  We study surface second-harmonic generation (SHG) from a singular plasmonic
structure consisting of touching metallic wires. We use the technique of
transformation optics and relate the structure to a rather simpler geometry, a
slab waveguide. This allows us to obtain an analytical solution to the problem,
revealing rich physical insights. We identify various conditions that govern
the SHG efficiency. Importantly, our analysis demonstrates that apart from the
mode-matching condition, phase-matching condition is relevant even for this
sub-wavelength structure. Furthermore, we identify a geometric factor which was
not identified before. We support our analysis with numerical simulations.
