Abstract

We synchronize an 8.06 GHz microwave signal from a voltage-controlled oscillator with an optical pulse train from a 77.5 MHz mode-locked Er-fiber laser using a fiber-based optical-microwave phase detector. The residual phase noise between the optical pulse train and the synchronized microwave signal is 133dBc/Hz (154dBc/Hz) at 1 Hz (5 kHz) offset frequency, which results in 838 as integrated rms timing jitter [1 Hz–1 MHz]. The long-term residual phase drift is 847 as (rms) measured over 2 h, which reaches 4×1019 fractional frequency instability at 1800 s averaging time. This method has a potential to provide both subfemtosecond-level short-term phase noise and long-term phase stability in microwave extraction from mode-locked fiber lasers.

© 2012 Optical Society of America

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  17. J. Kim and F. X. Kärtner, Opt. Lett. 35, 2022 (2010).
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    [CrossRef]

2012

A. J. Benedick, J. G. Fujimoto, and F. X. Kärtner, Nat. Photon. 6, 97 (2012).
[CrossRef]

2011

J. Taylor, S. Datta, A. Hati, C. Nelson, F. Quinlan, A. Joshi, and S. Diddams, IEEE Photon. J. 3, 140 (2011).
[CrossRef]

H. Jiang, J. Taylor, F. Quinlan, T. Fortier, and S. A. Diddams, IEEE Photon. J. 3, 1004 (2011).
[CrossRef]

T. M. Fortier, M. S. Kirchner, F. Quinlan, J. Taylor, J. C. Bergquist, T. Rosenband, N. Lemke, A. Ludlow, Y. Jiang, C. W. Oates, and S. A. Diddams, Nat. Photon. 5, 425 (2011).
[CrossRef]

Y. Song, C. Kim, K. Jung, H. Kim, and J. Kim, Opt. Express 19, 14518 (2011).
[CrossRef]

F. Quinlan, T. M. Fortier, M. S. Kirchner, J. A. Taylor, M. J. Thorpe, N. Lemke, A. D. Ludlow, Y. Jiang, and S. A. Diddams, Opt. Lett. 36, 3260 (2011).
[CrossRef]

A. Haboucha, W. Zhang, T. Li, M. Lours, A. N. Luiten, Y. Le Coq, and G. Santarelli, Opt. Lett. 36, 3654 (2011).
[CrossRef]

T. K. Kim, Y. Song, K. Jung, C. Kim, H. Kim, C. H. Nam, and J. Kim, Opt. Lett. 36, 4443 (2011).
[CrossRef]

K. Wu, P. P. Shum, S. Aditya, C. Ouyang, J. H. Wong, H. Q. Lam, and K. E. Lee, J. Lightwave Technol. 29, 3622 (2011).
[CrossRef]

W. Zhang, Z. Xu, M. Lours, R. Boudot, Y. Kersalé, A. N. Luiten, Y. Le Coq, and G. Santarelli, IEEE Trans. Ultrason. Ferroelectr. Freq. Control 58, 900 (2011).
[CrossRef]

2010

J. Kim and F. X. Kärtner, Opt. Lett. 35, 2022 (2010).
[CrossRef]

W. Zhang, Z. Xu, M. Lours, R. Boudot, Y. Kersalé, G. Santarelli, and Y. Le Coq, Appl. Phys. Lett. 96, 211105 (2010).
[CrossRef]

2009

2008

J. Kim, J. Cox, J. Chen, and F. X. Kärtner, Nat. Photon. 2, 733 (2008).
[CrossRef]

2004

1996

M. L. Dennis, I. N. Duling, and W. K. Burns, Electron. Lett. 32, 547 (1996).
[CrossRef]

Aditya, S.

Benedick, A. J.

A. J. Benedick, J. G. Fujimoto, and F. X. Kärtner, Nat. Photon. 6, 97 (2012).
[CrossRef]

Bergquist, J. C.

T. M. Fortier, M. S. Kirchner, F. Quinlan, J. Taylor, J. C. Bergquist, T. Rosenband, N. Lemke, A. Ludlow, Y. Jiang, C. W. Oates, and S. A. Diddams, Nat. Photon. 5, 425 (2011).
[CrossRef]

Boudot, R.

