Abstract

When illuminating a photodiode with modulated laser light, optical intensity fluctuations of the incident beam are converted into phase fluctuations of the output electrical signal. This amplitude to phase noise conversion (APC) thus imposes a stringent constraint on the relative intensity noise (RIN) of the laser carrier when dealing with ultra-low phase noise microwave generation. Although the APC vanishes under certain conditions, it exhibits random fluctuations preventing efficient long-term passive stabilization schemes. In this paper, we present a digital coherent modulation-demodulation system for automatic measurement and control of the APC of a photodetector. The system is demonstrated in the detection of ultra-short optical pulses with an InGaAs photodetector and enables stable generation of ultra-low phase noise microwave signals with RIN rejection beyond 50 dB. This simple system can be used in various optoelectronic schemes, making photodetection virtually insensitive to the RIN of the lasers. We utilize this system to investigate the impact of the radiofrequency (RF) transmission line at the output of the photodetector on the APC coefficient that can affect the accuracy of the measurement in certain cases.

© 2017 Optical Society of America

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2017 (5)

C. Wade, N. Šibalić, N. de Melo, J. Kondo, C. Adams, and K. Weatherill, “Real-time near-field terahertz imaging with atomic optical fluorescence,” Nat. Photonics 11, 40–43 (2017).
[Crossref]

M. Xin, K. Şafak, M. Y. Peng, A. Kalaydzhyan, P. T. Callahan, W. Wang, O. D. Mücke, and F. X. Kärtner, “Breaking the femtosecond barrier in multi-kilometer timing synchronization systems,” IEEE J. Select. Topics Quantum Electron. 23, 1–12 (2017).
[Crossref]

X. Xie, R. Bouchand, D. Nicolodi, M. Giunta, W. Hänsel, M. Lezius, A. Joshi, S. Datta, C. Alexandre, M. Lours, P.-A. Tremblin, G. Santarelli, R. Holzwarth, and Y. Le Coq, “Photonic microwave signals with zeptosecond-level absolute timing noise,” Nat. Photonics 11, 44–47 (2017).
[Crossref]

X. Xie, J. Zang, A. Beling, and J. Campbell, “Characterization of amplitude noise to phase noise conversion in charge-compensated modified uni-travelling carrier photodiodes,” J. Lightwave Technol. 35(9), 1718–1724 (2017).
[Crossref]

X. Xie, R. Bouchand, D. Nicolodi, M. Lours, C. Alexandre, and Y. Le Coq, “Phase noise characterization of sub-hertz linewidth lasers via digital cross correlation,” Opt. Lett. 42, 1217–1220 (2017).
[Crossref] [PubMed]

2016 (3)

J. Kim and Y. Song, “Ultralow-noise mode-locked fiber lasers and frequency combs: principles, status, and applications,” Adv. Opt. Photonics 8, 465–540 (2016).
[Crossref]

C. Lisdat, G. Grosche, N. Quintin, C. Shi, S. Raupach, C. Grebing, D. Nicolodi, F. Stefani, A. Al-Masoudi, S. Dörscher, S. Häfner, J.-L. Robyr, N. Chiodo, S. Bilicki, E. Bookjans, A. Koczwara, S. Koke, A. Kohl, F. Wiotte, F. Meynadier, E. Camisard, M. Abgrall, M. Lours, T. Legero, H. Schnatz, U. Sterr, H. Denker, C. Chardonnet, Y. Le Coq, G. Santarelli, A. Amy-Klein, R. Le Targat, J. Lodewyck, O. Lopez, and P.-E. Pottie, “A clock network for geodesy and fundamental science,” Nat. Commun. 7, 12443 (2016).
[Crossref] [PubMed]

A. Kalaydzhyan, M. Peng, and F. Kartner, “Ultrahigh precision synchronization of optical and microwave frequency sources,” J. Phys: Conf. Ser. 741, 012084 (2016).

2015 (2)

K. Şafak, M. Xin, P. Callahan, M. Peng, and F. Kärtner, “All fiber-coupled, long-term stable timing distribution for free-electron lasers with few-femtosecond jitter,” Struct. Dyn. 2, 041715 (2015).
[Crossref]

F. N. Baynes, F. Quinlan, T. M. Fortier, Q. Zhou, A. Beling, J. C. Campbell, and S. A. Diddams, “Attosecond timing in optical-to-electrical conversion,” Optica 2, 141–146 (2015).
[Crossref]

2014 (6)

Z. Abdallah, A. Rumeau, A. Fernandez, G. Cibiel, and O. Llopis, “Nonlinear equivalent-circuit modeling of a fast photodiode,” IEEE Photon. Technol. Lett. 26, 1041–1135 (2014).
[Crossref]

D.-H. Phung, M. Merzougui, C. Alexandre, and M. Lintz, “Phase measurement of a microwave optical modulation: Characterisation and reduction of amplitude-to-phase conversion in 1.5 μm high bandwidth photodiodes,” J. Lightwave Technol. 32, 3759–3767 (2014).
[Crossref]

D.-H. Phung and M. Lintz, “Comments on “frequency response of the noise conversion from relative intensity noise to phase noise in the photodetection of an optical pulse train”,” IEEE Photon. Technol. Lett. 26, 1994–1995 (2014).
[Crossref]

P. Ghelfi, F. Laghezza, F. Scotti, G. Serafino, A. Capria, S. Pinna, D. Onori, C. Porzi, M. Scaffardi, A. Malacarne, V. Vercesi, E. Lazzeri, F. Berizzi, and A. Bogoni, “A fully photonics-based coherent radar system,” Nature 507, 341–345 (2014).
[Crossref] [PubMed]

M. Y. Peng, A. Kalaydzhyan, and F. X. Kärtner, “Balanced optical-microwave phase detector for sub-femtosecond optical-rf synchronization,” Opt. Express 22, 27102–27111 (2014).
[Crossref] [PubMed]

W. Zhang, S. Seidelin, A. Joshi, S. Datta, G. Santarelli, and Y. Le Coq, “Dual photo-detector system for low phase noise microwave generation with femtosecond lasers,” Opt. Lett. 39, 1204–1207 (2014).
[Crossref] [PubMed]

2013 (2)

2012 (3)

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

K. Jung and J. Kim, “Subfemtosecond synchronization of microwave oscillators with mode-locked er-fiber lasers,” Opt. Lett. 37, 2958–2960 (2012).
[Crossref] [PubMed]

W. Zhang, T. Li, M. Lours, S. Seidelin, G. Santarelli, and Y. Le Coq, “Amplitude to phase conversion of ingaas pin photo-diodes for femtosecond lasers microwave signal generation,” Appl. Phys. B 106, 301–308 (2012).
[Crossref]

2011 (3)

2010 (1)

W. Zhang, Z. Xu, M. Lours, R. Boudot, Y. Kersalé, G. Santarelli, and Y. Le Coq, “Sub-100 attoseconds stability optics to microwave synchronization,” Appl. Phys. Lett. 96, 211105 (2010).
[Crossref]

2009 (1)

2008 (1)

D. Eliyahu, D. Seidel, and L. Maleki, “Rf amplitude and phase-noise reduction of an optical link and an opto-electronic oscillator,” IEEE Trans. Microw. Theory Techn. 56, 449–456 (2008).
[Crossref]

2007 (2)

E. N. Ivanov, J. J. McFerran, S. A. Diddams, and L. Hollberg, “Noise properties of microwave signals synthesized with femtosecond lasers,” IEEE Trans. Ultrason., Ferroelect., Freq. Contr. 54, 736–745 (2007).
[Crossref]

J. Capmany and D. Novak, “Microwave photonics combines two worlds,” Nat. Photonics 1, 319–330 (2007).
[Crossref]

2006 (1)

M. Currie and I. Vurgaftman, “Microwave phase retardation in saturated ingaas photodetectors,” IEEE Photon. Technol. Lett. 18, 1433–1435 (2006).
[Crossref]

2005 (1)

E. N. Ivanov, S. A. Diddams, and L. Hollberg, “Study of the excess noise associated with demodulation of ultra-short infrared pulses,” IEEE Trans. Ultrason., Ferroelect., Freq. Contr. 52, 1068–1074 (2005).
[Crossref]

1999 (1)

P.-L. Liu, K. J. Williams, M. Y. Frankel, and R. D. Esman, “Saturation characteristics of fast photodetectors,” IEEE Trans. Microw. Theory Techn. 47, 1297–1303 (1999).
[Crossref]

1998 (1)

C.-K. Sun, I.-H. Tan, and J. E. Bowers, “Ultrafast transport dynamics of pin photodetectors under high-power illumination,” IEEE Photon. Technol. Lett. 10, 135–137 (1998).
[Crossref]

1992 (1)

D. Kuhl, F. Hieronymi, E. H. Bottcher, T. Wolf, D. Bimberg, J. Kuhl, and M. Klingenstein, “Influence of space charges on the impulse response of ingaas metal-semiconductor-metal photodetectors,” J. Lightwave Technol. 10, 753–759 (1992).
[Crossref]

Abdallah, Z.

Z. Abdallah, A. Rumeau, A. Fernandez, G. Cibiel, and O. Llopis, “Nonlinear equivalent-circuit modeling of a fast photodiode,” IEEE Photon. Technol. Lett. 26, 1041–1135 (2014).
[Crossref]

Abgrall, M.

