marowsky, U. Brinkmann, D. Lo, A. Borsutzky, H. Wächter, M. W. Sigrist, E. Saldin, E. Schneidmiller, M. Yurkov, K. Midorikawa, J. Hein, R. Sauerbrey, and J. Helmcke, “Lasers and coherent light sources,” in Springer Handbook of Lasers and Optics, F. Träger, ed. (Springer, 2007), pp. 583–936.

Le Coq, Y.

W. Zhang, M. Lours, M. Fischer, R. Holzwarth, G. Santarelli, and Y. Le Coq, “Characterizing a fiber-based frequency comb with electro-optic modulator,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 59, 432–438 (2012).
[CrossRef]

W. Zhang, Z. Xu, M. Lours, R. Boudot, Y. Kersalé, A. N. Luiten, Y. Le Coq, and G. Santarelli, “Advanced noise reduction techniques for ultra-low phase noise optical-to-microwave division with femtosecond fiber combs,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 58, 900–908 (2011).
[CrossRef]

J. Millo, M. Abgrall, M. Lours, E. M. L. English, H. Jiang, J. Guéna, A. Clairon, S. Bize, Y. Le Coq, G. Santarelli, and M. E. Tobar, “Ultra-low noise microwave generation with fiber-based optical frequency comb and application to atomic fountain clock,” Appl. Phys. Lett. 94, 141105 (2009).
[CrossRef]

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]

Lo, D.

O. Svelto, S. Longhi, G. Della Valle, S. Kück, G. Huber, M. Pollnau, H. Hillmer, S. Hansmann, R. Engelbrecht, H. Brand, J. Kaiser, A. B. Peterson, R. Malz, S. Steinberg, G. Marowsky, U. Brinkmann, D. Lo, A. Borsutzky, H. Wächter, M. W. Sigrist, E. Saldin, E. Schneidmiller, M. Yurkov, K. Midorikawa, J. Hein, R. Sauerbrey, and J. Helmcke, “Lasers and coherent light sources,” in Springer Handbook of Lasers and Optics, F. Träger, ed. (Springer, 2007), pp. 583–936.

Longhi, S.

O. Svelto, S. Longhi, G. Della Valle, S. Kück, G. Huber, M. Pollnau, H. Hillmer, S. Hansmann, R. Engelbrecht, H. Brand, J. Kaiser, A. B. Peterson, R. Malz, S. Steinberg, G. Marowsky, U. Brinkmann, D. Lo, A. Borsutzky, H. Wächter, M. W. Sigrist, E. Saldin, E. Schneidmiller, M. Yurkov, K. Midorikawa, J. Hein, R. Sauerbrey, and J. Helmcke, “Lasers and coherent light sources,” in Springer Handbook of Lasers and Optics, F. Träger, ed. (Springer, 2007), pp. 583–936.

Lours, M.

W. Zhang, M. Lours, M. Fischer, R. Holzwarth, G. Santarelli, and Y. Le Coq, “Characterizing a fiber-based frequency comb with electro-optic modulator,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 59, 432–438 (2012).
[CrossRef]

W. Zhang, Z. Xu, M. Lours, R. Boudot, Y. Kersalé, A. N. Luiten, Y. Le Coq, and G. Santarelli, “Advanced noise reduction techniques for ultra-low phase noise optical-to-microwave division with femtosecond fiber combs,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 58, 900–908 (2011).
[CrossRef]

J. Millo, M. Abgrall, M. Lours, E. M. L. English, H. Jiang, J. Guéna, A. Clairon, S. Bize, Y. Le Coq, G. Santarelli, and M. E. Tobar, “Ultra-low noise microwave generation with fiber-based optical frequency comb and application to atomic fountain clock,” Appl. Phys. Lett. 94, 141105 (2009).
[CrossRef]

Luiten, A. N.

W. Zhang, Z. Xu, M. Lours, R. Boudot, Y. Kersalé, A. N. Luiten, Y. Le Coq, and G. Santarelli, “Advanced noise reduction techniques for ultra-low phase noise optical-to-microwave division with femtosecond fiber combs,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 58, 900–908 (2011).
[CrossRef]

Malz, R.

O. Svelto, S. Longhi, G. Della Valle, S. Kück, G. Huber, M. Pollnau, H. Hillmer, S. Hansmann, R. Engelbrecht, H. Brand, J. Kaiser, A. B. Peterson, R. Malz, S. Steinberg, G. Marowsky, U. Brinkmann, D. Lo, A. Borsutzky, H. Wächter, M. W. Sigrist, E. Saldin, E. Schneidmiller, M. Yurkov, K. Midorikawa, J. Hein, R. Sauerbrey, and J. Helmcke, “Lasers and coherent light sources,” in Springer Handbook of Lasers and Optics, F. Träger, ed. (Springer, 2007), pp. 583–936.

Marowsky, G.

O. Svelto, S. Longhi, G. Della Valle, S. Kück, G. Huber, M. Pollnau, H. Hillmer, S. Hansmann, R. Engelbrecht, H. Brand, J. Kaiser, A. B. Peterson, R. Malz, S. Steinberg, G. Marowsky, U. Brinkmann, D. Lo, A. Borsutzky, H. Wächter, M. W. Sigrist, E. Saldin, E. Schneidmiller, M. Yurkov, K. Midorikawa, J. Hein, R. Sauerbrey, and J. Helmcke, “Lasers and coherent light sources,” in Springer Handbook of Lasers and Optics, F. Träger, ed. (Springer, 2007), pp. 583–936.

McFerran, J. J.

