Abstract

In multi-branch combs, the comb outputs from the branches suffer from different fiber noises, which often limit the uncertainty of the combs referring a highly-stable optical frequency. To overcome this limitation, we introduced fiber noise difference cancellation to multi-branch fiber combs. We detected and phase-locked the beat notes between the branch outputs and a common 1542 nm continuous wave laser. A piezo-electric transducer-based fiber stretcher was installed in each branch except for the branch used as the cancellation reference. We fabricated two quasi-identical combs with this mechanism and confirmed the relative frequency uncertainty by comparing them. The cancellation improved the frequency uncertainty to a low level of 10−20 at a 100000-s averaging time.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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  2. D. J. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, “Carrier-envelope phase control of femtosecond mode-locked lasers and direct optical frequency synthesis,” Science 288(5466), 635–639 (2000).
    [Crossref] [PubMed]
  3. J. Stenger, H. Schnatz, C. Tamm, and H. R. Telle, “Ultraprecise measurement of optical frequency ratios,” Phys. Rev. Lett. 88(7), 073601 (2002).
    [Crossref] [PubMed]
  4. L.-S. Ma, Z. Bi, A. Bartels, L. Robertsson, M. Zucco, R. S. Windeler, G. Wilpers, C. Oates, L. Hollberg, and S. A. Diddams, “Optical frequency synthesis and comparison with uncertainty at the 10-19 level,” Science 303(5665), 1843–1845 (2004).
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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
  13. D. Nicolodi, B. Argence, W. Zhang, R. Le Targat, G. Santarelli, and Y. Le Coq, “Spectral purity transfer between optical wavelengths at the 10−18 level,” Nat. Photonics 8(3), 219–223 (2014).
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
  22. W. Zhang, M. Lours, M. Fischer, R. Holzwarth, G. Santarelli, and Y. Coq, “Characterizing a fiber-based frequency comb with electro-optic modulator,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 59(3), 432–438 (2012).
    [Crossref] [PubMed]
  23. C. Hagemann, C. Grebing, T. Kessler, S. Falke, N. Lemke, C. Lisdat, H. Schnatz, F. Riehle, and U. Sterr, “Providing 10−16 short-term stability of a 1.5 μm laser to optical clocks,” IEEE Trans. Instrum. Meas. 62(6), 1556–1562 (2013).
    [Crossref]
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    [Crossref]
  25. H. Leopardi, J. Davila-Rodriguez, F. Quinlan, J. Olson, J. A. Sherman, S. A. Diddams, and T. M. Fortier, “Single-branch Er:fiber frequency comb for precision optical metrology with 10−18 fractional instability,” Optica 4(8), 879–885 (2017).
    [Crossref]
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    [Crossref] [PubMed]
  27. L. A. M. Johnson, P. Gill, and H. S. Margolis, “Evaluating the performance of the NPL femtosecond frequency combs: agreement at the 10−21 level,” Metrologia 52(1), 62–71 (2015).
    [Crossref]
  28. Y. Yao, Y. Jiang, H. Yu, Z. Bi, and L. Ma, “Optical frequency divider with division uncertainty at the 10−21 level,” Natl. Sci. Rev. 3, 463–469 (2016).
  29. Y. Nakajima, H. Inaba, F.-L. Hong, A. Onae, K. Minoshima, T. Kobayashi, M. Nakazawa, and H. Matsumoto, “Optimized amplification of femtosecond optical pulses by dispersion management for octave-spanning optical frequency comb generation,” Opt. Commun. 281(17), 4484–4487 (2008).
    [Crossref]
  30. M. Hirano, T. Nakanishi, T. Okuno, and M. Onishi, “Silica-based highly nonlinear fibers and their application,” IEEE J. Sel. Top. Quantum Electron. 15, 103–113 (2009).
  31. K. Hosaka, H. Inaba, Y. Nakajima, M. Yasuda, T. Kohno, A. Onae, and F.-L. Hong, “Evaluation of the clock laser for an Yb lattice clock using an optic fiber comb,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 57(3), 606–612 (2010).
    [Crossref] [PubMed]
  32. L. S. Ma, P. Jungner, J. Ye, and J. L. Hall, “Delivering the same optical frequency at two places: accurate cancellation of phase noise introduced by an optical fiber or other time-varying path,” Opt. Lett. 19(21), 1777–1779 (1994).
    [Crossref] [PubMed]
  33. P. A. Williams, W. C. Swann, and N. R. Newbury, “High-stability transfer of an optical frequency over long fiber-optic links,” J. Opt. Soc. Am. B 25(8), 1284–1293 (2008).
    [Crossref]

2017 (3)

2016 (1)

Y. Yao, Y. Jiang, H. Yu, Z. Bi, and L. Ma, “Optical frequency divider with division uncertainty at the 10−21 level,” Natl. Sci. Rev. 3, 463–469 (2016).

2015 (2)

T. Nakamura, I. Ito, and Y. Kobayashi, “Offset-free broadband Yb:fiber optical frequency comb for optical clocks,” Opt. Express 23(15), 19376–19381 (2015).
[Crossref] [PubMed]

L. A. M. Johnson, P. Gill, and H. S. Margolis, “Evaluating the performance of the NPL femtosecond frequency combs: agreement at the 10−21 level,” Metrologia 52(1), 62–71 (2015).
[Crossref]

2014 (1)

D. Nicolodi, B. Argence, W. Zhang, R. Le Targat, G. Santarelli, and Y. Le Coq, “Spectral purity transfer between optical wavelengths at the 10−18 level,” Nat. Photonics 8(3), 219–223 (2014).
[Crossref]

2013 (2)

H. Inaba, K. Hosaka, M. Yasuda, Y. Nakajima, K. Iwakuni, D. Akamatsu, S. Okubo, T. Kohno, A. Onae, and F.-L. Hong, “Spectroscopy of 171Yb in an optical lattice based on laser linewidth transfer using a narrow linewidth frequency comb,” Opt. Express 21(7), 7891–7896 (2013).
[Crossref] [PubMed]