W. Zhang, Z. Xu, M. Lours, R. Boudot, Y. Kersalé, A. N. Luiten, Y. Le Coq, and G. Santarelli, IEEE Trans. Ultrason. Ferroelectr. Freq. Control 58, 900 (2011).
[CrossRef]

W. Zhang, Z. Xu, M. Lours, R. Boudot, Y. Kersalé, G. Santarelli, and Y. Le Coq, Appl. Phys. Lett. 96, 211105 (2010).
[CrossRef]

J. Millo, R. Boudot, M. Lours, P. Y. Bourgeois, A. N. Luiten, Y. Le Coq, Y. Kersalé, and G. Santarelli, Opt. Lett. 34, 3707 (2009).
[CrossRef]

Bourgeois, P. Y.

Burns, W. K.

M. L. Dennis, I. N. Duling, and W. K. Burns, Electron. Lett. 32, 547 (1996).
[CrossRef]

Chen, J.

J. Kim, J. Cox, J. Chen, and F. X. Kärtner, Nat. Photon. 2, 733 (2008).
[CrossRef]

Chou, C. WS.

T. M. Fortier, C. W. Nelson, A. Hati, F. Quinlan, J. Taylor, H. Jiang, C. WS. Chou, N. Lemke, A. Ludlow, D. Howe, C. Oates, and S. A. Diddams, in Proceedings of IEEE Photonics Conference (IEEE, 2011).
[CrossRef]

Cox, J.

J. Kim, J. Cox, J. Chen, and F. X. Kärtner, Nat. Photon. 2, 733 (2008).
[CrossRef]

Datta, S.

J. Taylor, S. Datta, A. Hati, C. Nelson, F. Quinlan, A. Joshi, and S. Diddams, IEEE Photon. J. 3, 140 (2011).
[CrossRef]

Dennis, M. L.

M. L. Dennis, I. N. Duling, and W. K. Burns, Electron. Lett. 32, 547 (1996).
[CrossRef]

Diddams, S.

J. Taylor, S. Datta, A. Hati, C. Nelson, F. Quinlan, A. Joshi, and S. Diddams, IEEE Photon. J. 3, 140 (2011).
[CrossRef]

Diddams, S. A.

T. M. Fortier, M. S. Kirchner, F. Quinlan, J. Taylor, J. C. Bergquist, T. Rosenband, N. Lemke, A. Ludlow, Y. Jiang, C. W. Oates, and S. A. Diddams, Nat. Photon. 5, 425 (2011).
[CrossRef]

H. Jiang, J. Taylor, F. Quinlan, T. Fortier, and S. A. Diddams, IEEE Photon. J. 3, 1004 (2011).
[CrossRef]

F. Quinlan, T. M. Fortier, M. S. Kirchner, J. A. Taylor, M. J. Thorpe, N. Lemke, A. D. Ludlow, Y. Jiang, and S. A. Diddams, Opt. Lett. 36, 3260 (2011).
[CrossRef]

T. M. Fortier, C. W. Nelson, A. Hati, F. Quinlan, J. Taylor, H. Jiang, C. WS. Chou, N. Lemke, A. Ludlow, D. Howe, C. Oates, and S. A. Diddams, in Proceedings of IEEE Photonics Conference (IEEE, 2011).
[CrossRef]

Duling, I. N.

M. L. Dennis, I. N. Duling, and W. K. Burns, Electron. Lett. 32, 547 (1996).
[CrossRef]

Fortier, T.

H. Jiang, J. Taylor, F. Quinlan, T. Fortier, and S. A. Diddams, IEEE Photon. J. 3, 1004 (2011).
[CrossRef]

Fortier, T. M.

T. M. Fortier, M. S. Kirchner, F. Quinlan, J. Taylor, J. C. Bergquist, T. Rosenband, N. Lemke, A. Ludlow, Y. Jiang, C. W. Oates, and S. A. Diddams, Nat. Photon. 5, 425 (2011).
[CrossRef]

F. Quinlan, T. M. Fortier, M. S. Kirchner, J. A. Taylor, M. J. Thorpe, N. Lemke, A. D. Ludlow, Y. Jiang, and S. A. Diddams, Opt. Lett. 36, 3260 (2011).
[CrossRef]

T. M. Fortier, C. W. Nelson, A. Hati, F. Quinlan, J. Taylor, H. Jiang, C. WS. Chou, N. Lemke, A. Ludlow, D. Howe, C. Oates, and S. A. Diddams, in Proceedings of IEEE Photonics Conference (IEEE, 2011).
[CrossRef]

Fujimoto, J. G.