J. J. McFerran, W. C. Swann, B. R. Washburn, and N. R. Newbury, “Suppression of pump-induced frequency noise in fiber-laser frequency combs leading to sub-radion fceo phase excursion,” Appl. Phys. B 86, 219–227 (2007).
[CrossRef]

Midorikawa, K.

O. Svelto, S. Longhi, G. Della Valle, S. Kück, G. Huber, M. Pollnau, H. Hillmer, S. Hansmann, R. Engelbrecht, H. Brand, J. Kaiser, A. B. Peterson, R. Malz, S. Steinberg, G. Marowsky, U. Brinkmann, D. Lo, A. Borsutzky, H. Wächter, M. W. Sigrist, E. Saldin, E. Schneidmiller, M. Yurkov, K. Midorikawa, J. Hein, R. Sauerbrey, and J. Helmcke, “Lasers and coherent light sources,” in Springer Handbook of Lasers and Optics, F. Träger, ed. (Springer, 2007), pp. 583–936.

Millo, J.

J. Millo, M. Abgrall, M. Lours, E. M. L. English, H. Jiang, J. Guéna, A. Clairon, S. Bize, Y. Le Coq, G. Santarelli, and M. E. Tobar, “Ultra-low noise microwave generation with fiber-based optical frequency comb and application to atomic fountain clock,” Appl. Phys. Lett. 94, 141105 (2009).
[CrossRef]

Moll, K. D.

M. J. Thorpe, K. D. Moll, R. J. Jones, B. Safdi, and J. Ye, “Broadband cavity ringdown spectroscopy for sensitive and rapid molecular detection,” Science 311, 1595–1599 (2006).
[CrossRef]

Newbury, N.

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

Newbury, N. R.

Nicholson, J. W.

Oehler, A. E. H.

Ozawa, A.

B. Bernhardt, A. Ozawa, P. Jacquet, M. Jacquey, Y. Kobayashi, T. Udem, R. Holzwarth, G. Guelachvili, T. W. Hänsch, and N. Picqué, “Cavity-enhanced dual-comb spectroscopy,” Nat. Photonics 4, 55–57 (2010).

Paschotta, R.

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

Pe’er, A.

M. C. Stowe, M. J. Thorpe, A. Pe’er, J. Ye, J. E. Stalnaker, V. Gerginov, and S. A. Diddams, “Direct frequency comb spectroscopy,” Adv. At. Mol.Opt. Phys. 55, 1–60 (2008).
[CrossRef]

Pekarek, S.

Peterson, A. B.

O. Svelto, S. Longhi, G. Della Valle, S. Kück, G. Huber, M. Pollnau, H. Hillmer, S. Hansmann, R. Engelbrecht, H. Brand, J. Kaiser, A. B. Peterson, R. Malz, S. Steinberg, G. Marowsky, U. Brinkmann, D. Lo, A. Borsutzky, H. Wächter, M. W. Sigrist, E. Saldin, E. Schneidmiller, M. Yurkov, K. Midorikawa, J. Hein, R. Sauerbrey, and J. Helmcke, “Lasers and coherent light sources,” in Springer Handbook of Lasers and Optics, F. Träger, ed. (Springer, 2007), pp. 583–936.

Picqué, N.

B. Bernhardt, A. Ozawa, P. Jacquet, M. Jacquey, Y. Kobayashi, T. Udem, R. Holzwarth, G. Guelachvili, T. W. Hänsch, and N. Picqué, “Cavity-enhanced dual-comb spectroscopy,” Nat. Photonics 4, 55–57 (2010).

Pollnau, M.

O. Svelto, S. Longhi, G. Della Valle, S. Kück, G. Huber, M. Pollnau, H. Hillmer, S. Hansmann, R. Engelbrecht, H. Brand, J. Kaiser, A. B. Peterson, R. Malz, S. Steinberg, G. Marowsky, U. Brinkmann, D. Lo, A. Borsutzky, H. Wächter, M. W. Sigrist, E. Saldin, E. Schneidmiller, M. Yurkov, K. Midorikawa, J. Hein, R. Sauerbrey, and J. Helmcke, “Lasers and coherent light sources,” in Springer Handbook of Lasers and Optics, F. Träger, ed. (Springer, 2007), pp. 583–936.

Rauschenberger, J.

Riehle, F.

F. Riehle, Frequency Standards, Basics and Applications(Wiley, 2004), Chap. 2.

Safdi, B.

M. J. Thorpe, K. D. Moll, R. J. Jones, B. Safdi, and J. Ye, “Broadband cavity ringdown spectroscopy for sensitive and rapid molecular detection,” Science 311, 1595–1599 (2006).
[CrossRef]

Saldin, E.

O. Svelto, S. Longhi, G. Della Valle, S. Kück, G. Huber, M. Pollnau, H. Hillmer, S. Hansmann, R. Engelbrecht, H. Brand, J. Kaiser, A. B. Peterson, R. Malz, S. Steinberg, G. Marowsky, U. Brinkmann, D. Lo, A. Borsutzky, H. Wächter, M. W. Sigrist, E. Saldin, E. Schneidmiller, M. Yurkov, K. Midorikawa, J. Hein, R. Sauerbrey, and J. Helmcke, “Lasers and coherent light sources,” in Springer Handbook of Lasers and Optics, F. Träger, ed. (Springer, 2007), pp. 583–936.

Santarelli, G.