C. Hagemann, C. Grebing, T. Kessler, S. Falke, N. Lemke, C. Lisdat, H. Schnatz, F. Riehle, and U. Sterr, “Providing 10−16 short-term stability of a 1.5 μm laser to optical clocks,” IEEE Trans. Instrum. Meas. 62(6), 1556–1562 (2013).
[Crossref]

2012 (3)

2010 (2)

Y. Nakajima, H. Inaba, K. Hosaka, K. Minoshima, A. Onae, M. Yasuda, T. Kohno, S. Kawato, T. Kobayashi, T. Katsuyama, and F.-L. Hong, “A multi-branch, fiber-based frequency comb with millihertz-level relative linewidths using an intra-cavity electro-optic modulator,” Opt. Express 18(2), 1667–1676 (2010).
[Crossref] [PubMed]

K. Hosaka, H. Inaba, Y. Nakajima, M. Yasuda, T. Kohno, A. Onae, and F.-L. Hong, “Evaluation of the clock laser for an Yb lattice clock using an optic fiber comb,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 57(3), 606–612 (2010).
[Crossref] [PubMed]

2009 (3)

M. Hirano, T. Nakanishi, T. Okuno, and M. Onishi, “Silica-based highly nonlinear fibers and their application,” IEEE J. Sel. Top. Quantum Electron. 15, 103–113 (2009).

M. J. Martin, S. M. Foreman, T. R. Schibli, and J. Ye, “Testing ultrafast mode-locking at microhertz relative optical linewidth,” Opt. Express 17(2), 558–568 (2009).
[Crossref] [PubMed]

T. Legero, C. Lisdat, J. S. R. Vellore Winfred, H. Schnatz, G. Grosche, F. Riehle, and U. Sterr, “Interrogation laser for a strontium lattice clock,” IEEE Trans. Instrum. Meas. 58(4), 1252–1257 (2009).
[Crossref]

2008 (3)

T. R. Schibli, I. Hartl, D. C. Yost, M. J. Martin, A. Marcinkevičius, M. E. Fermann, and J. Ye, “Optical frequency comb with submillihertz linewidth and more than 10 W average power,” Nat. Photonics 2(6), 355–359 (2008).
[Crossref]

Y. Nakajima, H. Inaba, F.-L. Hong, A. Onae, K. Minoshima, T. Kobayashi, M. Nakazawa, and H. Matsumoto, “Optimized amplification of femtosecond optical pulses by dispersion management for octave-spanning optical frequency comb generation,” Opt. Commun. 281(17), 4484–4487 (2008).
[Crossref]

P. A. Williams, W. C. Swann, and N. R. Newbury, “High-stability transfer of an optical frequency over long fiber-optic links,” J. Opt. Soc. Am. B 25(8), 1284–1293 (2008).
[Crossref]

2007 (1)

2006 (1)

2004 (4)

2003 (2)

2002 (1)

J. Stenger, H. Schnatz, C. Tamm, and H. R. Telle, “Ultraprecise measurement of optical frequency ratios,” Phys. Rev. Lett. 88(7), 073601 (2002).
[Crossref] [PubMed]

2000 (2)

D. J. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, “Carrier-envelope phase control of femtosecond mode-locked lasers and direct optical frequency synthesis,” Science 288(5466), 635–639 (2000).
[Crossref] [PubMed]

A. Apolonski, A. Poppe, G. Tempea, C. Spielmann, T. Udem, R. Holzwarth, T. W. Hänsch, and F. Krausz, “Controlling the phase evolution of few-cycle light pulses,” Phys. Rev. Lett. 85(4), 740–743 (2000).
[Crossref] [PubMed]

1999 (1)

1994 (1)

Akamatsu, D.

Apolonski, A.

A. Apolonski, A. Poppe, G. Tempea, C. Spielmann, T. Udem, R. Holzwarth, T. W. Hänsch, and F. Krausz, “Controlling the phase evolution of few-cycle light pulses,” Phys. Rev. Lett. 85(4), 740–743 (2000).
[Crossref] [PubMed]

Argence, B.

D. Nicolodi, B. Argence, W. Zhang, R. Le Targat, G. Santarelli, and Y. Le Coq, “Spectral purity transfer between optical wavelengths at the 10−18 level,” Nat. Photonics 8(3), 219–223 (2014).
[Crossref]

Bartels, A.

L.-S. Ma, Z. Bi, A. Bartels, L. Robertsson, M. Zucco, R. S. Windeler, G. Wilpers, C. Oates, L. Hollberg, and S. A. Diddams, “Optical frequency synthesis and comparison with uncertainty at the 10-19 level,” Science 303(5665), 1843–1845 (2004).
[Crossref] [PubMed]

A. Bartels, C. W. Oates, L. Hollberg, and S. A. Diddams, “Stabilization of femtosecond laser frequency combs with subhertz residual linewidths,” Opt. Lett. 29(10), 1081–1083 (2004).
[Crossref] [PubMed]

Benko, C.

Bi, Z.

Y. Yao, Y. Jiang, H. Yu, Z. Bi, and L. Ma, “Optical frequency divider with division uncertainty at the 10−21 level,” Natl. Sci. Rev. 3, 463–469 (2016).

L.-S. Ma, Z. Bi, A. Bartels, L. Robertsson, M. Zucco, R. S. Windeler, G. Wilpers, C. Oates, L. Hollberg, and S. A. Diddams, “Optical frequency synthesis and comparison with uncertainty at the 10-19 level,” Science 303(5665), 1843–1845 (2004).
[Crossref] [PubMed]

Coddington, I.

Coq, Y.

W. Zhang, M. Lours, M. Fischer, R. Holzwarth, G. Santarelli, and Y. Coq, “Characterizing a fiber-based frequency comb with electro-optic modulator,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 59(3), 432–438 (2012).
[Crossref] [PubMed]

Cundiff, S. T.

D. J. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, “Carrier-envelope phase control of femtosecond mode-locked lasers and direct optical frequency synthesis,” Science 288(5466), 635–639 (2000).
[Crossref] [PubMed]

Davila-Rodriguez, J.

Diddams, S. A.

