Casimir energy and geometry : beyond the Proximity Force Approximation

TL;DR

This paper reviews how the Casimir effect depends on geometry, especially deviations from the Proximity Force Approximation, using scattering formalism to improve theoretical and experimental understanding of complex surface interactions.

Contribution

It discusses the extension of scattering formalism to non-specular reflections and its application to lateral Casimir forces beyond PFA.

Findings

Scattering formalism effectively models non-planar Casimir interactions.

Non-specular reflections are crucial for accurate Casimir force predictions.

Lateral Casimir force measurements could demonstrate geometry effects beyond PFA.

Abstract

We review the relation between Casimir effect and geometry, emphasizing deviations from the commonly used Proximity Force Approximation (PFA). We use to this aim the scattering formalism which is nowadays the best tool available for accurate and reliable theory-experiment comparisons. We first recall the main lines of this formalism when the mirrors can be considered to obey specular reflection. We then discuss the more general case where non planar mirrors give rise to non-specular reflection with wavevectors and field polarisations mixed. The general formalism has already been fruitfully used for evaluating the effect of roughness on the Casimir force as well as the lateral Casimir force or Casimir torque appearing between corrugated surfaces. In this short review, we focus our attention on the case of the lateral force which should make possible in the future an experimental demonstration of the nontrivial (i.e. beyond PFA) interplay of geometry and Casimir effect.