Attenuation and dispersion of surface polaritons on gratings

Abstract

We present theoretical studies of the influence of a diffraction grating on the dispersion relation and lifetime of surface polaritons which propagate on a periodic metallic grating. Several issues are addressed. We compare the predictions of a perturbation-theoretic analysis with the results of a nonperturbative approach based on use of the extinction theorem. The grating-induced attenuation arises from radiative decay of the surface polariton; the radiative width of the mode is compared with the magnitude of the minigaps in the dispersion relation induced by the grating. We also compare grating-induced frequency shifts and damping rates calculated directly from the implicit dispersion relation with the width and position of reflectivity dips, as calculated from a nonperturbative treatment of the coupling of an incident photon to the grating. The effects of introducing asymmetry in the grating profile are also explored quantitatively.