Geometrical dependence in Casimir-Polder repulsion

Repulsion, induced from quantum vacuum fluctuations, for an anisotropically polarizable atom on the symmetry axis of an anisotropically polarizable annular disk is studied. There exist two torsion-free points on each side of the annular disk, where the interaction energy is orientation independent. The position of the second of the two torsion-free points, on either side of the disk, is shown to determine the orientation dependence of the atom at distances far from the plate, revealing a geometrical dependence. In the ring limit of the annular disk, an additional region of repulsion emerges.