Impact of anisotropy on the interaction of an atom with a one-dimensional nano-grating

We study the interaction of an atom with a one-dimensional nano-grating within the framework of macroscopic QED, with special emphasis on possible anisotropic contributions. To this end, we first derive the scattering Green's tensor of the grating by means of a Rayleigh expansion and discuss its symmetry properties and asymptotes. We then determine the Casimir--Polder potential of an atom with the grating. In particular, we find that strong anisotropy can lead to a repulsive Casimir--Polder potential in the normal direction.