Casimir interaction of dielectric gratings

TL;DR

This paper presents an exact theoretical solution for the Casimir force between arbitrary dielectric gratings, validated by experiments with silicon gratings and gold spheres, showing good agreement with measurements.

Contribution

It introduces a novel exact method for calculating Casimir forces between periodic dielectric structures, improving accuracy over approximate methods.

Findings

Exact solution matches experimental measurements

Good agreement with PFA predictions

Applicable to various dielectric grating configurations

Abstract

We derive an exact solution for the Casimir force between two arbitrary periodic dielectric gratings and illustrate our method by applying it to two nanostructured silicon gratings. We also reproduce the Casimir force gradient measured recently [1] between a silicon grating and a gold sphere taking into account the material dependence of the force. We find good agreement between our theoretical results and the measured values both in absolute force values and the ratios between the exact force and PFA predictions.