W. Zhang, M. Lours, M. Fischer, R. Holzwarth, G. Santarelli, and Y. Le Coq, “Characterizing a fiber-based frequency comb with electro-optic modulator,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 59, 432–438 (2012).
[CrossRef]

W. Zhang, Z. Xu, M. Lours, R. Boudot, Y. Kersalé, A. N. Luiten, Y. Le Coq, and G. Santarelli, “Advanced noise reduction techniques for ultra-low phase noise optical-to-microwave division with femtosecond fiber combs,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 58, 900–908 (2011).
[CrossRef]

J. Millo, M. Abgrall, M. Lours, E. M. L. English, H. Jiang, J. Guéna, A. Clairon, S. Bize, Y. Le Coq, G. Santarelli, and M. E. Tobar, “Ultra-low noise microwave generation with fiber-based optical frequency comb and application to atomic fountain clock,” Appl. Phys. Lett. 94, 141105 (2009).
[CrossRef]

Sauerbrey, R.

O. Svelto, S. Longhi, G. Della Valle, S. Kück, G. Huber, M. Pollnau, H. Hillmer, S. Hansmann, R. Engelbrecht, H. Brand, J. Kaiser, A. B. Peterson, R. Malz, S. Steinberg, G. Marowsky, U. Brinkmann, D. Lo, A. Borsutzky, H. Wächter, M. W. Sigrist, E. Saldin, E. Schneidmiller, M. Yurkov, K. Midorikawa, J. Hein, R. Sauerbrey, and J. Helmcke, “Lasers and coherent light sources,” in Springer Handbook of Lasers and Optics, F. Träger, ed. (Springer, 2007), pp. 583–936.

Schilt, S.

S. Schilt, N. Bucalovic, V. Dolgovskiy, C. Schori, M. C. Stumpf, G. Di Domenico, S. Pekarek, A. E. H. Oehler, T. Südmeyer, U. Keller, and P. Thomann, “Fully stabilized optical frequency comb with sub-radian CEO phase noise from a SESAM-modelocked 1.5 μm solid-state laser,” Opt. Express 19, 24171–24181 (2011).
[CrossRef]

S. Schilt, N. Bucalovic, L. Tombez, V. Dolgovskiy, C. Schori, G. Di Domenico, M. Zaffalon, and P. Thomann, “Frequency discriminators for the characterization of narrow-spectrum heterodyne beat signals: application to the measurement of a sub-hertz carrier-envelope-offset beat in an optical frequency comb,” Rev. Sci. Instrum. 82, 123116(2011).
[CrossRef]

V. Dolgovskiy, S. Schilt, G. Di Domenico, N. Bucalovic, C. Schori, and P. Thomann, “1.5 μm cavity-stabilized laser for ultra-stable microwave generation,” in Proceedings of 2011 Joint Conference of the IEEE International Frequency Control and the European Frequency and Time Forum (FCS), San Francisco, USA, May 2–5, 2011 (IEEE, 2011), pp. 1–3.

Schlatter, A.

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

Schnatz, H.

J. Ye, H. Schnatz, and L. W. Hollberg, “Optical frequency combs: from frequency metrology to optical phase control,” IEEE J. Sel. Top. Quantum Electron. 9, 1041–1058 (2003).
[CrossRef]

Schneidmiller, E.

O. Svelto, S. Longhi, G. Della Valle, S. Kück, G. Huber, M. Pollnau, H. Hillmer, S. Hansmann, R. Engelbrecht, H. Brand, J. Kaiser, A. B. Peterson, R. Malz, S. Steinberg, G. Marowsky, U. Brinkmann, D. Lo, A. Borsutzky, H. Wächter, M. W. Sigrist, E. Saldin, E. Schneidmiller, M. Yurkov, K. Midorikawa, J. Hein, R. Sauerbrey, and J. Helmcke, “Lasers and coherent light sources,” in Springer Handbook of Lasers and Optics, F. Träger, ed. (Springer, 2007), pp. 583–936.

Schori, C.

S. Schilt, N. Bucalovic, V. Dolgovskiy, C. Schori, M. C. Stumpf, G. Di Domenico, S. Pekarek, A. E. H. Oehler, T. Südmeyer, U. Keller, and P. Thomann, “Fully stabilized optical frequency comb with sub-radian CEO phase noise from a SESAM-modelocked 1.5 μm solid-state laser,” Opt. Express 19, 24171–24181 (2011).
[CrossRef]

S. Schilt, N. Bucalovic, L. Tombez, V. Dolgovskiy, C. Schori, G. Di Domenico, M. Zaffalon, and P. Thomann, “Frequency discriminators for the characterization of narrow-spectrum heterodyne beat signals: application to the measurement of a sub-hertz carrier-envelope-offset beat in an optical frequency comb,” Rev. Sci. Instrum. 82, 123116(2011).
[CrossRef]

V. Dolgovskiy, S. Schilt, G. Di Domenico, N. Bucalovic, C. Schori, and P. Thomann, “1.5 μm cavity-stabilized laser for ultra-stable microwave generation,” in Proceedings of 2011 Joint Conference of the IEEE International Frequency Control and the European Frequency and Time Forum (FCS), San Francisco, USA, May 2–5, 2011 (IEEE, 2011), pp. 1–3.

Sigrist, M. W.

O. Svelto, S. Longhi, G. Della Valle, S. Kück, G. Huber, M. Pollnau, H. Hillmer, S. Hansmann, R. Engelbrecht, H. Brand, J. Kaiser, A. B. Peterson, R. Malz, S. Steinberg, G. Marowsky, U. Brinkmann, D. Lo, A. Borsutzky, H. Wächter, M. W. Sigrist, E. Saldin, E. Schneidmiller, M. Yurkov, K. Midorikawa, J. Hein, R. Sauerbrey, and J. Helmcke, “Lasers and coherent light sources,” in Springer Handbook of Lasers and Optics, F. Träger, ed. (Springer, 2007), pp. 583–936.

