# Long-distance frequency transfer over an urban fiber link using optical phase stabilization

**ABSTRACT** We transferred the frequency of an ultra-stable laser over 86 km of urban fiber. The link is composed of two cascaded 43-km fibers connecting two laboratories, LNE-SYRTE and LPL in Paris area. In an effort to realistically demonstrate a link of 172 km without using spooled fiber extensions, we implemented a recirculation loop to double the length of the urban fiber link. The link is fed with a 1542-nm cavity stabilized fiber laser having a sub-Hz linewidth. The fiber-induced phase noise is measured and cancelled with an all fiber-based interferometer using commercial off the shelf pigtailed telecommunication components. The compensated link shows an Allan deviation of a few 10-16 at one second and a few 10-19 at 10,000 seconds.

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- Fabio Stefani, Olivier Lopez, Anthony Bercy, Won-Kyu Lee, Christian Chardonnet, Giorgio Santarelli, Paul-Eric Pottie, Anne Amy-Klein[Show abstract] [Hide abstract]

**ABSTRACT:**We theoretically and experimentally investigate relevant noise processes arising in optical fiber links, which fundamentally limit their relative stability. We derive the unsuppressed delay noise for three configurations of optical links: two-way method, Sagnac interferometry, and actively compensated link, respectively designed for frequency comparison, rotation sensing, and frequency transfer. We also consider an alternative two-way setup allowing real-time frequency comparison and demonstrate its effectiveness on a proof-of-principle experiment with a 25-km fiber spool. For these three configurations, we analyze the noise arising from uncommon fiber paths in the interferometric ensemble and design optimized interferometers. We demonstrate interferometers with very low temperature sensitivity of respectively -2.2, -0.03 and 1 fs/K. We use one of these optimized interferometers on a long haul compensated fiber link of 540km. We obtain a relative frequency stability of 3E-20 after 10,000 s of integration time.12/2014; - [Show abstract] [Hide abstract]

**ABSTRACT:**In this paper, the transmission of the time and/or frequency signals (e.g., 1 pulse per second and 10 MHz) coded on the optical carrier by means of an on-off intensity modulation in the two-way fiber-optic link is considered. It is assumed that the bidirectional optical amplification in the single piece of an erbium-doped fiber is exploited to compensate the attenuation of the optical path. Such configuration of the amplifiers, offering the highest possible symmetry of the propagation conditions in both directions, is well suited for the two-way transfer method exploiting the symmetry of the link. We proposed the method of estimating interfering signals and jitter, which appear at both sides of such bidirectional fiber link because of Rayleigh backscattering and amplified spontaneous emission. This method is further exploited for finding the gains of bidirectional amplifiers, allowing optimization of the performance of the link. The experiments done with 120- and 220-km-long links, incorporating one and three amplifiers, respectively, confirmed theoretical predictions and proved that the single-path bidirectional amplifiers without any components separating the directions are useful for time or RF frequency transfer. During the experiments, both field-deployed telecommunication cables and the fibers spooled in the laboratory were used. Presented methods of analysis and optimization are useful for designing and evaluating the fiber-optic links incorporating single-path bidirectional fiber-optic amplifiers and exploiting intensity modulation for time and/or frequency transfer.IEEE Transactions on Instrumentation and Measurement 01/2013; 62(1):253-262. · 1.71 Impact Factor - SourceAvailable from: Anthony BercyAnthony Bercy, Saïda Guellati-Khélifa, Fabio Stefani, Giorgio Santarelli, Christian Chardonnet, Paul-Eric Pottie, Olivier Lopez, Anne Amy-Klein[Show abstract] [Hide abstract]

**ABSTRACT:**We demonstrate in-line extraction of an ultra-stable frequency signal over an optical link of 92-km of installed telecommunication fibers, following the proposition of G. Grosche in 2010. We show that the residual frequency noise at the extraction end is noticeably below that at the main link output when the extraction is near the input end, as expected from a simple model of the noise compensation. We obtain relative frequency instabilities, expressed as overlapping Allan deviation, of 8x10-16 at 1 s averaging time and a few 10-19 at 1 day. These results are at the state-of-the-art for a link using urban telecommunication fibers. We also propose an improved scheme which delivers an ultra-stable signal of higher power, in order to feed a secondary link. In-line extraction opens the way to a broad distribution of an ultra-stable frequency reference, enabling a wide range of applications beyond metrology.Journal of the Optical Society of America B 02/2014; 31(4). · 2.21 Impact Factor

