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arXiv · 0906.5170

Casimir forces in the time domain II: Applications

Alexander P. McCauley·Alejandro W. Rodriguez·John D. Joannopoulos·Steven G. Johnson
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Abstract

Our preceding paper introduced a method to compute Casimir forces in arbitrary geometries and for arbitrary materials that was based on a finite-difference time-domain (FDTD) scheme. In this manuscript, we focus on the efficient implementation of our method for geometries of practical interest and extend our previous proof-of-concept algorithm in one dimension to problems in two and three dimensions, introducing a number of new optimizations. We consider Casimir piston-like problems with nonmonotonic and monotonic force dependence on sidewall separation, both for previously solved geometries to validate our method and also for new geometries involving magnetic sidewalls and/or cylindrical pistons. We include realistic dielectric materials to calculate the force between suspended silicon waveguides or on a suspended membrane with periodic grooves, also demonstrating the application of PML absorbing boundaries and/or periodic boundaries. In addition we apply this method to a realizable three-dimensional system in which a silica sphere is stably suspended in a fluid above an indented metallic substrate. More generally, the method allows off-the-shelf FDTD software, already supporting a wide variety of materials (including dielectric, magnetic, and even anisotropic materials) and boundary conditions, to be exploited for the Casimir problem.

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Alexander P. McCauley, Alejandro W. Rodriguez, John D. Joannopoulos, Steven G. Johnson. 2009-10-27. Casimir forces in the time domain II: Applications. https://doi.org/10.1103/physreva.81.012119

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