H. Leopardi, J. Davila-Rodriguez, F. Quinlan, J. Olson, J. A. Sherman, S. A. Diddams, and T. M. Fortier, “Single-branch Er:fiber frequency comb for precision optical metrology with 10−18 fractional instability,” Optica 4(8), 879–885 (2017).
[Crossref]

L.-S. Ma, Z. Bi, A. Bartels, L. Robertsson, M. Zucco, R. S. Windeler, G. Wilpers, C. Oates, L. Hollberg, and S. A. Diddams, “Optical frequency synthesis and comparison with uncertainty at the 10-19 level,” Science 303(5665), 1843–1845 (2004).
[Crossref] [PubMed]

A. Bartels, C. W. Oates, L. Hollberg, and S. A. Diddams, “Stabilization of femtosecond laser frequency combs with subhertz residual linewidths,” Opt. Lett. 29(10), 1081–1083 (2004).
[Crossref] [PubMed]

D. J. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, “Carrier-envelope phase control of femtosecond mode-locked lasers and direct optical frequency synthesis,” Science 288(5466), 635–639 (2000).
[Crossref] [PubMed]

Eikema, K. S. E.

Falke, S.

C. Hagemann, C. Grebing, T. Kessler, S. Falke, N. Lemke, C. Lisdat, H. Schnatz, F. Riehle, and U. Sterr, “Providing 10−16 short-term stability of a 1.5 μm laser to optical clocks,” IEEE Trans. Instrum. Meas. 62(6), 1556–1562 (2013).
[Crossref]

Fan, S.

Feder, K.

Feder, K. S.

Fejer, M. M.

Fermann, M. E.

Fischer, M.

W. Zhang, M. Lours, M. Fischer, R. Holzwarth, G. Santarelli, and Y. Coq, “Characterizing a fiber-based frequency comb with electro-optic modulator,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 59(3), 432–438 (2012).
[Crossref] [PubMed]

Foreman, S. M.

Fortier, T. M.

Fox, R. W.

Gill, P.

L. A. M. Johnson, P. Gill, and H. S. Margolis, “Evaluating the performance of the NPL femtosecond frequency combs: agreement at the 10−21 level,” Metrologia 52(1), 62–71 (2015).
[Crossref]

Grebing, C.

C. Hagemann, C. Grebing, T. Kessler, S. Falke, N. Lemke, C. Lisdat, H. Schnatz, F. Riehle, and U. Sterr, “Providing 10−16 short-term stability of a 1.5 μm laser to optical clocks,” IEEE Trans. Instrum. Meas. 62(6), 1556–1562 (2013).
[Crossref]

Grosche, G.

T. Legero, C. Lisdat, J. S. R. Vellore Winfred, H. Schnatz, G. Grosche, F. Riehle, and U. Sterr, “Interrogation laser for a strontium lattice clock,” IEEE Trans. Instrum. Meas. 58(4), 1252–1257 (2009).
[Crossref]

Guo, W.

Hagemann, C.

C. Hagemann, C. Grebing, T. Kessler, S. Falke, N. Lemke, C. Lisdat, H. Schnatz, F. Riehle, and U. Sterr, “Providing 10−16 short-term stability of a 1.5 μm laser to optical clocks,” IEEE Trans. Instrum. Meas. 62(6), 1556–1562 (2013).
[Crossref]

Hall, J. L.

D. J. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, “Carrier-envelope phase control of femtosecond mode-locked lasers and direct optical frequency synthesis,” Science 288(5466), 635–639 (2000).
[Crossref] [PubMed]

L. S. Ma, P. Jungner, J. Ye, and J. L. Hall, “Delivering the same optical frequency at two places: accurate cancellation of phase noise introduced by an optical fiber or other time-varying path,” Opt. Lett. 19(21), 1777–1779 (1994).
[Crossref] [PubMed]

Hänsch, T. W.

A. Apolonski, A. Poppe, G. Tempea, C. Spielmann, T. Udem, R. Holzwarth, T. W. Hänsch, and F. Krausz, “Controlling the phase evolution of few-cycle light pulses,” Phys. Rev. Lett. 85(4), 740–743 (2000).
[Crossref] [PubMed]

T. Udem, J. Reichert, R. Holzwarth, and T. W. Hänsch, “Accurate measurement of large optical frequency differences with a mode-locked laser,” Opt. Lett. 24(13), 881–883 (1999).
[Crossref] [PubMed]

Hartl, I.

Hirai, A.

Hirano, M.

M. Hirano, T. Nakanishi, T. Okuno, and M. Onishi, “Silica-based highly nonlinear fibers and their application,” IEEE J. Sel. Top. Quantum Electron. 15, 103–113 (2009).

Hollberg, L.

A. Bartels, C. W. Oates, L. Hollberg, and S. A. Diddams, “Stabilization of femtosecond laser frequency combs with subhertz residual linewidths,” Opt. Lett. 29(10), 1081–1083 (2004).
[Crossref] [PubMed]

L.-S. Ma, Z. Bi, A. Bartels, L. Robertsson, M. Zucco, R. S. Windeler, G. Wilpers, C. Oates, L. Hollberg, and S. A. Diddams, “Optical frequency synthesis and comparison with uncertainty at the 10-19 level,” Science 303(5665), 1843–1845 (2004).
[Crossref] [PubMed]

Holzwarth, R.

W. Zhang, M. Lours, M. Fischer, R. Holzwarth, G. Santarelli, and Y. Coq, “Characterizing a fiber-based frequency comb with electro-optic modulator,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 59(3), 432–438 (2012).
[Crossref] [PubMed]

A. Apolonski, A. Poppe, G. Tempea, C. Spielmann, T. Udem, R. Holzwarth, T. W. Hänsch, and F. Krausz, “Controlling the phase evolution of few-cycle light pulses,” Phys. Rev. Lett. 85(4), 740–743 (2000).
[Crossref] [PubMed]

T. Udem, J. Reichert, R. Holzwarth, and T. W. Hänsch, “Accurate measurement of large optical frequency differences with a mode-locked laser,” Opt. Lett. 24(13), 881–883 (1999).
[Crossref] [PubMed]

Hong, F.-L.

