Torque on birefringent plates induced by quantum fluctuations

Abstract

We present detailed numerical calculations of the mechanical torque induced by quantum fluctuations on two parallel birefringent plates with in plane optical anisotropy, separated by either vacuum or a liquid (ethanol). The torque is found to vary as sin (2θ), where θ represents the angle between the two optical axes, and its magnitude rapidly increases with decreasing plate separation d. For a 40 µm diameter disk, made out of either quartz or calcite, kept parallel to a Barium Titanate plate at d ≃ 100 nm, the maximum torque (at θ = π 4 ) is of the order of ≃ 10 −19 N·m. We propose an experiment to observe this torque when the Barium Titanate plate is immersed in ethanol and the other birefringent disk is placed on top of it. In this case the retarded van der Waals (or Casimir-Lifshitz) force between the two birefringent slabs is repulsive. The disk would float parallel to the plate at a distance where its net weight is counterbalanced by the retarded van der Waals repulsion, free to rotate in response to very small driving torques.

van der Waals Interactions on the Mesoscale: Open-Science Implementation, Anisotropy, Retardation, and Solvent Effects

“…The vdW interaction free energy between two semi-inifinte anisotropic uniaxial dielectric layers across a finite layer of thickness l was worked out in the nonretarded 11 and the fully retarded limit 19 as a function of their separation l and the angle between their principal dielectric anisotropy axes θ: G(l,θ). It then follows that the interaction free energy between two cylinders, G(l,θ), whose axes are contained within the two parallel boundaries at a separation l, but skewed at an angle θ is given by the second derivative d 2 G(l,θ)/dl 2 expanded to second order in the density of the two cylindrical arrays.…”

Structural anisotropy and orientation-induced Casimir repulsion in fluids

“…Therefore, while in some circumstances EMA can be a useful qualitative guide (and rigorously accurate in certain limits), it must be used with caution-ideally, as a supplement to exact calculations. Orientation dependence (and the resulting Casimir torque) between slabs has previously been considered for two birefringent plates with weak anisotropy [22][23][24], and for corrugated metallic plates [2]. Although the torques in these systems are in principle measurable, the change in the force with orientation is small, and the forces are always attractive.…”

General approach to Casimir force problems based on local reflection amplitudes and Huygens’ principle

“…Such a cavity would have sidewalls made of a uniaxial material, for example, a wire grid polarizer or a graphite crystal cut with in-plane optical anisotropy. When two such plates are placed close together with their optic axes rotated by an angle χ with respect to each other, both an orientationally dependent normal force and a torque tending to align the optic axes of the plates have been predicted [4,16,17]. In order to address this Casimir problem in the formalism presented in this paper, let us start with Eq.…”