The Casimir Force Between Electromagnetic Composite Materials

The Casimir effect originated from the fluctuations of zero point energy in vacuum isa macroscopic quantum effect, which results from the alteration of the quantizedelectromagnetic field in vacuum due to the change of boundary conditions.In recent years, with the application and development of micro/nano mechanicalsystems, it is easy to cause adhere together, further lead to the failure and even stoppingwork within the devices of the micro/nano structures for the existence of the attractiveCasimir force between two conductor slabs. In this case, with the introduction of theCasimir repulsive force, we hope to overcome this viscous effect in micro/nano mechanicalsystems, and further to avoid this problem. Along with the development of themanufacturing technology for the materials, with the help of changing the extraordinaryelectromagnetic properties of the electromagnetic metamaterials represented by thecomposite material made of particles, we can alter the magnitude of the Casimir forcebetween two slabs, and further obtain the repulsive Casimir force. It has injected newenergy to theoretical and experimental researches on the Casimir effect via introducingthese electromagnetic metamaterials, which has become a heated topic on the investigationof the Casimir effect.In this thesis, according to the theoretical formula for the Casimir force bwtween twoelectromagnetic material slabs deduced from the maxwell stress tensor method, we willinvestigate the mutual transitions of the attractive and repulsive the Casimir force betweenpermittivity-negative and permeability-negative material slabs, the Casimir force betweentwo composite materials containing elliposoid particles, and the Casimir force between twocomposite materials including the nonlocal metallic nanosphere particles respectively. The main contents of the thesis are arranged as follows:1. the Casimir force between permittivity-negative and permeability-negativematerial slabsThe Casimir force between magnetodielectric slabs (one slab is permittivity-negative,and the other is permeability-negative in the real frequency space) is investigated by meansof Casimir-Lifshitz Theory. For electromagnetic properties of these two slabs, we willchoose the scheme with the opposite electromagnetic structure to achieve the repulsiveCasimir force between these two slabs. Numerical results show that when the separationbetween these two slabs is small (or large), the Casimir force is repulsive for the oppositeelectromagnetic properties of these two slabs (one slab is mainly electric, and the other ismagnetic), while for the intermediate separation, the Casimir force is attractive for thesame electromagnetic properties of both slabs. With increasing the separation, there is arepulsive-attractive-repulsive transition, and there are equilibria with zero Casimir force,where the attractive and repulsive forces are equal. Therefore, if the separation betweentwo interacting slabs is manipulated in the small (or large) separation region, it is possibleto overcome the stiction in micromechanical and nanomechanical systems.2. the Casimir force between composite material slabs containing elliposoid particlesThe Casimir force between metal-dielectric composite materials containing metallicelliposoid particles is investigated by the Casimir-Lifshitz theory. For simplicity, thecomposite materials are considered to two microstructures. One is the symmetric, in whichthe metallic elliposoid particles and spherical dielectric particles are randomly distributed,and the electromagnetic parameters are described by the generalized Bruggeman effectivemedium approximation; the other is asymmetric, in which the metallic elliposoid particlesare randomly embedded in the dielectric host medium, and the electromagnetic parametersare described by the generalized Maxwell-Garnett approximation. As a consequence, theCasimir force can be controlled by the volume fraction and the shape of the metal particles.It is found that the Casimir force achieves a minimal value for spherical particles, and themagnitude of Casimir force can become strong for metallic elliposoid particles. In addition, the Casimir force for the metal-dielectric composites with the symmetric microstructureshows a fast change at the shape-dependent percolation threshold.3. the Casimir force between nonlocal composite material slabsThe Casimir force between two composite materials including the nonlocal metallicnanosphere particles is investigated. The equivalent permittivity and permeability of thenonlocal metallic nanosphere particle is derived from full-wave nonlocal Mie theory. Then,we adopt both the nonlocal Bruggeman effective medium approximation and the nonlocalMaxwell-Garnett approximation to obtain the effective permittivity and permeability of thecomposite materials, and further to calculate the Casimir force by Casimir-Lifshitz theory.Due to the excitation of the longitudinal modes inside nonlocal metallic nanosphereparticle, the attractive Casimir force between nonlocal composite materials is much weakerthan that of the local composites, and numerical results show that the relative errorsbetween local and nonlocal calculations of the Casimir force for the composite materialswith the same structure can be on the order of25%. Moreover, the nonlocal effects on theCasimir force are strongly dependent on the microstructures. For the symmetricmicrostructure, when the volume fraction of the nonlocal metallic nanosphere particles isnear the percolation threshold, the nonlocal effect will become significant due to themetal-insulator phase transition.