Plasmonic interferences sampled by a diffraction grating generate moiré fringes

We report on the formation of moir\'e patterns when observing the diffraction of surface plasmons by periodic gratings of finite extent with an imaging spectrometer that maps the light emission as a function of the wavelength and the propagation distance. This phenomenon results from the formation of standing waves upon the partial reflection of surface plasmons at the far end of the grating and their scattering by the periodic corrugations. The moir\'e fringes are created as a result of the incommensurability between the sampling pitch of the grating and the wavelength-dependent standing waves. We introduce a scalar model that supports these observations and provides physical insight into these results, including a method to estimate the complex Fresnel reflection coefficient of a surface plasmon at the edge of a grating.