Second harmonic generation by periodically-structured metal surfaces

We present an approach to calculating second harmonic generation from periodically-structured metal surfaces. It requires the numerical solution of Maxwell's equations at both the first and second harmonic, but the electronic response to these fields is treated by a parametrization scheme developed earlier. Several model systems are considered, including metal patches of various shapes or holes in a metal film. Detailed calculations using the finite-difference time-domain method lead to predictions of the frequency dependence of second harmonic generation for different diffracted beams and polarizations. There is more spectral structure than what is evident in the linear reflection or transmission.