H. Inaba, K. Hosaka, M. Yasuda, Y. Nakajima, K. Iwakuni, D. Akamatsu, S. Okubo, T. Kohno, A. Onae, and F.-L. Hong, “Spectroscopy of 171Yb in an optical lattice based on laser linewidth transfer using a narrow linewidth frequency comb,” Opt. Express 21(7), 7891–7896 (2013).
[Crossref] [PubMed]

K. Iwakuni, H. Inaba, Y. Nakajima, T. Kobayashi, K. Hosaka, A. Onae, and F.-L. Hong, “Narrow linewidth comb realized with a mode-locked fiber laser using an intra-cavity waveguide electro-optic modulator for high-speed control,” Opt. Express 20(13), 13769–13776 (2012).
[Crossref] [PubMed]

Y. Nakajima, H. Inaba, K. Hosaka, K. Minoshima, A. Onae, M. Yasuda, T. Kohno, S. Kawato, T. Kobayashi, T. Katsuyama, and F.-L. Hong, “A multi-branch, fiber-based frequency comb with millihertz-level relative linewidths using an intra-cavity electro-optic modulator,” Opt. Express 18(2), 1667–1676 (2010).
[Crossref] [PubMed]

K. Hosaka, H. Inaba, Y. Nakajima, M. Yasuda, T. Kohno, A. Onae, and F.-L. Hong, “Evaluation of the clock laser for an Yb lattice clock using an optic fiber comb,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 57(3), 606–612 (2010).
[Crossref] [PubMed]

Y. Nakajima, H. Inaba, F.-L. Hong, A. Onae, K. Minoshima, T. Kobayashi, M. Nakazawa, and H. Matsumoto, “Optimized amplification of femtosecond optical pulses by dispersion management for octave-spanning optical frequency comb generation,” Opt. Commun. 281(17), 4484–4487 (2008).
[Crossref]

T. R. Schibli, K. Minoshima, F.-L. Hong, H. Inaba, A. Onae, H. Matsumoto, I. Hartl, and M. E. Fermann, “Frequency metrology with a turnkey all-fiber system,” Opt. Lett. 29(21), 2467–2469 (2004).
[Crossref] [PubMed]

F.-L. Hong, K. Minoshima, A. Onae, H. Inaba, H. Takada, A. Hirai, H. Matsumoto, T. Sugiura, and M. Yoshida, “Broad-spectrum frequency comb generation and carrier-envelope offset frequency measurement by second-harmonic generation of a mode-locked fiber laser,” Opt. Lett. 28(17), 1516–1518 (2003).
[Crossref] [PubMed]

Hosaka, K.

Inaba, H.

H. Inaba, K. Hosaka, M. Yasuda, Y. Nakajima, K. Iwakuni, D. Akamatsu, S. Okubo, T. Kohno, A. Onae, and F.-L. Hong, “Spectroscopy of 171Yb in an optical lattice based on laser linewidth transfer using a narrow linewidth frequency comb,” Opt. Express 21(7), 7891–7896 (2013).
[Crossref] [PubMed]

K. Iwakuni, H. Inaba, Y. Nakajima, T. Kobayashi, K. Hosaka, A. Onae, and F.-L. Hong, “Narrow linewidth comb realized with a mode-locked fiber laser using an intra-cavity waveguide electro-optic modulator for high-speed control,” Opt. Express 20(13), 13769–13776 (2012).
[Crossref] [PubMed]

Y. Nakajima, H. Inaba, K. Hosaka, K. Minoshima, A. Onae, M. Yasuda, T. Kohno, S. Kawato, T. Kobayashi, T. Katsuyama, and F.-L. Hong, “A multi-branch, fiber-based frequency comb with millihertz-level relative linewidths using an intra-cavity electro-optic modulator,” Opt. Express 18(2), 1667–1676 (2010).
[Crossref] [PubMed]

K. Hosaka, H. Inaba, Y. Nakajima, M. Yasuda, T. Kohno, A. Onae, and F.-L. Hong, “Evaluation of the clock laser for an Yb lattice clock using an optic fiber comb,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 57(3), 606–612 (2010).
[Crossref] [PubMed]

Y. Nakajima, H. Inaba, F.-L. Hong, A. Onae, K. Minoshima, T. Kobayashi, M. Nakazawa, and H. Matsumoto, “Optimized amplification of femtosecond optical pulses by dispersion management for octave-spanning optical frequency comb generation,” Opt. Commun. 281(17), 4484–4487 (2008).
[Crossref]

T. R. Schibli, K. Minoshima, F.-L. Hong, H. Inaba, A. Onae, H. Matsumoto, I. Hartl, and M. E. Fermann, “Frequency metrology with a turnkey all-fiber system,” Opt. Lett. 29(21), 2467–2469 (2004).
[Crossref] [PubMed]

F.-L. Hong, K. Minoshima, A. Onae, H. Inaba, H. Takada, A. Hirai, H. Matsumoto, T. Sugiura, and M. Yoshida, “Broad-spectrum frequency comb generation and carrier-envelope offset frequency measurement by second-harmonic generation of a mode-locked fiber laser,” Opt. Lett. 28(17), 1516–1518 (2003).
[Crossref] [PubMed]

Ito, I.

Iwakuni, K.

Jiang, H.

Jiang, Y.

Y. Yao, Y. Jiang, H. Yu, Z. Bi, and L. Ma, “Optical frequency divider with division uncertainty at the 10−21 level,” Natl. Sci. Rev. 3, 463–469 (2016).

Johnson, L. A. M.

L. A. M. Johnson, P. Gill, and H. S. Margolis, “Evaluating the performance of the NPL femtosecond frequency combs: agreement at the 10−21 level,” Metrologia 52(1), 62–71 (2015).
[Crossref]

Jones, D. J.

D. J. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, “Carrier-envelope phase control of femtosecond mode-locked lasers and direct optical frequency synthesis,” Science 288(5466), 635–639 (2000).
[Crossref] [PubMed]

Jørgensen, C. G.

Jungner, P.

Katori, H.

