Surface scattering expansion for the Casimir-Polder interaction of a dielectric wedge

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 [Emig and 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.