  We present a tunable liquid crystal device that converts pure orbital angular
momentum eigenmodes of a light beam into equal-weight superpositions of
opposite-handed eigenmodes and vice versa. For specific input states, the
device may thus simulate the behavior of a {\pi}/2 phase retarder in a given
two-dimensional orbital angular momentum subspace, analogous to a quarter-wave
plate for optical polarization. A variant of the same device generates the same
final modes starting from a Gaussian input.
