Non-monotonic Casimir interaction: The role of amplifying dielectrics

TL;DR

This paper investigates how amplifying and absorptive dielectrics influence Casimir interactions between corrugated metallic plates, revealing non-monotonic forces and stable or unstable equilibria depending on the system configuration.

Contribution

It introduces a path-integral quantization approach to analyze non-monotonic Casimir forces caused by amplifying and absorptive dielectrics in various configurations.

Findings

Amplifying slabs increase Casimir interactions, absorptive slabs decrease them.

Normal Casimir force can be non-monotonic with amplifying slabs, leading to stable equilibrium.

Force behavior varies with boundary conditions and dielectric layering, affecting stability.

Abstract

The normal and the lateral Casimir interactions between corrugated ideal metallic plates in the presence of an amplifying or an absorptive dielectric slab has been studied by the path-integral quantization technique. The effect of the amplifying slab, which is located between corrugated conductors, is to increase the normal and lateral Casimir interactions, while the presence of the absorptive slab diminishes the interactions. These effects are more pronounced if the thickness of the slab increases, and also if the slab comes closer to one of the bounding conductors. When both bounding ideal conductors are flat, the normal Casimir force is non-monotonic in the presence of the amplifying slab and the system has a stable mechanical equilibrium state, while the force is attractive and is weakened by intervening the absorptive dielectric slab in the cavity. By replacing one of the flat conductors by a flat ideal permeable plate the force becomes non-monotonic and the system has an unstable mechanical equilibrium state in the presence of either an amplifying or an absorptive slab. When the left side plate is conductor and the right one is permeable, the force is non-monotonic in the presence of a double-layer DA (dissipative-amplifying) dielectric slab with a stable mechanical equilibrium state, while it is purely repulsive in the presence of a double-layer AD (amplifying-dissipative) dielectric slab.