Casimir energy between a plane and a sphere in electromagnetic vacuum

TL;DR

This paper calculates the Casimir energy between a plane and a sphere in electromagnetic vacuum, revealing significant deviations from the proximity-force approximation in realistic conditions.

Contribution

It develops a scattering formula using plane-waves and multipole basis for arbitrary sphere radius and distance, improving precision over previous scalar models.

Findings

Electromagnetic Casimir energy deviates from PFA more rapidly than scalar models predict.

The developed formula is valid for any sphere size and separation.

Results are relevant for precise Casimir force experiments.

Abstract

The Casimir energy is computed in the geometry of interest for the most precise experiments, a plane and a sphere in electromagnetic vacuum. The scattering formula is developed on adapted plane-waves and multipole basis, leading to an expression valid for arbitrary relative values of the sphere radius and inter-plate distance. In the limiting case of perfect reflection, the electromagnetic result is found to depart from the commonly used proximity-force approximation (PFA) significantly more rapidly than expected from scalar computations.