Stalnaker, J. E.

M. C. Stowe, M. J. Thorpe, A. Pe’er, J. Ye, J. E. Stalnaker, V. Gerginov, and S. A. Diddams, “Direct frequency comb spectroscopy,” Adv. At. Mol.Opt. Phys. 55, 1–60 (2008).
[CrossRef]

Stein, B.

D. R. Walker, T. Udem, C. Gohle, B. Stein, and T. W. Hänsch, “Frequency dependence of the fixed point in a fluctuating frequency comb,” Appl. Phys. B 89, 535–538 (2007).
[CrossRef]

Steinberg, S.

O. Svelto, S. Longhi, G. Della Valle, S. Kück, G. Huber, M. Pollnau, H. Hillmer, S. Hansmann, R. Engelbrecht, H. Brand, J. Kaiser, A. B. Peterson, R. Malz, S. Steinberg, G. Marowsky, U. Brinkmann, D. Lo, A. Borsutzky, H. Wächter, M. W. Sigrist, E. Saldin, E. Schneidmiller, M. Yurkov, K. Midorikawa, J. Hein, R. Sauerbrey, and J. Helmcke, “Lasers and coherent light sources,” in Springer Handbook of Lasers and Optics, F. Träger, ed. (Springer, 2007), pp. 583–936.

Steinmeyer, G.

F. W. Helbing, G. Steinmeyer, J. Stenger, H. R. Telle, and U. Keller, “Carrier–envelope-offset dynamics and stabilization of femtosecond pulses,” Appl. Phys. B. 74, S35–S42 (2002).
[CrossRef]

H. R. Telle, G. Steinmeyer, A. E. Dunlop, J. Stenger, D. H. Sutter, and U. Keller, “Carrier-envelope offset phase control: a novel concept for absolute optical frequency measurement and ultrashort pulse generation,” Appl. Phys. B 69, 327–332 (1999).
[CrossRef]

Stenger, J.

F. W. Helbing, G. Steinmeyer, J. Stenger, H. R. Telle, and U. Keller, “Carrier–envelope-offset dynamics and stabilization of femtosecond pulses,” Appl. Phys. B. 74, S35–S42 (2002).
[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]

H. R. Telle, G. Steinmeyer, A. E. Dunlop, J. Stenger, D. H. Sutter, and U. Keller, “Carrier-envelope offset phase control: a novel concept for absolute optical frequency measurement and ultrashort pulse generation,” Appl. Phys. B 69, 327–332 (1999).
[CrossRef]

Stowe, M. C.

M. C. Stowe, M. J. Thorpe, A. Pe’er, J. Ye, J. E. Stalnaker, V. Gerginov, and S. A. Diddams, “Direct frequency comb spectroscopy,” Adv. At. Mol.Opt. Phys. 55, 1–60 (2008).
[CrossRef]

Stumpf, M. C.

Südmeyer, T.

Sutter, D. H.

H. R. Telle, G. Steinmeyer, A. E. Dunlop, J. Stenger, D. H. Sutter, and U. Keller, “Carrier-envelope offset phase control: a novel concept for absolute optical frequency measurement and ultrashort pulse generation,” Appl. Phys. B 69, 327–332 (1999).
[CrossRef]

Svelto, O.

O. Svelto, S. Longhi, G. Della Valle, S. Kück, G. Huber, M. Pollnau, H. Hillmer, S. Hansmann, R. Engelbrecht, H. Brand, J. Kaiser, A. B. Peterson, R. Malz, S. Steinberg, G. Marowsky, U. Brinkmann, D. Lo, A. Borsutzky, H. Wächter, M. W. Sigrist, E. Saldin, E. Schneidmiller, M. Yurkov, K. Midorikawa, J. Hein, R. Sauerbrey, and J. Helmcke, “Lasers and coherent light sources,” in Springer Handbook of Lasers and Optics, F. Träger, ed. (Springer, 2007), pp. 583–936.

Swann, W. C.

J. J. McFerran, W. C. Swann, B. R. Washburn, and N. R. Newbury, “Suppression of pump-induced frequency noise in fiber-laser frequency combs leading to sub-radion fceo phase excursion,” Appl. Phys. B 86, 219–227 (2007).
[CrossRef]

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

B. R. Washburn, W. C. Swann, and N. R. Newbury, “Response dynamics of the frequency comb output from a femtosecond laser,” Opt. Express 13, 10622–10633 (2005).
[CrossRef]

Tauser, F.

Telle, H. R.

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

E. Benkler, H. R. Telle, A. Zach, and F. Tauser, “Circumvention of noise contributions in fiber laser baser frequency combs,” Opt. Express 13, 5662–5668 (2005).
[CrossRef]

N. Haverkamp, H. Hundertmark, C. Fallnich, and H. R. Telle, “Frequency stabilization of mode-locked Erbium fiber lasers using pump power control,” Appl. Phys. B 78, 321–324 (2004).
[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]

F. W. Helbing, G. Steinmeyer, J. Stenger, H. R. Telle, and U. Keller, “Carrier–envelope-offset dynamics and stabilization of femtosecond pulses,” Appl. Phys. B. 74, S35–S42 (2002).
[CrossRef]

H. R. Telle, G. Steinmeyer, A. E. Dunlop, J. Stenger, D. H. Sutter, and U. Keller, “Carrier-envelope offset phase control: a novel concept for absolute optical frequency measurement and ultrashort pulse generation,” Appl. Phys. B 69, 327–332 (1999).
[CrossRef]

Thomann, P.

