Optical-approximation analysis of sidewall-spacing effects on the force between two squares with parallel sidewalls

TL;DR

This paper uses ray-optics approximation to analyze how sidewall spacing affects the Casimir force between two metallic blocks, capturing key physics despite neglecting diffraction effects.

Contribution

It demonstrates that ray optics qualitatively reproduces non-monotonic force behavior and quantifies diffraction's impact compared to exact numerical results.

Findings

Force varies non-monotonically with sidewall distance h

Ray optics captures essential multi-body interaction physics

Diffraction effects significantly influence Casimir forces

Abstract

Using the ray-optics approximation, we analyze the Casimir force in a two dimensional domain formed by two metallic blocks adjacent to parallel metallic sidewalls, which are separated from the blocks by a finite distance h. For h > 0, the ray-optics approach is not exact because diffraction effects are neglected. Nevertheless, we show that ray optics is able to qualitatively reproduce a surprising effect recently identified in an exact numerical calculation: the force between the blocks varies non-monotonically with h. In this sense, the ray-optics approach captures an essential part of the physics of multi-body interactions in this system, unlike simpler pairwise-interaction approximations such as PFA. Furthermore, by comparison to the exact numerical results, we are able to quantify the impact of diffraction on Casimir forces in this geometry.