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Long-distance frequency transfer over an urban fiber link

using optical phase stabilization

H. Jiang,1 F. Kéfélian,2 S. Crane,1,3 O. Lopez,2 M. Lours,1 J. Millo,1 D. Holleville,1

P. Lemonde,1 Ch. Chardonnet,2 A. Amy-Klein,2 G. Santarelli1,*

1LNE-SYRTE, Observatoire de Paris, CNRS, 61 avenue de l'Observatoire, 75014 Paris, France

2Laboratoire de Physique des Lasers (LPL), UMR 7538, CNRS and Université Paris 13, 99 av. J.-

B. Clément, 93430 Villetaneuse, France

3Permanent address: United States Naval Observatory, 3450 Massachusetts Avenue NW,

Washington, DC 20392, USA

*Corresponding author: giorgio.santarelli@obspm.fr

We transferred the frequency of an ultra-stable laser over 86 km of urban fiber. The link is

composed of two cascaded 43-km fibers connecting two laboratories, LNE-SYRTE and LPL

in Paris area. In an effort to realistically demonstrate a link of 172 km without using spooled

fiber extensions, we implemented a recirculation loop to double the length of the urban fiber

link. The link is fed with a 1542-nm cavity stabilized fiber laser having a sub-Hz linewidth.

The fiber-induced phase noise is measured and cancelled with an all fiber-based

interferometer using commercial off the shelf pigtailed telecommunication components. The

compensated link shows an Allan deviation of a few 10-16 at one second and a few 10-19 at

10,000 seconds.

OCIS codes: 060.2360, 120.3930.

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1. INTRODUCTION

The transfer of ultra-stable frequencies between distant laboratories is required by many

applications in time and frequency metrology, fundamental physics, particle accelerators and

astrophysics. Remote clock comparisons are currently performed using satellites, either directly by

Two-Way Satellite Time and Frequency Transfer, or indirectly through the Global Positioning

System carrier phase measurement. However, both methods are limited by instability of 10-15 after

one day of averaging time [1] and are consequently insufficient to transfer modern cold atom

microwave frequency standards having demonstrated frequency stability of a few 10-16 at one day

[2].

Progress on satellite-based links may lower the noise floor to the 10-16 range at one day and

advanced space missions such as “ACES” (Atomic Clocks Ensemble in Space) [3] and “T2L2” [4]

are being designed to make comparisons in the high 10-17 at one day. However, even if achieved,

such performance would be insufficient for the next generation of optical clocks. Optical clocks

using a trapped single ion or cold atoms confined in lattice are expected to reach instability level of

10-17 or better at one day and will consequently require even more stable frequency transfer systems

[5,6]. Moreover the assets of the accuracy and stability of the optical clock are critically related to

an efficient way to compare remote clocks with short averaging time. Beyond metrology, high-

resolution clock comparison is essential for advanced tests in fundamental physics, such as tests of

the fundamental constants stability [7].

To overcome current space link limitations, the transmission of frequency standards over

optical fiber has been investigated for several years [8]. This technique takes advantage of the fact

that fiber has low attenuation, high reliability and the potential for phase noise cancellation.

Microwave frequency transmission using amplitude modulation of an optical carrier

demonstrated instability as low as 2×10-18 at one day over 86 km [9,10,11]. Direct optical frequency

transfer [12,13,14,15] can provide even better stability and be extended to greater distance. Indeed,

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optical frequency transfer is less sensitive to link attenuation, due to heterodyne detection. In

addition, the higher carrier frequency gives much better resolution for measuring link-induced

phase noise. In 2007, two pioneering experiments of optical frequency transfer over a fiber link of

more than 200 km were reported [13,14]. Both experiments used fiber spool extension of an urban

link and demonstrated the feasibility of a full optical link with instability in the 10-18 range. Since

last year several German research laboratories have been connected by 1000 km of dedicated fiber

from the national research network and the stabilization of the link is under development [16].

These are the first milestones towards continental scale fiber links.

