Abstract

We report a method to determine propagation delays of optical 10 Gb/s data traveling through a 75 km long amplified fiber link with an uncertainty of 4 ps. The one-way propagation delay is determined by two-way exchange and cross correlation of short (< 1 ms) bursts of 10 Gb/s data, with a single-shot time resolution better than 2.5 ps. We thus achieve a novel optical communications link suited for both long-haul high-capacity data transfer and time transfer with picosecond-range uncertainty. This opens up the perspective of synchronized optical telecommunication networks allowing picosecond-range time distribution and millimeter-range positioning.

© 2013 Optical Society of America

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2013

S. Droste, F. Ozimek, Th. Udem, K. Predehl, T. W. Hänsch, H. Schnatz, G. Grosche, and R. Holzwarth, “Optical-frequency transfer over a single-span 1840 km fiber link,” Phys. Rev. Lett.111(11), 110801 (2013).
[CrossRef] [PubMed]

O. Lopez, A. Kanj, P.-E. Pottie, D. Rovera, J. Achkar, C. Chardonnet, A. Amy-Klein, and G. Santarelli, “Simultaneous remote transfer of accurate timing and optical frequency over a public fiber network,” Appl. Phys. B110(1), 3–6 (2013).
[CrossRef]

L. Śliwczyński, P. Krehlik, A. Czubla, L. Buczek, and M. Lipinski, “Dissemination of time and RF frequency via a stabilized fibre optic link over a distance of 420 km,” Metrologia50(2), 133–145 (2013).
[CrossRef]

2012

M. Rost, D. Piester, W. Yang, T. Feldmann, T. Wübbena, and A. Bauch, “Time transfer through optical fibres over a distance of 73 km with an uncertainty below 100 ps,” Metrologia49(6), 772–778 (2012).
[CrossRef]

P. Krehlik, L. Sliwczynski, L. Buczek, and M. Lipinski, “Fiber-optic joint time and frequency transfer with active stabilization of the propagation delay,” IEEE Trans. Instrum. Meas.61(10), 2844–2851 (2012).
[CrossRef]

X. Fang, S. Misra, G. Xue, and D. Yang, “Smart Grid – the new and improved power grid: a survey,” IEEE Commun. Surv. Tutorials14(4), 944–980 (2012).
[CrossRef]

2008

1997

S. R. Jefferts, M. A. Weiss, J. Levine, S. Dilla, E. W. Bell, and T. E. Parker, “Two-way time and frequency transfer using optical fibers,” IEEE Trans. Instrum. Meas.46(2), 209–211 (1997).
[CrossRef]

1993

F. Devaux, Y. Sorel, and J. F. Kerdiles, “Simple measurement of fiber dispersion and of chirp parameter of intensity modulated light emitter,” J. Lightwave Technol.11(12), 1937–1940 (1993).
[CrossRef]

Achkar, J.

O. Lopez, A. Kanj, P.-E. Pottie, D. Rovera, J. Achkar, C. Chardonnet, A. Amy-Klein, and G. Santarelli, “Simultaneous remote transfer of accurate timing and optical frequency over a public fiber network,” Appl. Phys. B110(1), 3–6 (2013).
[CrossRef]

Amy-Klein, A.

O. Lopez, A. Kanj, P.-E. Pottie, D. Rovera, J. Achkar, C. Chardonnet, A. Amy-Klein, and G. Santarelli, “Simultaneous remote transfer of accurate timing and optical frequency over a public fiber network,” Appl. Phys. B110(1), 3–6 (2013).
[CrossRef]

Bauch, A.

M. Rost, D. Piester, W. Yang, T. Feldmann, T. Wübbena, and A. Bauch, “Time transfer through optical fibres over a distance of 73 km with an uncertainty below 100 ps,” Metrologia49(6), 772–778 (2012).
[CrossRef]

Bell, E. W.

S. R. Jefferts, M. A. Weiss, J. Levine, S. Dilla, E. W. Bell, and T. E. Parker, “Two-way time and frequency transfer using optical fibers,” IEEE Trans. Instrum. Meas.46(2), 209–211 (1997).
[CrossRef]

Buczek, L.

