Roughness correction to the Casimir force: Beyond the Proximity Force Approximation

Neto, Paulo A. Maia; Lambrecht, Astrid; Reynaud, Serge

doi:10.1209/epl/i2004-10433-9

Cited by 109 publications

(160 citation statements)

References 23 publications

(34 reference statements)

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“…The scattering theory as pointed out in [13] gives the largest deviations in comparison with PFA at large separations.…”

mentioning

confidence: 86%

“…While this is the most important factor, any lateral information of rough films has been ignored [13]. Numerical approaches today are rather limited to simple systems making them unsuitable for predicting roughness effects of real systems [14].…”

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confidence: 99%

“…where G(k) is derived in [13,15] yielding for the total energy , δ = + pp rough ppflat pp E E E [13,15]. The theory is valid under the following assumptions.…”

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confidence: 99%

“…At small separations the PFA becomes more accurate [13], but a comparison with the scattering theory is impossible since the . Thus, we investigate how much increasing w enhances the effects predicted by scattering theory compared to the PFA for surfaces with equal local slopes (increase ξ with increasing w so that ρ rms is constant).…”

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confidence: 99%

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Roughness corrections to the Casimir force: The importance of local surface slope

Zwol

Palasantzas

Hosson

2007

Applied Physics Letters

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This paper concentrates on a study where finite conductivity corrections are included in the theoretical description of the effects of roughness on the Casimir force. The roughness data were taken from gold films evaporated onto Silicon and polysterene spheres. We conclude that for a detailed comparison with experimental data, i.e. at the level of at least 5 % at short separations below 200 nm, the lateral dimensions of roughness for real films should be included in the theoretical considerations. Moreover, if the RMS roughness is considerable, high local surface slopes are shown to have a significant effect on the Casimir force.

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“…The scattering theory as pointed out in [13] gives the largest deviations in comparison with PFA at large separations.…”

mentioning

confidence: 86%

mentioning

confidence: 99%

“…where G(k) is derived in [13,15] yielding for the total energy , δ = + pp rough ppflat pp E E E [13,15]. The theory is valid under the following assumptions.…”

mentioning

confidence: 99%

mentioning

confidence: 99%

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Roughness corrections to the Casimir force: The importance of local surface slope

Zwol

Palasantzas

Hosson

2007

Applied Physics Letters

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“…We use the perturbative approach that we developed for analyzing the effect of stochastic roughness on the normal Casimir force [14,15]. This technique is valid as long as the corrugation amplitude a remains the smallest of length scales a ≪ L, λ C , λ P .…”

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confidence: 99%

Lateral Casimir Force beyond the Proximity-Force Approximation

Rodrigues¹,

Neto²,

et al. 2006

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We argue that the appropriate variable to study a non trivial geometry dependence of the Casimir force is the lateral component of the Casimir force, which we evaluate between two corrugated metallic plates outside the validity of the Proximity Force Approximation (PFA). The metallic plates are described by the plasma model, with arbitrary values for the plasma wavelength, the plate separation and the corrugation period, the corrugation amplitude remaining the smallest length scale. Our analysis shows that in realistic experimental situations the Proximity Force Approximation overestimates the force by up to 30%.Considerable experimental progress has been achieved [1] in the measurement of the Casimir force, opening the way for various applications in nano-science [2], particularly in the development of nano-or micro-electromechanical systems (NEMS or MEMS). Calculations are much simpler in the original Casimir geometry of two plane plates [3] which obeys a symmetry with respect to lateral translations and thus allows to derive the expression of the Casimir force from the reflection amplitudes which describe specular scattering on the plates [4].More general geometries open a far richer physics with a variety of extremely interesting theoretical predictions [5]. Up to now the experimental studies of the effect of geometry have been restricted to simple configurations which can be calculated with the help of the Proximity Force Approximation (PFA). This approximation is essentially equivalent to an averaging over plane-plane geometries and its result can be deduced from the force known in this geometry [6]. For example, it allows to evaluate the force between a plane and a sphere [7] provided the radius R of the sphere is much larger than the mirror separation R ≫ L. It is also valid for the description of the effect of roughness when the wavelengths associated with the plate deformations are large enough [8]. However PFA relies heavily on assuming some additivity of Casimir forces which is known to be generally not valid except for very smooth geometrical perturbations [9].The aim of the present paper is to study a configuration allowing a new test of QED theoretical predictions outside the PFA domain and independent of those already performed in the plane-plane geometry. The idea is to look for the lateral component of the Casimir force which appears, besides the usual normal component, when periodic corrugations with the same period are imprinted on the two metallic plates. This configuration contrasts with other ones, for example the normal Casimir force in the plane-sphere geometry or roughness corrections to it. There PFA can also be invalid, but this leads only to small corrections of the dominant normal Casimir force, which do not seem accessible experimentally at the moment. The lateral component of the Casimir force has recently been measured and analyzed within the PFA [10,11]. We find for experimentally realizable parameters that PFA overestimates the force by as much as 30%, which should allow for a ...

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Nanoelectromechanical Systems

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Roughness correction to the Casimir force: Beyond the Proximity Force Approximation

Cited by 109 publications

References 23 publications

Roughness corrections to the Casimir force: The importance of local surface slope

Roughness corrections to the Casimir force: The importance of local surface slope

Lateral Casimir Force beyond the Proximity-Force Approximation

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