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

Abstract

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 the peak, valley, and intermediate regimes, respectively. In the present paper, we investigate how these regimes are affected by the consideration of two nondispersive semi-infinite dielectrics, ${\ensuremath{\epsilon}}_{1}$ and ${\ensuremath{\epsilon}}_{2}$, separated by a corrugated interface. Specifically, we study the vdW interaction between a neutral anisotropic polarizable particle, embedded in dielectric ${\ensuremath{\epsilon}}_{2}$, and dielectric ${\ensuremath{\epsilon}}_{1}$. We show that when ${\ensuremath{\epsilon}}_{2}<{\ensuremath{\epsilon}}_{1}$, the peak, valley, and intermediate regimes have, apart from 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 ${\ensuremath{\epsilon}}_{2}>{\ensuremath{\epsilon}}_{1}$, one might expect a mere permutation between the peak and valley regimes in comparison to the case ${\ensuremath{\epsilon}}_{2}<{\ensuremath{\epsilon}}_{1}$. Surprisingly, we find that when ${\ensuremath{\epsilon}}_{2}>{\ensuremath{\epsilon}}_{1}$, 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.