In this paper, we report the transmission of a sub-Hz linewidth optical frequency reference

over an 86 km length, which we doubled in a second step to an extended length of 172 km through

a recirculation loop. After the description of the cavity-stabilized laser used to test the link, we

present the scheme of the link-induced phase noise compensation system. The frequency stability

performance of an 86-km urban fiber link is then reported and, finally, the link length is extended to

172 km and characterized.

2. LASER SOURCE

Two identical ultra low noise laser sources have been developed using 1542-nm 1-2-kHz linewidth

commercial fiber lasers stabilized on two identical ultra-stable cavities by the Pound-Drever-Hall

method [17]. The cavity consists of a 10-cm ULE spacer and two optically contacted ULE mirrors,

giving a measured finesse of ~ 800,000. The cavity, specially designed to minimize the vibration

sensitivity in all spatial directions [18], is mounted horizontally and sits on four Viton pads. It is

placed in a vacuum chamber with pressure below 10-7 mbar and the entire system is on a vibration-

isolation platform in an acoustical isolation box. About 2 μW of optical power, including ~ 30% in

the phase modulation sidebands, are typically sent onto the cavity with a coupling efficiency better

than 60%. A 350-kHz bandwidth locking is achieved using a double-pass acousto-optic modulator

with a cat’s eye retroreflector. The stabilized output of the laser can provide up to 10 mW of optical

power.

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To measure the laser frequency noise power spectral density, the two independent cavity

stabilized lasers are mixed on a photodetector, and the down-converted beat-note signal is measured

with a dynamic signal analyzer after frequency-to-voltage conversion. The phase noise power

spectral density versus Fourier frequency of the laser is presented on Fig. 1. Except for some

spurious peaks between 40 Hz and 100 Hz, it is largely below the phase noise of a 1-Hz linewidth

white frequency noise laser (dashed line on Fig. 1). The integrated phase noise from 1 Hz to 10 kHz

is below 0.2 rad rms (root mean square). The fractional frequency instability (Allan deviation) was

also calculated from the frequency counted beat-note signal and was found less than 2×10-15 at 1 s

and 10-14 at 100 s after a 0.3-Hz/s drift was removed.

3. COMPENSATED LINK SETUP

Fig. 2 shows the scheme of the compensated link based on the principle first described in [19]. The

ultra-stable laser light is divided into two parts using a fiber coupler. One arm provides the

reference signal for stability measurement and fiber-induced phase noise compensation, while the

other arm is connected to the link through an optical circulator (OC) followed by acousto-optic

modulator AOM1 (with frequency f1 ≈40 MHz). To compensate for the phase noise φp accumulated

along the fiber due to acoustical, mechanical and thermal perturbations, part of the signal at the

remote end is retraced back to the link through an optical circulator, after frequency shifting by

acousto-optic modulator AOM2 (with frequency f2=70 MHz). This return signal, which passes

twice through the link and experiences a phase noise 2φp, is mixed at the local end with the

reference signal on photodiode PD1. The beat note at frequency 2f1+f2 is phase locked to a stable

RF synthesizer using AOM1 driven by a voltage controlled oscillator. The phase-lock loop applies

the correction φc=-φp to the AOM1 frequency f1, thus to the optical signal phase and consequently

actively cancels the fiber-induced phase noise at the remote end of the fiber link. To magnify the

dynamic range of the servo loop and hence improve its robustness, a digital frequency divider by 40

has been used just ahead of the phase detector. The optical frequency (phase) instability of the link

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is defined as the difference between the local and remote end optical frequencies (phases). It is

measured on the beat-note at frequency f1+f2 provided by mixing the single trip and the reference

optical signals on photodiode PD2. Two polarization controllers are employed for optimizing the

beat-note signal amplitudes. The compensation system is entirely fibered and uses only commercial

off the shelf pigtailed telecommunications components.

4. TRANSMISSION OVER 86 KM

LPL and LNE-SYRTE, located in Paris area, are linked by a pair of 43-km telecommunication

fibers. Each fiber is composed of various sections of buried cables of the metropolitan network

spliced together. The attenuation of each fiber is about 12 dB. By connecting the two ends of the

fibers at LPL, the link length is extended to 86 km with local end and remote end both located in

LNE-SYRTE.

