Casimir effect across a layered medium

TL;DR

This paper extends the Lifshitz formula to layered inhomogeneous media, enabling calculation of Casimir forces in complex multilayer systems with improved accuracy and generality.

Contribution

It introduces a recursive method for Fresnel coefficients to analyze Casimir forces across multilayered inhomogeneous media, generalizing previous models.

Findings

Reproduces recent results for simple layered systems.

Provides a new formula for forces on multilayer stacks between planar objects.

Enhances theoretical tools for Casimir force calculations in complex media.

Abstract

Using nonstandard recursion relations for Fresnel coefficients involving successive stacks of layers, we extend the Lifshitz formula to configurations with an inhomogeneous, n-layered, medium separating two planar objects. The force on each object is the sum of a Lifshitz like force and a force arising from the inhomogeneity of the medium. The theory correctly reproduces very recently obtained results for the Casimir force/energy in some simple systems of this kind. As a by product, we obtain a formula for the force on an (unspecified) stack of layers between two planar objects which generalizes our previous result for the force on a slab in a planar cavity.