Surface-enhanced second-harmonic generation at a silver grating: A numerical study

This paper is the continuation of a previous article devoted to the rigorous electromagnetic theory of diffraction in nonlinear optics [R. Reinisch and M. Nevière, Phys. Rev. B 28, 1870 (1983)]. Now we present the corresponding numerical results using a plausible prescription to resolve remaining ambiguities in the boundary conditions. For the sake of specificity, we consider second-harmonic generation at a silver grating. The key point is that, in our formalism of diffraction in nonlinear optics, the groove depth of the grating is not considered as a perturbative parameter. As a consequence, we obtain the groove-depth dependence of the intensity of the propagating and evanescent diffracted orders at the second-harmonic frequency. We thus obtain the following important result: There exists an optimum groove depth for which the intensity of a given diffracted order at the signal frequency is the greatest. Using a dispersive outside medium (benzene), we obtain an enhancement of the second-harmonic efficiency (when compared to the flat-silver-interface case) as high as 2.85×${10}^4$.