Role of diffraction in the Casimir effect beyond the proximity force approximation

V. Henning, B. Spreng, M. Hartmann, G.-L. Ingold, and P. A. Maia Neto

J. Opt. Soc. Am. B 36, C77 (2019) DOI: 10.1364/JOSAB.36.000C77

We derive the leading-order correction to the proximity force approximation (PFA) result for the electromagnetic Casimir interaction in the plane–sphere geometry by developing the scattering approach in the plane-wave basis. Expressing the Casimir energy as a sum over round trips between plane and sphere, we find two distinct contributions to the correction. The first one results from the variation of the Mie reflection operator, calculated within the geometric optical Wentzel–Kramers–Brillouin (WKB) approximation, over the narrow Fourier interval associated with specular reflection at the vicinity of the point of closest approach on the spherical surface. The second contribution, accounting for roughly 90% of the total correction, results from the modification of the geometric optical WKB Mie scattering amplitude due to diffraction. Our derivation recovers the known leading-order correction to the PFA and shows that all contributing scattering channels are of a local nature.