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

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.