N. Ohmae, N. Kuse, M. E. Fermann, and H. Katori, “All-polarization-maintaining, single-port Er:fiber comb for high-stability comparison of optical lattice clocks,” Appl. Phys. Express 10(6), 062503 (2017).
[Crossref]

Katsuyama, T.

Kawato, S.

Kessler, T.

C. Hagemann, C. Grebing, T. Kessler, S. Falke, N. Lemke, C. Lisdat, H. Schnatz, F. Riehle, and U. Sterr, “Providing 10−16 short-term stability of a 1.5 μm laser to optical clocks,” IEEE Trans. Instrum. Meas. 62(6), 1556–1562 (2013).
[Crossref]

Knox, W. H.

Kobayashi, T.

Kobayashi, Y.

Kohno, T.

Krausz, F.

A. Apolonski, A. Poppe, G. Tempea, C. Spielmann, T. Udem, R. Holzwarth, T. W. Hänsch, and F. Krausz, “Controlling the phase evolution of few-cycle light pulses,” Phys. Rev. Lett. 85(4), 740–743 (2000).
[Crossref] [PubMed]

Kuse, N.

N. Ohmae, N. Kuse, M. E. Fermann, and H. Katori, “All-polarization-maintaining, single-port Er:fiber comb for high-stability comparison of optical lattice clocks,” Appl. Phys. Express 10(6), 062503 (2017).
[Crossref]

Langrock, C.

Le Coq, Y.

D. Nicolodi, B. Argence, W. Zhang, R. Le Targat, G. Santarelli, and Y. Le Coq, “Spectral purity transfer between optical wavelengths at the 10−18 level,” Nat. Photonics 8(3), 219–223 (2014).
[Crossref]

Le Targat, R.

D. Nicolodi, B. Argence, W. Zhang, R. Le Targat, G. Santarelli, and Y. Le Coq, “Spectral purity transfer between optical wavelengths at the 10−18 level,” Nat. Photonics 8(3), 219–223 (2014).
[Crossref]

Legero, T.

T. Legero, C. Lisdat, J. S. R. Vellore Winfred, H. Schnatz, G. Grosche, F. Riehle, and U. Sterr, “Interrogation laser for a strontium lattice clock,” IEEE Trans. Instrum. Meas. 58(4), 1252–1257 (2009).
[Crossref]

Leitenstorfer, A.

Lemke, N.

C. Hagemann, C. Grebing, T. Kessler, S. Falke, N. Lemke, C. Lisdat, H. Schnatz, F. Riehle, and U. Sterr, “Providing 10−16 short-term stability of a 1.5 μm laser to optical clocks,” IEEE Trans. Instrum. Meas. 62(6), 1556–1562 (2013).
[Crossref]

Leopardi, H.

Lisdat, C.

C. Hagemann, C. Grebing, T. Kessler, S. Falke, N. Lemke, C. Lisdat, H. Schnatz, F. Riehle, and U. Sterr, “Providing 10−16 short-term stability of a 1.5 μm laser to optical clocks,” IEEE Trans. Instrum. Meas. 62(6), 1556–1562 (2013).
[Crossref]

T. Legero, C. Lisdat, J. S. R. Vellore Winfred, H. Schnatz, G. Grosche, F. Riehle, and U. Sterr, “Interrogation laser for a strontium lattice clock,” IEEE Trans. Instrum. Meas. 58(4), 1252–1257 (2009).
[Crossref]

Lours, M.

W. Zhang, M. Lours, M. Fischer, R. Holzwarth, G. Santarelli, and Y. Coq, “Characterizing a fiber-based frequency comb with electro-optic modulator,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 59(3), 432–438 (2012).
[Crossref] [PubMed]

Ma, L.

Y. Yao, Y. Jiang, H. Yu, Z. Bi, and L. Ma, “Optical frequency divider with division uncertainty at the 10−21 level,” Natl. Sci. Rev. 3, 463–469 (2016).

Ma, L. S.

Ma, L.-S.

L.-S. Ma, Z. Bi, A. Bartels, L. Robertsson, M. Zucco, R. S. Windeler, G. Wilpers, C. Oates, L. Hollberg, and S. A. Diddams, “Optical frequency synthesis and comparison with uncertainty at the 10-19 level,” Science 303(5665), 1843–1845 (2004).
[Crossref] [PubMed]

Marcinkevicius, A.

T. R. Schibli, I. Hartl, D. C. Yost, M. J. Martin, A. Marcinkevičius, M. E. Fermann, and J. Ye, “Optical frequency comb with submillihertz linewidth and more than 10 W average power,” Nat. Photonics 2(6), 355–359 (2008).
[Crossref]

Margolis, H. S.

L. A. M. Johnson, P. Gill, and H. S. Margolis, “Evaluating the performance of the NPL femtosecond frequency combs: agreement at the 10−21 level,” Metrologia 52(1), 62–71 (2015).
[Crossref]

Martin, M. J.

Matsumoto, H.

McFerran, J. J.

Minoshima, K.

Nakajima, Y.

Nakamura, T.

Nakanishi, T.

M. Hirano, T. Nakanishi, T. Okuno, and M. Onishi, “Silica-based highly nonlinear fibers and their application,” IEEE J. Sel. Top. Quantum Electron. 15, 103–113 (2009).

Nakazawa, M.

Y. Nakajima, H. Inaba, F.-L. Hong, A. Onae, K. Minoshima, T. Kobayashi, M. Nakazawa, and H. Matsumoto, “Optimized amplification of femtosecond optical pulses by dispersion management for octave-spanning optical frequency comb generation,” Opt. Commun. 281(17), 4484–4487 (2008).
[Crossref]

Newbury, N. R.

Nicholson, J. W.

Nicolodi, D.

D. Nicolodi, B. Argence, W. Zhang, R. Le Targat, G. Santarelli, and Y. Le Coq, “Spectral purity transfer between optical wavelengths at the 10−18 level,” Nat. Photonics 8(3), 219–223 (2014).
[Crossref]

Oates, C.

L.-S. Ma, Z. Bi, A. Bartels, L. Robertsson, M. Zucco, R. S. Windeler, G. Wilpers, C. Oates, L. Hollberg, and S. A. Diddams, “Optical frequency synthesis and comparison with uncertainty at the 10-19 level,” Science 303(5665), 1843–1845 (2004).
[Crossref] [PubMed]

Oates, C. W.

