# Advancing numerics for the Casimir effect to experimentally relevant aspect ratios

## TL;DR

This paper improves numerical methods for calculating the Casimir force in sphere-plane geometries by symmetrizing the scattering operator, enabling more accurate and efficient computations relevant to experiments.

## Contribution

It introduces a symmetrization technique for the scattering matrix that enhances numerical efficiency and accuracy in Casimir force calculations for sphere-plane setups.

## Key findings

- Symmetrization reduces computational time significantly.
- Deviations from the proximity force approximation are quantified.
- Method improves numerical evaluation for experimentally relevant aspect ratios.

## Abstract

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 M et al. 2017, Phys. Rev. Lett. 119 043901] it was 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.