Edge Corrections to Electromagnetic Casimir Energies From General-Purpose Mathieu Function Routines

Abstract

Scattering theory methods make it possible to calculate the Casimir energy of a perfectly conducting elliptic cylinder opposite a perfectly conducting plane in terms of Mathieu functions. In the limit of zero radius, the elliptic cylinder becomes a finite-width strip, which allows for the study of edge effects. However, existing packages for computing Mathieu functions are insufficient for this calculation, because none can compute Mathieu functions of both the first and second kind for complex arguments. To address this shortcoming, we have written a general purpose Mathieu function package, based on algorithms developed by Alhargan [1,2]. We use these routines to find edge corrections to the proximity force approximation for the Casimir energy of a perfectly conducting strip opposite a perfectly conducting plane.

9 pages, 1 figure; fixed typos

References in corpus (8)

• Casimir forces between arbitrary compact objects
• The Casimir effect within scattering theory
• Casimir edge effects
• Casimir force between sharp-shaped conductors
• Interplay between geometry and temperature for inclined Casimir plates
• Electromagnetic Casimir Forces of Parabolic Cylinder and Knife-Edge Geometries
• On the Casimir interaction between holes
• Electromagnetic Casimir Energies of Semi-Infinite Planes