Ohmae, N.

N. Ohmae, N. Kuse, M. E. Fermann, and H. Katori, “All-polarization-maintaining, single-port Er:fiber comb for high-stability comparison of optical lattice clocks,” Appl. Phys. Express 10(6), 062503 (2017).
[Crossref]

Okubo, S.

Okuno, T.

M. Hirano, T. Nakanishi, T. Okuno, and M. Onishi, “Silica-based highly nonlinear fibers and their application,” IEEE J. Sel. Top. Quantum Electron. 15, 103–113 (2009).

Olson, J.

Onae, A.

H. Inaba, K. Hosaka, M. Yasuda, Y. Nakajima, K. Iwakuni, D. Akamatsu, S. Okubo, T. Kohno, A. Onae, and F.-L. Hong, “Spectroscopy of 171Yb in an optical lattice based on laser linewidth transfer using a narrow linewidth frequency comb,” Opt. Express 21(7), 7891–7896 (2013).
[Crossref] [PubMed]

K. Iwakuni, H. Inaba, Y. Nakajima, T. Kobayashi, K. Hosaka, A. Onae, and F.-L. Hong, “Narrow linewidth comb realized with a mode-locked fiber laser using an intra-cavity waveguide electro-optic modulator for high-speed control,” Opt. Express 20(13), 13769–13776 (2012).
[Crossref] [PubMed]

Y. Nakajima, H. Inaba, K. Hosaka, K. Minoshima, A. Onae, M. Yasuda, T. Kohno, S. Kawato, T. Kobayashi, T. Katsuyama, and F.-L. Hong, “A multi-branch, fiber-based frequency comb with millihertz-level relative linewidths using an intra-cavity electro-optic modulator,” Opt. Express 18(2), 1667–1676 (2010).
[Crossref] [PubMed]

K. Hosaka, H. Inaba, Y. Nakajima, M. Yasuda, T. Kohno, A. Onae, and F.-L. Hong, “Evaluation of the clock laser for an Yb lattice clock using an optic fiber comb,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 57(3), 606–612 (2010).
[Crossref] [PubMed]

Y. Nakajima, H. Inaba, F.-L. Hong, A. Onae, K. Minoshima, T. Kobayashi, M. Nakazawa, and H. Matsumoto, “Optimized amplification of femtosecond optical pulses by dispersion management for octave-spanning optical frequency comb generation,” Opt. Commun. 281(17), 4484–4487 (2008).
[Crossref]

T. R. Schibli, K. Minoshima, F.-L. Hong, H. Inaba, A. Onae, H. Matsumoto, I. Hartl, and M. E. Fermann, “Frequency metrology with a turnkey all-fiber system,” Opt. Lett. 29(21), 2467–2469 (2004).
[Crossref] [PubMed]

F.-L. Hong, K. Minoshima, A. Onae, H. Inaba, H. Takada, A. Hirai, H. Matsumoto, T. Sugiura, and M. Yoshida, “Broad-spectrum frequency comb generation and carrier-envelope offset frequency measurement by second-harmonic generation of a mode-locked fiber laser,” Opt. Lett. 28(17), 1516–1518 (2003).
[Crossref] [PubMed]

Onishi, M.

M. Hirano, T. Nakanishi, T. Okuno, and M. Onishi, “Silica-based highly nonlinear fibers and their application,” IEEE J. Sel. Top. Quantum Electron. 15, 103–113 (2009).

Pal, P.

Poppe, A.

A. Apolonski, A. Poppe, G. Tempea, C. Spielmann, T. Udem, R. Holzwarth, T. W. Hänsch, and F. Krausz, “Controlling the phase evolution of few-cycle light pulses,” Phys. Rev. Lett. 85(4), 740–743 (2000).
[Crossref] [PubMed]

Quinlan, F.

Ranka, J. K.

D. J. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, “Carrier-envelope phase control of femtosecond mode-locked lasers and direct optical frequency synthesis,” Science 288(5466), 635–639 (2000).
[Crossref] [PubMed]

Reichert, J.

Riehle, F.

C. Hagemann, C. Grebing, T. Kessler, S. Falke, N. Lemke, C. Lisdat, H. Schnatz, F. Riehle, and U. Sterr, “Providing 10−16 short-term stability of a 1.5 μm laser to optical clocks,” IEEE Trans. Instrum. Meas. 62(6), 1556–1562 (2013).
[Crossref]

T. Legero, C. Lisdat, J. S. R. Vellore Winfred, H. Schnatz, G. Grosche, F. Riehle, and U. Sterr, “Interrogation laser for a strontium lattice clock,” IEEE Trans. Instrum. Meas. 58(4), 1252–1257 (2009).
[Crossref]

Robertsson, L.

L.-S. Ma, Z. Bi, A. Bartels, L. Robertsson, M. Zucco, R. S. Windeler, G. Wilpers, C. Oates, L. Hollberg, and S. A. Diddams, “Optical frequency synthesis and comparison with uncertainty at the 10-19 level,” Science 303(5665), 1843–1845 (2004).
[Crossref] [PubMed]

Ruehl, A.

Santarelli, G.

D. Nicolodi, B. Argence, W. Zhang, R. Le Targat, G. Santarelli, and Y. Le Coq, “Spectral purity transfer between optical wavelengths at the 10−18 level,” Nat. Photonics 8(3), 219–223 (2014).
[Crossref]

W. Zhang, M. Lours, M. Fischer, R. Holzwarth, G. Santarelli, and Y. Coq, “Characterizing a fiber-based frequency comb with electro-optic modulator,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 59(3), 432–438 (2012).
[Crossref] [PubMed]

Schibli, T. R.

Schnatz, H.

