Abstract

We report a 32-times multiplication of optical pulse rate based on a cascaded optical fiber ring interferometer for generating ultra-low noise photonic microwaves. The optical power loss of the interleaver is approximately 0.5 dB, which is the lowest insertion loss for optical pulse interleaving to date. The time delay in each interleaver stage is precisely controlled by measuring the power ratio between the harmonics of the generated microwaves. In addition, the relationship between the phase noise reduction from the continuous-wave shot noise limit and interleaver delay errors is verified experimentally for the first time. Finally, a phase noise level of −173 dBc/Hz for a single multiplication channel at an offset frequency of 2 MHz was measured.

© 2017 Optical Society of America

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    [Crossref]
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    [Crossref]
  24. F. Quinlan, F. N. Baynes, T. M. Fortier, Q. Zhou, A. Cross, J. C. Campbell, and S. A. Diddams, “Optical amplification and pulse interleaving for low-noise photonic microwave generation,” Opt. Lett. 39(6), 1581–1584 (2014).
    [Crossref] [PubMed]
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    [Crossref] [PubMed]
  26. R. Bouchand, X. Xie, D. Nicolodi, P. Tremblin, G. Santarelli, C. Alexandre, M. Giunta, M. Lezius, W. Haensel, R. Holzwarth, D. Shubhashish, J. Abhay, and Y. Le Coq, “State-of-the-art ultra-low phase noise photonic microwave generation,” inProceedings of IEEE European Frequency and Time Forum (IEEE, 2016), pp. 1–3.
  27. T. M. Fortier, F. Quinlan, A. Hati, C. Nelson, J. A. Taylor, Y. Fu, J. Campbell, and S. A. Diddams, “Photonic microwave generation with high-power photodiodes,” Opt. Lett. 38(10), 1712–1714 (2013).
    [Crossref] [PubMed]

2015 (2)

E. Portuondo-Campa, G. Buchs, S. Kundermann, L. Balet, and S. Lecomte, “Ultra-low phase-noise microwave generation using a diode-pumped solid-state laser based frequency comb and a polarization-maintaining pulse interleaver,” Opt. Express 23(25), 32441–32451 (2015).
[Crossref] [PubMed]

Y. Zheng, Y. Ren, P. An, C. Chu, X. Li, C. Xue, J. Liu, and S. Yan, “Wide dynamic range experiments on a resonator fiber optic gyro based on closed-loop frequency locking technique,” Chin. Opt. Lett. 13(2), 20601 (2015).
[Crossref]

2014 (2)

F. Quinlan, F. N. Baynes, T. M. Fortier, Q. Zhou, A. Cross, J. C. Campbell, and S. A. Diddams, “Optical amplification and pulse interleaving for low-noise photonic microwave generation,” Opt. Lett. 39(6), 1581–1584 (2014).
[Crossref] [PubMed]

W. Sun, F. Quinlan, T. M. Fortier, J. D. Deschenes, Y. Fu, S. A. Diddams, and J. C. Campbell, “Broadband noise limit in the photodetection of ultralow jitter optical pulses,” Phys. Rev. Lett. 113(20), 203901 (2014).
[Crossref] [PubMed]

2013 (3)

2012 (1)

2011 (7)

2010 (2)

2009 (4)

S. Weyers, B. Lipphardt, and H. Schnatz, “Reaching the quantum limit in a fountain clock using a microwave oscillator phase locked to an ultrastable laser,” Phys. Rev. A 79(3), 031803 (2009).
[Crossref]

J. Millo, M. Abgrall, M. Lours, E. M. L. English, H. Jiang, J. Guéna, A. Clairon, M. E. Tobar, S. Bize, Y. Le Coq, and G. Santarelli, “Ultra-low noise microwave generation with fiber-based optical frequency comb and application to atomic fountain clock,” Appl. Phys. Lett. 94(14), 141105 (2009).
[Crossref]

S. A. Diddams, M. Kirchner, T. Fortier, D. Braje, A. M. Weiner, and L. Hollberg, “Improved signal-to-noise ratio of 10 GHz microwave signals generated with a mode-filtered femtosecond laser frequency comb,” Opt. Express 17(5), 3331–3340 (2009).
[Crossref] [PubMed]

J. Millo, R. Boudot, M. Lours, P. Y. Bourgeois, A. N. Luiten, Y. L. Coq, Y. Kersalé, and G. Santarelli, “Ultra-low-noise microwave extraction from fiber-based optical frequency comb,” Opt. Lett. 34(23), 3707–3709 (2009).
[Crossref] [PubMed]

2007 (1)

S. Min, Y. Zhao, and S. Fleming, “Repetition rate multiplication in figure-eight fibre laser with 3 dB couplers,” Opt. Commun. 277(2), 411–413 (2007).
[Crossref]

2005 (2)

A. Bartels, S. A. Diddams, C. W. Oates, G. Wilpers, J. C. Bergquist, W. H. Oskay, and L. Hollberg, “Femtosecond-laser-based synthesis of ultrastable microwave signals from optical frequency references,” Opt. Lett. 30(6), 667–669 (2005).
[Crossref] [PubMed]

B. Xia and L. R. Chen, “A direct temporal domain approach for pulse-repetition rate multiplication with arbitrary envelope shaping,” IEEE J. Sel. Top. Quantum Electron. 11(1), 165–172 (2005).
[Crossref]

2001 (1)

D. Wei, Y. Zhao, T. Li, and S. Jian, “A novel scheme for optical pulse multiplication using fiber coupler loop-connecting configuration,” Czech. J. Phys. 51(2), 155–162 (2001).
[Crossref]

Abgrall, M.

J. Millo, M. Abgrall, M. Lours, E. M. L. English, H. Jiang, J. Guéna, A. Clairon, M. E. Tobar, S. Bize, Y. Le Coq, and G. Santarelli, “Ultra-low noise microwave generation with fiber-based optical frequency comb and application to atomic fountain clock,” Appl. Phys. Lett. 94(14), 141105 (2009).
[Crossref]

Abhay, J.

R. Bouchand, X. Xie, D. Nicolodi, P. Tremblin, G. Santarelli, C. Alexandre, M. Giunta, M. Lezius, W. Haensel, R. Holzwarth, D. Shubhashish, J. Abhay, and Y. Le Coq, “State-of-the-art ultra-low phase noise photonic microwave generation,” inProceedings of IEEE European Frequency and Time Forum (IEEE, 2016), pp. 1–3.

