Implications of the Babinet Principle for Casimir interactions

Abstract

We formulate the Babinet Principle (BP) as a relation between scattering amplitudes and combine it with multiple scattering techniques to derive new properties of electromagnetic 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. Also, the BP suggests that Casimir edge effects are generically anomalously small. Furthermore, the BP can be used to relate any planar object to its complementary geometry, a relation we use to estimate Casimir forces between two screens with apertures.