C. Hagemann, C. Grebing, T. Kessler, S. Falke, N. Lemke, C. Lisdat, H. Schnatz, F. Riehle, and U. Sterr, “Providing 10−16 short-term stability of a 1.5 μm laser to optical clocks,” IEEE Trans. Instrum. Meas. 62(6), 1556–1562 (2013).
[Crossref]

T. Legero, C. Lisdat, J. S. R. Vellore Winfred, H. Schnatz, G. Grosche, F. Riehle, and U. Sterr, “Interrogation laser for a strontium lattice clock,” IEEE Trans. Instrum. Meas. 58(4), 1252–1257 (2009).
[Crossref]

J. Stenger, H. Schnatz, C. Tamm, and H. R. Telle, “Ultraprecise measurement of optical frequency ratios,” Phys. Rev. Lett. 88(7), 073601 (2002).
[Crossref] [PubMed]

Sherman, J. A.

Spielmann, C.

A. Apolonski, A. Poppe, G. Tempea, C. Spielmann, T. Udem, R. Holzwarth, T. W. Hänsch, and F. Krausz, “Controlling the phase evolution of few-cycle light pulses,” Phys. Rev. Lett. 85(4), 740–743 (2000).
[Crossref] [PubMed]

Stenger, J.

J. Stenger, H. Schnatz, C. Tamm, and H. R. Telle, “Ultraprecise measurement of optical frequency ratios,” Phys. Rev. Lett. 88(7), 073601 (2002).
[Crossref] [PubMed]

Stentz, A.

D. J. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, “Carrier-envelope phase control of femtosecond mode-locked lasers and direct optical frequency synthesis,” Science 288(5466), 635–639 (2000).
[Crossref] [PubMed]

Sterr, U.

C. Hagemann, C. Grebing, T. Kessler, S. Falke, N. Lemke, C. Lisdat, H. Schnatz, F. Riehle, and U. Sterr, “Providing 10−16 short-term stability of a 1.5 μm laser to optical clocks,” IEEE Trans. Instrum. Meas. 62(6), 1556–1562 (2013).
[Crossref]

T. Legero, C. Lisdat, J. S. R. Vellore Winfred, H. Schnatz, G. Grosche, F. Riehle, and U. Sterr, “Interrogation laser for a strontium lattice clock,” IEEE Trans. Instrum. Meas. 58(4), 1252–1257 (2009).
[Crossref]

Sugiura, T.

Swann, W. C.

Takada, H.

Tamm, C.

J. Stenger, H. Schnatz, C. Tamm, and H. R. Telle, “Ultraprecise measurement of optical frequency ratios,” Phys. Rev. Lett. 88(7), 073601 (2002).
[Crossref] [PubMed]

Tauser, F.

Telle, H. R.

J. Stenger, H. Schnatz, C. Tamm, and H. R. Telle, “Ultraprecise measurement of optical frequency ratios,” Phys. Rev. Lett. 88(7), 073601 (2002).
[Crossref] [PubMed]

Tempea, G.

A. Apolonski, A. Poppe, G. Tempea, C. Spielmann, T. Udem, R. Holzwarth, T. W. Hänsch, and F. Krausz, “Controlling the phase evolution of few-cycle light pulses,” Phys. Rev. Lett. 85(4), 740–743 (2000).
[Crossref] [PubMed]

Udem, T.

A. Apolonski, A. Poppe, G. Tempea, C. Spielmann, T. Udem, R. Holzwarth, T. W. Hänsch, and F. Krausz, “Controlling the phase evolution of few-cycle light pulses,” Phys. Rev. Lett. 85(4), 740–743 (2000).
[Crossref] [PubMed]

T. Udem, J. Reichert, R. Holzwarth, and T. W. Hänsch, “Accurate measurement of large optical frequency differences with a mode-locked laser,” Opt. Lett. 24(13), 881–883 (1999).
[Crossref] [PubMed]

Vellore Winfred, J. S. R.

T. Legero, C. Lisdat, J. S. R. Vellore Winfred, H. Schnatz, G. Grosche, F. Riehle, and U. Sterr, “Interrogation laser for a strontium lattice clock,” IEEE Trans. Instrum. Meas. 58(4), 1252–1257 (2009).
[Crossref]

Washburn, B. R.

Westbrook, P. S.

Williams, P. A.

Wilpers, G.

L.-S. Ma, Z. Bi, A. Bartels, L. Robertsson, M. Zucco, R. S. Windeler, G. Wilpers, C. Oates, L. Hollberg, and S. A. Diddams, “Optical frequency synthesis and comparison with uncertainty at the 10-19 level,” Science 303(5665), 1843–1845 (2004).
[Crossref] [PubMed]

Windeler, R. S.

L.-S. Ma, Z. Bi, A. Bartels, L. Robertsson, M. Zucco, R. S. Windeler, G. Wilpers, C. Oates, L. Hollberg, and S. A. Diddams, “Optical frequency synthesis and comparison with uncertainty at the 10-19 level,” Science 303(5665), 1843–1845 (2004).
[Crossref] [PubMed]

D. J. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, “Carrier-envelope phase control of femtosecond mode-locked lasers and direct optical frequency synthesis,” Science 288(5466), 635–639 (2000).
[Crossref] [PubMed]

Yan, L.

Yao, Y.

Y. Yao, Y. Jiang, H. Yu, Z. Bi, and L. Ma, “Optical frequency divider with division uncertainty at the 10−21 level,” Natl. Sci. Rev. 3, 463–469 (2016).

Yasuda, M.

Ye, J.

Yoshida, M.

Yost, D. C.

T. R. Schibli, I. Hartl, D. C. Yost, M. J. Martin, A. Marcinkevičius, M. E. Fermann, and J. Ye, “Optical frequency comb with submillihertz linewidth and more than 10 W average power,” Nat. Photonics 2(6), 355–359 (2008).
[Crossref]

Yu, H.

Y. Yao, Y. Jiang, H. Yu, Z. Bi, and L. Ma, “Optical frequency divider with division uncertainty at the 10−21 level,” Natl. Sci. Rev. 3, 463–469 (2016).

Zhang, L.

Zhang, S.

Zhang, W.