L. Śliwczyński, P. Krehlik, A. Czubla, L. Buczek, and M. Lipinski, “Dissemination of time and RF frequency via a stabilized fibre optic link over a distance of 420 km,” Metrologia50(2), 133–145 (2013).
[CrossRef]

P. Krehlik, L. Sliwczynski, L. Buczek, and M. Lipinski, “Fiber-optic joint time and frequency transfer with active stabilization of the propagation delay,” IEEE Trans. Instrum. Meas.61(10), 2844–2851 (2012).
[CrossRef]

Chardonnet, C.

O. Lopez, A. Kanj, P.-E. Pottie, D. Rovera, J. Achkar, C. Chardonnet, A. Amy-Klein, and G. Santarelli, “Simultaneous remote transfer of accurate timing and optical frequency over a public fiber network,” Appl. Phys. B110(1), 3–6 (2013).
[CrossRef]

Czubla, A.

L. Śliwczyński, P. Krehlik, A. Czubla, L. Buczek, and M. Lipinski, “Dissemination of time and RF frequency via a stabilized fibre optic link over a distance of 420 km,” Metrologia50(2), 133–145 (2013).
[CrossRef]

Devaux, F.

F. Devaux, Y. Sorel, and J. F. Kerdiles, “Simple measurement of fiber dispersion and of chirp parameter of intensity modulated light emitter,” J. Lightwave Technol.11(12), 1937–1940 (1993).
[CrossRef]

Dilla, S.

S. R. Jefferts, M. A. Weiss, J. Levine, S. Dilla, E. W. Bell, and T. E. Parker, “Two-way time and frequency transfer using optical fibers,” IEEE Trans. Instrum. Meas.46(2), 209–211 (1997).
[CrossRef]

Droste, S.

S. Droste, F. Ozimek, Th. Udem, K. Predehl, T. W. Hänsch, H. Schnatz, G. Grosche, and R. Holzwarth, “Optical-frequency transfer over a single-span 1840 km fiber link,” Phys. Rev. Lett.111(11), 110801 (2013).
[CrossRef] [PubMed]

Ebenhag, S. C.

S. C. Ebenhag, K. Jaldehag, C. Rieck, P. Jarlemark, P. O. Hedekvist, P. Löthberg, T. Fordell, and M. Merimaa, “Time transfer between UTC(SP) and TUC(MIKE) using frame detection in fiber-optical communication networks,” in Proceedings 43rd Precise Time and Time Interval Systems and Applications Meeting, Long Beach, California (2011), pp. 431–441.

Fang, X.

X. Fang, S. Misra, G. Xue, and D. Yang, “Smart Grid – the new and improved power grid: a survey,” IEEE Commun. Surv. Tutorials14(4), 944–980 (2012).
[CrossRef]

Feldmann, T.

M. Rost, D. Piester, W. Yang, T. Feldmann, T. Wübbena, and A. Bauch, “Time transfer through optical fibres over a distance of 73 km with an uncertainty below 100 ps,” Metrologia49(6), 772–778 (2012).
[CrossRef]

Fordell, T.

S. C. Ebenhag, K. Jaldehag, C. Rieck, P. Jarlemark, P. O. Hedekvist, P. Löthberg, T. Fordell, and M. Merimaa, “Time transfer between UTC(SP) and TUC(MIKE) using frame detection in fiber-optical communication networks,” in Proceedings 43rd Precise Time and Time Interval Systems and Applications Meeting, Long Beach, California (2011), pp. 431–441.

Grosche, G.

S. Droste, F. Ozimek, Th. Udem, K. Predehl, T. W. Hänsch, H. Schnatz, G. Grosche, and R. Holzwarth, “Optical-frequency transfer over a single-span 1840 km fiber link,” Phys. Rev. Lett.111(11), 110801 (2013).
[CrossRef] [PubMed]

Hänsch, T. W.

S. Droste, F. Ozimek, Th. Udem, K. Predehl, T. W. Hänsch, H. Schnatz, G. Grosche, and R. Holzwarth, “Optical-frequency transfer over a single-span 1840 km fiber link,” Phys. Rev. Lett.111(11), 110801 (2013).
[CrossRef] [PubMed]

Hedekvist, P. O.

S. C. Ebenhag, K. Jaldehag, C. Rieck, P. Jarlemark, P. O. Hedekvist, P. Löthberg, T. Fordell, and M. Merimaa, “Time transfer between UTC(SP) and TUC(MIKE) using frame detection in fiber-optical communication networks,” in Proceedings 43rd Precise Time and Time Interval Systems and Applications Meeting, Long Beach, California (2011), pp. 431–441.

