Noncontact Atomic Force Microscopy - Yale School of Engineering ...

Mo-0955
Multiple Scattering Casimir Force Calculations between Layered and
Corrugated Materials
Kimball A. Milton 1 , Inés Cavero-Peláez 2 , Prachi Parashar 1 , K.V. Shajesh 3 ,
and Jef Wagner 1
1 H.L. Dodge Department of Physics and Astronomy, University of Oklahoma, Norman, OK 73019, USA
2 Laboratoire Kastler Brossel, Université Pierre et Marie Curie, F-75252 Paris, France
3 St Edward's School, Vero Beach, FL 32963, USA
Multiple scattering methods have recently proven useful in calculating quantum vacuum
forces between distinct bodies. In fact, 40 years ago such an approach was used to derive
the Lifshitz formula for the force between parallel dielectric slabs. More generally,
numerical results can be readily obtained in many cases, but more remarkably, for weak
coupling (e.g., for dilute dielectrics), closed-form exact expressions can be derived,
reflecting the summation of Casimir-Polder forces or their analogues. We have recently
used such methods to derive forces between corrugated planar and cylindrical surfaces.
(See Fig. 1.) For scalar fields with Dirichlet boundary conditions, the forces can be
computed perturbatively in the corrugation amplitudes; 4 th order perturbative results
agree closely with the exact results for weak coupling. We are now extending such
calculations to electromagnetism and to general multilayered surfaces (see Fig. 2), where
again exact results can be obtained in many cases. These results will have important
applications to experimentally accessible situations, and to nanomachinery. The
extension to finite temperature will be explored in the near future.
Fig. 1 Fig. 2
Figure 1: Concentric corrugated gears. The corrugations have equal spatial frequency. The stable
equilibrium configuration occurs when the outer troughs align with the inner peaks. If the gears
are misaligned, a torque is exerted on one cylinder due to the other.
Figure 2: Multilayered surface. The Casimir energy between two such layered potentials can be
calculated in closed form.
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