Ms6127Bwithfigures

3. Results and discussion 
We measure the fractional stability of the compensated link by analyzing the phase variation 
between the local end 9.15 GHz and the remote end 9.25 GHz (Fig. 1). The beat signal at 9.25 GHz 
is down-converted to DC by mixing with the 9.15 GHz input and the 100 MHz LO. Figure 2 shows 
the residual phase noise spectral density of the compensated 86-km optical link (red trace) measured 
at 9.25 GHz, the system noise floor obtained after replacing the fiber link with an equivalent optical 
attenuator (black dotted trace) and the noise of the laser diode, photodiode and amplifier (blue 
dashed trace). The latter noise does not limit the compensation system. The red trace shows a rather 
dense distribution of spurious bright lines due to the polarization scrambling process and their multi 
frequency mixing products converted into phase variations. These unwanted lines are not a limiting 
factor for distant clocks comparisons. However, in order to transfer an ultra-stable oscillator, it is 
necessary to remove the spurious lines beyond 50-100Hz. This could be done by locking a 
commercially available low phase-noise oscillator to the transmitted signal with a bandwidth around 
50 Hz and reducing its phase-noise close to the carrier.
Figure 3 shows the temporal behaviour of the link propagation delay in open and closed loop 
over 4 days. The open loop signal was obtained simultaneously with the closed loop phase by 
measuring the temperature of the 2.5 km heated spool used for the correction and converting it in 
phase. The free-running fiber propagation delay spans over about 2 ns while the closed loop signal 
is confined well below 200 fs peak-to-peak. This demonstrates that the correction systems have a 
rejection factor close to 10
4
. Figure 4 shows the Allan deviation calculated from the propagation 
delay data measured on the 86-km compensated link. A 15 Hz low-pass filter is used to remove the 
spurious lines and the high frequency phase noise of the microwave signal before phase sampling. 
We obtain a frequency instability of the link of 1.3
×
10
-15
at 1 s integration time and much better 
than 10
-18
at one day integration time (red circles). This result is compared with previous results at 
1 GHz (blue squares) [11] together with the free running frequency stability of the link (black 
diamonds). This demonstrates that we have significantly improved the frequency stability of the 
link by using amplitude modulation at higher microwave frequencies and minimizing the unwanted 
fiber propagation effects. A linear fit calculated over the entire dataset show a frequency bias of 
about 2
×
10
-19
, compatible with zero within the errors bars. 
The ultimate link stability is still an open question and we need to analyze the different 
sources limiting the stability. To demonstrate the PMD deleterious effects on the fiber propagation, 
we have removed the polarization scrambler at the remote end and performed a phase measurement. 

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In this case the long-term stability of the link is severely degraded (black squares in figure 5) and 
reaches a Flicker floor at around 10
-17
. We have also replaced the negative dispersion fiber with an 
equivalent optical attenuator. In this case both short-term and long-term stability are affected (blue 
triangles in figure 5). The compensation system noise floor is shown in figure 5 (grey diamonds) 
where the 86-km link has been replaced by an equivalent optical attenuator. Below 2000 s, there is a 
good agreement between the 86-km stability link (red circles) and the compensation system floor. 
The signal-to-noise ratio at the optical detection is limiting this noise floor at short term. The 
frequency instability scales with approximately a 
τ
-2/3
slope. This noise level has been obtained with 
a careful control of the thermal environment of the electronics package and the uncommon sections 
of the optical paths. Over the long term, the optical link stability is no longer limited by the 
compensator floor. This long-term instability can be attributed to residual PMD effects or amplitude 
modulation to phase modulation (AM/PM) conversion in photodiodes and mixers [22, 23].