A. J. Benedick, J. G. Fujimoto, and F. X. Kärtner, Nat. Photon. 6, 97 (2012).
[CrossRef]

Haboucha, A.

Hati, A.

J. Taylor, S. Datta, A. Hati, C. Nelson, F. Quinlan, A. Joshi, and S. Diddams, IEEE Photon. J. 3, 140 (2011).
[CrossRef]

T. M. Fortier, C. W. Nelson, A. Hati, F. Quinlan, J. Taylor, H. Jiang, C. WS. Chou, N. Lemke, A. Ludlow, D. Howe, C. Oates, and S. A. Diddams, in Proceedings of IEEE Photonics Conference (IEEE, 2011).
[CrossRef]

Howe, D.

T. M. Fortier, C. W. Nelson, A. Hati, F. Quinlan, J. Taylor, H. Jiang, C. WS. Chou, N. Lemke, A. Ludlow, D. Howe, C. Oates, and S. A. Diddams, in Proceedings of IEEE Photonics Conference (IEEE, 2011).
[CrossRef]

Jiang, H.

H. Jiang, J. Taylor, F. Quinlan, T. Fortier, and S. A. Diddams, IEEE Photon. J. 3, 1004 (2011).
[CrossRef]

T. M. Fortier, C. W. Nelson, A. Hati, F. Quinlan, J. Taylor, H. Jiang, C. WS. Chou, N. Lemke, A. Ludlow, D. Howe, C. Oates, and S. A. Diddams, in Proceedings of IEEE Photonics Conference (IEEE, 2011).
[CrossRef]

Jiang, Y.

T. M. Fortier, M. S. Kirchner, F. Quinlan, J. Taylor, J. C. Bergquist, T. Rosenband, N. Lemke, A. Ludlow, Y. Jiang, C. W. Oates, and S. A. Diddams, Nat. Photon. 5, 425 (2011).
[CrossRef]

F. Quinlan, T. M. Fortier, M. S. Kirchner, J. A. Taylor, M. J. Thorpe, N. Lemke, A. D. Ludlow, Y. Jiang, and S. A. Diddams, Opt. Lett. 36, 3260 (2011).
[CrossRef]

Joshi, A.

J. Taylor, S. Datta, A. Hati, C. Nelson, F. Quinlan, A. Joshi, and S. Diddams, IEEE Photon. J. 3, 140 (2011).
[CrossRef]

Jung, K.

Kärtner, F. X.

A. J. Benedick, J. G. Fujimoto, and F. X. Kärtner, Nat. Photon. 6, 97 (2012).
[CrossRef]

J. Kim and F. X. Kärtner, Opt. Lett. 35, 2022 (2010).
[CrossRef]

J. Kim, J. Cox, J. Chen, and F. X. Kärtner, Nat. Photon. 2, 733 (2008).
[CrossRef]

J. Kim, F. X. Kärtner, and M. H. Perrott, Opt. Lett. 29, 2076 (2004).
[CrossRef]

Kersalé, Y.

W. Zhang, Z. Xu, M. Lours, R. Boudot, Y. Kersalé, A. N. Luiten, Y. Le Coq, and G. Santarelli, IEEE Trans. Ultrason. Ferroelectr. Freq. Control 58, 900 (2011).
[CrossRef]

W. Zhang, Z. Xu, M. Lours, R. Boudot, Y. Kersalé, G. Santarelli, and Y. Le Coq, Appl. Phys. Lett. 96, 211105 (2010).
[CrossRef]

J. Millo, R. Boudot, M. Lours, P. Y. Bourgeois, A. N. Luiten, Y. Le Coq, Y. Kersalé, and G. Santarelli, Opt. Lett. 34, 3707 (2009).
[CrossRef]

Kim, C.

Kim, H.

Kim, J.

Kim, T. K.

Kirchner, M. S.

F. Quinlan, T. M. Fortier, M. S. Kirchner, J. A. Taylor, M. J. Thorpe, N. Lemke, A. D. Ludlow, Y. Jiang, and S. A. Diddams, Opt. Lett. 36, 3260 (2011).
[CrossRef]

T. M. Fortier, M. S. Kirchner, F. Quinlan, J. Taylor, J. C. Bergquist, T. Rosenband, N. Lemke, A. Ludlow, Y. Jiang, C. W. Oates, and S. A. Diddams, Nat. Photon. 5, 425 (2011).
[CrossRef]

Lam, H. Q.

