  We employ transformation optics to study analytically nonlinear wave mixing
from a singular geometry of touching plasmonic wires. We obtain the analytic
solution of the near-field and complement it with a solution of the far-field
properties. We find, somewhat surprisingly, that optimal efficiency (in both
regimes) is obtained for the degenerate case of the Second-harmonic generation.
We exploit the analytic solution obtained to trace this behaviour to the
spatial overlap of the input fields near the geometric singularity.
