Exact eigenfunctions for square-wave gratings: Application to diffraction and surface-plasmon calculations

Abstract

We show that for dielectric or metallic gratings with square-wave geometry the photon eigenfunctions in the grating region can be expressed in analytical form. The knowledge of these eigenfunctions makes the diffraction calculation not only simple and direct, but also devoid of the many limitations encountered in other solution techniques. In particular, diffraction from deep gratings and the calculation of surface-plasmon excitations present no difficulties. Numerical results on diffraction efficiency are in good agreement with our experimental data. The near-field electromagnetic properties of Ag gratings are examined in detail. These results are of particular importance in understanding the optical behavior of molecules near a rough metal surface (for example, in surface-enhanced Raman scattering). It is shown that coincident with the excitation of surface plasmon, there is an enhancement of the local- (surface-) field intensity by a factor of 100-500. For molecules on a grating surface, such increase in local fields can imply an amplification of ${10}^{4}$-3\ifmmode\times\else\texttimes\fi{}${10}^{5}$ for the Raman scattering signal.