Le Coq, Y.

W. Zhang, Z. Xu, M. Lours, R. Boudot, Y. Kersalé, A. N. Luiten, Y. Le Coq, and G. Santarelli, IEEE Trans. Ultrason. Ferroelectr. Freq. Control 58, 900 (2011).
[CrossRef]

A. Haboucha, W. Zhang, T. Li, M. Lours, A. N. Luiten, Y. Le Coq, and G. Santarelli, Opt. Lett. 36, 3654 (2011).
[CrossRef]

W. Zhang, Z. Xu, M. Lours, R. Boudot, Y. Kersalé, G. Santarelli, and Y. Le Coq, Appl. Phys. Lett. 96, 211105 (2010).
[CrossRef]

J. Millo, R. Boudot, M. Lours, P. Y. Bourgeois, A. N. Luiten, Y. Le Coq, Y. Kersalé, and G. Santarelli, Opt. Lett. 34, 3707 (2009).
[CrossRef]

Lee, K. E.

Lemke, N.

T. M. Fortier, M. S. Kirchner, F. Quinlan, J. Taylor, J. C. Bergquist, T. Rosenband, N. Lemke, A. Ludlow, Y. Jiang, C. W. Oates, and S. A. Diddams, Nat. Photon. 5, 425 (2011).
[CrossRef]

F. Quinlan, T. M. Fortier, M. S. Kirchner, J. A. Taylor, M. J. Thorpe, N. Lemke, A. D. Ludlow, Y. Jiang, and S. A. Diddams, Opt. Lett. 36, 3260 (2011).
[CrossRef]

T. M. Fortier, C. W. Nelson, A. Hati, F. Quinlan, J. Taylor, H. Jiang, C. WS. Chou, N. Lemke, A. Ludlow, D. Howe, C. Oates, and S. A. Diddams, in Proceedings of IEEE Photonics Conference (IEEE, 2011).
[CrossRef]

Li, T.

Lorbeer, B.

B. Lorbeer, F. Ludwig, H. Schlarb, and A. Winter, in Proceedings of the Particle Accelerator Conference 2007 (IEEE, 2007), pp. 182–184.

Lours, M.

A. Haboucha, W. Zhang, T. Li, M. Lours, A. N. Luiten, Y. Le Coq, and G. Santarelli, Opt. Lett. 36, 3654 (2011).
[CrossRef]

W. Zhang, Z. Xu, M. Lours, R. Boudot, Y. Kersalé, A. N. Luiten, Y. Le Coq, and G. Santarelli, IEEE Trans. Ultrason. Ferroelectr. Freq. Control 58, 900 (2011).
[CrossRef]

W. Zhang, Z. Xu, M. Lours, R. Boudot, Y. Kersalé, G. Santarelli, and Y. Le Coq, Appl. Phys. Lett. 96, 211105 (2010).
[CrossRef]

J. Millo, R. Boudot, M. Lours, P. Y. Bourgeois, A. N. Luiten, Y. Le Coq, Y. Kersalé, and G. Santarelli, Opt. Lett. 34, 3707 (2009).
[CrossRef]

Ludlow, A.

T. M. Fortier, M. S. Kirchner, F. Quinlan, J. Taylor, J. C. Bergquist, T. Rosenband, N. Lemke, A. Ludlow, Y. Jiang, C. W. Oates, and S. A. Diddams, Nat. Photon. 5, 425 (2011).
[CrossRef]

T. M. Fortier, C. W. Nelson, A. Hati, F. Quinlan, J. Taylor, H. Jiang, C. WS. Chou, N. Lemke, A. Ludlow, D. Howe, C. Oates, and S. A. Diddams, in Proceedings of IEEE Photonics Conference (IEEE, 2011).
[CrossRef]

Ludlow, A. D.

Ludwig, F.

B. Lorbeer, F. Ludwig, H. Schlarb, and A. Winter, in Proceedings of the Particle Accelerator Conference 2007 (IEEE, 2007), pp. 182–184.

Luiten, A. N.

Millo, J.

Nam, C. H.

Nelson, C.