Holzwarth, R.

S. Droste, F. Ozimek, Th. Udem, K. Predehl, T. W. Hänsch, H. Schnatz, G. Grosche, and R. Holzwarth, “Optical-frequency transfer over a single-span 1840 km fiber link,” Phys. Rev. Lett.111(11), 110801 (2013).
[CrossRef] [PubMed]

Imaoka, A.

M. Kihara and A. Imaoka, “SDH-based time and frequency transfer system,” in Proceedings 9th European Frequency and Time Forum, Besancon, France (1995), pp. 317–322.

Jaldehag, K.

S. C. Ebenhag, K. Jaldehag, C. Rieck, P. Jarlemark, P. O. Hedekvist, P. Löthberg, T. Fordell, and M. Merimaa, “Time transfer between UTC(SP) and TUC(MIKE) using frame detection in fiber-optical communication networks,” in Proceedings 43rd Precise Time and Time Interval Systems and Applications Meeting, Long Beach, California (2011), pp. 431–441.

Jarlemark, P.

S. C. Ebenhag, K. Jaldehag, C. Rieck, P. Jarlemark, P. O. Hedekvist, P. Löthberg, T. Fordell, and M. Merimaa, “Time transfer between UTC(SP) and TUC(MIKE) using frame detection in fiber-optical communication networks,” in Proceedings 43rd Precise Time and Time Interval Systems and Applications Meeting, Long Beach, California (2011), pp. 431–441.

Jefferts, S. R.

S. R. Jefferts, M. A. Weiss, J. Levine, S. Dilla, E. W. Bell, and T. E. Parker, “Two-way time and frequency transfer using optical fibers,” IEEE Trans. Instrum. Meas.46(2), 209–211 (1997).
[CrossRef]

Jiang, Z.

G. Petit and Z. Jiang, “Precise point positioning for TAI computation,” Int. J. Navig. Obs.2008, 562878 (2008).
[CrossRef]

Kanj, A.

O. Lopez, A. Kanj, P.-E. Pottie, D. Rovera, J. Achkar, C. Chardonnet, A. Amy-Klein, and G. Santarelli, “Simultaneous remote transfer of accurate timing and optical frequency over a public fiber network,” Appl. Phys. B110(1), 3–6 (2013).
[CrossRef]

Kerdiles, J. F.

F. Devaux, Y. Sorel, and J. F. Kerdiles, “Simple measurement of fiber dispersion and of chirp parameter of intensity modulated light emitter,” J. Lightwave Technol.11(12), 1937–1940 (1993).
[CrossRef]

Kihara, M.

M. Kihara and A. Imaoka, “SDH-based time and frequency transfer system,” in Proceedings 9th European Frequency and Time Forum, Besancon, France (1995), pp. 317–322.

Krehlik, P.

L. Śliwczyński, P. Krehlik, A. Czubla, L. Buczek, and M. Lipinski, “Dissemination of time and RF frequency via a stabilized fibre optic link over a distance of 420 km,” Metrologia50(2), 133–145 (2013).
[CrossRef]

P. Krehlik, L. Sliwczynski, L. Buczek, and M. Lipinski, “Fiber-optic joint time and frequency transfer with active stabilization of the propagation delay,” IEEE Trans. Instrum. Meas.61(10), 2844–2851 (2012).
[CrossRef]

Levine, J.

S. R. Jefferts, M. A. Weiss, J. Levine, S. Dilla, E. W. Bell, and T. E. Parker, “Two-way time and frequency transfer using optical fibers,” IEEE Trans. Instrum. Meas.46(2), 209–211 (1997).
[CrossRef]

Lipinski, M.

L. Śliwczyński, P. Krehlik, A. Czubla, L. Buczek, and M. Lipinski, “Dissemination of time and RF frequency via a stabilized fibre optic link over a distance of 420 km,” Metrologia50(2), 133–145 (2013).
[CrossRef]

P. Krehlik, L. Sliwczynski, L. Buczek, and M. Lipinski, “Fiber-optic joint time and frequency transfer with active stabilization of the propagation delay,” IEEE Trans. Instrum. Meas.61(10), 2844–2851 (2012).
[CrossRef]

Lopez, O.

