Modal Approach to Casimir Forces in Periodic Structures

TL;DR

This paper introduces a modal method to compute finite temperature Casimir forces between periodically structured surfaces, validated against experiments and compared with approximation methods.

Contribution

It develops a novel modal approach to accurately calculate Casimir interactions in complex periodic geometries, improving upon existing approximation techniques.

Findings

The modal approach accurately predicts Casimir forces for patterned surfaces.

Comparison with experiments shows good agreement.

Deviations from proximity force approximation are quantified.

Abstract

We present a modal approach to calculate finite temperature Casimir interactions between two periodically modulated surfaces. The scattering formula is used and the reflection matrices of the patterned surfaces are calculated decomposing the electromagnetic field into the natural modes of the structures. The Casimir force gradient from a deeply etched silicon grating is evaluated using the modal approach and compared to experiment for validation. The Casimir force from a two dimensional periodic structure is computed and deviations from the proximity force approximation examined.