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Calculation of the Casimir Effect Based on FDTD Method

Author: WangWang
Tutor: HuangZhiXiang; WuXianLiang
School: Anhui University
Course: Electromagnetic Field and Microwave Technology
Keywords: Casimir effect zero-point energy finite difference time domainmethod Maxwell stress tensor fluctuation-dissipation theorem
CLC: TN011
Type: Master's thesis
Year: 2013
Downloads: 7
Quote: 0
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Abstract


The casimir effect has been one of the most robust findings in physic. There is an unknown repulsive force between two uncharged metallic plates in a vacuum, placed a few micrometers apart, we called it casimir force. After years’ research and development, also found that the attractive force of the casimir effect. There are two explanations of casimir effect in academic circle, one of explanations is based on the change in zero-point energy of the vacuum caused by this phenomenon:add a piece of uncharged metallic plate in vacuum, results in the alteration by the boundaries of the zero-point electromagnetic energy, and then impact of electromagnetic field fluctuations arising from fluctuations. Another explanation for casimir effect is the radiation pressure theory. According to this theory, both inside and outside of metallic plate in vacuum is influenced by radiation pressure. The casimir force generated by the difference of radiation pressure.Although the casimir force is very small, generally only10-10N. In fact, casimir force will affect micro-devices (the size of devices be below1um) greatly. And the miniaturization of devices is a hot issue in engineering, also will be the future development tendency. The casimir effect of nano-microscale structures or nano-microscale devices become one of important topics in the design of MEMS (micro-electromechanical systems). So the calculation of casimir force has been an important topic in engineering and physics. But it can only calculate casimir force of some basic geometry structures and some simple materials.This paper gives a new method to calculate the casimir force which combined with FDTD algorithm, this method based on the first theory. Compared with the traditional method, this method has more advantages in the calculation of complex structures and special materials. The precision of analytic method for calculating casimir force is high. Because we use the method combined with FDTD, so we can direct use FDTD software calculate casimir force. The FDTD method proposed by K.S.Yee basing on Maxwell’s differential equations is a very important approach in Computational electromagnetic. The advantage of this method is:easy to operate as well as be suitable for parallel programming. We choose FDTD software-MEEP with open source and modify it for applying to our calculations.MEEP is a simulation software based on the FDTD algorithm running on Linux environment, which is developed by MIT. We first install MEEP in Linux and configure it. Then we choose three simulation cases to verify its accuracy and effectiveness:1.The wave source spreads out in the rectangular waveguide.2. Silver column’s scattering\absorption\extinction cross section3.The transmission coefficient of the50nm dielectric plate.We first calculated the Casimir force between two-dimensional metal plate in the basic vacuum. Then we compared the calculated result with the observed experimental data. We found that the force and the performance trends between them are almost same. Therefore this method for calculating Casimir effect feasible is feasible. Besides, we calculate a classic Casimir piston structure to elaborate on the calculation steps of the method. Then we also compare to experimental data, fatherly verify the accuracy and effectiveness of the method.In the following, we calculated the Casimir force among several different geometry and different material objects respectively to indicate how do the geometry and material of object affect the Casimir. Finally calculate Casimir force of the dispersion medium.

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