O. Lopez, A. Kanj, P.-E. Pottie, D. Rovera, J. Achkar, C. Chardonnet, A. Amy-Klein, and G. Santarelli, “Simultaneous remote transfer of accurate timing and optical frequency over a public fiber network,” Appl. Phys. B110(1), 3–6 (2013).
[CrossRef]

Löthberg, P.

S. C. Ebenhag, K. Jaldehag, C. Rieck, P. Jarlemark, P. O. Hedekvist, P. Löthberg, T. Fordell, and M. Merimaa, “Time transfer between UTC(SP) and TUC(MIKE) using frame detection in fiber-optical communication networks,” in Proceedings 43rd Precise Time and Time Interval Systems and Applications Meeting, Long Beach, California (2011), pp. 431–441.

Merimaa, M.

S. C. Ebenhag, K. Jaldehag, C. Rieck, P. Jarlemark, P. O. Hedekvist, P. Löthberg, T. Fordell, and M. Merimaa, “Time transfer between UTC(SP) and TUC(MIKE) using frame detection in fiber-optical communication networks,” in Proceedings 43rd Precise Time and Time Interval Systems and Applications Meeting, Long Beach, California (2011), pp. 431–441.

Misra, S.

X. Fang, S. Misra, G. Xue, and D. Yang, “Smart Grid – the new and improved power grid: a survey,” IEEE Commun. Surv. Tutorials14(4), 944–980 (2012).
[CrossRef]

Newbury, N. R.

Ozimek, F.

S. Droste, F. Ozimek, Th. Udem, K. Predehl, T. W. Hänsch, H. Schnatz, G. Grosche, and R. Holzwarth, “Optical-frequency transfer over a single-span 1840 km fiber link,” Phys. Rev. Lett.111(11), 110801 (2013).
[CrossRef] [PubMed]

Parker, T. E.

S. R. Jefferts, M. A. Weiss, J. Levine, S. Dilla, E. W. Bell, and T. E. Parker, “Two-way time and frequency transfer using optical fibers,” IEEE Trans. Instrum. Meas.46(2), 209–211 (1997).
[CrossRef]

Petit, G.

G. Petit and Z. Jiang, “Precise point positioning for TAI computation,” Int. J. Navig. Obs.2008, 562878 (2008).
[CrossRef]

Piester, D.

M. Rost, D. Piester, W. Yang, T. Feldmann, T. Wübbena, and A. Bauch, “Time transfer through optical fibres over a distance of 73 km with an uncertainty below 100 ps,” Metrologia49(6), 772–778 (2012).
[CrossRef]

Pottie, P.-E.

O. Lopez, A. Kanj, P.-E. Pottie, D. Rovera, J. Achkar, C. Chardonnet, A. Amy-Klein, and G. Santarelli, “Simultaneous remote transfer of accurate timing and optical frequency over a public fiber network,” Appl. Phys. B110(1), 3–6 (2013).
[CrossRef]

Predehl, K.

S. Droste, F. Ozimek, Th. Udem, K. Predehl, T. W. Hänsch, H. Schnatz, G. Grosche, and R. Holzwarth, “Optical-frequency transfer over a single-span 1840 km fiber link,” Phys. Rev. Lett.111(11), 110801 (2013).
[CrossRef] [PubMed]

Rieck, C.

S. C. Ebenhag, K. Jaldehag, C. Rieck, P. Jarlemark, P. O. Hedekvist, P. Löthberg, T. Fordell, and M. Merimaa, “Time transfer between UTC(SP) and TUC(MIKE) using frame detection in fiber-optical communication networks,” in Proceedings 43rd Precise Time and Time Interval Systems and Applications Meeting, Long Beach, California (2011), pp. 431–441.

Rost, M.

M. Rost, D. Piester, W. Yang, T. Feldmann, T. Wübbena, and A. Bauch, “Time transfer through optical fibres over a distance of 73 km with an uncertainty below 100 ps,” Metrologia49(6), 772–778 (2012).
[CrossRef]

Rovera, D.

O. Lopez, A. Kanj, P.-E. Pottie, D. Rovera, J. Achkar, C. Chardonnet, A. Amy-Klein, and G. Santarelli, “Simultaneous remote transfer of accurate timing and optical frequency over a public fiber network,” Appl. Phys. B110(1), 3–6 (2013).
[CrossRef]

Santarelli, G.

