  Nematic liquid-crystal devices are a powerful tool to structure light in
different degrees of freedom, both in classical and quantum regimes. Most of
these devices exploit either the possibility of introducing a
position-dependent phase retardation with a homogeneous alignment of the optic
axis -- e.g., liquid-crystal-based spatial light modulators -- or conversely,
with a uniform but tunable retardation and patterned optic axis, e.g.,
$q$-plates. The pattern is the same in the latter case on the two alignment
layers. Here, a more general case is considered, wherein the front and back
alignment layers are patterned differently. This creates a non-symmetric device
which can exhibit different behaviours depending on the direction of beam
propagation and effective phase retardation. In particular, we fabricate
multi-$q$-plates by setting different topological charges on the two alignment
layers. The devices have been characterized by spatially resolved Stokes
polarimetry, with and without applied electric voltage, demonstrating new
functionalities.
