We present a method to compute Casimir forces in arbitrary geometries and for arbitrary materials based on the finite-difference time-domain (FDTD) scheme. The method involves the time evolution of electric and magnetic fields in response to a set of current sources, in a modified medium with frequency-independent conductivity. The advantage of this approach is that it allows one to exploit existing FDTD software, without modification, to compute Casimir forces. In this paper, we focus on the derivation, implementation choices, and essential properties of the time-domain algorithm, both considered analytically and illustrated in the simplest parallel-plate geometry.
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"In such a case, this approach for the roughness correction could be combined with numerical methods (e.g. FDTD  ) to account for the geometry of the system. Such a calculation would be computationally challenging, because it involves multiple scales. "
[Show abstract][Hide abstract]ABSTRACT: Quantum mechanics teaches us that vacuum is not empty. Rather, it contains all kinds of virtual particles. The energy of such particles is called zero point energy. If two surfaces come in close proximity of each other, they will create a difference between the zero point energies in between them and on the outside. Consequently the surfaces will be pushed toward each other. This phenomenon is known as the Casimir effect. It has turned out to be a generalization of the more familiar van der Waals force.
Present technology has only recently enabled us to measure the Casimir force directly. Part of this thesis is about a complication that arises in such measurements: a real surface does not have a nice, smooth shape, but it is often rough. Surface roughness influences the Casimir force mainly at relatively short distances of one ten millionth meter or less. This influence is predominantly determined by statistically rare high asperities in the surfaces. This thesis introduces a model that reproduces measurements of the Casimir force between rough surfaces.
The Casimir force is unavoidable: the existence of virtual particles cannot be shut down in any way. The smaller the distance between the surfaces, the larger the Casimir force. Hence at short distances it is of interest for technology of micro electromechanical systems (MEMS), such as micro switches or accelerometers. The Casmir force has a considerable influence on the motion of MEMS components at short distances. Surface roughness turns out to make this motion more predictable.
[Show abstract][Hide abstract]ABSTRACT: The Casimir force between an ellipsoid and a plate can be tuned by using the combination of anisotropic materials and nonlinear materials exhibiting the AC Kerr effect. The force was obtained numerically by using the FDTD method, based on the Maxwell's stress tensor. The results indicate that the force can be significantly varied by changing the intensity and location of the laser, as well as the properties of material. The sensitive changing between ellipsoid and plate structure with different materials' properties provides new possibilities of integrating optical devices into nano-electromechanical systems (NEMS).
Preview · Article · Jan 2014 · Progress In Electromagnetics Research M
"The thermal Casimir force, generated by thermal rather than quantum fluctuations of the electromagnetic field, has recently been confirmed . This development goes along with significant advances in calculating the Casimir force for complex geometries and materials [7,1415161718192021. A force analogous to the electromagnetic Casimir force occurs if the fluctuations of the confined medium are of thermal instead of quantum origin [5,22,23]. "
[Show abstract][Hide abstract]ABSTRACT: We study the fluctuation-induced, time-dependent force between two plates confining a correlated fluid which is driven out of equilibrium mechanically by harmonic vibrations of one of the plates. For a purely relaxational dynamics of the fluid we calculate the fluctuation-induced force generated by the vibrating plate on the plate at rest. The time-dependence of this force is characterized by a positive lag time with respect to the driving. We obtain two distinctive contributions to the force, one generated by diffusion of stress in the fluid and another related to resonant dissipation in the cavity. The relation to the dynamic Casimir effect of the electromagnetic field and possible experiments to measure the time-dependent Casimir force are discussed.