  We analyze theoretically 4-terminal electronic devices composed of two
crossed graphene nanoribbons (GNRs) and show that they can function as beam
splitters or mirrors. These features are identified for electrons in the
low-energy region where a single valence or conduction band is present. Our
modeling is based on $p_z$ orbital tight-binding with Slater--Koster type
matrix elements fitted to accurately reproduce the low-energy bands from
density functional theory calculations. We analyze systematically all devices
that can be constructed with either zigzag or armchair GNRs in AA and AB
stackings. From Green's function theory the elastic electron transport
properties are quantified as a function of the ribbon width. We find that
devices composed of relatively narrow zigzag GNRs and AA-stacked armchair GNRs
are the most interesting candidates to realize electron beam splitters with a
close to 50-50 ratio in the two outgoing terminals. Structures with wider
ribbons instead provide electron mirrors, where the electron wave is mostly
transferred into the outgoing terminal of the other ribbon, or electron filters
where the scattering depends sensitively on the wavelength of the propagating
electron. We also test the robustness of these transport properties against
variations in intersection angle, stacking pattern, lattice deformation
(uniaxial strain), inter-GNR separation, and electrostatic potential
differences between the layers. These generic features show that GNRs are
interesting basic components to construct electronic quantum optical setups.
