Scattering formalism in the Casimir interaction of gratings and Chern-Simons layers

Abstract

We describe scattering formalism to evaluate the Casimir energy of two gratings separated by a vacuum slit and the Casimir energy of two Chern- Simons layers in vacuum.

Casimir interaction of two dielectric half spaces with Chern-Simons boundary layers

“…is a matrix due to a change of the coordinate system x 1 = x, y 1 = −y, z 1 = −z + L (see for example [21,45]).…”

“…In Sec.2 we solve a diffraction problem for Chern-Simons layer at the boundary of dielectric half space characterized by a permittivity ε(ω), reflection and transmission coefficients for diffraction of an electromagnetic plane wave are derived. In Sec.3 we apply scattering formalism [11], [39] - [45] to derive formulas for the Casimir energy of two dielectric half spaces with Chern-Simons layers at plane-parallel boundaries separated by a vacuum slit L. We study Casimir forces for Au and Si half spaces with Chern-Simons boundary layers, crossing from the repulsive to the attractive Casimir force is analyzed.…”