Ackert, J.

Alexandre, C.

R. Bouchand, X. Xie, D. Nicolodi, P. Tremblin, G. Santarelli, C. Alexandre, M. Giunta, M. Lezius, W. Haensel, R. Holzwarth, D. Shubhashish, J. Abhay, and Y. Le Coq, “State-of-the-art ultra-low phase noise photonic microwave generation,” inProceedings of IEEE European Frequency and Time Forum (IEEE, 2016), pp. 1–3.

An, P.

Y. Zheng, Y. Ren, P. An, C. Chu, X. Li, C. Xue, J. Liu, and S. Yan, “Wide dynamic range experiments on a resonator fiber optic gyro based on closed-loop frequency locking technique,” Chin. Opt. Lett. 13(2), 20601 (2015).
[Crossref]

Balet, L.

Bartels, A.

Baynes, F. N.

Beling, A.

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, “Generation of ultrastable microwave via optical frequency division,” Nat. Photonics 5(7), 425–429 (2011).
[Crossref]

A. Bartels, S. A. Diddams, C. W. Oates, G. Wilpers, J. C. Bergquist, W. H. Oskay, and L. Hollberg, “Femtosecond-laser-based synthesis of ultrastable microwave signals from optical frequency references,” Opt. Lett. 30(6), 667–669 (2005).
[Crossref] [PubMed]

Bize, S.

J. Millo, M. Abgrall, M. Lours, E. M. L. English, H. Jiang, J. Guéna, A. Clairon, M. E. Tobar, S. Bize, Y. Le Coq, and G. Santarelli, “Ultra-low noise microwave generation with fiber-based optical frequency comb and application to atomic fountain clock,” Appl. Phys. Lett. 94(14), 141105 (2009).
[Crossref]

Bouchand, R.

R. Bouchand, X. Xie, D. Nicolodi, P. Tremblin, G. Santarelli, C. Alexandre, M. Giunta, M. Lezius, W. Haensel, R. Holzwarth, D. Shubhashish, J. Abhay, and Y. Le Coq, “State-of-the-art ultra-low phase noise photonic microwave generation,” inProceedings of IEEE European Frequency and Time Forum (IEEE, 2016), pp. 1–3.

Boudot, R.

Bourgeois, P. Y.

Bowers, J. E.

Braje, D.

Buchs, G.

Campbell, J.

Campbell, J. C.

W. Sun, F. Quinlan, T. M. Fortier, J. D. Deschenes, Y. Fu, S. A. Diddams, and J. C. Campbell, “Broadband noise limit in the photodetection of ultralow jitter optical pulses,” Phys. Rev. Lett. 113(20), 203901 (2014).
[Crossref] [PubMed]

F. Quinlan, F. N. Baynes, T. M. Fortier, Q. Zhou, A. Cross, J. C. Campbell, and S. A. Diddams, “Optical amplification and pulse interleaving for low-noise photonic microwave generation,” Opt. Lett. 39(6), 1581–1584 (2014).
[Crossref] [PubMed]

F. Quinlan, T. M. Fortier, H. Jiang, A. Hati, C. Nelson, Y. Fu, J. C. Campbell, and S. A. Diddams, “Exploiting shot noise correlations in the photodetection of ultrashort optical pulse trains,” Nat. Photonics 7(4), 290–293 (2013).
[Crossref]

Z. Li, Y. Fu, M. Piels, H. Pan, A. Beling, J. E. Bowers, and J. C. Campbell, “High-power high-linearity flip-chip bonded modified uni-traveling carrier photodiode,” Opt. Express 19(26), B385–B390 (2011).
[Crossref] [PubMed]

Chen, L. R.

B. Xia and L. R. Chen, “A direct temporal domain approach for pulse-repetition rate multiplication with arbitrary envelope shaping,” IEEE J. Sel. Top. Quantum Electron. 11(1), 165–172 (2005).
[Crossref]

Chrostowski, L.

Chu, C.

Y. Zheng, Y. Ren, P. An, C. Chu, X. Li, C. Xue, J. Liu, and S. Yan, “Wide dynamic range experiments on a resonator fiber optic gyro based on closed-loop frequency locking technique,” Chin. Opt. Lett. 13(2), 20601 (2015).
[Crossref]

Clairon, A.

J. Millo, M. Abgrall, M. Lours, E. M. L. English, H. Jiang, J. Guéna, A. Clairon, M. E. Tobar, S. Bize, Y. Le Coq, and G. Santarelli, “Ultra-low noise microwave generation with fiber-based optical frequency comb and application to atomic fountain clock,” Appl. Phys. Lett. 94(14), 141105 (2009).
[Crossref]

Coq, Y. L.

Cross, A.

Deschenes, J. D.

W. Sun, F. Quinlan, T. M. Fortier, J. D. Deschenes, Y. Fu, S. A. Diddams, and J. C. Campbell, “Broadband noise limit in the photodetection of ultralow jitter optical pulses,” Phys. Rev. Lett. 113(20), 203901 (2014).
[Crossref] [PubMed]

Diddams, S. A.

W. Sun, F. Quinlan, T. M. Fortier, J. D. Deschenes, Y. Fu, S. A. Diddams, and J. C. Campbell, “Broadband noise limit in the photodetection of ultralow jitter optical pulses,” Phys. Rev. Lett. 113(20), 203901 (2014).
[Crossref] [PubMed]

F. Quinlan, F. N. Baynes, T. M. Fortier, Q. Zhou, A. Cross, J. C. Campbell, and S. A. Diddams, “Optical amplification and pulse interleaving for low-noise photonic microwave generation,” Opt. Lett. 39(6), 1581–1584 (2014).
[Crossref] [PubMed]

F. Quinlan, T. M. Fortier, H. Jiang, and S. A. Diddams, “Analysis of shot noise in the detection of ultrashort optical pulse trains,” J. Opt. Soc. Am. B 30(6), 1775–1785 (2013).
[Crossref]

F. Quinlan, T. M. Fortier, H. Jiang, A. Hati, C. Nelson, Y. Fu, J. C. Campbell, and S. A. Diddams, “Exploiting shot noise correlations in the photodetection of ultrashort optical pulse trains,” Nat. Photonics 7(4), 290–293 (2013).
[Crossref]

