The Scattering Approach to the Casimir Force

TL;DR

This paper reviews the scattering approach as a powerful method for calculating the Casimir force in complex, realistic configurations, emphasizing its advantages over simpler approximations.

Contribution

It introduces the scattering approach for Casimir force calculations in arbitrary geometries and materials, surpassing the limitations of the Proximity Force Approximation.

Findings

Scattering approach effectively describes Casimir forces in complex geometries.

Material and shape dependence of Casimir forces are accurately accounted for.

Beyond Proximity Force Approximation results are demonstrated.

Abstract

We present the scattering approach which is nowadays the best tool for describing the Casimir force in realistic experimental configurations. After reminders on the simple geometries of 1d space and specular scatterers in 3d space, we discuss the case of stationary arbitrarily shaped mirrors in electromagnetic vacuum. We then review specific calculations based on the scattering approach, dealing for example with the forces or torques between nanostructured surfaces and with the force between a plane and a sphere. In these various cases, we account for the material dependence of the forces, and show that the geometry dependence goes beyond the trivial {\it Proximity Force Approximation} often used for discussing experiments.