Casimir force between hyperbolic metamaterials

The Casimir force between two hyperbolic metamaterials (HMMs) constructed by alternative metal- dielectric layers is investigated. Due to the existence of the hyperbolic dispersion, the electromagnetic response of HMMs becomes extremely dramatic, which is embodied by the nearly total reflection in such frequency region. As a result, the Casimir force between HMMs is much greater than that between ordinary dielectrics. In addition, it is shown that the Casimir force is proportional to the bandwidth of this hyperbolic dispersion, which is dependent on the filling factor as well as the characteristic frequencies of ingredient materials. Therefore, the relations between the force and these parameters are discussed. We show that the Casimir force can be controlled by tuning the bandwidth possessing hyperbolic dispersion of the structures. This work provides promising applications of HMMs on microelectromechanical systems and nanoelectromechanical systems.