Nonlinear electromagnetic response of corrugated metallic gratings

We describe a theoretical formalism to study the second-harmonic generation in periodically corrugated surfaces illuminated by a plane wave. The incident wave vector is contained in the plane perpendicular to the grating grooves. Our analysis is based on the most general expression for the nonlinear polarization of a homogeneous and isotropic medium. The diffraction problem is solved using a Rayleigh method, and the numerical technique is illustrated by examples for which the nonlinear susceptibilities are calculated with a free-electron model. (C) 2011 Optical Society of America