摘要
起源于真空零点能涨落的Casimir效应是真空中量子化的电磁场因边界条件的改变而产生的宏观量子效应。
近年来，随着微纳米机械系统的应用和发展，存在于两块导体板之间的Casimir吸引力容易使微纳米结构器件粘附在一起，引起微纳米机械系统失效，甚至停止工作。通过引入Casimir排斥力，有希望能够克服微纳米器件中的粘附作用，避免这类问题的产生。随着材料制造工艺的发展，通过改变以颗粒复合材料为代表的特异材料的非平凡电磁性质，可以改变两块材料板之间的Casimir力的大小，并进一步获得Casimir排斥力。这类材料的出现给Casimir效应理论和实验研究注入了新的活力，成为了研究Casimir效应一个热点。
根据麦克斯韦应力张量法得到的两块电磁材料板之间的Casimir力的理论公式，本文分别研究了电单负和磁单负材料板之间的Casimir吸引力和排斥力的相互转变，含有椭球金属颗粒的复合材料板之间的Casimir力，含有非局域金属纳米球颗粒的复合材料板之间的Casimir力。论文主要内容安排如下：
1.电单负和磁单负材料板之间的Casimir力
运用Casimir-Lifshitz理论，研究两块单负材料板（在实频区域内，一块是电单负材料板，另一块是磁单负材料板）之间的Casimir力。根据这两块材料板的电磁性质的特点，通过选择具有相反电磁结构的方案，可以在这两块材料板之间实现Casimir排斥力。研究结果表明，当两板之间的间距处于较大间距（或是较小间距）时，由于两板具有相反的电磁性质（一块板是电性为主，而另一块板是磁性为主），它们之间的Casimir力呈现为排斥力，当两板之间的间距处于中间间距时，两板具有相同的电磁性质，它们之间的Casimir力呈现吸引力。随着两板间距的增大，两板之间的Casimir力出现了排斥力-吸引力-排斥力的转变过程，并出现了吸引力与排斥力相等的平衡态。因此，如果能够把这两块单负材料板之间的间距控制在较大的间距（或是较小间距）时，希望避免在微纳米结构系统里出现的粘滞作用。
2.含有椭球金属颗粒的复合材料板之间的Casimir力
利用Casimir-Lifshitz理论，研究具有非均匀金属-介电复合材料板（含有椭球金属颗粒和球形介电颗粒）之间的Casimir力。为简单起见，只考虑两种几何微结构：一种是对称性微结构，椭球金属颗粒和球形介电颗粒是任意无规分布在一起，它的电磁参数可以用推广的Bruggeman有效媒质理论来描述；另一种是反对称性微结构，椭球金属颗粒任意嵌入在介电颗粒的基质里，它的电磁参数可以用推广的Maxwell-Garnett近似理论来描述。研究结果表明，通过调节金属颗粒的形状和体积分数可以有效调控Casimir力的大小。当金属颗粒为球形时，复合材料板之间的Casimir力取最小值；金属颗粒越偏离球形，Casimir力的数值越大。对于对称微结构颗粒分布的复合材料来说，当金属颗粒的体积分数处于依赖于形状因子的逾渗阈值附近时，复合材料板之间的Casimir力就会出现快速的增加。
3.非局域复合材料板之间的Casimir力
研究含有非局域金属纳米球颗粒的复合材料板之间的Casimir力。首先，基于全波的非局域Mie理论，推导得到非局域金属纳米球颗粒的等效介电常数和等效磁导率。然后，根据Casimir-Lifshitz理论，利用非局域的Bruggeman有效媒质理论和非局域的Maxwell-Garnett近似理论求得复合材料的有效介电常数和有效磁导率，继而计算两块复合材料板之间的Casimir力。由于金属钠米球颗粒内部纵模的激发，非局域复合材料板之间的Casimir力会比局域时的情况小很多。数值结果表明，复合材料板在局域和非局域情况下的Casimir力的相对误差最大会达到25%。两板之间的Casimir力的非局域效应强烈地依赖于材料的微结构组成。对于具有对称微结构的非局域复合材料来说，当金属钠米球颗粒的体积分数处于逾渗阈值附近时，由于复合材料板出现金属-绝缘相变，非局域效应尤其明显。
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 slabs
The 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 particles
The 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 slabs
The 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.
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