Advancing numerics for the Casimir effect to experimentally relevant aspect ratios

Within the scattering theoretical approach, the Casimir force is obtained numerically by an evaluation of the round trip of an electromagnetic wave between the objects involved. Recently, Hartmann et al (2017 Phys. Rev. Lett. 119 043901) have shown that a symmetrization of the scattering operator provides significant advantages for the numerical evaluation of the Casimir force in the experimentally relevant sphere–plane geometry. Here, we discuss in more detail how the symmetrization modifies the scattering matrix in the multipole basis and how computational time is reduced. As an application, we discuss how the Casimir force in the sphere–plane geometry deviates from the proximity force approximation as a function of the geometric parameters. (paper)