C. Lisdat, G. Grosche, N. Quintin, C. Shi, S. Raupach, C. Grebing, D. Nicolodi, F. Stefani, A. Al-Masoudi, S. Dörscher, S. Häfner, J.-L. Robyr, N. Chiodo, S. Bilicki, E. Bookjans, A. Koczwara, S. Koke, A. Kohl, F. Wiotte, F. Meynadier, E. Camisard, M. Abgrall, M. Lours, T. Legero, H. Schnatz, U. Sterr, H. Denker, C. Chardonnet, Y. Le Coq, G. Santarelli, A. Amy-Klein, R. Le Targat, J. Lodewyck, O. Lopez, and P.-E. Pottie, “A clock network for geodesy and fundamental science,” Nat. Commun. 7, 12443 (2016).
[Crossref] [PubMed]

Adams, C.

C. Wade, N. Šibalić, N. de Melo, J. Kondo, C. Adams, and K. Weatherill, “Real-time near-field terahertz imaging with atomic optical fluorescence,” Nat. Photonics 11, 40–43 (2017).
[Crossref]

Aditya, S.

Alexandre, C.

Al-Masoudi, A.

C. Lisdat, G. Grosche, N. Quintin, C. Shi, S. Raupach, C. Grebing, D. Nicolodi, F. Stefani, A. Al-Masoudi, S. Dörscher, S. Häfner, J.-L. Robyr, N. Chiodo, S. Bilicki, E. Bookjans, A. Koczwara, S. Koke, A. Kohl, F. Wiotte, F. Meynadier, E. Camisard, M. Abgrall, M. Lours, T. Legero, H. Schnatz, U. Sterr, H. Denker, C. Chardonnet, Y. Le Coq, G. Santarelli, A. Amy-Klein, R. Le Targat, J. Lodewyck, O. Lopez, and P.-E. Pottie, “A clock network for geodesy and fundamental science,” Nat. Commun. 7, 12443 (2016).
[Crossref] [PubMed]

Amy-Klein, A.

C. Lisdat, G. Grosche, N. Quintin, C. Shi, S. Raupach, C. Grebing, D. Nicolodi, F. Stefani, A. Al-Masoudi, S. Dörscher, S. Häfner, J.-L. Robyr, N. Chiodo, S. Bilicki, E. Bookjans, A. Koczwara, S. Koke, A. Kohl, F. Wiotte, F. Meynadier, E. Camisard, M. Abgrall, M. Lours, T. Legero, H. Schnatz, U. Sterr, H. Denker, C. Chardonnet, Y. Le Coq, G. Santarelli, A. Amy-Klein, R. Le Targat, J. Lodewyck, O. Lopez, and P.-E. Pottie, “A clock network for geodesy and fundamental science,” Nat. Commun. 7, 12443 (2016).
[Crossref] [PubMed]

Baynes, F. N.

Beling, A.

Berizzi, F.

P. Ghelfi, F. Laghezza, F. Scotti, G. Serafino, A. Capria, S. Pinna, D. Onori, C. Porzi, M. Scaffardi, A. Malacarne, V. Vercesi, E. Lazzeri, F. Berizzi, and A. Bogoni, “A fully photonics-based coherent radar system,” Nature 507, 341–345 (2014).
[Crossref] [PubMed]

Bilicki, S.

C. Lisdat, G. Grosche, N. Quintin, C. Shi, S. Raupach, C. Grebing, D. Nicolodi, F. Stefani, A. Al-Masoudi, S. Dörscher, S. Häfner, J.-L. Robyr, N. Chiodo, S. Bilicki, E. Bookjans, A. Koczwara, S. Koke, A. Kohl, F. Wiotte, F. Meynadier, E. Camisard, M. Abgrall, M. Lours, T. Legero, H. Schnatz, U. Sterr, H. Denker, C. Chardonnet, Y. Le Coq, G. Santarelli, A. Amy-Klein, R. Le Targat, J. Lodewyck, O. Lopez, and P.-E. Pottie, “A clock network for geodesy and fundamental science,” Nat. Commun. 7, 12443 (2016).
[Crossref] [PubMed]

Bimberg, D.

D. Kuhl, F. Hieronymi, E. H. Bottcher, T. Wolf, D. Bimberg, J. Kuhl, and M. Klingenstein, “Influence of space charges on the impulse response of ingaas metal-semiconductor-metal photodetectors,” J. Lightwave Technol. 10, 753–759 (1992).
[Crossref]

Bogoni, A.

P. Ghelfi, F. Laghezza, F. Scotti, G. Serafino, A. Capria, S. Pinna, D. Onori, C. Porzi, M. Scaffardi, A. Malacarne, V. Vercesi, E. Lazzeri, F. Berizzi, and A. Bogoni, “A fully photonics-based coherent radar system,” Nature 507, 341–345 (2014).
[Crossref] [PubMed]

Bookjans, E.

C. Lisdat, G. Grosche, N. Quintin, C. Shi, S. Raupach, C. Grebing, D. Nicolodi, F. Stefani, A. Al-Masoudi, S. Dörscher, S. Häfner, J.-L. Robyr, N. Chiodo, S. Bilicki, E. Bookjans, A. Koczwara, S. Koke, A. Kohl, F. Wiotte, F. Meynadier, E. Camisard, M. Abgrall, M. Lours, T. Legero, H. Schnatz, U. Sterr, H. Denker, C. Chardonnet, Y. Le Coq, G. Santarelli, A. Amy-Klein, R. Le Targat, J. Lodewyck, O. Lopez, and P.-E. Pottie, “A clock network for geodesy and fundamental science,” Nat. Commun. 7, 12443 (2016).
[Crossref] [PubMed]

Bottcher, E. H.

D. Kuhl, F. Hieronymi, E. H. Bottcher, T. Wolf, D. Bimberg, J. Kuhl, and M. Klingenstein, “Influence of space charges on the impulse response of ingaas metal-semiconductor-metal photodetectors,” J. Lightwave Technol. 10, 753–759 (1992).
[Crossref]

Bouchand, R.

X. Xie, R. Bouchand, D. Nicolodi, M. Giunta, W. Hänsel, M. Lezius, A. Joshi, S. Datta, C. Alexandre, M. Lours, P.-A. Tremblin, G. Santarelli, R. Holzwarth, and Y. Le Coq, “Photonic microwave signals with zeptosecond-level absolute timing noise,” Nat. Photonics 11, 44–47 (2017).
[Crossref]

X. Xie, R. Bouchand, D. Nicolodi, M. Lours, C. Alexandre, and Y. Le Coq, “Phase noise characterization of sub-hertz linewidth lasers via digital cross correlation,” Opt. Lett. 42, 1217–1220 (2017).
[Crossref] [PubMed]

Boudot, R.

W. Zhang, Z. Xu, M. Lours, R. Boudot, Y. Kersalé, G. Santarelli, and Y. Le Coq, “Sub-100 attoseconds stability optics to microwave synchronization,” Appl. Phys. Lett. 96, 211105 (2010).
[Crossref]

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

Bourgeois, P.

Bowers, J. E.

C.-K. Sun, I.-H. Tan, and J. E. Bowers, “Ultrafast transport dynamics of pin photodetectors under high-power illumination,” IEEE Photon. Technol. Lett. 10, 135–137 (1998).
[Crossref]

Brown, C. T. A.

Callahan, P.

