  Superconductors connected to normal metallic electrodes at the nanoscale
provide a potential source of non-locally entangled electron pairs. Such states
would arise from Cooper pairs splitting into two electrons with opposite spins
tunnelling into different leads. In an actual system the detection of these
processes is hindered by the elastic transmission of individual electrons
between the leads, yielding an opposite contribution to the non-local
conductance. Here we show that electromagnetic excitations on the
superconductor can play an important role in altering the balance between these
two processes, leading to a dominance of one upon the other depending on the
spatial symmetry of these excitations. These findings allow to understand some
intriguing recent experimental results and open the possibility to control
non-local transport through a superconductor by an appropriate design of the
experimental geometry.
