  By using two-way frequency transfer, we demonstrate ultra-high resolution
comparison of optical frequencies over a telecommunication fiber link of 100 km
operating simultaneously digital data transfer. We first propose and experiment
a bi-directional scheme using a single fiber. We show that the relative
stability at 1 s integration time is 7 10^18 and scales down to 5 10^21. The
same level of performance is reached when an optical link is implemented with
an active compensation of the fiber noise. We also implement a real-time
two-way frequency comparison over a uni-directional telecommunication network
using a pair of parallel fibers. The relative frequency stability is 10^15 at 1
s integration time and reaches 2 10^17 at 40 000 s. The fractional uncertainty
of the frequency comparisons was evaluated for the best case to 2 10^20. These
results open the way to accurate and high resolution frequency comparison of
optical clocks over intercontinental fiber networks.