K. Şafak, M. Xin, P. Callahan, M. Peng, and F. Kärtner, “All fiber-coupled, long-term stable timing distribution for free-electron lasers with few-femtosecond jitter,” Struct. Dyn. 2, 041715 (2015).
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M. Xin, K. Şafak, M. Y. Peng, A. Kalaydzhyan, P. T. Callahan, W. Wang, O. D. Mücke, and F. X. Kärtner, “Breaking the femtosecond barrier in multi-kilometer timing synchronization systems,” IEEE J. Select. Topics Quantum Electron. 23, 1–12 (2017).
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C. Lisdat, G. Grosche, N. Quintin, C. Shi, S. Raupach, C. Grebing, D. Nicolodi, F. Stefani, A. Al-Masoudi, S. Dörscher, S. Häfner, J.-L. Robyr, N. Chiodo, S. Bilicki, E. Bookjans, A. Koczwara, S. Koke, A. Kohl, F. Wiotte, F. Meynadier, E. Camisard, M. Abgrall, M. Lours, T. Legero, H. Schnatz, U. Sterr, H. Denker, C. Chardonnet, Y. Le Coq, G. Santarelli, A. Amy-Klein, R. Le Targat, J. Lodewyck, O. Lopez, and P.-E. Pottie, “A clock network for geodesy and fundamental science,” Nat. Commun. 7, 12443 (2016).
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P. Ghelfi, F. Laghezza, F. Scotti, G. Serafino, A. Capria, S. Pinna, D. Onori, C. Porzi, M. Scaffardi, A. Malacarne, V. Vercesi, E. Lazzeri, F. Berizzi, and A. Bogoni, “A fully photonics-based coherent radar system,” Nature 507, 341–345 (2014).
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C. Lisdat, G. Grosche, N. Quintin, C. Shi, S. Raupach, C. Grebing, D. Nicolodi, F. Stefani, A. Al-Masoudi, S. Dörscher, S. Häfner, J.-L. Robyr, N. Chiodo, S. Bilicki, E. Bookjans, A. Koczwara, S. Koke, A. Kohl, F. Wiotte, F. Meynadier, E. Camisard, M. Abgrall, M. Lours, T. Legero, H. Schnatz, U. Sterr, H. Denker, C. Chardonnet, Y. Le Coq, G. Santarelli, A. Amy-Klein, R. Le Targat, J. Lodewyck, O. Lopez, and P.-E. Pottie, “A clock network for geodesy and fundamental science,” Nat. Commun. 7, 12443 (2016).
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C. Lisdat, G. Grosche, N. Quintin, C. Shi, S. Raupach, C. Grebing, D. Nicolodi, F. Stefani, A. Al-Masoudi, S. Dörscher, S. Häfner, J.-L. Robyr, N. Chiodo, S. Bilicki, E. Bookjans, A. Koczwara, S. Koke, A. Kohl, F. Wiotte, F. Meynadier, E. Camisard, M. Abgrall, M. Lours, T. Legero, H. Schnatz, U. Sterr, H. Denker, C. Chardonnet, Y. Le Coq, G. Santarelli, A. Amy-Klein, R. Le Targat, J. Lodewyck, O. Lopez, and P.-E. Pottie, “A clock network for geodesy and fundamental science,” Nat. Commun. 7, 12443 (2016).
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W. Zhang, M. Lours, M. Fischer, R. Holzwarth, G. Santarelli, and Y. L. Coq, “Characterizing a fiber-based frequency comb with electro-optic modulator,” IEEE Trans. Ultrason., Ferroelect., Freq. Contr. 59, 432–438 (2012).
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W. Zhang, S. Seidelin, A. Joshi, S. Datta, G. Santarelli, and Y. Le Coq, “Dual photo-detector system for low phase noise microwave generation with femtosecond lasers,” Opt. Lett. 39, 1204–1207 (2014).
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C. Wade, N. Šibalić, N. de Melo, J. Kondo, C. Adams, and K. Weatherill, “Real-time near-field terahertz imaging with atomic optical fluorescence,” Nat. Photonics 11, 40–43 (2017).
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E. N. Ivanov, S. A. Diddams, and L. Hollberg, “Study of the excess noise associated with demodulation of ultra-short infrared pulses,” IEEE Trans. Ultrason., Ferroelect., Freq. Contr. 52, 1068–1074 (2005).
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C. Lisdat, G. Grosche, N. Quintin, C. Shi, S. Raupach, C. Grebing, D. Nicolodi, F. Stefani, A. Al-Masoudi, S. Dörscher, S. Häfner, J.-L. Robyr, N. Chiodo, S. Bilicki, E. Bookjans, A. Koczwara, S. Koke, A. Kohl, F. Wiotte, F. Meynadier, E. Camisard, M. Abgrall, M. Lours, T. Legero, H. Schnatz, U. Sterr, H. Denker, C. Chardonnet, Y. Le Coq, G. Santarelli, A. Amy-Klein, R. Le Targat, J. Lodewyck, O. Lopez, and P.-E. Pottie, “A clock network for geodesy and fundamental science,” Nat. Commun. 7, 12443 (2016).
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Z. Abdallah, A. Rumeau, A. Fernandez, G. Cibiel, and O. Llopis, “Nonlinear equivalent-circuit modeling of a fast photodiode,” IEEE Photon. Technol. Lett. 26, 1041–1135 (2014).
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Fischer, M.

W. Zhang, M. Lours, M. Fischer, R. Holzwarth, G. Santarelli, and Y. L. Coq, “Characterizing a fiber-based frequency comb with electro-optic modulator,” IEEE Trans. Ultrason., Ferroelect., Freq. Contr. 59, 432–438 (2012).
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Fortier, T. M.

Frankel, M. Y.

P.-L. Liu, K. J. Williams, M. Y. Frankel, and R. D. Esman, “Saturation characteristics of fast photodetectors,” IEEE Trans. Microw. Theory Techn. 47, 1297–1303 (1999).
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Ghelfi, P.

P. Ghelfi, F. Laghezza, F. Scotti, G. Serafino, A. Capria, S. Pinna, D. Onori, C. Porzi, M. Scaffardi, A. Malacarne, V. Vercesi, E. Lazzeri, F. Berizzi, and A. Bogoni, “A fully photonics-based coherent radar system,” Nature 507, 341–345 (2014).
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Gill, P.

Giunta, M.

X. Xie, R. Bouchand, D. Nicolodi, M. Giunta, W. Hänsel, M. Lezius, A. Joshi, S. Datta, C. Alexandre, M. Lours, P.-A. Tremblin, G. Santarelli, R. Holzwarth, and Y. Le Coq, “Photonic microwave signals with zeptosecond-level absolute timing noise,” Nat. Photonics 11, 44–47 (2017).
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C. Lisdat, G. Grosche, N. Quintin, C. Shi, S. Raupach, C. Grebing, D. Nicolodi, F. Stefani, A. Al-Masoudi, S. Dörscher, S. Häfner, J.-L. Robyr, N. Chiodo, S. Bilicki, E. Bookjans, A. Koczwara, S. Koke, A. Kohl, F. Wiotte, F. Meynadier, E. Camisard, M. Abgrall, M. Lours, T. Legero, H. Schnatz, U. Sterr, H. Denker, C. Chardonnet, Y. Le Coq, G. Santarelli, A. Amy-Klein, R. Le Targat, J. Lodewyck, O. Lopez, and P.-E. Pottie, “A clock network for geodesy and fundamental science,” Nat. Commun. 7, 12443 (2016).
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C. Lisdat, G. Grosche, N. Quintin, C. Shi, S. Raupach, C. Grebing, D. Nicolodi, F. Stefani, A. Al-Masoudi, S. Dörscher, S. Häfner, J.-L. Robyr, N. Chiodo, S. Bilicki, E. Bookjans, A. Koczwara, S. Koke, A. Kohl, F. Wiotte, F. Meynadier, E. Camisard, M. Abgrall, M. Lours, T. Legero, H. Schnatz, U. Sterr, H. Denker, C. Chardonnet, Y. Le Coq, G. Santarelli, A. Amy-Klein, R. Le Targat, J. Lodewyck, O. Lopez, and P.-E. Pottie, “A clock network for geodesy and fundamental science,” Nat. Commun. 7, 12443 (2016).
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Haboucha, A.

Häfner, S.

C. Lisdat, G. Grosche, N. Quintin, C. Shi, S. Raupach, C. Grebing, D. Nicolodi, F. Stefani, A. Al-Masoudi, S. Dörscher, S. Häfner, J.-L. Robyr, N. Chiodo, S. Bilicki, E. Bookjans, A. Koczwara, S. Koke, A. Kohl, F. Wiotte, F. Meynadier, E. Camisard, M. Abgrall, M. Lours, T. Legero, H. Schnatz, U. Sterr, H. Denker, C. Chardonnet, Y. Le Coq, G. Santarelli, A. Amy-Klein, R. Le Targat, J. Lodewyck, O. Lopez, and P.-E. Pottie, “A clock network for geodesy and fundamental science,” Nat. Commun. 7, 12443 (2016).
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X. Xie, R. Bouchand, D. Nicolodi, M. Giunta, W. Hänsel, M. Lezius, A. Joshi, S. Datta, C. Alexandre, M. Lours, P.-A. Tremblin, G. Santarelli, R. Holzwarth, and Y. Le Coq, “Photonic microwave signals with zeptosecond-level absolute timing noise,” Nat. Photonics 11, 44–47 (2017).
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Hati, A.

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

J. Taylor, S. Datta, A. Hati, C. Nelson, F. Quinlan, A. Joshi, and S. Diddams, “Characterization of power-to-phase conversion in high-speed p-i-n photodiodes,” IEEE Photon. J. 3, 140–151 (2011).
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Hieronymi, F.

D. Kuhl, F. Hieronymi, E. H. Bottcher, T. Wolf, D. Bimberg, J. Kuhl, and M. Klingenstein, “Influence of space charges on the impulse response of ingaas metal-semiconductor-metal photodetectors,” J. Lightwave Technol. 10, 753–759 (1992).
[Crossref]

Hollberg, L.

E. N. Ivanov, J. J. McFerran, S. A. Diddams, and L. Hollberg, “Noise properties of microwave signals synthesized with femtosecond lasers,” IEEE Trans. Ultrason., Ferroelect., Freq. Contr. 54, 736–745 (2007).
[Crossref]

E. N. Ivanov, S. A. Diddams, and L. Hollberg, “Study of the excess noise associated with demodulation of ultra-short infrared pulses,” IEEE Trans. Ultrason., Ferroelect., Freq. Contr. 52, 1068–1074 (2005).
[Crossref]

Holzwarth, R.

X. Xie, R. Bouchand, D. Nicolodi, M. Giunta, W. Hänsel, M. Lezius, A. Joshi, S. Datta, C. Alexandre, M. Lours, P.-A. Tremblin, G. Santarelli, R. Holzwarth, and Y. Le Coq, “Photonic microwave signals with zeptosecond-level absolute timing noise,” Nat. Photonics 11, 44–47 (2017).
[Crossref]

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

Ivanov, E. N.

