The Casimir-Lifshitz formula for rectangular dielectric waveguide

TL;DR

This paper derives a generalized Casimir-Lifshitz formula for a rectangular dielectric waveguide, enabling precise energy calculations and extending the formula's applicability to complex dielectric geometries.

Contribution

It introduces a surface mode technique to derive a new Lifshitz formula for rectangular dielectric waveguides, accounting for their unique dielectric properties.

Findings

Recovered classical perfect reflector results in asymptotic limit

Extended Lifshitz formula to complex dielectric geometries

Provided a method for precise Casimir energy calculations in waveguides

Abstract

We analyze the Casimir-Lifshitz effect associated with the electromagnetic field in the presence of a rectangular waveguide consisting of two distinct dielectric materials in a $(3+1)$-dimensional spacetime. We employ the surface mode technique to derive a generalized Lifshitz formula for this specific geometry. Our formulation accounts for the unique dielectric properties of the materials composing the waveguide, leading to a precise calculation of the Casimir-Lifshitz energy. In the asymptotic limit, our results recover the classical expressions for perfect reflecting boundaries. This work extends the applicability of the Lifshitz formula to more complex systems and provides valuable insights into the influence of dielectric materials on the electromagnetic Casimir effect.