S. Schilt, N. Bucalovic, L. Tombez, V. Dolgovskiy, C. Schori, G. Di Domenico, M. Zaffalon, and P. Thomann, “Frequency discriminators for the characterization of narrow-spectrum heterodyne beat signals: application to the measurement of a sub-hertz carrier-envelope-offset beat in an optical frequency comb,” Rev. Sci. Instrum. 82, 123116(2011).
[CrossRef]

S. Schilt, N. Bucalovic, V. Dolgovskiy, C. Schori, M. C. Stumpf, G. Di Domenico, S. Pekarek, A. E. H. Oehler, T. Südmeyer, U. Keller, and P. Thomann, “Fully stabilized optical frequency comb with sub-radian CEO phase noise from a SESAM-modelocked 1.5 μm solid-state laser,” Opt. Express 19, 24171–24181 (2011).
[CrossRef]

V. Dolgovskiy, S. Schilt, G. Di Domenico, N. Bucalovic, C. Schori, and P. Thomann, “1.5 μm cavity-stabilized laser for ultra-stable microwave generation,” in Proceedings of 2011 Joint Conference of the IEEE International Frequency Control and the European Frequency and Time Forum (FCS), San Francisco, USA, May 2–5, 2011 (IEEE, 2011), pp. 1–3.

Thorpe, M. J.

M. C. Stowe, M. J. Thorpe, A. Pe’er, J. Ye, J. E. Stalnaker, V. Gerginov, and S. A. Diddams, “Direct frequency comb spectroscopy,” Adv. At. Mol.Opt. Phys. 55, 1–60 (2008).
[CrossRef]

M. J. Thorpe, K. D. Moll, R. J. Jones, B. Safdi, and J. Ye, “Broadband cavity ringdown spectroscopy for sensitive and rapid molecular detection,” Science 311, 1595–1599 (2006).
[CrossRef]

Tobar, M. E.

J. Millo, M. Abgrall, M. Lours, E. M. L. English, H. Jiang, J. Guéna, A. Clairon, S. Bize, Y. Le Coq, G. Santarelli, and M. E. Tobar, “Ultra-low noise microwave generation with fiber-based optical frequency comb and application to atomic fountain clock,” Appl. Phys. Lett. 94, 141105 (2009).
[CrossRef]

Tombez, L.

S. Schilt, N. Bucalovic, L. Tombez, V. Dolgovskiy, C. Schori, G. Di Domenico, M. Zaffalon, and P. Thomann, “Frequency discriminators for the characterization of narrow-spectrum heterodyne beat signals: application to the measurement of a sub-hertz carrier-envelope-offset beat in an optical frequency comb,” Rev. Sci. Instrum. 82, 123116(2011).
[CrossRef]

Udem, T.

B. Bernhardt, A. Ozawa, P. Jacquet, M. Jacquey, Y. Kobayashi, T. Udem, R. Holzwarth, G. Guelachvili, T. W. Hänsch, and N. Picqué, “Cavity-enhanced dual-comb spectroscopy,” Nat. Photonics 4, 55–57 (2010).

D. R. Walker, T. Udem, C. Gohle, B. Stein, and T. W. Hänsch, “Frequency dependence of the fixed point in a fluctuating frequency comb,” Appl. Phys. B 89, 535–538 (2007).
[CrossRef]

Wächter, H.

O. Svelto, S. Longhi, G. Della Valle, S. Kück, G. Huber, M. Pollnau, H. Hillmer, S. Hansmann, R. Engelbrecht, H. Brand, J. Kaiser, A. B. Peterson, R. Malz, S. Steinberg, G. Marowsky, U. Brinkmann, D. Lo, A. Borsutzky, H. Wächter, M. W. Sigrist, E. Saldin, E. Schneidmiller, M. Yurkov, K. Midorikawa, J. Hein, R. Sauerbrey, and J. Helmcke, “Lasers and coherent light sources,” in Springer Handbook of Lasers and Optics, F. Träger, ed. (Springer, 2007), pp. 583–936.

Walker, D. R.

D. R. Walker, T. Udem, C. Gohle, B. Stein, and T. W. Hänsch, “Frequency dependence of the fixed point in a fluctuating frequency comb,” Appl. Phys. B 89, 535–538 (2007).
[CrossRef]

Washburn, B.

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

Washburn, B. R.

J. J. McFerran, W. C. Swann, B. R. Washburn, and N. R. Newbury, “Suppression of pump-induced frequency noise in fiber-laser frequency combs leading to sub-radion fceo phase excursion,” Appl. Phys. B 86, 219–227 (2007).
[CrossRef]

B. R. Washburn, W. C. Swann, and N. R. Newbury, “Response dynamics of the frequency comb output from a femtosecond laser,” Opt. Express 13, 10622–10633 (2005).
[CrossRef]

Xu, Z.

W. Zhang, Z. Xu, M. Lours, R. Boudot, Y. Kersalé, A. N. Luiten, Y. Le Coq, and G. Santarelli, “Advanced noise reduction techniques for ultra-low phase noise optical-to-microwave division with femtosecond fiber combs,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 58, 900–908 (2011).
[CrossRef]

Yan, M.

Ye, J.

