  We determine exactly the non-retarded Casimir-Polder interaction between a
neutral but polarizable particle and a perfectly reflecting sheet containing a
circular hole. The calculation reveals a strong dependence of the interaction
on the orientation of the particle's electric dipole moment with respect to the
surface. For a dipole moment that is polarized perpendicularly to the surface
the interaction potential has two saddle points lying above and below the plane
of the surface, on a line through the centre of the aperture. For a dipole
moment that is polarized parallel to the surface there is only one saddle point
right in the middle of the aperture. Provided the particles' motion could be
confined to a line through the middle of the aperture, this effect could
potentially be used for population-sensitive trapping of particles.
