Casimir forces in the time domain: Applications

McCauley, Alexander P.; Rodríguez, Alejandro W.; Joannopoulos, John D.; Johnson, Steven G.

doi:10.1103/physreva.81.012119

Cited by 48 publications

(68 citation statements)

References 25 publications

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“…In particular, the accuracy of the resulting force would only be limited by the magnitude of any measurement error, because the remaining postprocessing steps can be performed with very high accuracy using well known techniques (14). With respect to measurement errors, we believe these to be well within the bounds necessary to obtain forces with accuracies better than or similar to those of our previous (and current) numerical experiments (14,26,28,30,31,42). Some of these may include: electronic noise, finite-size effects associated with any measurement device (e.g., antenna width), and surface roughness.…”

Section: A Casimir Analog Computermentioning

confidence: 63%

“…30 and demonstrated for various geometries in ref. 31. The other application, discussed below, involves the possibility of computing the force via real experiments (in contrast to numerical experiments), in the spirit of analog computations.…”

Section: Correspondencementioning

confidence: 99%

“…On the theoretical side, this correspondence makes it easier to understand Casimir systems from the perspective of conventional classical electromagnetism, based on real-frequency responses, in contrast to the standard point of view based on Wick rotations (imaginary frequencies). Furthermore, it has already led to a finite-difference time-domain numerical method for calculation of Casimir forces in arbitrary geometries and materials (30,31).In this paper, we focus on the derivation of this correspondence along with a third application of that idea: a technique for calculation of Casimir forces based on experimental S-matrix (microwave antenna) measurements in centimeter-scale models. Note that an experiment (centimeter-scale model) of the sort proposed here is not a Casimir "simulator," in that one is not measuring forces but rather a quantity that is mathematically related to the Casimir force-in this sense, it is an analog computer.…”

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confidence: 99%

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Theoretical ingredients of a Casimir analog computer

Rodríguez¹,

McCauley²,

Joannopoulos³

et al. 2010

Proc. Natl. Acad. Sci. U.S.A.

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We derive a correspondence between the contour integration of the Casimir stress tensor in the complex-frequency plane and the electromagnetic response of a physical dissipative medium in a finite real-frequency bandwidth. The consequences of this correspondence are at least threefold: First, the correspondence makes it easier to understand Casimir systems from the perspective of conventional classical electromagnetism, based on real-frequency responses, in contrast to the standard imaginary-frequency point of view based on Wick rotations. Second, it forms the starting point of finite-difference time-domain numerical techniques for calculation of Casimir forces in arbitrary geometries. Finally, this correspondence is also key to a technique for computing quantum Casimir forces at micrometer scales using antenna measurements at tabletop (e.g., centimeter) scales, forming a type of analog computer for the Casimir force. Superficially, relationships between the Casimir force and the classical electromagnetic Green's function are well known, so one might expect that any experimental measurement of the Green's function would suffice to calculate the Casimir force. However, we show that the standard forms of this relationship lead to infeasible experiments involving infinite bandwidth or exponentially growing fields, and a fundamentally different formulation is therefore required.C asimir forces arise due to quantum fluctuations of the electromagnetic field (1-4) and can play a significant role in the physics of neutral, macroscopic bodies at micrometer separations, such as in new generations of micro-electromechanical systems (5, 6). These forces have previously been studied both in delicate experiments at micron and submicron length scales (7-10) and also in theoretical calculations that are only recently becoming feasible for complex nonplanar geometries (11)(12)(13)(14)(15)(16)(17)(18)(19)(20)(21)(22). Theoretical efforts to predict Casimir forces for geometries very unlike the standard case of parallel plates have begun to yield fruit, having demonstrated a number of interesting results for strong-curvature structures (17,(23)(24)(25)(26)(27)(28)(29). But theoretical challenges still remain, more so in geometries involving multiple bodies and/or multiple length scales (14).In this paper, we describe a correspondence between the calculation of Casimir forces for vacuum-separated objects and a similar electromagnetic-force calculation in which the objects are instead separated by a conducting fluid, as illustrated in Fig. 1. The requirement that the geometry be mapped in this fashion is a practical consideration for any calculation based on the time domain (real frequencies). In fact, it is the theoretical equivalent of a crucial and well-known technique for accurate numerical evaluation of Casimir forces, in which the force integrand is deformed via contour integration and commonly evaluated over the imaginary-frequency axis (2, 14). Our formulation circumvents difficulties with all previous expressions of Casimir...

