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

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