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 -2.2, -0.03, and 1 fs/K. We use one of these optimized interferometers on a long haul compensated fiber link of 540 km. We obtain a relative frequency stability of 3*10^-20 after 10000s of integration time

Received Month X, XXXX; revised Month X, XXXX; accepted Month X, XXXX; posted Month X, XXXX (Doc. ID XXXXX); published Month X, XXXX 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 [1]. 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 8×10 -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.