O. Lopez, A. Kanj, P.-E. Pottie, D. Rovera, J. Achkar, C. Chardonnet, A. Amy-Klein, and G. Santarelli, “Simultaneous remote transfer of accurate timing and optical frequency over a public fiber network,” Appl. Phys. B110(1), 3–6 (2013).
[CrossRef]

Schnatz, H.

S. Droste, F. Ozimek, Th. Udem, K. Predehl, T. W. Hänsch, H. Schnatz, G. Grosche, and R. Holzwarth, “Optical-frequency transfer over a single-span 1840 km fiber link,” Phys. Rev. Lett.111(11), 110801 (2013).
[CrossRef] [PubMed]

Sliwczynski, L.

L. Śliwczyński, P. Krehlik, A. Czubla, L. Buczek, and M. Lipinski, “Dissemination of time and RF frequency via a stabilized fibre optic link over a distance of 420 km,” Metrologia50(2), 133–145 (2013).
[CrossRef]

P. Krehlik, L. Sliwczynski, L. Buczek, and M. Lipinski, “Fiber-optic joint time and frequency transfer with active stabilization of the propagation delay,” IEEE Trans. Instrum. Meas.61(10), 2844–2851 (2012).
[CrossRef]

Sorel, Y.

F. Devaux, Y. Sorel, and J. F. Kerdiles, “Simple measurement of fiber dispersion and of chirp parameter of intensity modulated light emitter,” J. Lightwave Technol.11(12), 1937–1940 (1993).
[CrossRef]

Swann, W. C.

Udem, Th.

S. Droste, F. Ozimek, Th. Udem, K. Predehl, T. W. Hänsch, H. Schnatz, G. Grosche, and R. Holzwarth, “Optical-frequency transfer over a single-span 1840 km fiber link,” Phys. Rev. Lett.111(11), 110801 (2013).
[CrossRef] [PubMed]

Weiss, M. A.

S. R. Jefferts, M. A. Weiss, J. Levine, S. Dilla, E. W. Bell, and T. E. Parker, “Two-way time and frequency transfer using optical fibers,” IEEE Trans. Instrum. Meas.46(2), 209–211 (1997).
[CrossRef]

Williams, P. A.

Wübbena, T.

M. Rost, D. Piester, W. Yang, T. Feldmann, T. Wübbena, and A. Bauch, “Time transfer through optical fibres over a distance of 73 km with an uncertainty below 100 ps,” Metrologia49(6), 772–778 (2012).
[CrossRef]

Xue, G.

X. Fang, S. Misra, G. Xue, and D. Yang, “Smart Grid – the new and improved power grid: a survey,” IEEE Commun. Surv. Tutorials14(4), 944–980 (2012).
[CrossRef]

Yang, D.

X. Fang, S. Misra, G. Xue, and D. Yang, “Smart Grid – the new and improved power grid: a survey,” IEEE Commun. Surv. Tutorials14(4), 944–980 (2012).
[CrossRef]

Yang, W.

M. Rost, D. Piester, W. Yang, T. Feldmann, T. Wübbena, and A. Bauch, “Time transfer through optical fibres over a distance of 73 km with an uncertainty below 100 ps,” Metrologia49(6), 772–778 (2012).
[CrossRef]

Appl. Phys. B

O. Lopez, A. Kanj, P.-E. Pottie, D. Rovera, J. Achkar, C. Chardonnet, A. Amy-Klein, and G. Santarelli, “Simultaneous remote transfer of accurate timing and optical frequency over a public fiber network,” Appl. Phys. B110(1), 3–6 (2013).
[CrossRef]

IEEE Commun. Surv. Tutorials

X. Fang, S. Misra, G. Xue, and D. Yang, “Smart Grid – the new and improved power grid: a survey,” IEEE Commun. Surv. Tutorials14(4), 944–980 (2012).
[CrossRef]

IEEE Trans. Instrum. Meas.