T. M. Fortier, F. Quinlan, A. Hati, C. Nelson, J. A. Taylor, Y. Fu, J. Campbell, and S. A. Diddams, “Photonic microwave generation with high-power photodiodes,” Opt. Lett. 38(10), 1712–1714 (2013).
[Crossref] [PubMed]

F. Quinlan, T. M. Fortier, M. S. Kirchner, J. A. Taylor, M. J. Thorpe, N. Lemke, A. D. Ludlow, Y. Jiang, S. A. Diddams, and S. A. Diddams, “Ultralow phase noise microwave generation with an Er:fiber-based optical frequency divider,” Opt. Lett. 36(16), 3260–3262 (2011).
[Crossref] [PubMed]

F. Quinlan, T. M. Fortier, M. S. Kirchner, J. A. Taylor, M. J. Thorpe, N. Lemke, A. D. Ludlow, Y. Jiang, S. A. Diddams, and S. A. Diddams, “Ultralow phase noise microwave generation with an Er:fiber-based optical frequency divider,” Opt. Lett. 36(16), 3260–3262 (2011).
[Crossref] [PubMed]

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, “Generation of ultrastable microwave via optical frequency division,” Nat. Photonics 5(7), 425–429 (2011).
[Crossref]

S. A. Diddams, “The evolving optical frequency comb,” J. Opt. Soc. Am. B 27(11), B51–B62 (2010).
[Crossref]

S. A. Diddams, M. Kirchner, T. Fortier, D. Braje, A. M. Weiner, and L. Hollberg, “Improved signal-to-noise ratio of 10 GHz microwave signals generated with a mode-filtered femtosecond laser frequency comb,” Opt. Express 17(5), 3331–3340 (2009).
[Crossref] [PubMed]

A. Bartels, S. A. Diddams, C. W. Oates, G. Wilpers, J. C. Bergquist, W. H. Oskay, and L. Hollberg, “Femtosecond-laser-based synthesis of ultrastable microwave signals from optical frequency references,” Opt. Lett. 30(6), 667–669 (2005).
[Crossref] [PubMed]

Digonnet, M. J. F.

English, E. M. L.

J. Millo, M. Abgrall, M. Lours, E. M. L. English, H. Jiang, J. Guéna, A. Clairon, M. E. Tobar, S. Bize, Y. Le Coq, and G. Santarelli, “Ultra-low noise microwave generation with fiber-based optical frequency comb and application to atomic fountain clock,” Appl. Phys. Lett. 94(14), 141105 (2009).
[Crossref]

Fan, S.

Fleming, S.

S. Min, Y. Zhao, and S. Fleming, “Repetition rate multiplication in figure-eight fibre laser with 3 dB couplers,” Opt. Commun. 277(2), 411–413 (2007).
[Crossref]

Fortier, T.

Fortier, T. M.

W. Sun, F. Quinlan, T. M. Fortier, J. D. Deschenes, Y. Fu, S. A. Diddams, and J. C. Campbell, “Broadband noise limit in the photodetection of ultralow jitter optical pulses,” Phys. Rev. Lett. 113(20), 203901 (2014).
[Crossref] [PubMed]

F. Quinlan, F. N. Baynes, T. M. Fortier, Q. Zhou, A. Cross, J. C. Campbell, and S. A. Diddams, “Optical amplification and pulse interleaving for low-noise photonic microwave generation,” Opt. Lett. 39(6), 1581–1584 (2014).
[Crossref] [PubMed]

F. Quinlan, T. M. Fortier, H. Jiang, and S. A. Diddams, “Analysis of shot noise in the detection of ultrashort optical pulse trains,” J. Opt. Soc. Am. B 30(6), 1775–1785 (2013).
[Crossref]

F. Quinlan, T. M. Fortier, H. Jiang, A. Hati, C. Nelson, Y. Fu, J. C. Campbell, and S. A. Diddams, “Exploiting shot noise correlations in the photodetection of ultrashort optical pulse trains,” Nat. Photonics 7(4), 290–293 (2013).
[Crossref]

T. M. Fortier, F. Quinlan, A. Hati, C. Nelson, J. A. Taylor, Y. Fu, J. Campbell, and S. A. Diddams, “Photonic microwave generation with high-power photodiodes,” Opt. Lett. 38(10), 1712–1714 (2013).
[Crossref] [PubMed]

F. Quinlan, T. M. Fortier, M. S. Kirchner, J. A. Taylor, M. J. Thorpe, N. Lemke, A. D. Ludlow, Y. Jiang, S. A. Diddams, and S. A. Diddams, “Ultralow phase noise microwave generation with an Er:fiber-based optical frequency divider,” Opt. Lett. 36(16), 3260–3262 (2011).
[Crossref] [PubMed]

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, “Generation of ultrastable microwave via optical frequency division,” Nat. Photonics 5(7), 425–429 (2011).
[Crossref]

Fu, Y.

W. Sun, F. Quinlan, T. M. Fortier, J. D. Deschenes, Y. Fu, S. A. Diddams, and J. C. Campbell, “Broadband noise limit in the photodetection of ultralow jitter optical pulses,” Phys. Rev. Lett. 113(20), 203901 (2014).
[Crossref] [PubMed]

F. Quinlan, T. M. Fortier, H. Jiang, A. Hati, C. Nelson, Y. Fu, J. C. Campbell, and S. A. Diddams, “Exploiting shot noise correlations in the photodetection of ultrashort optical pulse trains,” Nat. Photonics 7(4), 290–293 (2013).
[Crossref]

T. M. Fortier, F. Quinlan, A. Hati, C. Nelson, J. A. Taylor, Y. Fu, J. Campbell, and S. A. Diddams, “Photonic microwave generation with high-power photodiodes,” Opt. Lett. 38(10), 1712–1714 (2013).
[Crossref] [PubMed]

Z. Li, Y. Fu, M. Piels, H. Pan, A. Beling, J. E. Bowers, and J. C. Campbell, “High-power high-linearity flip-chip bonded modified uni-traveling carrier photodiode,” Opt. Express 19(26), B385–B390 (2011).
[Crossref] [PubMed]

Gad, M.

