A New Angle on Second Harmonic Generation from a Small Hole in a Metal Film

Bethe’s theory treats a subwavelength aperture in a metal film as the combination of a parallel magnetic dipole and transverse electric dipole. For linear optics, this gives the usual dipole transmission; however, for nonlinear optics, it is interesting to consider how these two components interact. While many works have studied the nonlinear harmonic generation for metal nanoapertures, here we show that the Lorentz force dominates the second harmonic generation by an order of magnitude at angled incidence where the generation is maximized. The angular dependence matches that of the magnetic and electric dipoles accounting for Lambert’s cosine law. The theoretical analysis and numerical calculations agree well with past experiments.