The Casimir force between a microfabricated elliptic cylinder and a plate

Abstract

We investigate the Casimir force between a microfabricated elliptic cylinder (cylindrical lens) and a plate made of real materials. After a brief discussion of the fabrication procedure, which typically results in elliptic rather than circular cylinders, the Lifshitz-type formulas for the Casimir force and for its gradient are derived. In the specific case of equal semiaxes, the resulting formulas coincide with those derived previously for circular cylinders. The nanofabrication procedure may also result in asymmetric cylindrical lenses obtained from parts of two different cylinders, or rotated through some angle about the axis of the cylinder. In these cases the Lifshitz-type formulas for the Casimir force between a lens and a plate and for its gradient are also derived, and the influence of lens asymmetry is determined. Additionally, we obtain an expression for the shift of the natural frequency of a micromachined oscillator with an attached elliptic cylindrical lens interacting with a plate via the Casimir force in a nonlinear regime.

22 pages, 4 figures, to appear in Phys. Rev. A

References in corpus (13)

• Casimir forces between arbitrary compact objects
• Novel constraints on light elementary particles and extra-dimensional physics from the Casimir effect
• Effect of the Casimir-Polder force on the collective oscillations of a trapped Bose-Einstein condensate
• The Casimir effect for a sphere and a cylinder in front of plane and corrections to the proximity force theorem
• Casimir interaction of dielectric gratings
• Halving the Casimir force with conductive oxides
• Limits on Nonstandard Forces in the Submicrometer Range
• Kramers-Kronig relations for plasma-like permittivities and the Casimir force
• Microscopic theory of the Casimir force at thermal equilibrium: large-separation asymptotics
• Control of the Casimir Force Using Semiconductor Test Bodies
• Exact Casimir-Polder potential between a particle and an ideal metal cylindrical shell and the proximity force approximation
• Possibility to measure thermal effects in the Casimir force
• Casimir experiments showing saturation effects

Cited by in corpus (7)

• Gradient of the Casimir force between Au surfaces of a sphere and a plate measured using atomic force microscope in a frequency shift technique
• The Casimir energy between nanostructured gratings of arbitrary periodic profile
• Casimir forces between cylinders at different temperatures
• Repulsive and attractive Casimir interactions in liquids
• New constraints on Yukawa-type interactions from the Casimir effect
• Electromagnetic Casimir Forces in Elliptic Cylinder Geometries
• Universal Casimir attraction between filaments at the cell scale