Research On The Casimir Effect For The Planar Structures Containing Metamaterials

Casimir effect is a macroscopic quantum effect that results from the change of zero-point energy due to the existence of the boundaries. In recent years, with the development of micro- and nanoelectromechanical systems and nanotechnology, Casimir forces that raise from quantum vacuum fluctuation have more influences on the system, and significant potential applications of the Casimir force, such as the actuator, have drawn extensive attention. Recently some composite materials namely metamaterials with special electromagnetic properties, including left-handed materials and single-negative materials, have been fabricated experimentally. The metamaterials have simultaneously negative permittivity and permeability , or negative permeability (permittivity) but positive permittivity (permeability) over a band of frequencies, and they still satisfy the Maxwell equations. Therefore these new types of materials attract a great deal of attention, and more possible applications have been proposed. Real metamaterials must exhibit frequency dispersion, and the values of material characteristic frequencies influence the material reflection property, and it is expected that the magnitude and the directions of Casimir force will be accordingly influenced. In this dissertation, we study the Casimir effect for the planar structures containing metamaterials, including the adjusting of the magnitude of the Casimir forces, the formation of attraction and repulsion and the transformation between them. The main work is summarized in detail as follows.The extension of the calculation for the Casimir force between the parallel slabs to the metamaterial system is discussed. We have considered the analytic property of the integrand in the complex plane for the calculation of the Casimir force when the metamaterials are concerned, and based on the theory of the Casimir effect for real media situation, we obtained the formula of the Casimir force for the planar structures containing metamaterials.We discussed the attraction effect between the left-handed material slabs which have simultaneously negative permittivity and permeability and thereby the refractive index is negative. The medium with negative refractive index in which the solutions to the wave equation satisfy causality must exhibit frequency dispersion, that is, the medium has negative refractive index within a frequency band. For the left-handed materials characterized by dispersive permittivity and permeability of the Drude-Lorentz type, the structure of dispersion curve over the negative refraction frequency band is determined by the plasma frequency, the resonant frequency and the damping frequency. The different widths and depths of the negative refraction frequency band correspond to different medium reflection properties, and thus influences the magnitude of Casimir effect between the slabs. We analyzed the strength of the Casimir effect from the point of view of the dependence of material reflection on different factors, and obtained the relationship between the structure characters of the dispersion curve over the negative refraction band and the Casimir effect. Generally, the greater width and depth of the negative refraction region may correspond to the larger forces. In addition, it is no longer easy to relate the structure characters of dispersion curve over the negative refraction frequency band to the Casimir effect when the frequency regions of negative permittivity and negative permeability of left-handed materials are not the same, since left-handed materials turns into single-negative material, and more stop band replacing the propagation band makes the case quite complicated. A comparison is shown between the Casimir forces for left-handed material and for ordinary dielectric slabs, which have the opposite values of refractive indices for the chosen frequency. The force between two left-handed material slabs having sufficiently wide negative refraction frequency band is generally stronger than the force between two ordinary dielectric slabs.The formation of the repulsive Casimir effect between two parallel slabs has been studied when the metamaterials are concerned. With the development of the experimental techniques, the attractive Casimir forces could lead to restriction in micro- and nanoelectromechanical systems, and therefore, the repulsive forces may avoid that limits and are of possible practical significance. The repulsion is to be expected when the two parallel slabs have different electromagnetic properties. By studying different cases containing ordinary materials and metamaterials, we found that the repulsive behavior may possibly appear when the wave impedances, which are used to demonstrate the difference of electric and magnetic properties between two slabs, are smaller and larger than the impedance of vacuum, respectively, and moreover, the greater the difference between two wave impedances, the more easily the repulsive force is obtained. Therefore, one can adjust the values of the characteristic frequencies of the metamaterials to obtain the repulsive Casimir forces.The dependence of directions of the Casimir forces on the distance between the slabs has been investigated, and special emphasis is put on a case of the transformation between the attraction and the repulsion, i.e., the restoring Casimir force. We discussed the asymptotic long- and short-distance laws of Casimir forces, and then studied the sign change of the forces between metamaterial slabs with the changing slab separation. In general, the Casimir force is always attractive at short distances, and as the slabs get further away from each other, the attractive force may become repulsive at certain distance. The restoring Casimir force, which is the force that changes from repulsion to attraction with the increasing slab separation, may be found to exist between perfectly conducting material and metamaterial slabs. This restoring force is a natural power for the system oscillation in vacuum and also can be used for system stabilization.