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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.
Polarisable atoms and molecules experience the Casimir-Polder force near magnetoelectric bodies, a force that is induced by quantum fluctuations of the electromagnetic field and the matter. Atoms and molecules in relative motion to a magnetoelectric
We present a modal approach to calculate finite temperature Casimir interactions between two periodically modulated surfaces. The scattering formula is used and the reflection matrices of the patterned surfaces are calculated decomposing the electrom
We investigate the Dirichlet-scalar equivalent of Casimir-Polder forces between an atom and a surface with arbitrary uniaxial corrugations. The complexity of the problem can be reduced to a one-dimensional Greens function equation along the corrugati
Barash has calculated the Casimir forces between parallel birefringent plates with optical axes parallel to the plate boundaries [Izv. Vyssh. Uchebn. Zaved., Radiofiz., {bf 12}, 1637 (1978)]. The interesting new feature of the solution compared to th
We perform a theoretical analysis of a setup intended to measure the repulsive (outward) Casimir forces predicted to exist inside of perfectly conducting rectangular cavities. We consider the roles of the conductivity of the real metals, of the tempe