Fig. 3 shows the 86-km link optical phase noise power spectral density versus Fourier frequency,

without and with compensation. The beat note provided by PD2 is frequency divided by 40 and

down mixed to DC, the phase noise power spectral density is then measured with a dynamic signal

analyzer. It exhibits a roughly 1/f 2 roll-off from 1 Hz to 100 Hz with a wide bump between 10 Hz

and 100 Hz, and 1/f 4 behavior above 100 Hz. The integrated phase noise from 1 Hz to 1 kHz is

equal to 19.2 rad and 0.4 rad (rms), without and with compensation respectively (corresponding to

15 fs and 0.3 fs rms timing jitter). Beyond 1 kHz, the phase noise rolls down to the measurement

system floor and is negligible. The 0.4 rad (rms) corresponds to 85% of the optical power in the

carrier. The phase noise of the transmitted laser is only slightly degraded by the transfer and the

laser coherence time is therefore preserved at the output of the compensated link. This is an

important point for applications requiring distribution of narrow linewidth sources.

Laser phase noise can corrupt the link-induced phase noise measurement. Indeed, on PD2

are mixed two optical signals coming from the same source but delayed by 430-µs (due to the 86-

km propagation in the fiber). This generates on the beat-note signal a delayed self-heterodyne

interferometric phase noise [20] due to the laser phase noise, in addition to the link-induced phase

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noise to be compensated. This additional phase noise contribution can be calculated from the laser

phase noise (shown on Fig. 1) and is displayed in Fig. 3 (c). It shows that the laser phase noise is

sufficiently low and does not limit the performance of the stabilization.

Fig. 4 displays the experimental fiber-induced optical phase noise rejection for the 86-km

link versus Fourier frequency calculated by dividing the phase noise power spectral densities of the

compensated and uncompensated links. We have performed the Laplace domain analysis of the

compensation scheme and obtain an analytical expression of the rejection transfer function (black

dashed line on Fig. 4) [21]. This analysis reveals that the optimum proportional gain is about the

inverse of the link single trip time (2300 for an 86-km link) and that the rejection frequency

bandwidth is limited to 1/4ttrip (~ 600 Hz) where ttrip is the one-way trip delay in agreement with

[14]. Moreover, this analysis shows that the integrator used in the phase-lock loop improves

rejection only in a limited frequency range. Indeed, as already pointed out in [14], at low frequency

the rejection is limited by the link delay and scales as (f.ttrip)2 (red dotted line on Fig. 4)

independently of the loop gain. Our calculations are in good agreement with the measurements as

shown on Fig. 4.

For long term frequency stability characterization, the Allan deviation is the most common tool

and is typically obtained using frequency counter measurements. The original Allan deviation

defined in [22] can only be calculated from frequency samples obtained with a classical, or “π-type”,

counter using a uniform average over the measurement gate time. Indeed, modern enhanced-

resolution, or “Λ-type”, counters have been shown to lead [23], not to the classical Allan deviation,

but to a quantity proportional to the modified Allan deviation [24]. Consequently, we measure the

classical Allan deviation of the fractional frequency instability introduced by the link with a four-

channel π-type frequency counter. This counter is dead-time free in order to avoid bias in the

calculation of the Allan deviation [25]. We measure simultaneously the frequency instability of the

compensated link and the frequency instability of the compensation signal (at the voltage controlled

oscillator output), which represents the free running fiber frequency noise. The beat-note between

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the remote end and local end optical signals provided by PD2 is frequency divided by 40 and band

limited by a tracking filter based on a low noise quartz oscillator giving a measurement bandwidth

of ~10 Hz. This bandwidth is larger than the inverse of the gate time.

Fig. 5 shows the fractional frequency overlapping Allan deviation of the 86-km link with and

without compensation for several days of continuous operation. The Allan deviation scales down

with a 1/τ slope from 1 s to 100 s. The bump at 250 s, which corresponds to the half cycle time of

the air conditioning system, is due to thermal effects in the sections of the interferometric system

that are not actively compensated. After 1000 s of averaging time, the Allan deviation levels off in

the low 10-19 range probably also limited by the uncompensated section of the system. Without

filtering, the Allan deviation is 10 times higher. This is consistent with the fact that the Allan

deviation of a white phase noise is proportional to the square root of the noise bandwidth.

5. TRANSMISSION OVER 172 KM

Previous extended link results have been demonstrated by adding spooled fiber to an urban link

[13,14,15]. To simulate a longer link with a more realistic phase noise, we devised a new scheme,

represented in Fig. 6, to pass twice through the 86-km link leading to a full urban link of 172 km.

