  We investigate the Dirichlet-scalar equivalent of Casimir-Polder forces
between an atom and a surface with arbitrary uniaxial corrugations. The
complexity of the problem can be reduced to a one-dimensional Green's function
equation along the corrugation which can be solved numerically. Our technique
is fully nonperturbative in the height profile of the corrugation. We present
explicit results for experimentally relevant sinusoidal and sawtooth
corrugations. Parameterizing the deviations from the planar limit in terms of
an anomalous dimension which measures the power-law deviation from the planar
case, we observe up to order-one anomalous dimensions at small and intermediate
scales and a universal regime at larger distances. This large-distance
universality can be understood from the fact that the relevant fluctuations
average over corrugation structures smaller than the atom-wall distance.
