It is shown that thermally excited plasmon-polariton modes can strongly mediate, enhance and emph{tune} the near-field radiation transfer between two closely separated graphene sheets. The dependence of near-field heat exchange on doping and electron
relaxation time is analyzed in the near infra-red within the framework of fluctuational electrodynamics. The dominant contribution to heat transfer can be controlled to arise from either interband or intraband processes. We predict maximum transfer at low doping and for plasmons in two graphene sheets in resonance, with orders-of-magnitude enhancement (e.g. $10^2$ to $10^3$ for separations between $0.1mu m$ to $10nm$) over the Stefan-Boltzmann law, known as the far field limit. Strong, tunable, near-field transfer offers the promise of an externally controllable thermal switch as well as a novel hybrid graphene-graphene thermoelectric/thermophotovoltaic energy conversion platform.
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.
