  Laguerre-Gauss beams, and more generally the orbital angular momentum of
light (OAM) provide valuable research tools for optical manipulation,
processing, imaging and communication. Here we explore the high-efficiency
frequency conversion of OAM in a four-wave mixing process in rubidium vapour.
Conservation of the OAM in the two pump beams determines the total OAM shared
by the generated light fields at 420 nm and 5.2 um - but not its distribution
between them. We experimentally investigate the spiral bandwidth of the
generated light modes as a function of pump OAM. A small pump OAM is
transferred almost completely to the 420 nm beam. Increasing the total pump OAM
broadens the OAM spectrum of the generated light, indicating OAM entanglement
between the generated light fields. This clears the path to high-efficiency OAM
entanglement between widely disparate wavelengths.