S. R. Jefferts, M. A. Weiss, J. Levine, S. Dilla, E. W. Bell, and T. E. Parker, “Two-way time and frequency transfer using optical fibers,” IEEE Trans. Instrum. Meas.46(2), 209–211 (1997).
[CrossRef]

P. Krehlik, L. Sliwczynski, L. Buczek, and M. Lipinski, “Fiber-optic joint time and frequency transfer with active stabilization of the propagation delay,” IEEE Trans. Instrum. Meas.61(10), 2844–2851 (2012).
[CrossRef]

Int. J. Navig. Obs.

G. Petit and Z. Jiang, “Precise point positioning for TAI computation,” Int. J. Navig. Obs.2008, 562878 (2008).
[CrossRef]

J. Lightwave Technol.

F. Devaux, Y. Sorel, and J. F. Kerdiles, “Simple measurement of fiber dispersion and of chirp parameter of intensity modulated light emitter,” J. Lightwave Technol.11(12), 1937–1940 (1993).
[CrossRef]

J. Opt. Soc. Am. B

Metrologia

M. Rost, D. Piester, W. Yang, T. Feldmann, T. Wübbena, and A. Bauch, “Time transfer through optical fibres over a distance of 73 km with an uncertainty below 100 ps,” Metrologia49(6), 772–778 (2012).
[CrossRef]

L. Śliwczyński, P. Krehlik, A. Czubla, L. Buczek, and M. Lipinski, “Dissemination of time and RF frequency via a stabilized fibre optic link over a distance of 420 km,” Metrologia50(2), 133–145 (2013).
[CrossRef]

Phys. Rev. Lett.

S. Droste, F. Ozimek, Th. Udem, K. Predehl, T. W. Hänsch, H. Schnatz, G. Grosche, and R. Holzwarth, “Optical-frequency transfer over a single-span 1840 km fiber link,” Phys. Rev. Lett.111(11), 110801 (2013).
[CrossRef] [PubMed]

Other

Global Navigation Space Systems: Reliance and Vulnerabilities (The Royal Academy of Engineering, 2011).

T. E. Parker and V. Zhang, “Sources of instabilities in two-way satellite time transfer,” in Proceedings IEEE International Frequency Control Symposium and Exposition (Institute of Electrical and Electronics Engineers, 2005), pp. 745–751.
[CrossRef]

W. J. Riley, Handbook of Frequency Stability Analysis (NIST Spec. Publ. 1065, July 2008).

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Figures (4)

Fig. 1
Fig. 1

(a) Experimental setup for 10 Gb/s data transmission and picosecond-uncertainty delay measurements over 75 km distance. Solid lines represent optical connections, whereas electrical connections are indicated by dashed lines. E/O, electrical-to-optical converter; O/E optical-to-electrical converter; BERT, bit-error-rate tester; WM, wavelength multiplexer; SOA, semiconductor optical amplifier; OI, optical isolator; VOA, variable optical attenuator. Both the upstream and downstream channels are equipped with a polarization and power control (PPC) unit (inset). The PPC contains a VOA, and can furthermore be configured to rotate the state of polarization (SOP) by either 0° or 90° by use of an optical circulator (OC) and a Faraday rotator mirror (FRM). The VOAs and PPCs allow maintaining a constant optical power level in the system as well as the determination of PMD. (b) Schematic of the signal propagation directions and delays in the setup shown in (a) with the fiber spools removed. (c) Same as in (b), but with the reference points A, B and C now defined such that they coincide with the DPO channels 3, 1 and 2, respectively. In the definition of the instrument delays tAX, t(X) denotes the point in time at which the PRBS arrives at location X. (d) Signal propagation delays with the fiber spools inserted in the link. The link delay asymmetry is modeled by an additional delay ΔL in the return path.

Fig. 2
Fig. 2

Delay determination by cross correlation of PRBSs. PRBS captured by the real-time DPO in location A [Fig. 1(a)] at sampling rates of 50 GS/s [red dots, Fig. 2(a)] and 12.5 GS/s [blue dots, Fig. 2(b)], respectively. Red curves are interpolations of the 50 GS/s data and serve to guide the eye. Similar signals are captured at channels 1 and 2 of the real-time DPO (which correspond to locations B and C, respectively). (c) Normalized cross correlation spectrum of the PRBS signals at locations A and B. Blue dots represent the correlation spectrum of the PRBSs captured at 12.5 GS/s with respect to the Rb-clock-stabilized time base of the DPO. Red dots are the high-resolution (50 GS/s) data obtained with the delayed-reference method (see Sec. 2.2), and are shown together with their interpolating function which is used to fit the blue data points and determine the peak position (indicated by the vertical grey line), which yields a direct reference determination of the OWD. The delay offset in the abscissa label arises during the analysis and has no further physical meaning. (d) Cross correlation spectrum of the PRBS signals at locations A and C, and the fitted peak position, which corresponds to the RTD. (e) Eye diagrams captured with a sampling oscilloscope of the PRBS signals at locations A, B and C, respectively. For data transmission, only the signals in A and B are relevant.