M. C. Stowe, M. J. Thorpe, A. Pe’er, J. Ye, J. E. Stalnaker, V. Gerginov, and S. A. Diddams, “Direct frequency comb spectroscopy,” Adv. At. Mol.Opt. Phys. 55, 1–60 (2008).
[CrossRef]

M. J. Thorpe, K. D. Moll, R. J. Jones, B. Safdi, and J. Ye, “Broadband cavity ringdown spectroscopy for sensitive and rapid molecular detection,” Science 311, 1595–1599 (2006).
[CrossRef]

J. Ye, H. Schnatz, and L. W. Hollberg, “Optical frequency combs: from frequency metrology to optical phase control,” IEEE J. Sel. Top. Quantum Electron. 9, 1041–1058 (2003).
[CrossRef]

J. Rauschenberger, T. Fortier, D. Jones, J. Ye, and S. Cundiff, “Control of the frequency comb from a modelocked Erbium-doped fiber laser,” Opt. Express 10, 1404–1410 (2002).

Yurkov, M.

O. Svelto, S. Longhi, G. Della Valle, S. Kück, G. Huber, M. Pollnau, H. Hillmer, S. Hansmann, R. Engelbrecht, H. Brand, J. Kaiser, A. B. Peterson, R. Malz, S. Steinberg, G. Marowsky, U. Brinkmann, D. Lo, A. Borsutzky, H. Wächter, M. W. Sigrist, E. Saldin, E. Schneidmiller, M. Yurkov, K. Midorikawa, J. Hein, R. Sauerbrey, and J. Helmcke, “Lasers and coherent light sources,” in Springer Handbook of Lasers and Optics, F. Träger, ed. (Springer, 2007), pp. 583–936.

Zach, A.

Zaffalon, M.

S. Schilt, N. Bucalovic, L. Tombez, V. Dolgovskiy, C. Schori, G. Di Domenico, M. Zaffalon, and P. Thomann, “Frequency discriminators for the characterization of narrow-spectrum heterodyne beat signals: application to the measurement of a sub-hertz carrier-envelope-offset beat in an optical frequency comb,” Rev. Sci. Instrum. 82, 123116(2011).
[CrossRef]

Zeller, S. C.

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

Zhang, W.

W. Zhang, M. Lours, M. Fischer, R. Holzwarth, G. Santarelli, and Y. Le Coq, “Characterizing a fiber-based frequency comb with electro-optic modulator,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 59, 432–438 (2012).
[CrossRef]

W. Zhang, Z. Xu, M. Lours, R. Boudot, Y. Kersalé, A. N. Luiten, Y. Le Coq, and G. Santarelli, “Advanced noise reduction techniques for ultra-low phase noise optical-to-microwave division with femtosecond fiber combs,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 58, 900–908 (2011).
[CrossRef]

Adv. At. Mol.Opt. Phys.

M. C. Stowe, M. J. Thorpe, A. Pe’er, J. Ye, J. E. Stalnaker, V. Gerginov, and S. A. Diddams, “Direct frequency comb spectroscopy,” Adv. At. Mol.Opt. Phys. 55, 1–60 (2008).
[CrossRef]

Appl. Phys. B

R. Paschotta, A. Schlatter, S. C. Zeller, H. R. Telle, and U. Keller, “Optical phase noise and carrier-envelope offset 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]

H. R. Telle, G. Steinmeyer, A. E. Dunlop, J. Stenger, D. H. Sutter, and U. Keller, “Carrier-envelope offset phase control: a novel concept for absolute optical frequency measurement and ultrashort pulse generation,” Appl. Phys. B 69, 327–332 (1999).
[CrossRef]

D. R. Walker, T. Udem, C. Gohle, B. Stein, and T. W. Hänsch, “Frequency dependence of the fixed point in a fluctuating frequency comb,” Appl. Phys. B 89, 535–538 (2007).
[CrossRef]

N. Haverkamp, H. Hundertmark, C. Fallnich, and H. R. Telle, “Frequency stabilization of mode-locked Erbium fiber lasers using pump power control,” Appl. Phys. B 78, 321–324 (2004).
[CrossRef]

J. J. McFerran, W. C. Swann, B. R. Washburn, and N. R. Newbury, “Suppression of pump-induced frequency noise in fiber-laser frequency combs leading to sub-radion fceo phase excursion,” Appl. Phys. B 86, 219–227 (2007).
[CrossRef]

Appl. Phys. B.

F. W. Helbing, G. Steinmeyer, J. Stenger, H. R. Telle, and U. Keller, “Carrier–envelope-offset dynamics and stabilization of femtosecond pulses,” Appl. Phys. B. 74, S35–S42 (2002).
[CrossRef]

Appl. Phys. Lett.

J. Millo, M. Abgrall, M. Lours, E. M. L. English, H. Jiang, J. Guéna, A. Clairon, S. Bize, Y. Le Coq, G. Santarelli, and M. E. Tobar, “Ultra-low noise microwave generation with fiber-based optical frequency comb and application to atomic fountain clock,” Appl. Phys. Lett. 94, 141105 (2009).
[CrossRef]

IEEE J. Quantum Electron.

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

IEEE J. Sel. Top. Quantum Electron.

