时域积分方程法研究石墨烯太赫兹频段色散特性

发布时间：2018-03-16 16:40

本文选题：太赫兹　切入点：石墨烯　出处：《南京邮电大学》2017年硕士论文　论文类型：学位论文

【摘要】：新型纳米碳基材料石墨烯无限薄,表现出色散特性,在电磁、太赫兹通信系统等方面具有重要的应用前景。本文针对石墨烯器件的应用需求与数值分析的发展需要,提出一种分析石墨烯太赫兹频段色散特性的数值方法,研究内容涉及以下部分:对石墨烯的色散特性进行准确建模,使用Kubo公式计算其由带内和带间表面电导率构成的频域表面电导率。使用矢量匹配法,以实极点-留数和/或复极点-留数共轭对的形式展开石墨烯频域表面电导率和阻抗,通过改变矢量匹配法的拟合项数来研究项数对拟合精度的影响,同时对不同温度和化学势下的石墨烯频域表面阻抗进行有理近似,以此探讨这些参数对频域表面阻抗的影响。在此基础上,使用矢量匹配法来拟合石墨烯在太赫兹频段下的频域表面阻抗,仿真结果表明通过较少的拟合项数即可达到比较精确的拟合结果。在上述研究基础上,将石墨烯的频域表面阻抗经傅里叶逆变换获得时域表面阻抗,根据表面阻抗边界条件建立分析石墨烯的阶数步进时域积分方程,通过时域表面阻抗与时域电流作卷积体现石墨烯的色散特性。使用Laguerre多项式等性质进行推导,获得时域表面阻抗与时域电流卷积项的解析公式。使用加权Laguerre多项式作为时间基函数,使用Galerkin法进行空间和时间测试,推导出从积分方程建立到矩阵方程形成的主要公式。仿真结果表明时域电流是无条件稳定的,此外,对比石墨烯与金属平板的时域结果,表明石墨烯是色散的,对比由频域矩量法所得到的仿真结果,进一步验证本文所提出的分析石墨烯的阶数步进时域积分方程法的正确性。
[Abstract]:The novel nano-carbon based material graphene is infinitely thin and has excellent dispersion properties. It has an important application prospect in electromagnetic and terahertz communication systems. This paper aims at the development of graphene devices and numerical analysis. A numerical method for analyzing the dispersion characteristics of graphene terahertz band is presented. The research involves the following parts: the dispersion characteristics of graphene are modeled accurately. The frequency domain surface conductivity of graphene is calculated by using the Kubo formula, which consists of the in-band and inter-band surface conductivities. Using vector matching method, the surface conductivity and impedance of graphene in frequency domain are developed in the form of real pole-residue and / or complex pole-residue conjugate pairs. By changing the fitting term number of vector matching method, the influence of term number on fitting accuracy is studied. At the same time, the surface impedance of graphene in frequency domain under different temperature and chemical potential is obtained by rational approximation. The influence of these parameters on the surface impedance in frequency domain is discussed. On this basis, the frequency domain surface impedance of graphene in terahertz band is fitted by vector matching method. The simulation results show that more accurate fitting results can be obtained by using fewer fitting terms. On the basis of the above research, the surface impedance of graphene in frequency domain is obtained by Fourier inverse transform, and the surface impedance of graphene in time domain is obtained by inverse Fourier transform. According to the boundary condition of surface impedance, the order step time domain integral equation of graphene is established, and the dispersion characteristic of graphene is reflected by convolution of time domain surface impedance and time domain current. The properties of graphene are deduced by using Laguerre polynomials. The analytical formulas of the time domain surface impedance and the time domain current convolution term are obtained. The weighted Laguerre polynomial is used as the time basis function and the Galerkin method is used to carry out the space and time measurements. The main formulas from integral equation to matrix equation are derived. The simulation results show that the time domain current is unconditionally stable. In addition, compared with the time domain results of graphene and metal plate, it is shown that graphene is dispersive. By comparing the simulation results obtained from the method of moments in frequency domain, the correctness of the order step time domain integral equation method for graphene analysis proposed in this paper is further verified.
【学位授予单位】：南京邮电大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O613.71;O241.8

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