Electromagnetic normal modes and Casimir effects in layered structures

Abstract

We derive a general procedure for finding the electromagnetic normal modes in layered structures. We apply this procedure to planar, spherical and cylindrical structures. These normal modes are important in a variety of applications. They are the only input needed in calculations of Casimir interactions. We present explicit expression for the condition for modes and Casimir energy for a large number of specific geometries. The layers are allowed to be two-dimensional so graphene and graphene-like sheets as well as two-dimensional electron gases can be handled within the formalism. Also forces on atoms in layered structures are obtained. One side-result is the van der Waals and Casimir-Polder interaction between two atoms.

50 pages, 21 figures, more than 400 equations

References in corpus (7)

• Dispersion forces in macroscopic quantum electrodynamics
• Thermal Casimir vs Casimir-Polder forces: Equilibrium and non-equilibrium forces
• Retarded interactions in Graphene systems
• The Casimir Problem of Spherical Dielectrics: Numerical Evaluation for General Permittivities
• Dynamics of thermal Casimir-Polder forces on polar molecules
• Casimir experiments showing saturation effects
• Thin films versus 2D sheets in layered structures: graphene and 2D metallic sheets

Cited by in corpus (5)

• The Casimir-Polder effect for a stack of conductive planes
• Casimir effects in systems containing 2D layers, like graphene and 2D electron gases
• The Casimir effect for stack of graphenes
• Stability of Suspended Graphene under Casimir Force
• Special features of the thermal Casimir effect across a uniaxial anisotropic film