  Light carrying orbital angular momentum (OAM) has been shown to be of use in
a disparate range of fields ranging from astronomy to optical trapping, and as
a promising new dimension for multiplexing signals in optical communications
and data storage. A challenge to many of these applications is a reliable and
dynamic method that sorts incident OAM states without altering them. Here we
report a wavelength-independent technique capable of dynamically filtering
individual OAM states based on the resonant transmission of a tunable optical
cavity. The cavity length is piezo-controlled to facilitate dynamic
reconfiguration, and the sorting process leaves both the transmitted and
reflected signals in their original states for subsequent processing. As a
result, we also show that a reconfigurable sorting network can be constructed
by cascading such optical resonators to handle multiple OAM states
simultaneously. This approach to sorting OAM states is amenable to integration
into optical communication networks and has implications in quantum optics,
astronomy, optical data storage and optical trapping.