J. Taylor, S. Datta, A. Hati, C. Nelson, F. Quinlan, A. Joshi, and S. Diddams, IEEE Photon. J. 3, 140 (2011).
[CrossRef]

Nelson, C. W.

T. M. Fortier, C. W. Nelson, A. Hati, F. Quinlan, J. Taylor, H. Jiang, C. WS. Chou, N. Lemke, A. Ludlow, D. Howe, C. Oates, and S. A. Diddams, in Proceedings of IEEE Photonics Conference (IEEE, 2011).
[CrossRef]

Oates, C.

T. M. Fortier, C. W. Nelson, A. Hati, F. Quinlan, J. Taylor, H. Jiang, C. WS. Chou, N. Lemke, A. Ludlow, D. Howe, C. Oates, and S. A. Diddams, in Proceedings of IEEE Photonics Conference (IEEE, 2011).
[CrossRef]

Oates, C. W.

T. M. Fortier, M. S. Kirchner, F. Quinlan, J. Taylor, J. C. Bergquist, T. Rosenband, N. Lemke, A. Ludlow, Y. Jiang, C. W. Oates, and S. A. Diddams, Nat. Photon. 5, 425 (2011).
[CrossRef]

Ouyang, C.

Perrott, M. H.

Quinlan, F.

H. Jiang, J. Taylor, F. Quinlan, T. Fortier, and S. A. Diddams, IEEE Photon. J. 3, 1004 (2011).
[CrossRef]

T. M. Fortier, M. S. Kirchner, F. Quinlan, J. Taylor, J. C. Bergquist, T. Rosenband, N. Lemke, A. Ludlow, Y. Jiang, C. W. Oates, and S. A. Diddams, Nat. Photon. 5, 425 (2011).
[CrossRef]

J. Taylor, S. Datta, A. Hati, C. Nelson, F. Quinlan, A. Joshi, and S. Diddams, IEEE Photon. J. 3, 140 (2011).
[CrossRef]

F. Quinlan, T. M. Fortier, M. S. Kirchner, J. A. Taylor, M. J. Thorpe, N. Lemke, A. D. Ludlow, Y. Jiang, and S. A. Diddams, Opt. Lett. 36, 3260 (2011).
[CrossRef]

T. M. Fortier, C. W. Nelson, A. Hati, F. Quinlan, J. Taylor, H. Jiang, C. WS. Chou, N. Lemke, A. Ludlow, D. Howe, C. Oates, and S. A. Diddams, in Proceedings of IEEE Photonics Conference (IEEE, 2011).
[CrossRef]

Rosenband, T.

T. M. Fortier, M. S. Kirchner, F. Quinlan, J. Taylor, J. C. Bergquist, T. Rosenband, N. Lemke, A. Ludlow, Y. Jiang, C. W. Oates, and S. A. Diddams, Nat. Photon. 5, 425 (2011).
[CrossRef]

Santarelli, G.

W. Zhang, Z. Xu, M. Lours, R. Boudot, Y. Kersalé, A. N. Luiten, Y. Le Coq, and G. Santarelli, IEEE Trans. Ultrason. Ferroelectr. Freq. Control 58, 900 (2011).
[CrossRef]

A. Haboucha, W. Zhang, T. Li, M. Lours, A. N. Luiten, Y. Le Coq, and G. Santarelli, Opt. Lett. 36, 3654 (2011).
[CrossRef]

W. Zhang, Z. Xu, M. Lours, R. Boudot, Y. Kersalé, G. Santarelli, and Y. Le Coq, Appl. Phys. Lett. 96, 211105 (2010).
[CrossRef]

J. Millo, R. Boudot, M. Lours, P. Y. Bourgeois, A. N. Luiten, Y. Le Coq, Y. Kersalé, and G. Santarelli, Opt. Lett. 34, 3707 (2009).
[CrossRef]

Schlarb, H.

B. Lorbeer, F. Ludwig, H. Schlarb, and A. Winter, in Proceedings of the Particle Accelerator Conference 2007 (IEEE, 2007), pp. 182–184.

Shum, P. P.

Song, Y.

Taylor, J.

