Second-harmonic generation in reflection from a metallic grating

Abstract

We present a nonperturbative theory of second-harmonic generation in reflection from a metallic grating. $p$-polarized light of frequency $\omega$ is assumed to be incident on the grating surface from the vacuum side, with the plane of incidence perpendicular to the grooves of the grating. We employ the method of reduced Rayleigh equations to solve Maxwell's equations in the presence of a nonlinear polarization and calculate the diffracted field at the frequency $2\omega$. In the vicinity of the frequency where the incident photon couples to surface polaritons on the grating we obtain an enhancement of the second-harmonic intensity by a factor of ~${10}^4$ over its value for a flat surface. The effect of the surface current density in the nonlinear polarization on the enhancement is analyzed. Numerical results are presented for a grating of silver.