  We study the van der Waals (vdW) interaction between a polarizable particle
and a grounded conducting corrugated surface. For sinusoidal corrugations, one
knows that, under the action of the lateral vdW force, an isotropic particle is
always attracted to the nearest corrugation peak, with such behavior called in
the present paper as peak regime. Here, considering an anisotropic polarizable
particle, and making analytical calculations valid beyond the proximity force
approximation (PFA), we show that the attraction is not only toward the peaks,
but, for certain particle orientations and distances from the surface, the
lateral force attracts the particle to the nearest corrugation valley (valley
regime), or even to an intermediate point between a peak and a valley
(intermediate regime). We also show that in the configurations of transition
between the peak and valley regimes the lateral vdW force vanishes, even in the
presence of a corrugated surface. In addition, we find that these new regimes
occur in general, for periodic and nonperiodic corrugated surfaces. Moreover,
we demonstrate that similar regimes arise in the classical interaction between
a neutral polarized particle and a rough surface. The description of these
valley and intermediate regimes, which are out of reach of the predictions
based on the PFA, may be relevant for a better understanding of the interaction
between anisotropic particles and corrugated surfaces in classical and quantum
physics, with experimental verifications feasible in both domains.
