  We present a technique for coherence transfer of laser light through a
branching fiber link, where the optical phase noise induced by environmental
perturbations via the fiber link is passively compensated by remote users
without the requirements of any active servo components. At each remote site,
an acousto-optic modulator (AOM) is simultaneously taken as a frequency
distinguisher for distinguishing its unique frequency from other sites' and as
an optical actuator for compensating the phase noise coming from the optical
fiber. With this configuration, we incorporate a long outside loop path
consisting of a fiber-pigtailed AOM into the loop, enabling the significant
reduction of the outside loop phase noise in the passive way. To further
address the residual out-of-loop phase noise coming from the interferometer and
the two-way optical frequency comparison setup, we design a low-noise active
temperature stabilization system. Measurements with a back-to-back system show
that the stability in our stabilization system is $2\times10^{-16}$ at 1 s,
reaching $2\times10^{-20}$ after 10,000 s. Adopting these techniques, we
demonstrate transfer of a laser light through a branching fiber network with 50
km and 145 km two fiber links. After being compensated for the 145 km fiber
link, the relative frequency instability is $3.4\times10^{-15}$ at the 1 s
averaging time and scales down to $3.7\times10^{-19}$ at the 10,000 s averaging
time. This proposed technique is suitable for the simultaneous transfer of an
optical signal to a number of independent users within a local area.