E. N. Ivanov, J. J. McFerran, S. A. Diddams, and L. Hollberg, “Noise properties of microwave signals synthesized with femtosecond lasers,” IEEE Trans. Ultrason., Ferroelect., Freq. Contr. 54, 736–745 (2007).
[Crossref]

E. N. Ivanov, S. A. Diddams, and L. Hollberg, “Study of the excess noise associated with demodulation of ultra-short infrared pulses,” IEEE Trans. Ultrason., Ferroelect., Freq. Contr. 52, 1068–1074 (2005).
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X. Xie, R. Bouchand, D. Nicolodi, M. Giunta, W. Hänsel, M. Lezius, A. Joshi, S. Datta, C. Alexandre, M. Lours, P.-A. Tremblin, G. Santarelli, R. Holzwarth, and Y. Le Coq, “Photonic microwave signals with zeptosecond-level absolute timing noise,” Nat. Photonics 11, 44–47 (2017).
[Crossref]

W. Zhang, S. Seidelin, A. Joshi, S. Datta, G. Santarelli, and Y. Le Coq, “Dual photo-detector system for low phase noise microwave generation with femtosecond lasers,” Opt. Lett. 39, 1204–1207 (2014).
[Crossref] [PubMed]

J. Taylor, S. Datta, A. Hati, C. Nelson, F. Quinlan, A. Joshi, and S. Diddams, “Characterization of power-to-phase conversion in high-speed p-i-n photodiodes,” IEEE Photon. J. 3, 140–151 (2011).
[Crossref]

Jung, K.

Kalaydzhyan, A.

M. Xin, K. Şafak, M. Y. Peng, A. Kalaydzhyan, P. T. Callahan, W. Wang, O. D. Mücke, and F. X. Kärtner, “Breaking the femtosecond barrier in multi-kilometer timing synchronization systems,” IEEE J. Select. Topics Quantum Electron. 23, 1–12 (2017).
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A. Kalaydzhyan, M. Peng, and F. Kartner, “Ultrahigh precision synchronization of optical and microwave frequency sources,” J. Phys: Conf. Ser. 741, 012084 (2016).

M. Y. Peng, A. Kalaydzhyan, and F. X. Kärtner, “Balanced optical-microwave phase detector for sub-femtosecond optical-rf synchronization,” Opt. Express 22, 27102–27111 (2014).
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Kartner, F.

A. Kalaydzhyan, M. Peng, and F. Kartner, “Ultrahigh precision synchronization of optical and microwave frequency sources,” J. Phys: Conf. Ser. 741, 012084 (2016).

Kärtner, F.

K. Şafak, M. Xin, P. Callahan, M. Peng, and F. Kärtner, “All fiber-coupled, long-term stable timing distribution for free-electron lasers with few-femtosecond jitter,” Struct. Dyn. 2, 041715 (2015).
[Crossref]

Kärtner, F. X.

M. Xin, K. Şafak, M. Y. Peng, A. Kalaydzhyan, P. T. Callahan, W. Wang, O. D. Mücke, and F. X. Kärtner, “Breaking the femtosecond barrier in multi-kilometer timing synchronization systems,” IEEE J. Select. Topics Quantum Electron. 23, 1–12 (2017).
[Crossref]

M. Y. Peng, A. Kalaydzhyan, and F. X. Kärtner, “Balanced optical-microwave phase detector for sub-femtosecond optical-rf synchronization,” Opt. Express 22, 27102–27111 (2014).
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Kersalé, Y.

W. Zhang, Z. Xu, M. Lours, R. Boudot, Y. Kersalé, G. Santarelli, and Y. Le Coq, “Sub-100 attoseconds stability optics to microwave synchronization,” Appl. Phys. Lett. 96, 211105 (2010).
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J. Millo, R. Boudot, M. Lours, P. Bourgeois, A. Luiten, Y. L. Coq, Y. Kersalé, and G. Santarelli, “Ultra-low-noise microwave extraction from fiber-based optical frequency comb,” Opt. Lett. 34, 3707–3709 (2009).
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J. Kim and Y. Song, “Ultralow-noise mode-locked fiber lasers and frequency combs: principles, status, and applications,” Adv. Opt. Photonics 8, 465–540 (2016).
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K. Jung and J. Kim, “Subfemtosecond synchronization of microwave oscillators with mode-locked er-fiber lasers,” Opt. Lett. 37, 2958–2960 (2012).
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D. Kuhl, F. Hieronymi, E. H. Bottcher, T. Wolf, D. Bimberg, J. Kuhl, and M. Klingenstein, “Influence of space charges on the impulse response of ingaas metal-semiconductor-metal photodetectors,” J. Lightwave Technol. 10, 753–759 (1992).
[Crossref]

Koczwara, A.

C. Lisdat, G. Grosche, N. Quintin, C. Shi, S. Raupach, C. Grebing, D. Nicolodi, F. Stefani, A. Al-Masoudi, S. Dörscher, S. Häfner, J.-L. Robyr, N. Chiodo, S. Bilicki, E. Bookjans, A. Koczwara, S. Koke, A. Kohl, F. Wiotte, F. Meynadier, E. Camisard, M. Abgrall, M. Lours, T. Legero, H. Schnatz, U. Sterr, H. Denker, C. Chardonnet, Y. Le Coq, G. Santarelli, A. Amy-Klein, R. Le Targat, J. Lodewyck, O. Lopez, and P.-E. Pottie, “A clock network for geodesy and fundamental science,” Nat. Commun. 7, 12443 (2016).
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Kohl, A.

C. Lisdat, G. Grosche, N. Quintin, C. Shi, S. Raupach, C. Grebing, D. Nicolodi, F. Stefani, A. Al-Masoudi, S. Dörscher, S. Häfner, J.-L. Robyr, N. Chiodo, S. Bilicki, E. Bookjans, A. Koczwara, S. Koke, A. Kohl, F. Wiotte, F. Meynadier, E. Camisard, M. Abgrall, M. Lours, T. Legero, H. Schnatz, U. Sterr, H. Denker, C. Chardonnet, Y. Le Coq, G. Santarelli, A. Amy-Klein, R. Le Targat, J. Lodewyck, O. Lopez, and P.-E. Pottie, “A clock network for geodesy and fundamental science,” Nat. Commun. 7, 12443 (2016).
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C. Lisdat, G. Grosche, N. Quintin, C. Shi, S. Raupach, C. Grebing, D. Nicolodi, F. Stefani, A. Al-Masoudi, S. Dörscher, S. Häfner, J.-L. Robyr, N. Chiodo, S. Bilicki, E. Bookjans, A. Koczwara, S. Koke, A. Kohl, F. Wiotte, F. Meynadier, E. Camisard, M. Abgrall, M. Lours, T. Legero, H. Schnatz, U. Sterr, H. Denker, C. Chardonnet, Y. Le Coq, G. Santarelli, A. Amy-Klein, R. Le Targat, J. Lodewyck, O. Lopez, and P.-E. Pottie, “A clock network for geodesy and fundamental science,” Nat. Commun. 7, 12443 (2016).
[Crossref] [PubMed]

Kondo, J.

C. Wade, N. Šibalić, N. de Melo, J. Kondo, C. Adams, and K. Weatherill, “Real-time near-field terahertz imaging with atomic optical fluorescence,” Nat. Photonics 11, 40–43 (2017).
[Crossref]

Kuhl, D.

D. Kuhl, F. Hieronymi, E. H. Bottcher, T. Wolf, D. Bimberg, J. Kuhl, and M. Klingenstein, “Influence of space charges on the impulse response of ingaas metal-semiconductor-metal photodetectors,” J. Lightwave Technol. 10, 753–759 (1992).
[Crossref]

Kuhl, J.

D. Kuhl, F. Hieronymi, E. H. Bottcher, T. Wolf, D. Bimberg, J. Kuhl, and M. Klingenstein, “Influence of space charges on the impulse response of ingaas metal-semiconductor-metal photodetectors,” J. Lightwave Technol. 10, 753–759 (1992).
[Crossref]

Laghezza, F.

P. Ghelfi, F. Laghezza, F. Scotti, G. Serafino, A. Capria, S. Pinna, D. Onori, C. Porzi, M. Scaffardi, A. Malacarne, V. Vercesi, E. Lazzeri, F. Berizzi, and A. Bogoni, “A fully photonics-based coherent radar system,” Nature 507, 341–345 (2014).
[Crossref] [PubMed]

Lam, H. Q.

Lazzeri, E.

P. Ghelfi, F. Laghezza, F. Scotti, G. Serafino, A. Capria, S. Pinna, D. Onori, C. Porzi, M. Scaffardi, A. Malacarne, V. Vercesi, E. Lazzeri, F. Berizzi, and A. Bogoni, “A fully photonics-based coherent radar system,” Nature 507, 341–345 (2014).
[Crossref] [PubMed]

Le Coq, Y.

