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 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.