Article

# Casimir forces in the time domain: Theory

Physical Review A (Impact Factor: 2.99). 07/2009; DOI: 10.1103/PhysRevA.80.012115

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**ABSTRACT:**Using the dipole scattering theory, we study the dependence of the Casimir force on the separation between arrays of planar scatterers. The reflection amplitude near zero frequency is computed by taking into account the interaction between scatterers that are organized in an array. The absolute values of amplitude can be described as linearly increasing functions of frequency that cross the origin, with their slopes depending on the values of incidence angle and polarization. The argument value of the reflection amplitude is determined from the absolute value of the reflection amplitude, on the basis of the assumption that the reflection amplitude is analytical in the upper half of a complex frequency plane. The numerical results show that, for a large separation between the arrays, the strength of the Casimir force between arrays of metal disks is inversely proportional to the sixth power of the separation between the arrays.Journal of the Physical Society of Japan 05/2013; 82(5):4002-. · 1.48 Impact Factor - [Show abstract] [Hide abstract]

**ABSTRACT:**Our previous article [Phys. Rev. A 80, 012115 (2009)] 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 article, 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 pistonlike 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 perfectly matched layer (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.Physical Review A 01/2010; 81(1):012119-012119. · 2.99 Impact Factor - [Show abstract] [Hide abstract]

**ABSTRACT:**Whether intentionally introduced to exert control over particles and macroscopic objects, such as for trapping or cooling, or whether arising from the quantum and thermal fluctuations of charges in otherwise neutral bodies, leading to unwanted stiction between nearby mechanical parts, electromagnetic interactions play a fundamental role in many naturally occurring processes and technologies. In this review, we survey recent progress in the understanding and experimental observation of optomechanical and quantum-fluctuation forces. Although both of these effects arise from exchange of electromagnetic momentum, their dramatically different origins, involving either real or virtual photons, lead to different physical manifestations and design principles. Specifically, we describe recent predictions and measurements of attractive and repulsive optomechanical forces, based on the bonding and antibonding interactions of evanescent waves, as well as predictions of modified and even repulsive Casimir forces between nanostructured bodies. Finally, we discuss the potential impact and interplay of these forces in emerging experimental regimes of micromechanical devices.Annalen der Physik 09/2014; · 1.51 Impact Factor

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