X. Xie, R. Bouchand, D. Nicolodi, M. Giunta, W. Hänsel, M. Lezius, A. Joshi, S. Datta, C. Alexandre, M. Lours, P.-A. Tremblin, G. Santarelli, R. Holzwarth, and Y. Le Coq, “Photonic microwave signals with zeptosecond-level absolute timing noise,” Nat. Photonics 11, 44–47 (2017).
[Crossref]

X. Xie, R. Bouchand, D. Nicolodi, M. Lours, C. Alexandre, and Y. Le Coq, “Phase noise characterization of sub-hertz linewidth lasers via digital cross correlation,” Opt. Lett. 42, 1217–1220 (2017).
[Crossref] [PubMed]

C. Lisdat, G. Grosche, N. Quintin, C. Shi, S. Raupach, C. Grebing, D. Nicolodi, F. Stefani, A. Al-Masoudi, S. Dörscher, S. Häfner, J.-L. Robyr, N. Chiodo, S. Bilicki, E. Bookjans, A. Koczwara, S. Koke, A. Kohl, F. Wiotte, F. Meynadier, E. Camisard, M. Abgrall, M. Lours, T. Legero, H. Schnatz, U. Sterr, H. Denker, C. Chardonnet, Y. Le Coq, G. Santarelli, A. Amy-Klein, R. Le Targat, J. Lodewyck, O. Lopez, and P.-E. Pottie, “A clock network for geodesy and fundamental science,” Nat. Commun. 7, 12443 (2016).
[Crossref] [PubMed]

W. Zhang, S. Seidelin, A. Joshi, S. Datta, G. Santarelli, and Y. Le Coq, “Dual photo-detector system for low phase noise microwave generation with femtosecond lasers,” Opt. Lett. 39, 1204–1207 (2014).
[Crossref] [PubMed]

W. Zhang, T. Li, M. Lours, S. Seidelin, G. Santarelli, and Y. Le Coq, “Amplitude to phase conversion of ingaas pin photo-diodes for femtosecond lasers microwave signal generation,” Appl. Phys. B 106, 301–308 (2012).
[Crossref]

A. Haboucha, W. Zhang, T. Li, M. Lours, A. Luiten, Y. Le Coq, and G. Santarelli, “Optical-fiber pulse rate multiplier for ultra-low phase-noise signal generation,” Opt. Lett. 36, 3654 (2011).
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W. Zhang, Z. Xu, M. Lours, R. Boudot, Y. Kersalé, G. Santarelli, and Y. Le Coq, “Sub-100 attoseconds stability optics to microwave synchronization,” Appl. Phys. Lett. 96, 211105 (2010).
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Le Targat, R.

C. Lisdat, G. Grosche, N. Quintin, C. Shi, S. Raupach, C. Grebing, D. Nicolodi, F. Stefani, A. Al-Masoudi, S. Dörscher, S. Häfner, J.-L. Robyr, N. Chiodo, S. Bilicki, E. Bookjans, A. Koczwara, S. Koke, A. Kohl, F. Wiotte, F. Meynadier, E. Camisard, M. Abgrall, M. Lours, T. Legero, H. Schnatz, U. Sterr, H. Denker, C. Chardonnet, Y. Le Coq, G. Santarelli, A. Amy-Klein, R. Le Targat, J. Lodewyck, O. Lopez, and P.-E. Pottie, “A clock network for geodesy and fundamental science,” Nat. Commun. 7, 12443 (2016).
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Legero, T.

C. Lisdat, G. Grosche, N. Quintin, C. Shi, S. Raupach, C. Grebing, D. Nicolodi, F. Stefani, A. Al-Masoudi, S. Dörscher, S. Häfner, J.-L. Robyr, N. Chiodo, S. Bilicki, E. Bookjans, A. Koczwara, S. Koke, A. Kohl, F. Wiotte, F. Meynadier, E. Camisard, M. Abgrall, M. Lours, T. Legero, H. Schnatz, U. Sterr, H. Denker, C. Chardonnet, Y. Le Coq, G. Santarelli, A. Amy-Klein, R. Le Targat, J. Lodewyck, O. Lopez, and P.-E. Pottie, “A clock network for geodesy and fundamental science,” Nat. Commun. 7, 12443 (2016).
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Lezius, M.

X. Xie, R. Bouchand, D. Nicolodi, M. Giunta, W. Hänsel, M. Lezius, A. Joshi, S. Datta, C. Alexandre, M. Lours, P.-A. Tremblin, G. Santarelli, R. Holzwarth, and Y. Le Coq, “Photonic microwave signals with zeptosecond-level absolute timing noise,” Nat. Photonics 11, 44–47 (2017).
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Li, T.

W. Zhang, T. Li, M. Lours, S. Seidelin, G. Santarelli, and Y. Le Coq, “Amplitude to phase conversion of ingaas pin photo-diodes for femtosecond lasers microwave signal generation,” Appl. Phys. B 106, 301–308 (2012).
[Crossref]

A. Haboucha, W. Zhang, T. Li, M. Lours, A. Luiten, Y. Le Coq, and G. Santarelli, “Optical-fiber pulse rate multiplier for ultra-low phase-noise signal generation,” Opt. Lett. 36, 3654 (2011).
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Lintz, M.

D.-H. Phung, M. Merzougui, C. Alexandre, and M. Lintz, “Phase measurement of a microwave optical modulation: Characterisation and reduction of amplitude-to-phase conversion in 1.5 μm high bandwidth photodiodes,” J. Lightwave Technol. 32, 3759–3767 (2014).
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D.-H. Phung and M. Lintz, “Comments on “frequency response of the noise conversion from relative intensity noise to phase noise in the photodetection of an optical pulse train”,” IEEE Photon. Technol. Lett. 26, 1994–1995 (2014).
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Lisdat, C.

C. Lisdat, G. Grosche, N. Quintin, C. Shi, S. Raupach, C. Grebing, D. Nicolodi, F. Stefani, A. Al-Masoudi, S. Dörscher, S. Häfner, J.-L. Robyr, N. Chiodo, S. Bilicki, E. Bookjans, A. Koczwara, S. Koke, A. Kohl, F. Wiotte, F. Meynadier, E. Camisard, M. Abgrall, M. Lours, T. Legero, H. Schnatz, U. Sterr, H. Denker, C. Chardonnet, Y. Le Coq, G. Santarelli, A. Amy-Klein, R. Le Targat, J. Lodewyck, O. Lopez, and P.-E. Pottie, “A clock network for geodesy and fundamental science,” Nat. Commun. 7, 12443 (2016).
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P.-L. Liu, K. J. Williams, M. Y. Frankel, and R. D. Esman, “Saturation characteristics of fast photodetectors,” IEEE Trans. Microw. Theory Techn. 47, 1297–1303 (1999).
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Z. Abdallah, A. Rumeau, A. Fernandez, G. Cibiel, and O. Llopis, “Nonlinear equivalent-circuit modeling of a fast photodiode,” IEEE Photon. Technol. Lett. 26, 1041–1135 (2014).
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Lodewyck, J.

C. Lisdat, G. Grosche, N. Quintin, C. Shi, S. Raupach, C. Grebing, D. Nicolodi, F. Stefani, A. Al-Masoudi, S. Dörscher, S. Häfner, J.-L. Robyr, N. Chiodo, S. Bilicki, E. Bookjans, A. Koczwara, S. Koke, A. Kohl, F. Wiotte, F. Meynadier, E. Camisard, M. Abgrall, M. Lours, T. Legero, H. Schnatz, U. Sterr, H. Denker, C. Chardonnet, Y. Le Coq, G. Santarelli, A. Amy-Klein, R. Le Targat, J. Lodewyck, O. Lopez, and P.-E. Pottie, “A clock network for geodesy and fundamental science,” Nat. Commun. 7, 12443 (2016).
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Lopez, O.

C. Lisdat, G. Grosche, N. Quintin, C. Shi, S. Raupach, C. Grebing, D. Nicolodi, F. Stefani, A. Al-Masoudi, S. Dörscher, S. Häfner, J.-L. Robyr, N. Chiodo, S. Bilicki, E. Bookjans, A. Koczwara, S. Koke, A. Kohl, F. Wiotte, F. Meynadier, E. Camisard, M. Abgrall, M. Lours, T. Legero, H. Schnatz, U. Sterr, H. Denker, C. Chardonnet, Y. Le Coq, G. Santarelli, A. Amy-Klein, R. Le Targat, J. Lodewyck, O. Lopez, and P.-E. Pottie, “A clock network for geodesy and fundamental science,” Nat. Commun. 7, 12443 (2016).
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Lours, M.

