Repulsive Casimir forces with finite-thickness slabs

TL;DR

This paper investigates how finite thickness affects Casimir forces between various slabs, revealing conditions for repulsion and stable equilibrium points, with potential tunability via material and geometric parameters.

Contribution

It extends Lifshitz theory to analyze Casimir forces involving finite-thickness slabs, including magnetic and chiral metamaterials, highlighting how thickness influences force behavior and stability.

Findings

Repulsive Casimir force at large distances with 1/d^5 dependence.

Stable equilibrium points can be tuned by slab thickness.

Finite thickness affects force magnitude and distance dependence, especially with substrates.

Abstract

We use the extended Lifshitz theory to study the behaviors of the Casimir forces between finite-thickness effective medium slabs. We first study the interaction between a semi-infinite Drude metal and a finite-thickness magnetic slab with or without substrate. For no substrate, the large distance $d$ dependence of the force is repulsive and goes as $1/d^5$; for the Drude metal substrate, a stable equilibrium point appears at an intermediate distance which can be tuned by the thickness of the slab. We then study the interaction between two identical chiral metamaterial slabs with and without substrate. For no substrate, the finite thickness of the slabs $D$ does not influence significantly the repulsive character of the force at short distances, while the attractive character at large distances becomes weaker and behaves as $1/d^6$; for the Drude metal substrate, the finite thickness of the slabs $D$ does not influence the repulsive force too much at short distances until $D=0.05\lambda_0$.