M. Gad, J. Ackert, D. Yevick, L. Chrostowski, and P. Jessop, “Ring resonator wavelength division multiplexing interleaver,” J. Lightwave Technol. 29(14), 2102–2108 (2011).
[Crossref]

M. Gad, D. Yevick, and P. Jessop, “High sensitivity ring resonator gyroscopes,” Fiber Integr. Opt. 30, 395–410 (2011).

Giunta, M.

R. Bouchand, X. Xie, D. Nicolodi, P. Tremblin, G. Santarelli, C. Alexandre, M. Giunta, M. Lezius, W. Haensel, R. Holzwarth, D. Shubhashish, J. Abhay, and Y. Le Coq, “State-of-the-art ultra-low phase noise photonic microwave generation,” inProceedings of IEEE European Frequency and Time Forum (IEEE, 2016), pp. 1–3.

Guéna, J.

J. Millo, M. Abgrall, M. Lours, E. M. L. English, H. Jiang, J. Guéna, A. Clairon, M. E. Tobar, S. Bize, Y. Le Coq, and G. Santarelli, “Ultra-low noise microwave generation with fiber-based optical frequency comb and application to atomic fountain clock,” Appl. Phys. Lett. 94(14), 141105 (2009).
[Crossref]

Haboucha, A.

Haensel, W.

R. Bouchand, X. Xie, D. Nicolodi, P. Tremblin, G. Santarelli, C. Alexandre, M. Giunta, M. Lezius, W. Haensel, R. Holzwarth, D. Shubhashish, J. Abhay, and Y. Le Coq, “State-of-the-art ultra-low phase noise photonic microwave generation,” inProceedings of IEEE European Frequency and Time Forum (IEEE, 2016), pp. 1–3.

Hati, A.

F. Quinlan, T. M. Fortier, H. Jiang, A. Hati, C. Nelson, Y. Fu, J. C. Campbell, and S. A. Diddams, “Exploiting shot noise correlations in the photodetection of ultrashort optical pulse trains,” Nat. Photonics 7(4), 290–293 (2013).
[Crossref]

T. M. Fortier, F. Quinlan, A. Hati, C. Nelson, J. A. Taylor, Y. Fu, J. Campbell, and S. A. Diddams, “Photonic microwave generation with high-power photodiodes,” Opt. Lett. 38(10), 1712–1714 (2013).
[Crossref] [PubMed]

Hollberg, L.

Holzwarth, R.

R. Bouchand, X. Xie, D. Nicolodi, P. Tremblin, G. Santarelli, C. Alexandre, M. Giunta, M. Lezius, W. Haensel, R. Holzwarth, D. Shubhashish, J. Abhay, and Y. Le Coq, “State-of-the-art ultra-low phase noise photonic microwave generation,” inProceedings of IEEE European Frequency and Time Forum (IEEE, 2016), pp. 1–3.

Jessop, P.

M. Gad, D. Yevick, and P. Jessop, “High sensitivity ring resonator gyroscopes,” Fiber Integr. Opt. 30, 395–410 (2011).

M. Gad, J. Ackert, D. Yevick, L. Chrostowski, and P. Jessop, “Ring resonator wavelength division multiplexing interleaver,” J. Lightwave Technol. 29(14), 2102–2108 (2011).
[Crossref]

Jian, S.

D. Wei, Y. Zhao, T. Li, and S. Jian, “A novel scheme for optical pulse multiplication using fiber coupler loop-connecting configuration,” Czech. J. Phys. 51(2), 155–162 (2001).
[Crossref]

Jiang, H.

F. Quinlan, T. M. Fortier, H. Jiang, A. Hati, C. Nelson, Y. Fu, J. C. Campbell, and S. A. Diddams, “Exploiting shot noise correlations in the photodetection of ultrashort optical pulse trains,” Nat. Photonics 7(4), 290–293 (2013).
[Crossref]

F. Quinlan, T. M. Fortier, H. Jiang, and S. A. Diddams, “Analysis of shot noise in the detection of ultrashort optical pulse trains,” J. Opt. Soc. Am. B 30(6), 1775–1785 (2013).
[Crossref]

J. Millo, M. Abgrall, M. Lours, E. M. L. English, H. Jiang, J. Guéna, A. Clairon, M. E. Tobar, S. Bize, Y. Le Coq, and G. Santarelli, “Ultra-low noise microwave generation with fiber-based optical frequency comb and application to atomic fountain clock,” Appl. Phys. Lett. 94(14), 141105 (2009).
[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, “Generation of ultrastable microwave via optical frequency division,” Nat. Photonics 5(7), 425–429 (2011).
[Crossref]

F. Quinlan, T. M. Fortier, M. S. Kirchner, J. A. Taylor, M. J. Thorpe, N. Lemke, A. D. Ludlow, Y. Jiang, S. A. Diddams, and S. A. Diddams, “Ultralow phase noise microwave generation with an Er:fiber-based optical frequency divider,” Opt. Lett. 36(16), 3260–3262 (2011).
[Crossref] [PubMed]

Kärtner, F. X.

Kersalé, Y.

Kim, J.

Kirchner, M.

Kirchner, M. S.

F. Quinlan, T. M. Fortier, M. S. Kirchner, J. A. Taylor, M. J. Thorpe, N. Lemke, A. D. Ludlow, Y. Jiang, S. A. Diddams, and S. A. Diddams, “Ultralow phase noise microwave generation with an Er:fiber-based optical frequency divider,” Opt. Lett. 36(16), 3260–3262 (2011).
[Crossref] [PubMed]

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, “Generation of ultrastable microwave via optical frequency division,” Nat. Photonics 5(7), 425–429 (2011).
[Crossref]

Kundermann, S.

Lallana, P. C.

C. Vázquez, J. Montalvo, and P. C. Lallana, “Ring resonators with Sagnac loops for photonic processing in DWDM backbone networks,” inProceedings of IEEE International Symposium on Intelligent Signal Processing (IEEE, 2007), pp. 1–5.
[Crossref]

Le Coq, Y.

