The Casimir Effect Between Non-Parallel Plates by Geometric Optics

Abstract

The first two authors have developed a technique which uses the complex geometry of the space of oriented affine lines in R 3 to describe the reflection of rays off a surface. This can be viewed as a parametric approach to geometric optics which has many possible applications. Recently, Jaffe and Scardicchio have developed a geometric optics approximation to the Casimir effect and the main purpose of this paper is to show that the quantities involved can be easily computed by this complex formalism. To illustrate this, we determine explicitly and in closed form the geometric optics approximation of the Casimir force between two non-parallel plates. By making one of the plates finite, we regularize the divergence that is caused by the intersection of the planes. In the parallel plate limit, we prove that our expression reduces to Casimir's original result.

Stabilizing Diamagnetic Levitation of a Graphene Flake through the Casimir Effect

“…The calculation of the Casimir energy between an inclined plate and a flat plate can be a computationally intensive task [28][29][30]. As an alternative approach, the PFA is employed.…”

Stable Position of a Micro Torsion Balance under the Casimir Force

“…The Casimir energy between non-parallel plates using GOA was obtained by Guilfoyle et al as follows (see details in Ref. [14]):…”

“…The integer m 1 is defined by the smallest even integer satisfying inequality (13) or the smallest odd m 1 satisfying inequality (14). The integer m 2 is defined as the smallest integer between an integer m 0 satisfying inequality ( 12) and m 1 .…”

Reflection of a wave off a surface

“…The formalism developed above lends itself to a number of applications, including the construction of caustics [4] and the computation of the geometric optics approximation of the Casimir force [5].…”