  In a recent paper, it was shown that, under the action of the lateral van der
Waals (vdW) force due to a perfectly conducting corrugated surface, a neutral
anisotropic polarizable particle in vacuum can be attracted not only to the
nearest corrugation peak, but also to a valley, or an intermediate point
between a peak and a valley, with such behaviors called peak, valley and
intermediate regimes, respectively. In the present paper, we investigate how
these regimes are affected by the consideration of two non-dispersive
semi-infinite dielectrics $\epsilon_{1}$ and $\epsilon_{2}$, separated by a
corrugated interface. Specifically, we study the vdW interaction between a
neutral anisotropic polarizable particle, embedded in the dielectric
$\epsilon_{2}$, and the dielectric $\epsilon_{1}$. We show that when
$\epsilon_{2}<\epsilon_{1}$ the peak, valley and intermediate regimes have,
unless numerical factors, behaviors similar to those found for the situation
where the particle is in vacuum and interacting with a conducting medium. For
the case $\epsilon_{2}>\epsilon_{1}$, one might expect a mere permute between
the peak and valley regimes, in comparison to the case
$\epsilon_{2}<\epsilon_{1}$. Surprisingly, we find that when
$\epsilon_{2}>\epsilon_{1}$ the regimes exhibit a very different and nontrivial
behavior. Moreover, we show that similar regimes arise in the classical case
involving a neutral polarized particle. The description of how the peak, valley
and intermediate regimes are affected by the presence of dielectrics may be
relevant for a better understanding of the interaction between anisotropic
particles and corrugated surfaces.
