Surface-enhanced second-harmonic diffraction: Selective enhancement by spatial harmonics

Surface-enhanced second-harmonic diffraction from a corrugated silver surface is studied as a function of the Fourier decomposition of the surface profile. Numerical results are obtained using the reduced Rayleigh equations for the linear and second-harmonic fields. Scattering of the surface-plasmon-polariton (SPP)-enhanced, evanescent nonlinear polarization wave into radiative channels is shown to provide a sensitive probe of spatial-harmonic content. The presence of a specific higher harmonic in the surface profile allows preferential scattering of the enhanced nonlinear polarization into a certain diffraction order where a higher-order scattering mechanism might otherwise be operative. The propagating orders can thereby be selectively enhanced, in some cases, by many orders of magnitude. Calculations are presented for symmetric profiles and a range of grating periods. The nature of these selective enhancements suggests that optimized profiles for second-harmonic diffraction into a particular order can be formed by a superposition of two appropriately selected Fourier components. To explore this possibility, gratings with groove densities of 1200 and 1290 grooves/mm were studied by first determining the enhancement of each of the propagating orders at their respective optimum groove depths, assuming a purely sinusoidal profile. A search for the maximum enhancement of each order was then performed by varying the amplitudes of the grating fundamental and relevant order-enhancing higher harmonic. For the two periods considered, optimized profiles were found. The degree of coupling to the SPP at the second-harmonic frequency is shown to be important in determining the optimized profile as demonstrated by the substantially different enhancing properties of these similar groove-density gratings.