Casimir energy between nanostructured gratings of arbitrary periodic profile

Abstract

We study the lateral dependence of the Casimir energy for different corrugated gratings of arbitrary periodic profile. To this end we model the profiles as stacks of horizontal rectangular slices following the profiles' shape and evaluate numerically the Casimir energy between them for different relative lateral displacements of the two corrugated plates. We compare our results with predictions obtained within the proximity force approximation (PFA). At comparable separation of the corrugated plates and geometric parameters, we find a strong dependence of the Casimir energy on the shape of the corrugation profiles.

Casimir torque between nanostructured plates

“…Recently, exact expressions of the Casimir force between dielectric nanostructures have been developed for the normal and the lateral regime [14,[18][19][20][21] that compare very well with recent experiments performed with deep [22,23] and shallow corrugations [24].…”

“…The latter allows to compute Casimir forces between arbitrarily shaped bodies taking into account the material properties. The lateral force has been shown to be maximized if rectangular structures are imprinted [14]. The lateral force has been proposed to be employed in noncontact rack-and-pinion devices with high potential for applications [15][16][17].…”

Thermal Casimir force between nanostructured surfaces

“…Figure 7 shows the measured data points from this experiment together with the results of our calculations for this sample both at T = 300 K (red curve) and T = 0 K (blue curve). In the calculation we take into account the exact trapezoidal shape of the corrugation profile via a generalization of the formalism presented above [18]. As the range of separation distances is the same as in the experiment with deep trenches, the situation now corresponds to a regime where L > a.…”

Casimir-Lifshitz force out of thermal equilibrium between dielectric gratings

“…More recently, nanostructured surfaces have been theoretically considered in the contexts of both force [32][33][34][35] and heat transfer [36,37]. Experimentally, the force has been measured between a sphere and a dielectric [38,39] or metallic [40] grating.…”