A. Haboucha, W. Zhang, T. Li, M. Lours, A. N. Luiten, Y. Le Coq, and G. Santarelli, “Optical-fiber pulse rate multiplier for ultralow phase-noise signal generation,” Opt. Lett. 36(18), 3654–3656 (2011).
[Crossref] [PubMed]

J. Millo, M. Abgrall, M. Lours, E. M. L. English, H. Jiang, J. Guéna, A. Clairon, M. E. Tobar, S. Bize, Y. Le Coq, and G. Santarelli, “Ultra-low noise microwave generation with fiber-based optical frequency comb and application to atomic fountain clock,” Appl. Phys. Lett. 94(14), 141105 (2009).
[Crossref]

R. Bouchand, X. Xie, D. Nicolodi, P. Tremblin, G. Santarelli, C. Alexandre, M. Giunta, M. Lezius, W. Haensel, R. Holzwarth, D. Shubhashish, J. Abhay, and Y. Le Coq, “State-of-the-art ultra-low phase noise photonic microwave generation,” inProceedings of IEEE European Frequency and Time Forum (IEEE, 2016), pp. 1–3.

Lecomte, S.

Lemke, N.

F. Quinlan, T. M. Fortier, M. S. Kirchner, J. A. Taylor, M. J. Thorpe, N. Lemke, A. D. Ludlow, Y. Jiang, S. A. Diddams, and S. A. Diddams, “Ultralow phase noise microwave generation with an Er:fiber-based optical frequency divider,” Opt. Lett. 36(16), 3260–3262 (2011).
[Crossref] [PubMed]

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, “Generation of ultrastable microwave via optical frequency division,” Nat. Photonics 5(7), 425–429 (2011).
[Crossref]

Lezius, M.

R. Bouchand, X. Xie, D. Nicolodi, P. Tremblin, G. Santarelli, C. Alexandre, M. Giunta, M. Lezius, W. Haensel, R. Holzwarth, D. Shubhashish, J. Abhay, and Y. Le Coq, “State-of-the-art ultra-low phase noise photonic microwave generation,” inProceedings of IEEE European Frequency and Time Forum (IEEE, 2016), pp. 1–3.

Li, T.

A. Haboucha, W. Zhang, T. Li, M. Lours, A. N. Luiten, Y. Le Coq, and G. Santarelli, “Optical-fiber pulse rate multiplier for ultralow phase-noise signal generation,” Opt. Lett. 36(18), 3654–3656 (2011).
[Crossref] [PubMed]

D. Wei, Y. Zhao, T. Li, and S. Jian, “A novel scheme for optical pulse multiplication using fiber coupler loop-connecting configuration,” Czech. J. Phys. 51(2), 155–162 (2001).
[Crossref]

Li, X.

Y. Zheng, Y. Ren, P. An, C. Chu, X. Li, C. Xue, J. Liu, and S. Yan, “Wide dynamic range experiments on a resonator fiber optic gyro based on closed-loop frequency locking technique,” Chin. Opt. Lett. 13(2), 20601 (2015).
[Crossref]

Li, Z.

Lipphardt, B.

S. Weyers, B. Lipphardt, and H. Schnatz, “Reaching the quantum limit in a fountain clock using a microwave oscillator phase locked to an ultrastable laser,” Phys. Rev. A 79(3), 031803 (2009).
[Crossref]

Liu, J.

Y. Zheng, Y. Ren, P. An, C. Chu, X. Li, C. Xue, J. Liu, and S. Yan, “Wide dynamic range experiments on a resonator fiber optic gyro based on closed-loop frequency locking technique,” Chin. Opt. Lett. 13(2), 20601 (2015).
[Crossref]

Lours, M.

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, “Generation of ultrastable microwave via optical frequency division,” Nat. Photonics 5(7), 425–429 (2011).
[Crossref]

Ludlow, A. D.

Luiten, A. N.

Millo, J.

J. Millo, R. Boudot, M. Lours, P. Y. Bourgeois, A. N. Luiten, Y. L. Coq, Y. Kersalé, and G. Santarelli, “Ultra-low-noise microwave extraction from fiber-based optical frequency comb,” Opt. Lett. 34(23), 3707–3709 (2009).
[Crossref] [PubMed]

J. Millo, M. Abgrall, M. Lours, E. M. L. English, H. Jiang, J. Guéna, A. Clairon, M. E. Tobar, S. Bize, Y. Le Coq, and G. Santarelli, “Ultra-low noise microwave generation with fiber-based optical frequency comb and application to atomic fountain clock,” Appl. Phys. Lett. 94(14), 141105 (2009).
[Crossref]

Min, S.

S. Min, Y. Zhao, and S. Fleming, “Repetition rate multiplication in figure-eight fibre laser with 3 dB couplers,” Opt. Commun. 277(2), 411–413 (2007).
[Crossref]

Montalvo, J.

C. Vázquez, J. Montalvo, and P. C. Lallana, “Ring resonators with Sagnac loops for photonic processing in DWDM backbone networks,” inProceedings of IEEE International Symposium on Intelligent Signal Processing (IEEE, 2007), pp. 1–5.
[Crossref]

Nelson, C.

F. Quinlan, T. M. Fortier, H. Jiang, A. Hati, C. Nelson, Y. Fu, J. C. Campbell, and S. A. Diddams, “Exploiting shot noise correlations in the photodetection of ultrashort optical pulse trains,” Nat. Photonics 7(4), 290–293 (2013).
[Crossref]

T. M. Fortier, F. Quinlan, A. Hati, C. Nelson, J. A. Taylor, Y. Fu, J. Campbell, and S. A. Diddams, “Photonic microwave generation with high-power photodiodes,” Opt. Lett. 38(10), 1712–1714 (2013).
[Crossref] [PubMed]

Newbury, N. R.

N. R. Newbury, “Searching for applications with a fine-tooth comb,” Nat. Photonics 5(4), 186–188 (2011).
[Crossref]

Nicolodi, D.

R. Bouchand, X. Xie, D. Nicolodi, P. Tremblin, G. Santarelli, C. Alexandre, M. Giunta, M. Lezius, W. Haensel, R. Holzwarth, D. Shubhashish, J. Abhay, and Y. Le Coq, “State-of-the-art ultra-low phase noise photonic microwave generation,” inProceedings of IEEE European Frequency and Time Forum (IEEE, 2016), pp. 1–3.