The optical signal is fed into the 86-km link through an optical coupler. At the end of the 86-km

link, a “frequency shifter mirror” is connected. This “mirror” consists of a unidirectional loop based

on an optical circulator and an acousto-optic modulator. An Erbium doped fiber amplifier (EDFA1)

with 17-dB gain is also implemented in order to compensate for losses due to recirculation (12 dB

due to the double pass combiner losses, 5 dB due to the optical circulator and AOM2 losses). As a

result, this is equivalent to a 172-km span link without intermediate optical amplifier and the

resulting phase noise is similar to the noise of a real 172-km telecom network link. A second optical

amplifier (EDFA2) was added at the remote end to amplify the return signal. Temperature

variations in EDFAs induce phase fluctuations, which degrade the long-term frequency stability. In

order to correctly compensate for this effect, the output optical signal should pass once through the

EDFAs when the round trip signal should pass twice. This is naturally the case for EDFA1, but not

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for EDFA2. This is overcome by adding a recirculation loop around EDFA2. To easily identify the

output and round trip signals AOM3 is inserted in this loop. At the output of PD1 the beat-note

signal at frequency 2(f1+f2)+f3+f4 is appropriate for link compensation while at the output of PD2

the beat-note signal at f1+f2 is used to derive the link stability (fi is the frequency of the AOM i).

This set-up could be simplified by using a bi-directional EDFA.

Fig. 7 displays the 172-km link phase noise power spectral density, without and with

compensation. As expected, the correction bandwidth is half the one obtained for the 86-km link

due to a double roundtrip delay. Moreover, at low frequency, the fiber-induced phase noise

rejection is 4 times lower than with the 86-km link, in agreement with the delay-limitation effect

discussed in section 4. The integrated phase noise from 1 Hz to 1 kHz is equal to 53 rad and 2.4 rad

(rms), without and with compensation respectively.

Fig. 8 shows the fractional frequency instability of the 172-km link. The Allan deviation is

about 4×10-16 at 1 second and in the range of 10-19 at 1 hour with a 10-Hz measurement bandwidth.

The system floor is measured by replacing the urban fiber with an optical attenuator having the

equivalent attenuation.

In addition to data obtained with π-type counter we have used a Λ-type counter, without the

10-Hz filter, to allow comparison with the results of [14,15] obtained with 76 km of urban fiber,

175 km of spooled fiber and four in-line EDFA. To avoid dead-time, the gate time of the counter

was set equal to the averaging time for averaging time ≤ 100 s. Data obtained with Λ-type counter

are shown with green star points on Fig. 8. They are better than with π-type counter, due to an

additional filtering of the phase noise. The Allan deviation is calculated for every averaging time

with the classical formula and not with the modified Allan deviation (as in reference [14,15] for

averaging time >10s). Indeed, when original Allan deviation formula is used, Λ-type counters report

directly a quantity similar to the modified Allan deviation. For comparison, the use of the modified

Allan deviation would lead in our case to a reduction factor of 2/3 on the Allan deviation for

averaging time above 100 s. Results are found similar to the data presented in [14,15]. Data

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obtained with longer averaging times show that frequency instability keeps falling off until 5000 s

and reach 3×10-19 with the Λ-type counter at 3000 s.

Comparison between the two configurations is not straightforward. First, the link noise

process is not time stationary due to urban environmental fluctuations. Moreover when the length of

the fiber is virtually doubled by the recirculation technique the phase noise power spectral density

of the free running link is twice the one of a single pass double length fiber, as detailed below.

Under the assumption that the fiber phase noise is uniformly spatially distributed, the phase

noise power spectral density is proportional to the length of the fiber. However, with the

recirculation technique the laser wave experiences twice the phase fluctuation at each point of the

fiber. These two contributions of each point are correlated for times longer than the single span

fiber delay tfiber, they therefore add up coherently. Consequently, for Fourier frequencies below

1/4tfiber, the phase noise power spectral density of a 2L-km link realized by recirculation is expected

to be four times that of an L-km fiber. One can therefore anticipate that the phase noise power

spectral density for the recirculated link is twice larger than would be expected for a real link of

172-km. Consequently the stability results obtained for the recirculated link should be considered

as an upper bound for a real link of the same length.

