The Casimir energy between nanostructured gratings of arbitrary periodic profile

TL;DR

This paper investigates how the Casimir energy between nanostructured gratings varies with different arbitrary periodic profiles and lateral displacements, revealing a strong dependence on the shape of the corrugations.

Contribution

It introduces a numerical method modeling arbitrary periodic profiles as stacks of rectangular slices to evaluate Casimir energy beyond the proximity force approximation.

Findings

Casimir energy strongly depends on the shape of the corrugation profiles.

The numerical model captures deviations from PFA predictions.

Shape effects are significant at comparable separations and geometric parameters.

Abstract

We study the lateral dependence of the Casimir energy for different corrugated gratings of arbitrary periodic profile. To this end we model the profiles as stacks of horizontal rectangular slices following the profiles' shape and evaluate numerically the Casimir energy between them for different relative lateral displacements of the two corrugated plates. We compare our results with predictions obtained within the proximity force approximation (PFA). At comparable separation of the corrugated plates and geometric parameters, we find a strong dependence of the Casimir energy on the shape of the corrugation profiles.