The Research Of The Casimir Effect In Three Dimensional Structure Based On FDTD Method

Casimir effect, first discovered by the Dutch physicist Casimir in 1948, is an observable macroscopic quantum effect. Its known form is the attraction of a pair of neutral parallel conducting plates, due to the quantum vacuum fluctuations in the electromagnetic field. Then, the Casimir force has played an important role in various fields of physics over decades and various numerical calculations have been developed. There are three main calculation methods:the surface mode summation method (SMSM), the theory of Lifshitz method (LM) and Maxwell stress tensor method (MSTM). With the advances of fabrication techniques in the micro-electro-mechanical systems (MEMS) for the past years, people have begun to research repulsive force to conquer the stiction problem between dielectric and metallic surfaces in close spacing. Therefore, repulsive Casimir force received unprecedented attention in the practical systems.Nowadays, how to generate and tune the repulsive Casimir force are the hot topics in most research works. Obtained numerically by using the FDTD method, based on the Maxwell stress tensor and harmonic expansion, the Casimir force of a three dimensional structure is calculated. The numerical results show the efficiency and high precision of the method, and the condition of which can be used as a tool for obtaining the repulsive Casimir force. Besides, anisotropic materials and nonlinear materials exhibiting the AC Kerr effect are taken into consideration. The main research woks are as follow.1. The basic theories of the Casimir effect are briefly described including its root, physical background and application in various fields. Based on these basic theories, the typical two dimensional piston structure is analyzed, and a three dimensional structure that can achieve repulsive Casimir force is built.2. The progress of FDTD method and Yee cell are discussed, and the basic principle of Maxwell stress tensor to solve the force is described. Then based on the Maxwell stress tensor and combined with harmonic expansion method, the FDTD algorithm of the three dimensional structure is derived. In this case, the three dimensional problem in cylindrical coordinates is reduced to a two dimensional problem, greatly increase the speed of computation.3. The influences to the Casimir effect, such as structural parameters, center to center separation, properties of materials and embedded mediums, are discussed. Especially the Kerr effect is introduced to better tune the Casimir force between the anisotropic materials, which providing new possibilities of integrating optical devices into nano-electro-mechanical system (NEMS).