  Manipulation of orbital angular momentum (OAM) of light is essential in
OAM-based optical systems. Especially, OAM divider, which can convert the
incoming OAM mode into one or several new smaller modes in proportion at
different spatial paths, is very useful in OAM-based optical networks. However,
this useful tool was never reported yet. For the first time, we put forward a
passive OAM divider based on coordinate transformation. The device consists of
a Cartesian to log-polar coordinate converter and an inverse converter. The
first converter converts the OAM light into a rectangular-shaped plane light
with a transverse phase gradient. And the second converter converts the plane
light into multiple diffracted light. The OAM of zeroth-order diffracted light
is the product of the input OAM and the scaling parameter. The residual light
is output from other diffracted orders. Furthermore, we extend the scheme to
realize equal N-dividing of OAM and arbitrary dividing of OAM. The ability of
dividing OAM shows huge potential for OAM-based classical and quantum
information processing.