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Section: A Casimir Analog Computermentioning

confidence: 63%

Section: Correspondencementioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

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Theoretical ingredients of a Casimir analog computer

Rodríguez¹,

McCauley²,

Joannopoulos³

et al. 2010

Proc. Natl. Acad. Sci. U.S.A.

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“…Such micro-sphere interactions are predicted to possess a variety of unusual Casimir effects, including repulsive forces, [6][7][8] a strong interplay with material dispersion [4], and strong temperature dependences [9], and may have applications in microfluidic particle suspensions [10,11]. A typical situation considered in this paper is depicted in Fig.…”

Section: Introductionmentioning

confidence: 99%

Casimir microsphere diclusters and three-body effects in fluids

et al. 2011

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Our previous article [Phys. Rev. Lett. 104, 060401 (2010)] predicted that Casimir forces induced by the material-dispersion properties of certain dielectrics can give rise to stable configurations of objects. This phenomenon was illustrated via a dicluster configuration of non-touching objects consisting of two spheres immersed in a fluid and suspended against gravity above a plate. Here, we examine these predictions from the perspective of a practical experiment and consider the influence of non-additive, three-body, and nonzero-temperature effects on the stability of the two spheres. We conclude that the presence of Brownian motion reduces the set of experimentally realizable silicon/teflon spherical diclusters to those consisting of layered micro-spheres, such as the hollowcore (spherical shells) considered here.

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Finite‐Difference Time‐Domain Solution of Maxwell's Equations

Taflove

Hagness

2016

Wiley Encyclopedia of Electrical and Electronics Engineering

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For over 100 years after the publication of Maxwell's equations in 1865, essentially all solution techniques for electromagnetic fields and waves were based on Fourier‐domain concepts, assuming a priori a time‐harmonic (sinusoidal steady‐state) field variation and possibly the existence of a particular Green's function or a set of spatial modes. In 1966, Kane Yee's seminal paper introduced a complete paradigm shift in how to solve Maxwell's equations, reporting a field evolution‐in‐time technique that subsequently evolved into the finite‐difference time‐domain (FDTD) method. In the decades since the publication of Yee's paper, there has been an explosion of interest in FDTD and related grid‐based time‐marched solutions of Maxwell's equations among scientists and engineers. During this period, FDTD modeling has evolved to an advanced stage enabling large‐scale simulations of full‐wave time‐domain electromagnetic wave interactions with volumetrically complex structures over large frequency ranges, spatial scales, and timescales. Currently, FDTD modeling spans the electromagnetic spectrum from ultralow frequencies to visible light. FDTD modeling is routinely conducted as an invaluable virtual laboratory bench in scientific inquiry and exploration in electrodynamics; as an integral part of the electromagnetic engineering design and optimization process; and as a powerful forward solver in imaging and sensing inverse problems. This article reviews the technical basis of the key features of FDTD solution techniques for Maxwell's equations and provides 18 modeling examples spanning the electromagnetic spectrum to illustrate the power, flexibility, and robust nature of FDTD computational electrodynamics simulations.

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Casimir forces in the time domain: Applications

Cited by 48 publications

References 25 publications

Theoretical ingredients of a Casimir analog computer

Theoretical ingredients of a Casimir analog computer

Casimir microsphere diclusters and three-body effects in fluids

Finite‐Difference Time‐Domain Solution of Maxwell's Equations

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