6. DISCUSSION

It is conceivable to extend the length of the link up to continental scales, 1000 km or more.

In a single segment approach however, major difficulties will arise. Firstly, fiber attenuation will

make mandatory in-line bidirectional amplifiers in order to provide sufficient power at the output

and allow phase locking at the local end. As discussed in section 5, bidirectional amplifiers phase

noise is cancelled within the control bandwidth. However, when cascading amplifiers, amplified

spontaneous emission can be very large and will require the use of narrow band optical filters to

overcome a significant degradation of the signal-to-noise ratio at both ends [14, 15]. Secondly, the

reduced bandwidth of the servo-loop and the reduced noise rejection level both due to the delay

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effect (See Section 4) will degrade the performance of the transmission. We have empirically

observed that the phase noise exhibits a 1/f2 dependence in the free running link. Assuming a linear

dependence of the phase noise power on the length of the link L Allan deviation scales as L3/2

[14,15]. One could hence expect an Allan deviation below 10-14 at one second for a 1000-km single

segment link in a 10-Hz measurement bandwidth, averaging down as 1/τ to the noise floor of the

system.

An alternative approach is to split the long distance link in shorter compensated segments

using intermediate stations. Each one will achieve three functions, to send back part of the received

signal to the previous station, to amplify (and filter if necessary) the received signal, to compensate

the phase noise induced by the following segment. The maximum distance of each segment will

depend on the fiber phase noise distribution, attenuation and on the total link length. This multiple

segment approach allows for an increased correction bandwidth and enhances the resolution of the

system. This would enable much better performance down to a level where the coherence of the

laser itself can be transferred, as demonstrated in section 4.

Beside the limitations due to the length of the link an other possible source of transmission

degradation is related to spurious back reflections which always occurs in a fiber system. They are

due to connector interfaces (typically -40dB to -60 dB), Rayleigh backscattering (typically -40 dB

with SMF fiber) and splicing points. These effects can be enhanced when online bidirectional

amplifiers are used. However, optical frequency transfer over fiber is not sensitive to single back-

reflection as back-reflected waves do not receive the correct frequency offsets from the AOMs in

our scheme and are consequently easily discriminated. This is not the case when double back-

reflections are considered. Double back-reflected waves lead to additional phase and amplitude

noise that is proportional to the fraction of the optical field double back-reflected. Since double

back-reflections occur identically on the way there and the way back, the double back-reflection

optical phase noise are also cancelled by the compensation system. Consequently, back-reflections,

even strong, do not limit the stability of the link.

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7. CONCLUSION

We have demonstrated a long-distance link for metrological optical frequency transfer using optical

phase stabilization over a dedicated fiber that lies buried beneath the urban environment of Paris,

France. Frequency transfer was demonstrated with instability of 1.5×10-16 at 1 s and integrates down

to the range of 10-19 at 500 s over 86 km. We have simulated a link at twice this distance via

recirculation in the fiber to represent the phase noise of a 172-km urban link. It shows instability of

4×10-16 at 1 s and a few 10-19 at 10,000 s, which is better than the anticipated performance of optical

clocks.

To broaden the use of this technique to more users and reach longer distances, an appealing

solution is to use the existing research, educational as well as commercial optical communication

networks that connect a large number of physics laboratories. This will require addressing several

difficulties. For instance, such a link will have to coexist with telecommunication traffic via the use

of wavelength division multiplexing. Another crucial point is that fibers in classical optical

telecommunication networks are used in a unidirectional way, whereas the compensation technique

will require bi-directional operation. Yet one more significant hurdle being that restricted access to

the fiber network infrastructure will require the design of an ultra-stable link that functions in a

virtually flawless fashion. We are currently developing solutions to make compatible the frequency

transfer technique and the optical communication networks, in particular to bypass unidirectional

optical amplifiers and to allow the transparent coexistence of the ultrastable signal and the data

modulated signal. This is the next challenging step towards a network for ultra stable frequency

transfer.

ACKNOWLEDGMENTS

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We acknowledge funding support from the Agence Nationale de la Recherche (ANR BLAN06-

3_144016). SYRTE is a Unité Mixte de Recherche of CNRS, Observatoire de Paris and UPMC.

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