  The Talbot self-imaging phenomenon is a fundamental interference effect that
is natural to all waves with a periodic structure. We theoretically and
experimentally study the Talbot effect for optical waves in the transverse
angular domain using whispering-gallery modes of step-index multimode fibers,
which carry a high orbital angular momentum and fulfill the required quadratic
dispersion relation. By using the complex interference along the core-cladding
interface of these fibers, we experimentally demonstrate that the high-order
fractional Talbot effect can be used to implement 9- and 30-port beamsplitters
using only off-the-shelf components in a compact arrangement. In addition, we
show that the beamsplitters can be efficiently interfaced with single-mode
fibers, such that our work not only extends the recent developments on the
angular Talbot effect to widely available step-index multimode fibers, but also
demonstrates a powerful application as a signal multiplexer, which becomes more
compact as the number of channels is increased.