X. Xie, R. Bouchand, D. Nicolodi, M. Giunta, W. Hänsel, M. Lezius, A. Joshi, S. Datta, C. Alexandre, M. Lours, P.-A. Tremblin, G. Santarelli, R. Holzwarth, and Y. Le Coq, “Photonic microwave signals with zeptosecond-level absolute timing noise,” Nat. Photonics 11, 44–47 (2017).
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X. Xie, R. Bouchand, D. Nicolodi, M. Lours, C. Alexandre, and Y. Le Coq, “Phase noise characterization of sub-hertz linewidth lasers via digital cross correlation,” Opt. Lett. 42, 1217–1220 (2017).
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C. Lisdat, G. Grosche, N. Quintin, C. Shi, S. Raupach, C. Grebing, D. Nicolodi, F. Stefani, A. Al-Masoudi, S. Dörscher, S. Häfner, J.-L. Robyr, N. Chiodo, S. Bilicki, E. Bookjans, A. Koczwara, S. Koke, A. Kohl, F. Wiotte, F. Meynadier, E. Camisard, M. Abgrall, M. Lours, T. Legero, H. Schnatz, U. Sterr, H. Denker, C. Chardonnet, Y. Le Coq, G. Santarelli, A. Amy-Klein, R. Le Targat, J. Lodewyck, O. Lopez, and P.-E. Pottie, “A clock network for geodesy and fundamental science,” Nat. Commun. 7, 12443 (2016).
[Crossref] [PubMed]

W. Zhang, T. Li, M. Lours, S. Seidelin, G. Santarelli, and Y. Le Coq, “Amplitude to phase conversion of ingaas pin photo-diodes for femtosecond lasers microwave signal generation,” Appl. Phys. B 106, 301–308 (2012).
[Crossref]

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

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

W. Zhang, Z. Xu, M. Lours, R. Boudot, Y. Kersalé, G. Santarelli, and Y. Le Coq, “Sub-100 attoseconds stability optics to microwave synchronization,” Appl. Phys. Lett. 96, 211105 (2010).
[Crossref]

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

Malacarne, A.

P. Ghelfi, F. Laghezza, F. Scotti, G. Serafino, A. Capria, S. Pinna, D. Onori, C. Porzi, M. Scaffardi, A. Malacarne, V. Vercesi, E. Lazzeri, F. Berizzi, and A. Bogoni, “A fully photonics-based coherent radar system,” Nature 507, 341–345 (2014).
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Maleki, L.

D. Eliyahu, D. Seidel, and L. Maleki, “Rf amplitude and phase-noise reduction of an optical link and an opto-electronic oscillator,” IEEE Trans. Microw. Theory Techn. 56, 449–456 (2008).
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Margolis, H. S.

Marra, G.

McFerran, J. J.

E. N. Ivanov, J. J. McFerran, S. A. Diddams, and L. Hollberg, “Noise properties of microwave signals synthesized with femtosecond lasers,” IEEE Trans. Ultrason., Ferroelect., Freq. Contr. 54, 736–745 (2007).
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Merzougui, M.

Meynadier, F.

C. Lisdat, G. Grosche, N. Quintin, C. Shi, S. Raupach, C. Grebing, D. Nicolodi, F. Stefani, A. Al-Masoudi, S. Dörscher, S. Häfner, J.-L. Robyr, N. Chiodo, S. Bilicki, E. Bookjans, A. Koczwara, S. Koke, A. Kohl, F. Wiotte, F. Meynadier, E. Camisard, M. Abgrall, M. Lours, T. Legero, H. Schnatz, U. Sterr, H. Denker, C. Chardonnet, Y. Le Coq, G. Santarelli, A. Amy-Klein, R. Le Targat, J. Lodewyck, O. Lopez, and P.-E. Pottie, “A clock network for geodesy and fundamental science,” Nat. Commun. 7, 12443 (2016).
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Millo, J.

Mücke, O. D.

M. Xin, K. Şafak, M. Y. Peng, A. Kalaydzhyan, P. T. Callahan, W. Wang, O. D. Mücke, and F. X. Kärtner, “Breaking the femtosecond barrier in multi-kilometer timing synchronization systems,” IEEE J. Select. Topics Quantum Electron. 23, 1–12 (2017).
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J. Taylor, S. Datta, A. Hati, C. Nelson, F. Quinlan, A. Joshi, and S. Diddams, “Characterization of power-to-phase conversion in high-speed p-i-n photodiodes,” IEEE Photon. J. 3, 140–151 (2011).
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Nicolodi, D.

X. Xie, R. Bouchand, D. Nicolodi, M. Giunta, W. Hänsel, M. Lezius, A. Joshi, S. Datta, C. Alexandre, M. Lours, P.-A. Tremblin, G. Santarelli, R. Holzwarth, and Y. Le Coq, “Photonic microwave signals with zeptosecond-level absolute timing noise,” Nat. Photonics 11, 44–47 (2017).
[Crossref]

X. Xie, R. Bouchand, D. Nicolodi, M. Lours, C. Alexandre, and Y. Le Coq, “Phase noise characterization of sub-hertz linewidth lasers via digital cross correlation,” Opt. Lett. 42, 1217–1220 (2017).
[Crossref] [PubMed]

C. Lisdat, G. Grosche, N. Quintin, C. Shi, S. Raupach, C. Grebing, D. Nicolodi, F. Stefani, A. Al-Masoudi, S. Dörscher, S. Häfner, J.-L. Robyr, N. Chiodo, S. Bilicki, E. Bookjans, A. Koczwara, S. Koke, A. Kohl, F. Wiotte, F. Meynadier, E. Camisard, M. Abgrall, M. Lours, T. Legero, H. Schnatz, U. Sterr, H. Denker, C. Chardonnet, Y. Le Coq, G. Santarelli, A. Amy-Klein, R. Le Targat, J. Lodewyck, O. Lopez, and P.-E. Pottie, “A clock network for geodesy and fundamental science,” Nat. Commun. 7, 12443 (2016).
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P. Ghelfi, F. Laghezza, F. Scotti, G. Serafino, A. Capria, S. Pinna, D. Onori, C. Porzi, M. Scaffardi, A. Malacarne, V. Vercesi, E. Lazzeri, F. Berizzi, and A. Bogoni, “A fully photonics-based coherent radar system,” Nature 507, 341–345 (2014).
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Ouyang, C.

Peng, M.

A. Kalaydzhyan, M. Peng, and F. Kartner, “Ultrahigh precision synchronization of optical and microwave frequency sources,” J. Phys: Conf. Ser. 741, 012084 (2016).

K. Şafak, M. Xin, P. Callahan, M. Peng, and F. Kärtner, “All fiber-coupled, long-term stable timing distribution for free-electron lasers with few-femtosecond jitter,” Struct. Dyn. 2, 041715 (2015).
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Peng, M. Y.

M. Xin, K. Şafak, M. Y. Peng, A. Kalaydzhyan, P. T. Callahan, W. Wang, O. D. Mücke, and F. X. Kärtner, “Breaking the femtosecond barrier in multi-kilometer timing synchronization systems,” IEEE J. Select. Topics Quantum Electron. 23, 1–12 (2017).
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M. Y. Peng, A. Kalaydzhyan, and F. X. Kärtner, “Balanced optical-microwave phase detector for sub-femtosecond optical-rf synchronization,” Opt. Express 22, 27102–27111 (2014).
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Phung, D.-H.

D.-H. Phung, M. Merzougui, C. Alexandre, and M. Lintz, “Phase measurement of a microwave optical modulation: Characterisation and reduction of amplitude-to-phase conversion in 1.5 μm high bandwidth photodiodes,” J. Lightwave Technol. 32, 3759–3767 (2014).
[Crossref]

D.-H. Phung and M. Lintz, “Comments on “frequency response of the noise conversion from relative intensity noise to phase noise in the photodetection of an optical pulse train”,” IEEE Photon. Technol. Lett. 26, 1994–1995 (2014).
[Crossref]

Pinna, S.

P. Ghelfi, F. Laghezza, F. Scotti, G. Serafino, A. Capria, S. Pinna, D. Onori, C. Porzi, M. Scaffardi, A. Malacarne, V. Vercesi, E. Lazzeri, F. Berizzi, and A. Bogoni, “A fully photonics-based coherent radar system,” Nature 507, 341–345 (2014).
[Crossref] [PubMed]

Porzi, C.

P. Ghelfi, F. Laghezza, F. Scotti, G. Serafino, A. Capria, S. Pinna, D. Onori, C. Porzi, M. Scaffardi, A. Malacarne, V. Vercesi, E. Lazzeri, F. Berizzi, and A. Bogoni, “A fully photonics-based coherent radar system,” Nature 507, 341–345 (2014).
[Crossref] [PubMed]

Pottie, P.-E.

C. Lisdat, G. Grosche, N. Quintin, C. Shi, S. Raupach, C. Grebing, D. Nicolodi, F. Stefani, A. Al-Masoudi, S. Dörscher, S. Häfner, J.-L. Robyr, N. Chiodo, S. Bilicki, E. Bookjans, A. Koczwara, S. Koke, A. Kohl, F. Wiotte, F. Meynadier, E. Camisard, M. Abgrall, M. Lours, T. Legero, H. Schnatz, U. Sterr, H. Denker, C. Chardonnet, Y. Le Coq, G. Santarelli, A. Amy-Klein, R. Le Targat, J. Lodewyck, O. Lopez, and P.-E. Pottie, “A clock network for geodesy and fundamental science,” Nat. Commun. 7, 12443 (2016).
[Crossref] [PubMed]

Quinlan, F.

Quintin, N.

