Casimir forces in the time domain II: Applications

TL;DR

This paper extends a finite-difference time-domain method for calculating Casimir forces to complex 2D and 3D geometries, demonstrating its effectiveness on practical structures with realistic materials and boundary conditions.

Contribution

It introduces new optimizations for the FDTD-based Casimir force calculation method, enabling efficient analysis of complex geometries with realistic materials in three dimensions.

Findings

Validated the method on known geometries

Applied to new geometries with magnetic and cylindrical features

Demonstrated calculations with realistic dielectric materials

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.