Experimental and theoretical investigation of the angular dependence of the Casimir force between sinusoidally corrugated surfaces

Abstract

In the current work we present the complete results for the measurement of normal Casimir force between shallow and smooth sinusoidally corrugated gold coated sphere and a plate at various angles between the corrugations using an atomic force microscope. All measured data were compared with the theoretical approach using the proximity force approximation and theory based on derivative expansion. In both cases real material properties of the surfaces and non-zero temperature were taken into account. Special attention is paid to the description of electrostatic interactions between corrugated surfaces at different angles between corrugations and samples preparation and characterization. The measured forces are found to be in good agreement with the theory including correlation effects of geometry and material properties and deviate significantly from the predictions of the proximity force approximation approach. This provides the quantitative confirmation for the observation of diffraction-type effects that are disregarded within the PFA approach. The obtained results open new opportunities for control of the Casimir effect in micromechanical systems.

Casimir free energy of metallic films: Discriminating between Drude and plasma model approaches

“…2 we present the common computational results, obtained using the Drude or the plasma model approach for the magnitude of the nonrelativistic Casimir energy (27) of a Au film in vacuum, multiplied by the separation squared, as a function of a (the dashed line).…”

“…It was originally formulated for the plane parallel boundary surfaces and recently generalized for the bodies of arbitrary geometrical shape [22,23]. This generalization was used for interpretation of experiments on measuring the Casimir interaction between sinusoidally [24][25][26][27] and rectangular [28,29] corrugated surfaces.…”

Calculating Casimir interactions for periodic surface-relief gratings using theCmethod

“…As the experiments have become more sensitive, it has become necessary to do the theoretical analysis outside the range of validity of the PFA. Recently a derivative expansion (DE) approach has been introduced [16][17][18], which reproduces the PFA and gives the next order correction, and which has successfully explained a number of new recent experiments [13,14]. The first theoretical calculation of the Casimir force between geometrically patterned surfaces not using the PFA was reported in 2001 [19,20], which described the normal and lateral forces between two aligned corrugated surfaces in terms of a perturbative expansion in the profile height.…”

“…There have been a number of experiments showing that the magnitude of the Casimir force could be varied by changing the surface geometry of the interacting objects [5][6][7][8][9][10][11][12][13][14]. To investigate the impact of curvature and corrugation, the Casimir forces have been measured between a sphere and a sinusoidal grating [5] and between two corrugated surfaces for both aligned [6,7] and crossed [13,14] corrugations.…”

“…To investigate the impact of curvature and corrugation, the Casimir forces have been measured between a sphere and a sinusoidal grating [5] and between two corrugated surfaces for both aligned [6,7] and crossed [13,14] corrugations.…”