J. Ye, H. Schnatz, and L. W. Hollberg, “Optical frequency combs: from frequency metrology to optical phase control,” IEEE J. Sel. Top. Quantum Electron. 9, 1041–1058 (2003).
[CrossRef]

IEEE Trans. Ultrason. Ferroelectr. Freq. Control

W. Zhang, M. Lours, M. Fischer, R. Holzwarth, G. Santarelli, and Y. Le Coq, “Characterizing a fiber-based frequency comb with electro-optic modulator,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 59, 432–438 (2012).
[CrossRef]

W. Zhang, Z. Xu, M. Lours, R. Boudot, Y. Kersalé, A. N. Luiten, Y. Le Coq, and G. Santarelli, “Advanced noise reduction techniques for ultra-low phase noise optical-to-microwave division with femtosecond fiber combs,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 58, 900–908 (2011).
[CrossRef]

J. Opt. Soc. Am. B

Metrologia

L. Hollberg, S. Diddams, A. Bartels, T. Fortier, and K. Kim, “The measurement of optical frequencies,” Metrologia 42, S105–S124 (2005).
[CrossRef]

Nat. Photonics

B. Bernhardt, A. Ozawa, P. Jacquet, M. Jacquey, Y. Kobayashi, T. Udem, R. Holzwarth, G. Guelachvili, T. W. Hänsch, and N. Picqué, “Cavity-enhanced dual-comb spectroscopy,” Nat. Photonics 4, 55–57 (2010).

Opt. Express

Rev. Mod. Phys.

J. Bechhoefer, “Feedback for physicists: a tutorial essay on control,” Rev. Mod. Phys. 77, 783–836 (2005).
[CrossRef]

T. W. Hänsch, “Nobel lecture: passion for precision,” Rev. Mod. Phys. 78, 1297–1309 (2006).
[CrossRef]

Rev. Sci. Instrum.

S. Schilt, N. Bucalovic, L. Tombez, V. Dolgovskiy, C. Schori, G. Di Domenico, M. Zaffalon, and P. Thomann, “Frequency discriminators for the characterization of narrow-spectrum heterodyne beat signals: application to the measurement of a sub-hertz carrier-envelope-offset beat in an optical frequency comb,” Rev. Sci. Instrum. 82, 123116(2011).
[CrossRef]

Science

M. J. Thorpe, K. D. Moll, R. J. Jones, B. Safdi, and J. Ye, “Broadband cavity ringdown spectroscopy for sensitive and rapid molecular detection,” Science 311, 1595–1599 (2006).
[CrossRef]

Other

V. Dolgovskiy, S. Schilt, G. Di Domenico, N. Bucalovic, C. Schori, and P. Thomann, “1.5 μm cavity-stabilized laser for ultra-stable microwave generation,” in Proceedings of 2011 Joint Conference of the IEEE International Frequency Control and the European Frequency and Time Forum (FCS), San Francisco, USA, May 2–5, 2011 (IEEE, 2011), pp. 1–3.

F. Riehle, Frequency Standards, Basics and Applications(Wiley, 2004), Chap. 2.

O. Svelto, S. Longhi, G. Della Valle, S. Kück, G. Huber, M. Pollnau, H. Hillmer, S. Hansmann, R. Engelbrecht, H. Brand, J. Kaiser, A. B. Peterson, R. Malz, S. Steinberg, G. Marowsky, U. Brinkmann, D. Lo, A. Borsutzky, H. Wächter, M. W. Sigrist, E. Saldin, E. Schneidmiller, M. Yurkov, K. Midorikawa, J. Hein, R. Sauerbrey, and J. Helmcke, “Lasers and coherent light sources,” in Springer Handbook of Lasers and Optics, F. Träger, ed. (Springer, 2007), pp. 583–936.

E. Rubiola, and F. Vernotte, “The cross-spectrum experimental method,” http://arxiv.org/abs/1003.0113 .

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Figures (9)

Fig. 1.
Fig. 1.

Transfer functions in amplitude (left plots) and phase (right plots) of fCEO (light thick curve, left vertical axis) and frep (dark thin curve, right vertical axis) in the Er:fiber comb for cavity length modulation, applied through (a) a modulation of the PZT drive voltage and (b) for pump laser modulation. The points on the left vertical axes represent the DC values separately obtained from a static measurement.

Fig. 2.
Fig. 2.

Spectral distribution of the comb quasi-fixed point obtained for cavity length modulation (left vertical scale, thin blue curve) and for laser pump power modulation (right vertical scale, thick red curve). The points on the left vertical axis represent the static fixed points obtained from the ratio of the DC tuning coefficients of fCEO and frep. The quasi-fixed point for cavity length modulation presents many sign reversals that result from mechanical resonances in the PZT. The solid curve corresponds to positive values of Nq-fixPZT and the dashed curve to negative values of Nq-fixPZT.

Fig. 3.
Fig. 3.

Schematic representation of the two coupled stabilization loops in the Er:fiber comb. Loop (1) stabilizes the CEO frequency and loop (2) the repetition rate.

Fig. 4.
Fig. 4.

Measured frequency noise PSD of the repetition rate (@250 MHz) in the free-running and stabilized Er:fiber comb (with and without CEO stabilization). At high frequencies, the measurement is limited by the instrumental noise floor of the HF2PLL discriminator (dashed line).

Fig. 5.
Fig. 5.

Frequency noise PSD of the repetition rate in the fully stabilized Er:fiber comb: comparison between the experimental measurement (thick grey curve) and the calculation from the theoretical model (thin dark curve).

Fig. 6.
Fig. 6.

Measured individual contributions of the CEO and repetition rate frequency noise PSD (SδfCEOδfCEO and SN·δfrepN·δfrep) to an optical comb line at 1.56 μm and comparison with the measured frequency noise of the optical comb line (SδνNδνN) experimentally assessed from the heterodyne beat with a cavity-stabilized laser.

Fig. 7.
Fig. 7.