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, “Generation of ultrastable microwave via optical frequency division,” Nat. Photonics 5(7), 425–429 (2011).
[Crossref]

A. Bartels, S. A. Diddams, C. W. Oates, G. Wilpers, J. C. Bergquist, W. H. Oskay, and L. Hollberg, “Femtosecond-laser-based synthesis of ultrastable microwave signals from optical frequency references,” Opt. Lett. 30(6), 667–669 (2005).
[Crossref] [PubMed]

Oskay, W. H.

Pan, H.

Piels, M.

Portuondo-Campa, E.

Quinlan, F.

F. Quinlan, F. N. Baynes, T. M. Fortier, Q. Zhou, A. Cross, J. C. Campbell, and S. A. Diddams, “Optical amplification and pulse interleaving for low-noise photonic microwave generation,” Opt. Lett. 39(6), 1581–1584 (2014).
[Crossref] [PubMed]

W. Sun, F. Quinlan, T. M. Fortier, J. D. Deschenes, Y. Fu, S. A. Diddams, and J. C. Campbell, “Broadband noise limit in the photodetection of ultralow jitter optical pulses,” Phys. Rev. Lett. 113(20), 203901 (2014).
[Crossref] [PubMed]

F. Quinlan, T. M. Fortier, H. Jiang, A. Hati, C. Nelson, Y. Fu, J. C. Campbell, and S. A. Diddams, “Exploiting shot noise correlations in the photodetection of ultrashort optical pulse trains,” Nat. Photonics 7(4), 290–293 (2013).
[Crossref]

F. Quinlan, T. M. Fortier, H. Jiang, and S. A. Diddams, “Analysis of shot noise in the detection of ultrashort optical pulse trains,” J. Opt. Soc. Am. B 30(6), 1775–1785 (2013).
[Crossref]

T. M. Fortier, F. Quinlan, A. Hati, C. Nelson, J. A. Taylor, Y. Fu, J. Campbell, and S. A. Diddams, “Photonic microwave generation with high-power photodiodes,” Opt. Lett. 38(10), 1712–1714 (2013).
[Crossref] [PubMed]

F. Quinlan, T. M. Fortier, M. S. Kirchner, J. A. Taylor, M. J. Thorpe, N. Lemke, A. D. Ludlow, Y. Jiang, S. A. Diddams, and S. A. Diddams, “Ultralow phase noise microwave generation with an Er:fiber-based optical frequency divider,” Opt. Lett. 36(16), 3260–3262 (2011).
[Crossref] [PubMed]

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, “Generation of ultrastable microwave via optical frequency division,” Nat. Photonics 5(7), 425–429 (2011).
[Crossref]

Ren, Y.

Y. Zheng, Y. Ren, P. An, C. Chu, X. Li, C. Xue, J. Liu, and S. Yan, “Wide dynamic range experiments on a resonator fiber optic gyro based on closed-loop frequency locking technique,” Chin. Opt. Lett. 13(2), 20601 (2015).
[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, “Generation of ultrastable microwave via optical frequency division,” Nat. Photonics 5(7), 425–429 (2011).
[Crossref]

Santarelli, G.

A. Haboucha, W. Zhang, T. Li, M. Lours, A. N. Luiten, Y. Le Coq, and G. Santarelli, “Optical-fiber pulse rate multiplier for ultralow phase-noise signal generation,” Opt. Lett. 36(18), 3654–3656 (2011).
[Crossref] [PubMed]

J. Millo, R. Boudot, M. Lours, P. Y. Bourgeois, A. N. Luiten, Y. L. Coq, Y. Kersalé, and G. Santarelli, “Ultra-low-noise microwave extraction from fiber-based optical frequency comb,” Opt. Lett. 34(23), 3707–3709 (2009).
[Crossref] [PubMed]

J. Millo, M. Abgrall, M. Lours, E. M. L. English, H. Jiang, J. Guéna, A. Clairon, M. E. Tobar, S. Bize, Y. Le Coq, and G. Santarelli, “Ultra-low noise microwave generation with fiber-based optical frequency comb and application to atomic fountain clock,” Appl. Phys. Lett. 94(14), 141105 (2009).
[Crossref]

R. Bouchand, X. Xie, D. Nicolodi, P. Tremblin, G. Santarelli, C. Alexandre, M. Giunta, M. Lezius, W. Haensel, R. Holzwarth, D. Shubhashish, J. Abhay, and Y. Le Coq, “State-of-the-art ultra-low phase noise photonic microwave generation,” inProceedings of IEEE European Frequency and Time Forum (IEEE, 2016), pp. 1–3.

Schnatz, H.

S. Weyers, B. Lipphardt, and H. Schnatz, “Reaching the quantum limit in a fountain clock using a microwave oscillator phase locked to an ultrastable laser,” Phys. Rev. A 79(3), 031803 (2009).
[Crossref]

Shubhashish, D.

R. Bouchand, X. Xie, D. Nicolodi, P. Tremblin, G. Santarelli, C. Alexandre, M. Giunta, M. Lezius, W. Haensel, R. Holzwarth, D. Shubhashish, J. Abhay, and Y. Le Coq, “State-of-the-art ultra-low phase noise photonic microwave generation,” inProceedings of IEEE European Frequency and Time Forum (IEEE, 2016), pp. 1–3.

Sun, W.

W. Sun, F. Quinlan, T. M. Fortier, J. D. Deschenes, Y. Fu, S. A. Diddams, and J. C. Campbell, “Broadband noise limit in the photodetection of ultralow jitter optical pulses,” Phys. Rev. Lett. 113(20), 203901 (2014).
[Crossref] [PubMed]

Taylor, J.

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, “Generation of ultrastable microwave via optical frequency division,” Nat. Photonics 5(7), 425–429 (2011).
[Crossref]

Taylor, J. A.

Terrel, M. A.

Thorpe, M. J.

Tobar, M. E.

J. Millo, M. Abgrall, M. Lours, E. M. L. English, H. Jiang, J. Guéna, A. Clairon, M. E. Tobar, S. Bize, Y. Le Coq, and G. Santarelli, “Ultra-low noise microwave generation with fiber-based optical frequency comb and application to atomic fountain clock,” Appl. Phys. Lett. 94(14), 141105 (2009).
[Crossref]

Tremblin, P.

