Corrected Proximity-Force Approximation for Lateral Casimir Forces

TL;DR

This paper introduces a correction to the proximity-force approximation (PFA) that accurately predicts lateral Casimir forces between a sphere and a grating for larger separation ratios, enhancing estimation in experiments and engineering.

Contribution

A new correction to the PFA is proposed, extending its accuracy for lateral Casimir force predictions up to a separation-to-radius ratio of 0.5.

Findings

Corrected PFA accurately predicts lateral Casimir forces for separation ratios up to 0.5.

The correction improves upon the traditional PFA in relevant experimental regimes.

Inhomogeneity-induced forces in gradient gratings are beyond the corrected PFA.

Abstract

The widely-adopted proximity-force approximation (PFA) to estimate normal Casimir forces is known to be asymptotically exact at vanishing separations. In this letter, we propose a correction to the PFA, which is sufficiently accurate in predicting displacement-induced lateral Casimir forces between a sphere and a grating, for separation-to-radius ratio up to 0.5, far beyond the limit within which the application of PFA is previously restricted. Our result allows convenient estimation of Casimir interactions and thus shall be useful in relevant experimental and engineering Casimir applications. We also study the PFA for gradient gratings, and we find that the inhomogeneity-induced lateral Casimir force is beyond the corrected PFA.