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

Abstract

Quantum fluctuations of the electromagnetic field give rise to the force between parallel plates: the Casimir force. We theoretically calculate the Casimir force between two parallel isotropic plates when the space between the plates is filled with anisotropic material. Our result shows that the Casimir force, especially in the direction of the force, can be significantly affected by the anisotropy of the intervening material. We also discuss the combined influence of dispersion and anisotropy, and analyze the impact of the external electric filed on the Casimir force by affecting the anisotropy of the intervening material by Kerr electro-optical effect.

The Casimir force between parallel plates separated by anisotropic media with in-plane optical axis

“…In one of our previous studies, the exact impact of the anisotropy of the intervening media on the Casimir force effect was calculated and the result showed that repulsive-attractive transition of the Casimir force could appear in this case and both the magnitude and the direction of the Casimir force were affected by the anisotropy of the intervening media [20]. In a subsequent work [21], we reinvestigated this problem when frequency-dependent permittivities were considered. We also discussed the influence of the external electric field on the Casimir force by affecting the anisotropy of the intervening media though the Kerr effect in that work [21].…”

“…In a subsequent work [21], we reinvestigated this problem when frequency-dependent permittivities were considered. We also discussed the influence of the external electric field on the Casimir force by affecting the anisotropy of the intervening media though the Kerr effect in that work [21]. The thermal Casimir force between two parallel isotropic plates separated by a uniaxial anisotropic film was investigated by Mostepanenko [22].…”

“…To evaluate the Casimir force in our case, we will use the surface mode method. It should be noted that there are many equivalent methods which can be used to calculate the Casimir force in this situation [7][8][9][10][11][12][14][15][16][20][21][22]. We choose this method because it is as practical as other methods and has been used on similar problems many times in our previous works [11,12,15,16,20,21].…”

“…Owing to the fact that the three regions in fig. 1(b) are considered to be homogenous, the electric and magnetic field with surface mode q can be written as [20,21,24]…”

“…According to the method in [4,12,15,16,20,21], the Casimir interaction energy at zero temperature could be expressed as (since only the intervening medium is considered to be anisotropic, we can let φ = 0, which can simplify the equations without losing generality)…”