Fig. 3
Fig. 3

(a). Time differences ζ(t) – tAB(t) obtained for the 75 km link at different times t during one day of measurements. Green and blue data points are obtained using wavelength combinations (λ1, λ3) and (λ1, λ2), respectively. The delay asymmetry due to dispersion is removed using Eqs. (1) and (2), assuming the value for the chromatic dispersion found from Eq. (3) after PMD correction. Filled symbols indicate the use of FRMs in the PPCs [Fig. 1(a)], whereas open symbols correspond to data acquired without FRMs. Horizontal dashed lines represent the mean of each group of four data points; differential delays ΔP1j are derived from the difference of these means as indicated by the arrows. Pairs of data points with identical symbols (but with opposite wavelength combinations) correspond to data which are combined using Eq. (4) to obtain the results of Fig. 4(d). (b) Variation of ΔI during the measurements. Only the data corresponding to the circles/disks are used for calibration; triangle data are used for drift monitoring only and are relative to the first data point. Symbol filling and color correspond to that used in (a). (c) Variation of t′AB during the measurements with respect to t′AB(t = 0 s) (first eight data points) and t′AB(t = 7230 s) (final eight data points). (d) Temperature T and relative humidity H during the measurements: solid curve, T measured at the O/E converter at location B; dashed curve, T measured inside spool housing; dotted curve, H measured at the optical workbench. The steep temperature drop near t = 12500 s is due to the laboratory heating system being switched off at 5 pm local time.

Fig. 4
Fig. 4

Data transmission performance and accuracy of the OWD determination achieved using our method. (a) BER measurements for back-to-back (green dots), 25 km (red squares), 50 km (blue diamonds) and 75 km (brown triangles) fiber links. Error-free transmission (BER < 10−9) of 10 Gb/s data is achieved for the back-to-back, 25 km and 50 km links. For the 75 km link a BER slightly above 10−9 is achieved due to power limitations in the setup; however, the BER data show no sign of a noise floor, and with a slightly higher power level (or with dispersion compensation) a BER below 10−9 should be reached. (b) Delay differences θABtAB (blue symbols) for the 25 km link. Gray stars represent the offset of the reference measurements tAB (which is zero by definition) and its measurement uncertainty. (c),(d) Same as (b), but for the 50 km and 75 km links, respectively. In (d), the symbols correspond directly to those in Fig. 3(a). For example, the first measurement value of θABtAB (filled diamond) is found from combining the two filled-diamond values in Fig. 3(a), which were obtained using different wavelength combinations and with the FRMs installed.

Tables (1)

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Table 1 Uncertainty budget for θAB

Equations (4)

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τ(λ)τ( λ 1 )= L 2c [ 2( λ λ 1 ) λ 1 n ( λ 1 )+ ( λ λ 1 ) 2 ( n ( λ 1 )+ λ 1 n ( λ 1 ) ) ].
ζ 1j = 1 2 ( t AC 1j +τ( λ 1 )τ( λ j ) Δ 1j ),
D( λ 1 )= λ 1 c n ( λ 1 ) = 2 λ 1 L( λ 2 2 λ 3 2 ) { ( t AC 12 Δ 12 )( t AC 13 Δ 13 ) }+ λ 1 2 ( λ 2 + λ 3 2 λ 1 ) n ( λ 1 ) c( λ 2 + λ 3 ) .
θ AB = 1 2( λ 2 2 λ 3 2 ) [{ ( t AC 12 Δ 12 )( t AC 13 Δ 13 ) } λ 1 2 +( t AC 13 Δ 13 ) λ 2 2 ( t AC 12 Δ 12 ) λ 3 2 L λ 1 2 ( λ 1 λ 2 )( λ 1 λ 3 )( λ 2 λ 3 ) n ( λ 1 )/c].

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