D. Nicolodi, B. Argence, W. Zhang, R. Le Targat, G. Santarelli, and Y. Le Coq, “Spectral purity transfer between optical wavelengths at the 10−18 level,” Nat. Photonics 8(3), 219–223 (2014).
[Crossref]

W. Zhang, M. Lours, M. Fischer, R. Holzwarth, G. Santarelli, and Y. Coq, “Characterizing a fiber-based frequency comb with electro-optic modulator,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 59(3), 432–438 (2012).
[Crossref] [PubMed]

Zhang, X.

Zhang, Y.

Zinth, W.

Zucco, M.

L.-S. Ma, Z. Bi, A. Bartels, L. Robertsson, M. Zucco, R. S. Windeler, G. Wilpers, C. Oates, L. Hollberg, and S. A. Diddams, “Optical frequency synthesis and comparison with uncertainty at the 10-19 level,” Science 303(5665), 1843–1845 (2004).
[Crossref] [PubMed]

Appl. Phys. Express (1)

N. Ohmae, N. Kuse, M. E. Fermann, and H. Katori, “All-polarization-maintaining, single-port Er:fiber comb for high-stability comparison of optical lattice clocks,” Appl. Phys. Express 10(6), 062503 (2017).
[Crossref]

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

M. Hirano, T. Nakanishi, T. Okuno, and M. Onishi, “Silica-based highly nonlinear fibers and their application,” IEEE J. Sel. Top. Quantum Electron. 15, 103–113 (2009).

IEEE Trans. Instrum. Meas. (2)

C. Hagemann, C. Grebing, T. Kessler, S. Falke, N. Lemke, C. Lisdat, H. Schnatz, F. Riehle, and U. Sterr, “Providing 10−16 short-term stability of a 1.5 μm laser to optical clocks,” IEEE Trans. Instrum. Meas. 62(6), 1556–1562 (2013).
[Crossref]

T. Legero, C. Lisdat, J. S. R. Vellore Winfred, H. Schnatz, G. Grosche, F. Riehle, and U. Sterr, “Interrogation laser for a strontium lattice clock,” IEEE Trans. Instrum. Meas. 58(4), 1252–1257 (2009).
[Crossref]

IEEE Trans. Ultrason. Ferroelectr. Freq. Control (2)

W. Zhang, M. Lours, M. Fischer, R. Holzwarth, G. Santarelli, and Y. Coq, “Characterizing a fiber-based frequency comb with electro-optic modulator,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 59(3), 432–438 (2012).
[Crossref] [PubMed]

K. Hosaka, H. Inaba, Y. Nakajima, M. Yasuda, T. Kohno, A. Onae, and F.-L. Hong, “Evaluation of the clock laser for an Yb lattice clock using an optic fiber comb,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 57(3), 606–612 (2010).
[Crossref] [PubMed]

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

Metrologia (1)

L. A. M. Johnson, P. Gill, and H. S. Margolis, “Evaluating the performance of the NPL femtosecond frequency combs: agreement at the 10−21 level,” Metrologia 52(1), 62–71 (2015).
[Crossref]

Nat. Photonics (2)

D. Nicolodi, B. Argence, W. Zhang, R. Le Targat, G. Santarelli, and Y. Le Coq, “Spectral purity transfer between optical wavelengths at the 10−18 level,” Nat. Photonics 8(3), 219–223 (2014).
[Crossref]

T. R. Schibli, I. Hartl, D. C. Yost, M. J. Martin, A. Marcinkevičius, M. E. Fermann, and J. Ye, “Optical frequency comb with submillihertz linewidth and more than 10 W average power,” Nat. Photonics 2(6), 355–359 (2008).
[Crossref]

Natl. Sci. Rev. (1)

Y. Yao, Y. Jiang, H. Yu, Z. Bi, and L. Ma, “Optical frequency divider with division uncertainty at the 10−21 level,” Natl. Sci. Rev. 3, 463–469 (2016).

Opt. Commun. (1)

Y. Nakajima, H. Inaba, F.-L. Hong, A. Onae, K. Minoshima, T. Kobayashi, M. Nakazawa, and H. Matsumoto, “Optimized amplification of femtosecond optical pulses by dispersion management for octave-spanning optical frequency comb generation,” Opt. Commun. 281(17), 4484–4487 (2008).
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Opt. Express (9)

T. Nakamura, I. Ito, and Y. Kobayashi, “Offset-free broadband Yb:fiber optical frequency comb for optical clocks,” Opt. Express 23(15), 19376–19381 (2015).
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Figures (7)

Fig. 1
Fig. 1 Schematic diagram of experimental setup for reducing uncertainty in a multi-branch configuration. Black solid, and blue dotted lines denote optical fiber, and free-space parts, respectively. Black and red dashed lines are electronics parts for comb stabilization and fiber noise difference cancellation, respectively. TEC, temperature controller; WG-EOM, waveguide-type electro-optic phase modulator; LD, laser diode; EDFA, erbium-doped fiber amplifier; HNLF, highly nonlinear fiber; PD, photo detector; FNDC, (inter-branch) fiber noise difference cancellation.

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Fig. 2
Fig. 2 Schematic diagram of experimental setup for optical comparison of two quasi-identical combs. BS, beam splitter; BPF, band pass filter; DBM, double balanced mixer.

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Fig. 3
Fig. 3 Illustration of frequency arrangement of the two combs and the FNDC reference and ultrastable reference lasers.

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Fig. 4
Fig. 4 Out-of-loop beat frequency between two combs from application branches with and without FNDC. The FNDC was turned on around a measurement time of 1000 sec. The averaging time was 1-s.

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Fig. 5
Fig. 5 Frequency instabilities given by Allan deviation with and without FNDC in beat-locking and application branches. All stability values are normalized to the carrier frequencies and are divided by the square root of 2 to obtain the stabilities for the individual combs.

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Fig. 6
Fig. 6 Power spectral density of phase noise of the out-of-loop beat at 1700 nm (black solid line) [12] and integrated Allan variance (red dashed line) without FNDC. The Allan variance is calculated from the phase noise PSD. The Allan variance is normalized by a wavelength of 1700 nm.

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Fig. 7
Fig. 7 Frequency instabilities given by the modified Allan deviation with FNDC in beat-locking and application branches. All stability values are normalized to the carrier frequencies and are divided by the square root of 2 to obtain stabilities for the individual combs.

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