R. Bouchand, X. Xie, D. Nicolodi, P. Tremblin, G. Santarelli, C. Alexandre, M. Giunta, M. Lezius, W. Haensel, R. Holzwarth, D. Shubhashish, J. Abhay, and Y. Le Coq, “State-of-the-art ultra-low phase noise photonic microwave generation,” inProceedings of IEEE European Frequency and Time Forum (IEEE, 2016), pp. 1–3.

Vázquez, C.

C. Vázquez, J. Montalvo, and P. C. Lallana, “Ring resonators with Sagnac loops for photonic processing in DWDM backbone networks,” inProceedings of IEEE International Symposium on Intelligent Signal Processing (IEEE, 2007), pp. 1–5.
[Crossref]

Wei, D.

D. Wei, Y. Zhao, T. Li, and S. Jian, “A novel scheme for optical pulse multiplication using fiber coupler loop-connecting configuration,” Czech. J. Phys. 51(2), 155–162 (2001).
[Crossref]

Weiner, A. M.

Weyers, S.

S. Weyers, B. Lipphardt, and H. Schnatz, “Reaching the quantum limit in a fountain clock using a microwave oscillator phase locked to an ultrastable laser,” Phys. Rev. A 79(3), 031803 (2009).
[Crossref]

Wilpers, G.

Xia, B.

B. Xia and L. R. Chen, “A direct temporal domain approach for pulse-repetition rate multiplication with arbitrary envelope shaping,” IEEE J. Sel. Top. Quantum Electron. 11(1), 165–172 (2005).
[Crossref]

Xie, X.

R. Bouchand, X. Xie, D. Nicolodi, P. Tremblin, G. Santarelli, C. Alexandre, M. Giunta, M. Lezius, W. Haensel, R. Holzwarth, D. Shubhashish, J. Abhay, and Y. Le Coq, “State-of-the-art ultra-low phase noise photonic microwave generation,” inProceedings of IEEE European Frequency and Time Forum (IEEE, 2016), pp. 1–3.

Xue, C.

Y. Zheng, Y. Ren, P. An, C. Chu, X. Li, C. Xue, J. Liu, and S. Yan, “Wide dynamic range experiments on a resonator fiber optic gyro based on closed-loop frequency locking technique,” Chin. Opt. Lett. 13(2), 20601 (2015).
[Crossref]

Yan, S.

Y. Zheng, Y. Ren, P. An, C. Chu, X. Li, C. Xue, J. Liu, and S. Yan, “Wide dynamic range experiments on a resonator fiber optic gyro based on closed-loop frequency locking technique,” Chin. Opt. Lett. 13(2), 20601 (2015).
[Crossref]

Yevick, D.

M. Gad, D. Yevick, and P. Jessop, “High sensitivity ring resonator gyroscopes,” Fiber Integr. Opt. 30, 395–410 (2011).

M. Gad, J. Ackert, D. Yevick, L. Chrostowski, and P. Jessop, “Ring resonator wavelength division multiplexing interleaver,” J. Lightwave Technol. 29(14), 2102–2108 (2011).
[Crossref]

Zhang, W.

Zhao, Y.

S. Min, Y. Zhao, and S. Fleming, “Repetition rate multiplication in figure-eight fibre laser with 3 dB couplers,” Opt. Commun. 277(2), 411–413 (2007).
[Crossref]

D. Wei, Y. Zhao, T. Li, and S. Jian, “A novel scheme for optical pulse multiplication using fiber coupler loop-connecting configuration,” Czech. J. Phys. 51(2), 155–162 (2001).
[Crossref]

Zheng, Y.

Y. Zheng, Y. Ren, P. An, C. Chu, X. Li, C. Xue, J. Liu, and S. Yan, “Wide dynamic range experiments on a resonator fiber optic gyro based on closed-loop frequency locking technique,” Chin. Opt. Lett. 13(2), 20601 (2015).
[Crossref]

Zhou, Q.

Appl. Phys. Lett. (1)

J. Millo, M. Abgrall, M. Lours, E. M. L. English, H. Jiang, J. Guéna, A. Clairon, M. E. Tobar, S. Bize, Y. Le Coq, and G. Santarelli, “Ultra-low noise microwave generation with fiber-based optical frequency comb and application to atomic fountain clock,” Appl. Phys. Lett. 94(14), 141105 (2009).
[Crossref]

Chin. Opt. Lett. (1)

Y. Zheng, Y. Ren, P. An, C. Chu, X. Li, C. Xue, J. Liu, and S. Yan, “Wide dynamic range experiments on a resonator fiber optic gyro based on closed-loop frequency locking technique,” Chin. Opt. Lett. 13(2), 20601 (2015).
[Crossref]

Czech. J. Phys. (1)

D. Wei, Y. Zhao, T. Li, and S. Jian, “A novel scheme for optical pulse multiplication using fiber coupler loop-connecting configuration,” Czech. J. Phys. 51(2), 155–162 (2001).
[Crossref]

Fiber Integr. Opt. (1)

M. Gad, D. Yevick, and P. Jessop, “High sensitivity ring resonator gyroscopes,” Fiber Integr. Opt. 30, 395–410 (2011).

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

B. Xia and L. R. Chen, “A direct temporal domain approach for pulse-repetition rate multiplication with arbitrary envelope shaping,” IEEE J. Sel. Top. Quantum Electron. 11(1), 165–172 (2005).
[Crossref]

J. Lightwave Technol. (2)

J. Opt. Soc. Am. B (2)

Nat. Photonics (3)

N. R. Newbury, “Searching for applications with a fine-tooth comb,” Nat. Photonics 5(4), 186–188 (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, “Generation of ultrastable microwave via optical frequency division,” Nat. Photonics 5(7), 425–429 (2011).
[Crossref]

F. Quinlan, T. M. Fortier, H. Jiang, A. Hati, C. Nelson, Y. Fu, J. C. Campbell, and S. A. Diddams, “Exploiting shot noise correlations in the photodetection of ultrashort optical pulse trains,” Nat. Photonics 7(4), 290–293 (2013).
[Crossref]

Opt. Commun. (1)

S. Min, Y. Zhao, and S. Fleming, “Repetition rate multiplication in figure-eight fibre laser with 3 dB couplers,” Opt. Commun. 277(2), 411–413 (2007).
[Crossref]

Opt. Express (3)

Opt. Lett. (7)

