A quasi-analytical modal approach for computing Casimir interactions in periodic nanostructures

TL;DR

This paper introduces an analytical modal method for calculating Casimir forces in periodic nanostructures, enhancing accuracy and analytical insight over previous approaches.

Contribution

It develops a nearly fully analytical modal approach using exact eigenvectors and simple transcendental equations, improving calculations of Casimir interactions in nanostructures.

Findings

Exact eigenvectors improve accuracy

Eigenvalues solved via simple transcendental equations

Analytical predictions for large separation limits

Abstract

We present an almost fully analytical technique for computing Casimir interactions between periodic lamellar gratings based on a modal approach. Our method improves on previous work on Casimir modal approaches for nanostructures by using the exact form of the eigenvectors of such structures, and computing eigenvalues by solving numerically a simple transcendental equation. In some cases eigenvalues can be solved for exactly, such as the zero frequency limit of gratings modeled by a Drude permittivity. Our technique also allows us to predict analytically the behavior of the Casimir interaction in limiting cases, such as the large separation asymptotics. The method can be generalized to more complex grating structures, and may provide a deeper understanding of the geometry-composition-temperature interplay in Casimir forces between nanostructures.