Casimir force between parallel plates separated by anisotropic media

Abstract

The Casimir force between two parallel plates separated by anisotropic media is investigated. We theoretically calculate the Casimir force between two parallel plates when the interspace between the plates is filled with anisotropic media. Our result shows that the anisotropy of the material between the plates can significantly affect the Casimir force, especially the direction of the force.If ignoring the anisotropy of the in-between material makes the force to be repulsive (attractive), by contrast, taking the anisotropy into account may produce an extra attractive (repulsive) force.The physical explanation for this phenomenon is also discussed.

The Impact of the Anisotropy of the Media between Parallel Plates on the Casimir Force

“…The relative dielectric pemittivities of the plates and the anisotropic media between them can be expressed by following matrices [11,12,14,17,21,24]. The relative dielectric pemittivities of the plates and the anisotropic media between them can be expressed by following matrices [11,12,14,17,21,24]. The relative dielectric pemittivities of the plates and the anisotropic media between them can be expressed by following matrices [11,12,14,17,21,24].…”

“…where the subscripts z and x indicate the components of the permittivity tensors parallel and perpendicular to the optical axis, respectively. Due to the fact that all of the regions in Figure 2 are considered to be homogenous, the electric and magnetic fields with the surface mode q can be written as [21,25].…”

“…According to the method that used in [4,11,14,21], the Casimir interaction energy at zero temperature can be expressed as (the detailed mathematical derivation of (22) can be found in Appendix A)…”

“…Therefore, in this case, still, the magnitude as well as the direction of the Casimir force could be significantly affected by the anisotropy of the intervening material. In our previous work [21], we only roughly divided the force into two parts, which, in fact, is not the best way to analyze the impact of the anisotropy. In order to see it more clearly, in this paper, we expand the function Φ about δ to the first order:…”

“…Accordingly, this makes the condition for repulsive force more complicated. One of our recent works shows that it is still possible to have repulsive force in this case and that the force can be significantly affected by the anisotropy of the media between the plates [21]. As we know liquid like nitrobenzene can be anisotropic under an external field [22][23][24].…”