Casimir energy between a plane and a sphere in electromagnetic vacuum

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 interplate 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.