J. Taylor, S. Datta, A. Hati, C. Nelson, F. Quinlan, A. Joshi, and S. Diddams, IEEE Photon. J. 3, 140 (2011).
[CrossRef]

T. M. Fortier, M. S. Kirchner, F. Quinlan, J. Taylor, J. C. Bergquist, T. Rosenband, N. Lemke, A. Ludlow, Y. Jiang, C. W. Oates, and S. A. Diddams, Nat. Photon. 5, 425 (2011).
[CrossRef]

H. Jiang, J. Taylor, F. Quinlan, T. Fortier, and S. A. Diddams, IEEE Photon. J. 3, 1004 (2011).
[CrossRef]

T. M. Fortier, C. W. Nelson, A. Hati, F. Quinlan, J. Taylor, H. Jiang, C. WS. Chou, N. Lemke, A. Ludlow, D. Howe, C. Oates, and S. A. Diddams, in Proceedings of IEEE Photonics Conference (IEEE, 2011).
[CrossRef]

Taylor, J. A.

Thorpe, M. J.

Winter, A.

B. Lorbeer, F. Ludwig, H. Schlarb, and A. Winter, in Proceedings of the Particle Accelerator Conference 2007 (IEEE, 2007), pp. 182–184.

Wong, J. H.

Wu, K.

Xu, Z.

W. Zhang, Z. Xu, M. Lours, R. Boudot, Y. Kersalé, A. N. Luiten, Y. Le Coq, and G. Santarelli, IEEE Trans. Ultrason. Ferroelectr. Freq. Control 58, 900 (2011).
[CrossRef]

W. Zhang, Z. Xu, M. Lours, R. Boudot, Y. Kersalé, G. Santarelli, and Y. Le Coq, Appl. Phys. Lett. 96, 211105 (2010).
[CrossRef]

Zhang, W.

W. Zhang, Z. Xu, M. Lours, R. Boudot, Y. Kersalé, A. N. Luiten, Y. Le Coq, and G. Santarelli, IEEE Trans. Ultrason. Ferroelectr. Freq. Control 58, 900 (2011).
[CrossRef]

A. Haboucha, W. Zhang, T. Li, M. Lours, A. N. Luiten, Y. Le Coq, and G. Santarelli, Opt. Lett. 36, 3654 (2011).
[CrossRef]

W. Zhang, Z. Xu, M. Lours, R. Boudot, Y. Kersalé, G. Santarelli, and Y. Le Coq, Appl. Phys. Lett. 96, 211105 (2010).
[CrossRef]

Appl. Phys. Lett.

W. Zhang, Z. Xu, M. Lours, R. Boudot, Y. Kersalé, G. Santarelli, and Y. Le Coq, Appl. Phys. Lett. 96, 211105 (2010).
[CrossRef]

Electron. Lett.

M. L. Dennis, I. N. Duling, and W. K. Burns, Electron. Lett. 32, 547 (1996).
[CrossRef]

IEEE Photon. J.

J. Taylor, S. Datta, A. Hati, C. Nelson, F. Quinlan, A. Joshi, and S. Diddams, IEEE Photon. J. 3, 140 (2011).
[CrossRef]

H. Jiang, J. Taylor, F. Quinlan, T. Fortier, and S. A. Diddams, IEEE Photon. J. 3, 1004 (2011).
[CrossRef]

IEEE Trans. Ultrason. Ferroelectr. Freq. Control

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For example, “PSI sapphire loaded cavity oscillator,” http://psi.com.au/media/pdfs/SLCO-BCS Brochure.pdf .

For example, “OEwaves Opto-Electronic Oscillator,” http://oewaves.com/products/item/84-compact-opto-electronic-oscillator-oeo.html .

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Figures (4)

Fig. 1.
Fig. 1.

Fiber-based optical-microwave phase detector.

Fig. 2.
Fig. 2.

Optical-microwave synchronization and out-of-loop phase noise/drift measurement setup.

Fig. 3.
Fig. 3.

Single-sideband (SSB) phase noise measurement results: (i) phase noise of free-running VCO, (ii) out-of-loop residual phase noise of VCO locked to the Er-fiber laser (integrated rms timing jitter=838 as [1 Hz–1 MHz]), (iii) background noise of optical phase detector when microwave signal is not applied, (iv) in-loop residual phase noise.

Fig. 4.
Fig. 4.

Long-term residual phase drift measurement result between the optical pulse train and the synchronized microwave signal. (a) Measurement over 2 h [847 as (rms) drift]; (b) Fractional frequency instability (overlapping Allan deviation) based on the measured result in (a).

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