Effect of the Heterogeneity of Metamaterials on Casimir-Lifshitz Interaction

TL;DR

This paper investigates how the structural heterogeneity of metamaterials influences Casimir-Lifshitz forces, revealing oscillatory behavior and lateral forces that depend on the patterning at nanometer scales.

Contribution

It extends perturbation theory to account for non-uniform magnetic permeability, analyzing the impact of patterned heterogeneity on Casimir-Lifshitz interactions.

Findings

Patterned structures induce oscillatory Casimir-Lifshitz forces.

Non-uniformity leads to lateral Casimir-Lifshitz forces.

Results suggest revisiting previous experiments to include heterogeneity effects.

Abstract

The Casimir-Lifshitz interaction between metamaterials is studied using a model that takes into account the structural heterogeneity of the dielectric and magnetic properties of the bodies. A recently developed perturbation theory for the Casimir-Lifshitz interaction between arbitrary material bodies is generalized to include non-uniform magnetic permeability profiles, and used to study the interaction between the magneto-dielectric heterostructures within the leading order. The metamaterials are modeled as two dimensional arrays of domains with varying permittivity and permeability. In the case of two semi-infinite bodies with flat boundaries, the patterned structure of the material properties is found to cause the normal Casimir-Lifshitz force to develop an oscillatory behavior when the distance between the two bodies is comparable to the wavelength of the patterned features in the metamaterials. The non-uniformity also leads to the emergence of lateral Casimir-Lifshitz forces, which tend to strengthen as the gap size becomes smaller. Our results suggest that the recent studies on Casimir-Lifshitz forces between metamaterials, which have been performed with the aim of examining the possibility of observing the repulsive force, should be revisited to include the effect of the patterned structure at the wavelength of several hundred nanometers that coincides with the relevant gap size in the experiments.