Implications of the Babinet Principle for Casimir Interactions

TL;DR

This paper applies the Babinet Principle to electromagnetic scattering to derive new insights into Casimir forces, revealing that perforated mirrors experience roughly half the force of uniform mirrors and suggesting small edge effects.

Contribution

It formulates the Babinet Principle for electromagnetic scattering and uses it to analyze Casimir forces involving perforated and self-complementary mirrors.

Findings

Casimir force on perforated mirrors is about half that on uniform mirrors.

Casimir edge effects are predicted to be very small.

The Babinet Principle can estimate Casimir forces between perforated surfaces.

Abstract

We formulate the Babinet Principle (BP) as a relation between the scattering amplitudes for electromagnetic waves, and combine it with multiple scattering techniques to derive new properties of Casimir forces. We show that the Casimir force exerted by a planar conductor or dielectric on a self- complementary perforated planar mirror is approximately half that on a uniform mirror independent of the distance between them. The BP suggests that Casimir edge effects are anomalously small, supporting results obtained earlier in special cases. Finally, we illustrate how the BP can be used to estimate Casimir forces between perforated planar mirrors.