Comparison of the frequency noise of the CEO-free heterodyne beat (νNfCEO=N·frep) experimentally measured (thick grey curve) and calculated from the model (thin dark curve). In order to overcome the limitation in the frequency noise of the free-running repetition rate used in the model that results from the instrumental noise floor (see Fig. 5), the frequency noise PSD of frep was obtained from the CEO-free optical beat at 1.56 μm (N·frep with N770,000) divided by N2.

Fig. 8.
Fig. 8.

(a) Measured individual contributions of the CEO and repetition rate frequency noise PSDs (SΔfCEOΔfCEO and SN·ΔfrepN·Δfrep) to an optical comb line at 1.56 μm and comparison with the measured frequency noise of the optical comb line (SΔνNΔνN) experimentally assessed from the heterodyne beat between a cavity-stabilized laser and the free-running comb. (b) Frequency dependence of the sum of the complex coherences ΓΔ(ω)=(γΔfCEON·Δfrep+γN·ΔfrepΔfCEO) between the frequency variations of the CEO and repetition rate in the free-running comb (left vertical axis). The correlation between the phase of the variations of fCEO and frep induced by pump current modulation is also shown, represented by cos{φCEO(ω)φrep(ω)} (right vertical axis), where φCEO and φrep are the phases of the transfer functions of Fig. 1.

Fig. 9.
Fig. 9.

Frequency noise PSD of a comb line at 1.56 μm calculated from the model in the presence and absence of coupling between the two servo loops. The frequency noise spectrum experimentally measured for a 1.56 μm comb line from the heterodyne beat between the comb and an ultrastable laser is also shown for comparison (thick grey curve). In order to overcome the limitation in the frequency noise of the free-running repetition rate used in the model that results from the instrumental noise floor (see Fig. 5), the frequency noise PSD of frep was obtained from the CEO-free optical beat at 1.56 μm (N·frep with N770,000) divided by N2.

Equations (20)

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

(f˜CEO(ω)f˜rep(ω))=(CfCEOupump(ω)CfCEOuPZT(ω)Cfrepupump(ω)CfrepuPZT(ω))(u˜pump(ω)u˜PZT(ω)).
Nfixx=(fCEOx)/(frepx).
Nq-fixx(ω)=Re[CfCEOx(ω)Cfrepx(ω)].
|Δν˜N(ω)|=|Cfrepx(ω)·x˜(ω)|{Im[CfCEOx(ω)Cfrepx(ω)]}2+(NNq-fixx(ω))2,
f˜jstab=f˜jfree+f˜jcor+f˜jcoupl.
(f˜1cor+f˜1couplf˜2cor+f˜2coupl)=(C11C12C21C22)·(G100G2)·(D100D2)·(Δf˜1Δf˜2).
δf˜j=(1+Kj)(Δf˜j+KkΔf˜kCjkCkk)1KjKkCjkCkjCjjCkk,
(Sδf1δf1Sδf1δf2Sδf2δf1Sδf2δf2)=(H11H12H21H22)+·(SΔf1Δf1SΔf1Δf2SΔf2Δf1SΔf2Δf2)·(H11H12H21H22),
Hjj(ω)=(1+Kj)·(1KjKkCjkCkjCjjCkk)1,Hjk(ω)=(1+Kj)KkCjkCkk(1KjKkCjkCkjCjjCkk)1
SΔνNΔνN=SΔfCEOΔfCEO+SN·ΔfrepN·Δfrep+SΔfCEON·Δfrep+SN·ΔfrepΔfCEO,
SΔνNΔνN=SΔfCEOΔfCEO+SN·ΔfrepN·Δfrep+(γΔfCEON·Δfrep+γN·ΔfrepΔfCEO)SΔfCEOΔfCEO·SN·ΔfrepN·Δfrep.
ΓΔ(ω)=γΔfCEON·Δfrep+γN·ΔfrepΔfCEO=SΔνNΔνNSΔfCEOΔfCEOSN·ΔfrepN·ΔfrepSΔfCEOΔfCEO·SN·ΔfrepN·Δfrep.
(f˜1cor+f˜1couplf˜2cor+f˜2coupl)=(C11C12C21C22)·(G100G2)·(D100D2)·(Δf˜1Δf˜1refΔf˜2Δf˜2ref).
δf˜jcomb=(1+Kj)(Δf˜j+KkΔf˜kCjkCkk)1KjKkCjkCkjCjjCkk,
δf˜jref=Δf˜jrefKj(1+KkCjkCkjCjjCkk)1KjKkCjkCkjCjjCkkΔf˜krefKk(1+Kj)CjkCkk1KjKkCjkCkjCjjCkk.
|δf˜j|=|δf˜jcomb|2+|δf˜jref|2.
Sδfj=Sδfjcombδfjcomb+Sδfjrefδfjref,
(Sδf1combδf1combSδf1combδf2combSδf2combδf1combSδf2combδf2comb)=(H11H12H21H22)+·(SΔf1Δf1SΔf1Δf2SΔf2Δf1SΔf2Δf2)·(H11H12H21H22),
(Sδf1ref,δf1refSδf1ref,δf2refSδf2ref,δf1refSδf2ref,δf2ref)=(H11refH12refH21refH22ref)+·(SΔf1refΔf1refSΔf1refΔf2refSΔf2refΔf1refSΔf2refΔf2ref)·(H11refH12refH21refH22ref),
Hjj(ω)=(1+Kj)1KjKkCjkCkjCjjCkk,Hjk(ω)=Hjkref(ω)=(1+Kj)KkCjkCkk1KjKkCjkCkjCjjCkk,Hjjref(ω)=Kj(1+KkCjkCkjCjjCkk)1KjKkCjkCkjCjjCkk.

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