C. Lisdat, G. Grosche, N. Quintin, C. Shi, S. Raupach, C. Grebing, D. Nicolodi, F. Stefani, A. Al-Masoudi, S. Dörscher, S. Häfner, J.-L. Robyr, N. Chiodo, S. Bilicki, E. Bookjans, A. Koczwara, S. Koke, A. Kohl, F. Wiotte, F. Meynadier, E. Camisard, M. Abgrall, M. Lours, T. Legero, H. Schnatz, U. Sterr, H. Denker, C. Chardonnet, Y. Le Coq, G. Santarelli, A. Amy-Klein, R. Le Targat, J. Lodewyck, O. Lopez, and P.-E. Pottie, “A clock network for geodesy and fundamental science,” Nat. Commun. 7, 12443 (2016).
[Crossref] [PubMed]

Raupach, S.

C. Lisdat, G. Grosche, N. Quintin, C. Shi, S. Raupach, C. Grebing, D. Nicolodi, F. Stefani, A. Al-Masoudi, S. Dörscher, S. Häfner, J.-L. Robyr, N. Chiodo, S. Bilicki, E. Bookjans, A. Koczwara, S. Koke, A. Kohl, F. Wiotte, F. Meynadier, E. Camisard, M. Abgrall, M. Lours, T. Legero, H. Schnatz, U. Sterr, H. Denker, C. Chardonnet, Y. Le Coq, G. Santarelli, A. Amy-Klein, R. Le Targat, J. Lodewyck, O. Lopez, and P.-E. Pottie, “A clock network for geodesy and fundamental science,” Nat. Commun. 7, 12443 (2016).
[Crossref] [PubMed]

Robyr, J.-L.

C. Lisdat, G. Grosche, N. Quintin, C. Shi, S. Raupach, C. Grebing, D. Nicolodi, F. Stefani, A. Al-Masoudi, S. Dörscher, S. Häfner, J.-L. Robyr, N. Chiodo, S. Bilicki, E. Bookjans, A. Koczwara, S. Koke, A. Kohl, F. Wiotte, F. Meynadier, E. Camisard, M. Abgrall, M. Lours, T. Legero, H. Schnatz, U. Sterr, H. Denker, C. Chardonnet, Y. Le Coq, G. Santarelli, A. Amy-Klein, R. Le Targat, J. Lodewyck, O. Lopez, and P.-E. Pottie, “A clock network for geodesy and fundamental science,” Nat. Commun. 7, 12443 (2016).
[Crossref] [PubMed]

Rumeau, A.

Z. Abdallah, A. Rumeau, A. Fernandez, G. Cibiel, and O. Llopis, “Nonlinear equivalent-circuit modeling of a fast photodiode,” IEEE Photon. Technol. Lett. 26, 1041–1135 (2014).
[Crossref]

Safak, K.

M. Xin, K. Şafak, M. Y. Peng, A. Kalaydzhyan, P. T. Callahan, W. Wang, O. D. Mücke, and F. X. Kärtner, “Breaking the femtosecond barrier in multi-kilometer timing synchronization systems,” IEEE J. Select. Topics Quantum Electron. 23, 1–12 (2017).
[Crossref]

K. Şafak, M. Xin, P. Callahan, M. Peng, and F. Kärtner, “All fiber-coupled, long-term stable timing distribution for free-electron lasers with few-femtosecond jitter,” Struct. Dyn. 2, 041715 (2015).
[Crossref]

Santarelli, G.

X. Xie, R. Bouchand, D. Nicolodi, M. Giunta, W. Hänsel, M. Lezius, A. Joshi, S. Datta, C. Alexandre, M. Lours, P.-A. Tremblin, G. Santarelli, R. Holzwarth, and Y. Le Coq, “Photonic microwave signals with zeptosecond-level absolute timing noise,” Nat. Photonics 11, 44–47 (2017).
[Crossref]

C. Lisdat, G. Grosche, N. Quintin, C. Shi, S. Raupach, C. Grebing, D. Nicolodi, F. Stefani, A. Al-Masoudi, S. Dörscher, S. Häfner, J.-L. Robyr, N. Chiodo, S. Bilicki, E. Bookjans, A. Koczwara, S. Koke, A. Kohl, F. Wiotte, F. Meynadier, E. Camisard, M. Abgrall, M. Lours, T. Legero, H. Schnatz, U. Sterr, H. Denker, C. Chardonnet, Y. Le Coq, G. Santarelli, A. Amy-Klein, R. Le Targat, J. Lodewyck, O. Lopez, and P.-E. Pottie, “A clock network for geodesy and fundamental science,” Nat. Commun. 7, 12443 (2016).
[Crossref] [PubMed]

W. Zhang, S. Seidelin, A. Joshi, S. Datta, G. Santarelli, and Y. Le Coq, “Dual photo-detector system for low phase noise microwave generation with femtosecond lasers,” Opt. Lett. 39, 1204–1207 (2014).
[Crossref] [PubMed]

W. Zhang, T. Li, M. Lours, S. Seidelin, G. Santarelli, and Y. Le Coq, “Amplitude to phase conversion of ingaas pin photo-diodes for femtosecond lasers microwave signal generation,” Appl. Phys. B 106, 301–308 (2012).
[Crossref]

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

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

W. Zhang, Z. Xu, M. Lours, R. Boudot, Y. Kersalé, G. Santarelli, and Y. Le Coq, “Sub-100 attoseconds stability optics to microwave synchronization,” Appl. Phys. Lett. 96, 211105 (2010).
[Crossref]

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

Scaffardi, M.

P. Ghelfi, F. Laghezza, F. Scotti, G. Serafino, A. Capria, S. Pinna, D. Onori, C. Porzi, M. Scaffardi, A. Malacarne, V. Vercesi, E. Lazzeri, F. Berizzi, and A. Bogoni, “A fully photonics-based coherent radar system,” Nature 507, 341–345 (2014).
[Crossref] [PubMed]

Schnatz, H.

C. Lisdat, G. Grosche, N. Quintin, C. Shi, S. Raupach, C. Grebing, D. Nicolodi, F. Stefani, A. Al-Masoudi, S. Dörscher, S. Häfner, J.-L. Robyr, N. Chiodo, S. Bilicki, E. Bookjans, A. Koczwara, S. Koke, A. Kohl, F. Wiotte, F. Meynadier, E. Camisard, M. Abgrall, M. Lours, T. Legero, H. Schnatz, U. Sterr, H. Denker, C. Chardonnet, Y. Le Coq, G. Santarelli, A. Amy-Klein, R. Le Targat, J. Lodewyck, O. Lopez, and P.-E. Pottie, “A clock network for geodesy and fundamental science,” Nat. Commun. 7, 12443 (2016).
[Crossref] [PubMed]

Scotti, F.

P. Ghelfi, F. Laghezza, F. Scotti, G. Serafino, A. Capria, S. Pinna, D. Onori, C. Porzi, M. Scaffardi, A. Malacarne, V. Vercesi, E. Lazzeri, F. Berizzi, and A. Bogoni, “A fully photonics-based coherent radar system,” Nature 507, 341–345 (2014).
[Crossref] [PubMed]

Seidel, D.

D. Eliyahu, D. Seidel, and L. Maleki, “Rf amplitude and phase-noise reduction of an optical link and an opto-electronic oscillator,” IEEE Trans. Microw. Theory Techn. 56, 449–456 (2008).
[Crossref]

Seidelin, S.

W. Zhang, S. Seidelin, A. Joshi, S. Datta, G. Santarelli, and Y. Le Coq, “Dual photo-detector system for low phase noise microwave generation with femtosecond lasers,” Opt. Lett. 39, 1204–1207 (2014).
[Crossref] [PubMed]

W. Zhang, T. Li, M. Lours, S. Seidelin, G. Santarelli, and Y. Le Coq, “Amplitude to phase conversion of ingaas pin photo-diodes for femtosecond lasers microwave signal generation,” Appl. Phys. B 106, 301–308 (2012).
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C. Lisdat, G. Grosche, N. Quintin, C. Shi, S. Raupach, C. Grebing, D. Nicolodi, F. Stefani, A. Al-Masoudi, S. Dörscher, S. Häfner, J.-L. Robyr, N. Chiodo, S. Bilicki, E. Bookjans, A. Koczwara, S. Koke, A. Kohl, F. Wiotte, F. Meynadier, E. Camisard, M. Abgrall, M. Lours, T. Legero, H. Schnatz, U. Sterr, H. Denker, C. Chardonnet, Y. Le Coq, G. Santarelli, A. Amy-Klein, R. Le Targat, J. Lodewyck, O. Lopez, and P.-E. Pottie, “A clock network for geodesy and fundamental science,” Nat. Commun. 7, 12443 (2016).
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[Crossref]

Vercesi, V.

