  Wave propagation on the surface of cylinders exhibits interferometric self
imaging, much like the Talbot effect in the near-field diffraction at periodic
gratings. We report the experimental observation of the cylindrical Talbot
carpet in weakly-guiding ring-core fibers for classical light fields. We
further show that the ring-core fiber acts as a high-order optical beamsplitter
for single photons, whose output can be controlled by the relative phase
between the input light fields. By also demonstrating high-quality two-photon
interference between indistinguishable photons sent into the ring-core fiber,
our findings open the door to applications in optical telecommunications as a
compact beam multiplexer as well as in quantum information processing tasks as
a scalable realization of a linear optical network.
