Sum frequency generation from touching wires: a transformation optics approach.

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 far-field properties. We find, somewhat surprisingly, that optimal efficiency (in both regimes) is obtained for the degenerate case of second-harmonic generation. We exploit the analytic solution obtained to trace this behavior to the spatial overlap of input fields near the geometric singularity.