Digital Doppler-cancellation servo for ultra-stable optical frequency dissemination over fiber

Progress made in optical references, including ultra-stable Fabry-Perot cavities, optical frequency combs and optical atomic clocks, have driven the need for ultra-stable optical fiber networks. Telecom-wavelength ultra-pure optical signal transport has been demonstrated on distances ranging from the laboratory scale to the continental scale. In this manuscript, we present a Doppler-cancellation setup based on a digital phase-locked loop for ultra-stable optical signal dissemination over fiber. The optical phase stabilization setup is based on a usual heterodyne Michelson-interferometer setup, while the Software Defined Radio (SDR) implementation of the phase-locked loop is based on a compact commercial board embedding a field programmable gate array, analog-to-digital and digital-to-analog converters. Using three different configurations including an undersampling method, we demonstrate a 20 m long fiber link with residual fractional frequency instability as low as $10^{-18}$ at 1000 s, and an optical phase noise of $-70$ dBc/Hz at 1 Hz with a telecom frequency carrier.