  Efficiently discriminating beams carrying different orbital angular momentum
(OAM) is of fundamental importance for various applications including high
capacity optical communication and quantum information processing. We design
and experimentally verify a distinguished method for effectively splitting
different OAM-carried beams by introducing Dove prisms in a ring cavity.
Because of rotational symmetry broken of two OAM-carried beams with opposite
topological charges, their transmission spectra will split. When mode and
impedance matches between the cavity and one OAM-carried beam are achieved,
this beam will transmit through the cavity, and other beam will be reflected
without being destroyed their spatial shapes. In this case, the cavity acts
like a polarized beam splitter. The transmitting beam can be selected at your
will. The splitting efficiency can reach unity if the cavity is lossless and it
completely matches with the beam. Beams carry multi-OAMs can also be
effectively split by cascading ring cavities.
