Regimes of the lateral van der Waals force in the presence of dielectrics

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