Lateral Optical Forces on Linearly-Polarized Emitters near a Reciprocal Substrate

We theoretically investigate the emergence of lateral (recoil) forces acting on generic dipole-type emitters in the vicinity of a reciprocal translation-invariant substrate. Surprisingly, we find that for linearly-polarized electric dipoles the lateral force invariably vanishes, independent of the anisotropy (e.g., tilted optical axes) or chirality of the substrate. We identify a novel opportunity to have a recoil force relying on a superposition of two linearly-polarized and collinear electric and magnetic dipoles. Counterintuitively, it is shown that when such an emitter stands above a uniaxial dielectric half-space with tilted optical axes it may experience a recoil force oriented along the direction perpendicular to the plane defined by the interface normal and the substrate optical axis.