  The orbital angular momentum (OAM) spatial degree of freedom of light has
been widely explored in many applications, including telecommunications,
quantum information and light-based micro-manipulation. The ability to separate
and distinguish between the different transverse spatial modes is called mode
sorting or mode demultiplexing, and it is essential to recover the encoded
information in such applications. An ideal $d$ mode sorter should be able to
faithfully distinguish between the different $d$ spatial modes, with minimal
losses, have $d$ outputs, and have fast response times. All previous mode
sorters rely on bulk optical elements such as spatial light modulators, which
cannot be quickly tuned and have additional losses if they are to be integrated
with optical fiber systems. Here we propose and experimentally demonstrate, to
the best of our knowledge, the first all-in-fiber method for OAM mode sorting
with ultra-fast dynamic reconfigurability. Our scheme first decomposes the OAM
mode in fiber-optical linearly polarized (LP) modes, and then
interferometrically recombines them to determine the topological charge, thus
correctly sorting the OAM mode. In addition, our setup can also be used to
perform ultra-fast routing of the OAM modes. These results show a novel and
fiber integrated form of optical spatial mode sorting that can be readily used
for many new applications in classical and quantum information processing.