P. Ghelfi, F. Laghezza, F. Scotti, G. Serafino, A. Capria, S. Pinna, D. Onori, C. Porzi, M. Scaffardi, A. Malacarne, V. Vercesi, E. Lazzeri, F. Berizzi, and A. Bogoni, “A fully photonics-based coherent radar system,” Nature 507, 341–345 (2014).
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M. Xin, K. Şafak, M. Y. Peng, A. Kalaydzhyan, P. T. Callahan, W. Wang, O. D. Mücke, and F. X. Kärtner, “Breaking the femtosecond barrier in multi-kilometer timing synchronization systems,” IEEE J. Select. Topics Quantum Electron. 23, 1–12 (2017).
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C. Wade, N. Šibalić, N. de Melo, J. Kondo, C. Adams, and K. Weatherill, “Real-time near-field terahertz imaging with atomic optical fluorescence,” Nat. Photonics 11, 40–43 (2017).
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Adv. Opt. Photonics (1)

J. Kim and Y. Song, “Ultralow-noise mode-locked fiber lasers and frequency combs: principles, status, and applications,” Adv. Opt. Photonics 8, 465–540 (2016).
[Crossref]

Appl. Phys. B (1)

W. Zhang, T. Li, M. Lours, S. Seidelin, G. Santarelli, and Y. Le Coq, “Amplitude to phase conversion of ingaas pin photo-diodes for femtosecond lasers microwave signal generation,” Appl. Phys. B 106, 301–308 (2012).
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Appl. Phys. Lett. (1)

W. Zhang, Z. Xu, M. Lours, R. Boudot, Y. Kersalé, G. Santarelli, and Y. Le Coq, “Sub-100 attoseconds stability optics to microwave synchronization,” Appl. Phys. Lett. 96, 211105 (2010).
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IEEE J. Select. Topics Quantum Electron. (1)

M. Xin, K. Şafak, M. Y. Peng, A. Kalaydzhyan, P. T. Callahan, W. Wang, O. D. Mücke, and F. X. Kärtner, “Breaking the femtosecond barrier in multi-kilometer timing synchronization systems,” IEEE J. Select. Topics Quantum Electron. 23, 1–12 (2017).
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IEEE Photon. J. (1)

J. Taylor, S. Datta, A. Hati, C. Nelson, F. Quinlan, A. Joshi, and S. Diddams, “Characterization of power-to-phase conversion in high-speed p-i-n photodiodes,” IEEE Photon. J. 3, 140–151 (2011).
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IEEE Trans. Ultrason., Ferroelect., Freq. Contr. (3)

E. N. Ivanov, S. A. Diddams, and L. Hollberg, “Study of the excess noise associated with demodulation of ultra-short infrared pulses,” IEEE Trans. Ultrason., Ferroelect., Freq. Contr. 52, 1068–1074 (2005).
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J. Phys: Conf. Ser. (1)

A. Kalaydzhyan, M. Peng, and F. Kartner, “Ultrahigh precision synchronization of optical and microwave frequency sources,” J. Phys: Conf. Ser. 741, 012084 (2016).

Nat. Commun. (1)

C. Lisdat, G. Grosche, N. Quintin, C. Shi, S. Raupach, C. Grebing, D. Nicolodi, F. Stefani, A. Al-Masoudi, S. Dörscher, S. Häfner, J.-L. Robyr, N. Chiodo, S. Bilicki, E. Bookjans, A. Koczwara, S. Koke, A. Kohl, F. Wiotte, F. Meynadier, E. Camisard, M. Abgrall, M. Lours, T. Legero, H. Schnatz, U. Sterr, H. Denker, C. Chardonnet, Y. Le Coq, G. Santarelli, A. Amy-Klein, R. Le Targat, J. Lodewyck, O. Lopez, and P.-E. Pottie, “A clock network for geodesy and fundamental science,” Nat. Commun. 7, 12443 (2016).
[Crossref] [PubMed]

Nat. Photonics (3)

C. Wade, N. Šibalić, N. de Melo, J. Kondo, C. Adams, and K. Weatherill, “Real-time near-field terahertz imaging with atomic optical fluorescence,” Nat. Photonics 11, 40–43 (2017).
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X. Xie, R. Bouchand, D. Nicolodi, M. Giunta, W. Hänsel, M. Lezius, A. Joshi, S. Datta, C. Alexandre, M. Lours, P.-A. Tremblin, G. Santarelli, R. Holzwarth, and Y. Le Coq, “Photonic microwave signals with zeptosecond-level absolute timing noise,” Nat. Photonics 11, 44–47 (2017).
[Crossref]

Nature (1)

P. Ghelfi, F. Laghezza, F. Scotti, G. Serafino, A. Capria, S. Pinna, D. Onori, C. Porzi, M. Scaffardi, A. Malacarne, V. Vercesi, E. Lazzeri, F. Berizzi, and A. Bogoni, “A fully photonics-based coherent radar system,” Nature 507, 341–345 (2014).
[Crossref] [PubMed]

Opt. Express (2)

Opt. Lett. (6)

Optica (1)

Struct. Dyn. (1)

K. Şafak, M. Xin, P. Callahan, M. Peng, and F. Kärtner, “All fiber-coupled, long-term stable timing distribution for free-electron lasers with few-femtosecond jitter,” Struct. Dyn. 2, 041715 (2015).
[Crossref]

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Figures (9)

Fig. 1
Fig. 1 Power of the 12 GHz harmonics (Left panel) and electrical response (Right panel) obtained after the photodiode under test when detecting the modulated light of an optical frequency comb (4 GHz repetition rate). The electrical responses are measured when the bias voltage is 8 V.
Fig. 2
Fig. 2 Optical intensity noise up-conversion. The baseband laser RIN (black line) is transferred to the amplitude noise (green line) and phase noise (red line) of the 12 GHz RF carrier. The noise power spectral densities of the 12 GHz RF carrier are measured using a heterodyne cross-correlation scheme similar to [7]. The laser RIN is measured on a Fast-Fourier-Transform analyser after linear photodetection.
Fig. 3
Fig. 3 Setup for the automatic characterization of APC ocurring during the photodetection of a train of ultra-short optical pulses. DCF: dispersion compensation fibre; DDS: direct digital synthesizer; : error signal; f0: carrier envelope frequency; νn: frequency of the nth comb line; νCW : frequency of the continuous wave laser reference; GND: ground; VBias: bias voltage; IPh: photocurrent; ATT: mechanical fibred optical attenuator; CPL: coupler; XC: cross-correlation; LO: local oscillator; USRP: universal software radio peripheral.
Fig. 4
Fig. 4 Simplified block diagram of the digital processing taking place in the USRP for obtaining the amplitude modulation and phase modulation indices. ADC: analogue-to-digital converter; DDC: digital down-converter; DPLL: digital phase lock-loop; atan2: two-argument arctangent function; FIR: finite impulse response filter; DEC: decimation (by 200).
Fig. 5
Fig. 5 Top panel: APC coefficient of the photodetector under study for 8 V (blue dots) and 16 V (green dots) bias voltage. It is measured automatically via the USRP, each point taking approximately 5 seconds. Bottom panel: APC rejection. The data obtained via the USRP system (dotted line) agree well with the rejection inferred from the RIN and the RF carrier phase noise (red dots). The shaded blue area represents the statistical error on the APC coefficient measurement.
Fig. 6
Fig. 6 Impact of isolation and impedance mismatch on the APC coefficient. We measure the APC coefficient at the two different outputs of a coupler when the RF transmission line is improperly isolated (Case A, less than 1 dB of isolation) and properly isolated (Case B, isolation ∼ 20 dB). In Case A (circles), there is a significant discrepancy of the APC coefficient obtained at the two coupler outputs while in Case B (squares) the two curves overlap up to the accuracy of the APC coefficient measurement.
Fig. 7
Fig. 7 Left panel: comparison of the APC coefficient characteristics for three different bias-tees (5541A from Picosecond Pulse Labs; 8810SMF from Aeroflex, Inc. and SHFDX65 from SHF Communications Technologies AG) at the output of the photodiode under test. Right panel: electrical pulses obtained after each bias-tee. One can see that the electrical reponse depends on the model of the bias-tee used. Although the peak power remains unchanged, the negative transients in the tail of the response are particularly affected by the choice of bias-tee. Those electrical responses are measured using a sampling oscilloscope clocked by the repetition rate of the optical frequency comb.
Fig. 8
Fig. 8 Left panel: residual 12 GHz microwave carrier phase noise characterized by cross-correlation (red line). The RIN (green line) is shown for appreciating qualitatively the rejection of amplitude to phase noise conversion. Right panel: inloop power spectral density of the APC coefficient with (red line) and without (blue line) the active control.
Fig. 9
Fig. 9 Top panel: dynamics of the amplitude to phase conversion coefficient without (blue) and with (transparent red) active control over 650 seconds of acquisition. A zoom on a short time scale (0.1 second) is shown in the inset to emphasize that the high frequency behaviour of α is similar for both cases, although it seems the red stream is wider than the blue stream on the long time acquisition (due to the large number of samples and to the graphical linewidth). Bottom panel: overlapping two-sample (Allan) deviation of the amplitude to phase coefficient computed over the same acquisitions without (blue) and with (red) active control. The error bars are too small to be represented on this graph.

Tables (1)

Tables Icon

Table 1 Overview of the RIN rejection and residual phase noise recently reported in the literature in the case of BOM-PD and DP when extracting a microwave signal from an optical frequency comb. Note that in all those works except in the method presented here and in [7], the APC coefficient (and then the RIN rejection) is inferred a posteriori from the overall microwave phase noise results.

Equations (2)

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

α 2 = S ϕ ( f ) S I ( f ) [ rad 2 ]
RIN ( f ) = 10 log [ S I ( f ) ] + 20 log [ α ] 3 RINrejection [ dBc / Hz ]

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