A. Haboucha, W. Zhang, T. Li, M. Lours, A. N. Luiten, Y. Le Coq, and G. Santarelli, “Optical-fiber pulse rate multiplier for ultralow phase-noise signal generation,” Opt. Lett. 36(18), 3654–3656 (2011).
[Crossref] [PubMed]

F. Quinlan, T. M. Fortier, M. S. Kirchner, J. A. Taylor, M. J. Thorpe, N. Lemke, A. D. Ludlow, Y. Jiang, S. A. Diddams, and S. A. Diddams, “Ultralow phase noise microwave generation with an Er:fiber-based optical frequency divider,” Opt. Lett. 36(16), 3260–3262 (2011).
[Crossref] [PubMed]

J. Kim and F. X. Kärtner, “Microwave signal extraction from femtosecond mode-locked lasers with attosecond relative timing drift,” Opt. Lett. 35(12), 2022–2024 (2010).
[Crossref] [PubMed]

A. Bartels, S. A. Diddams, C. W. Oates, G. Wilpers, J. C. Bergquist, W. H. Oskay, and L. Hollberg, “Femtosecond-laser-based synthesis of ultrastable microwave signals from optical frequency references,” Opt. Lett. 30(6), 667–669 (2005).
[Crossref] [PubMed]

J. Millo, R. Boudot, M. Lours, P. Y. Bourgeois, A. N. Luiten, Y. L. Coq, Y. Kersalé, and G. Santarelli, “Ultra-low-noise microwave extraction from fiber-based optical frequency comb,” Opt. Lett. 34(23), 3707–3709 (2009).
[Crossref] [PubMed]

F. Quinlan, F. N. Baynes, T. M. Fortier, Q. Zhou, A. Cross, J. C. Campbell, and S. A. Diddams, “Optical amplification and pulse interleaving for low-noise photonic microwave generation,” Opt. Lett. 39(6), 1581–1584 (2014).
[Crossref] [PubMed]

T. M. Fortier, F. Quinlan, A. Hati, C. Nelson, J. A. Taylor, Y. Fu, J. Campbell, and S. A. Diddams, “Photonic microwave generation with high-power photodiodes,” Opt. Lett. 38(10), 1712–1714 (2013).
[Crossref] [PubMed]

Phys. Rev. A (1)

S. Weyers, B. Lipphardt, and H. Schnatz, “Reaching the quantum limit in a fountain clock using a microwave oscillator phase locked to an ultrastable laser,” Phys. Rev. A 79(3), 031803 (2009).
[Crossref]

Phys. Rev. Lett. (1)

W. Sun, F. Quinlan, T. M. Fortier, J. D. Deschenes, Y. Fu, S. A. Diddams, and J. C. Campbell, “Broadband noise limit in the photodetection of ultralow jitter optical pulses,” Phys. Rev. Lett. 113(20), 203901 (2014).
[Crossref] [PubMed]

Other (2)

R. Bouchand, X. Xie, D. Nicolodi, P. Tremblin, G. Santarelli, C. Alexandre, M. Giunta, M. Lezius, W. Haensel, R. Holzwarth, D. Shubhashish, J. Abhay, and Y. Le Coq, “State-of-the-art ultra-low phase noise photonic microwave generation,” inProceedings of IEEE European Frequency and Time Forum (IEEE, 2016), pp. 1–3.

C. Vázquez, J. Montalvo, and P. C. Lallana, “Ring resonators with Sagnac loops for photonic processing in DWDM backbone networks,” inProceedings of IEEE International Symposium on Intelligent Signal Processing (IEEE, 2007), pp. 1–5.
[Crossref]

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Figures (9)

Fig. 1
Fig. 1 Structure of fiber ring interferometer.
Fig. 2
Fig. 2 Optical pulse train (black) before multiplication and (red) after multiplication.
Fig. 3
Fig. 3 Power ratio of 54th and 53rd harmonics of generated microwaves using a first-stage interleaver as a function of interleaver delay errors.
Fig. 4
Fig. 4 Photodiode output microwave powers of 8 GHz signal as a function of input optical power.
Fig. 5
Fig. 5 Experimental setup for measuring the residual phase noise of photodetection. OC: optical coupler, OA: optical attenuator, MI: microwave isolator, BPF: band-pass filter, MA: microwave amplifier, PS: phase shifter.
Fig. 6
Fig. 6 Measured phase noise of photodetection system with different interleaver delay errors.
Fig. 7
Fig. 7 Calculated photodetection-limited phase noise deviation (red trace) and that with added noise floor of test set (black trace). The measured data are plotted as black points. The error bars result from the variance in the phase noise measurements.
Fig. 8
Fig. 8 Experimental setup for measuring the residual phase noise of multiplication channel.
Fig. 9
Fig. 9 Measured phase noise of multiplication channel (red trace) and the measured noise floor of photodetection system (green trace). The black trace corresponds to the noise floor of the test set.

Equations (6)

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( E 3 E 4 )=( α i βα i βα α )( E 1 E 2 )
a 1 (t)= | E 1 | 2 = a 0 (t) n= + δ(tnT)
a 3 (t)= | E 3 | 2 =α[ a 0 (t) n= + δ(tnT) ]+( βα )( βα )[ a 0 (t) n= + δ(tnT t L ) ] +( βα )α( βα )[ a 0 (t) n= + δ(tnT2 t L ) ]+.... + ( βα ) 2 α m1 [ a 0 (t) n= + δ(tnTm t L ) ] = a 0 (t) n= + [ αδ(tnT)+ m=1 (βα) 2 α m1 δ(tnTm t L ) ]
a 3 (t)= a 0 (t) n= + [ (α+ q=1 + (βα) 2 α 2q1 )δ(tnT)+ q=0 + (βα) 2 α 2q δ(tnT T 2 ) ]
α+ q=1 + (βα) 2 α 2q1 = q=0 + (βα) 2 α 2q α= β 2 1+2β
I n (n f rr )= A 0 (n f rr )[α e 2πi f rr nt + (βα) 2 e 2πi f rr n(t+ t L ) + (βα) 2 α e 2πi f rr n(t+ t L 2) + ...+ (βα) 2 α m1 e 2πi f rr n(t+ t L m) ] = A 0 (n f rr )[ α+ (βα) 2 m=1 α m1 e 2πi f rr n t L m ] e 2πi f rr nt with A 0 (f)=F( a 0 (t))

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