Conditions of effective medium theory in calculating Casimir force between hyperbolic metamaterials

Abstract

Hyperbolic metamaterials (HMMs) are artificial subwavelength-structured media that exhibit excellent hyperbolic properties. The Casimir force for HMMs can be predicted by effective medium theory (EMT), which simplifies the calculations considerably. However, the conditions of EMT in the Casimir force between HMMs have not been investigated. In this work, we compare the exact results of the Casimir force calculated by the transfer matrix method (TMM) with those from EMT. The numerical results suggest that EMT can accurately calculate the Casimir force only when the gap distance is 100 times larger than the period of a unit cell. When the gap distance and period of unit cell values are comparable, EMT is not suitable for TMM, and the main error occurs in the hyperbolic band. Furthermore, the effect of the filling ratio on the applicable conditions of EMT is also studied. This work demonstrates the conditions of EMT in calculating the Casimir force between HMMs and provides help for the development of micro- and nanoelectromechanical systems.