Surface Scattering Expansion for the Casimir-Polder Interaction of a Dielectric Wedge

TL;DR

This paper develops a numerical method to compute the Casimir-Polder interaction between a polarizable particle and a dielectric wedge, revealing a close relation to the perfect conductor case, thus advancing understanding of edge effects in fluctuation-induced forces.

Contribution

It introduces a basis-free numerical implementation of a multiple scattering expansion to evaluate the CP potential for dielectric wedges across various dielectric constants.

Findings

CP potential for smoothed dielectric wedge relates to perfect conductor wedge

Numerical estimates obtained for a wide range of dielectric constants

Potential of a perfect electric conductor wedge is exactly known

Abstract

The electromagnetic scattering amplitude of a dielectric wedge is not known in closed form. This makes the computation of the Casimir-Polder (CP) interaction between a polarizable particle and a dielectric wedge challenging. This geometry is a prototype for the effect of edges on fluctuation-induced interactions, and hence it is important to employ new methods for this problem. Using a recently developed multiple scattering expansion [T. Emig and G. Bimonte, Phys. Rev. Lett. 130, 200401 (2023)], here we implement a basis-free numerical evaluation of this expansion to obtain precise estimates of the CP potential for a wedge over a wide range of dielectric constants. A remarkable finding is that the CP potential for a dielectric wedge with a smoothed edge is closely related to the potential of a sharp wedge made of a perfect electric conductor. The latter potential is known exactly, making this relation particularly useful in practice.