  We show that for the two widely used configurations of the double-$\Lambda$
atom-light coupling scheme, one where the control fields are applied in the
same $\Lambda$-subsystem and another where they applied in different
$\Lambda$-subsystems, the forward propagation of the probe and signal fields is
described by the same set of equations. We then use optimal control theory to
find the spatially-dependent optimal control fields which maximize the
conversion efficiency from the probe to the signal field, for a given optical
density. The present work is expected to find application in the implementation
of efficient frequency and orbital angular momentum conversion devices for
quantum information processing, as well as to be useful to many other
applications using the double-$\Lambda$ atom-light coupling scheme.
