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## Symplectic FDTD algorithm for the simulations of double dispersive materials

Wang Hui, Huang Zhi-Xiang, Wu Xian-Liang, Ren Xin-Gang, Wu Bo
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• #### 摘要

结合有耗的Drude-Lorentz色散模型，提出了处理双色散模型的辛时域有限差分算法. 基于矩阵分裂，辛传播算子和辅助差分方程技术，结合严格而巧妙的公式推导，构建了算法框架，并给出了详细的公式推导过程. 为了验证本文算法的有效性和精确性，首先计算了一维空间双色散平板的透射系数，并与解析解对比，结果较好地符合，证明了该算法是有效而精确的. 然后计算了三维空间中有实际意义的银分裂环，金属银的介电参数由Drude 模型拟合. 计算了该结构的透射系数，反射系数和吸收系数，得到了银分裂环的谐振频率和吸收频率，为实际实验结果提供了可供参考的计算结果.

#### Abstract

Combined with the Lossy Drude-Lorentz dispersive model, a symplectic finite-difference time-domain (SFDTD) algorithm is proposed to deal with the double dispersive model. Based on matrix splitting, symplectic integrator propagator and the auxiliary differential equation (ADE) technique, with the rigorous and artful formula derivation, the algorithm is constructed, and detailed formulations are provided. Excellent agreement is achieved between the SFDTD-calculated and exact theoretical results when transmittance coefficient in simulation of double dispersive film in one dimension is calculated. As to numerical results for a more realistic structure in three dimensions, the simulation of periodic arrays of silver split-ring resonators using the Drude dispersion model are also included. The transmittance, reflectance, and absorptance of the structure are presented to test the efficiency of the proposed method. Our method can be used as an efficiency simulation tool for checking the experimental data.

#### 作者及机构信息

###### 1. 安徽大学计算智能与信号处理教育部重点实验室, 合肥 230039; 2. 合肥师范学院电子信息工程学院, 合肥 230061; 3. 香港大学电机电子工程学院, 香港, 薄扶林道
• 基金项目: 国家自然科学基金（批准号：51277001，61101064）、教育部新世纪优秀人才基金（批准号：NCET-12-0596）、教育部博士点基金（批准号：20123401110009）、安徽省杰出青年基金（批准号：1108085J01）和安徽省高校重点项目（批准号：KJ2012A103）资助的课题.

#### Authors and contacts

###### 1. The Key Laboratory of Intelligent Computing and Signal Processing, Ministry of Education, Anhui University, Hefei 230039, China; 2. Department of Physics and Engineering, Hefei Normal College, Hefei 230061, China; 3. Department of Electrical and Electronic Engineering, The University of Hong Kong, Pokfulam Road, Hong Kong, China
• Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 51277001, 61101064), the NCET (Grant No. NCET-12-0596), the DFMEC (Grant No. 20123401110009), the Fund for Distinguished Young Scholars of Anhui Province, China (Grant No. 1108085J01), and the Key Program of the Higher Education Institutions of Anhui Province, China (Grant No. KJ2012A103).

#### 参考文献

 [1] Ai F, Bai Y, Xu F, Qiao L J, Zhou J 2008 Acta Phys. Sin. 57 4189 (in Chinese)[艾芬, 白洋, 徐芳, 乔利杰, 周济 2008 物理学报57 4189] [2] Liu R, Shi J H, Plum E, Fedotov V, Zheludev N 2012 Acta Phys. Sin. 61 154101 (in Chinese)[刘冉, 史金辉, E. Plum, V.A.Fedotov, N.I.Zheludev 2012 物理学报61 154101] [3] Wang W S, Zhang L W, Ran J, Zhang Y W 2013 Acta Phys. Sin. 62 184203 (in Chinese)[王五松, 张利伟, 冉佳, 张冶文2013 物理学报62 184203] [4] Taflove A, Hagness S C 2005 Computational Electrodynamics: The Finite-Difference Time-Domain Method, third ed. (Boston: Artech House) [5] Sullivan D M, Hagness S C 2005 Electromagnetic Simulation Using the FDTD Method (New York: IEEE Press) [6] Prokopidis K P, Tsiboukis T D 2007 Appl. Comput. Eletron. 22 287 [7] Deinega A, John S 2012 Opt. Lett. 37 112 [8] Vial A, Grimault A-S, Macías D, Barchiesi D, Chapelle M L 2005 Phys. Rev. B 71 085416 [9] Sha W, Huang Z X, Chen M S, Wu X L 2008 IEEE Trans. Antennas Propag. 56 493 [10] Hirono T, Lui W, Seki S, Yoshikuni Y 2001 IEEE Trans. Microw. Thory Tech. 49 1640 [11] Wang H, Huang Z X, Wu X L, Ren X G 2011 Chin. Phys. B 20 114701 [12] Ren X G, Huang Z X, Wu X L, Lu S L, Wang H, Wu L, Li S 2012 Comput. Phys. Commun. 183 1192

#### 施引文献

•  [1] Ai F, Bai Y, Xu F, Qiao L J, Zhou J 2008 Acta Phys. Sin. 57 4189 (in Chinese)[艾芬, 白洋, 徐芳, 乔利杰, 周济 2008 物理学报57 4189] [2] Liu R, Shi J H, Plum E, Fedotov V, Zheludev N 2012 Acta Phys. Sin. 61 154101 (in Chinese)[刘冉, 史金辉, E. Plum, V.A.Fedotov, N.I.Zheludev 2012 物理学报61 154101] [3] Wang W S, Zhang L W, Ran J, Zhang Y W 2013 Acta Phys. Sin. 62 184203 (in Chinese)[王五松, 张利伟, 冉佳, 张冶文2013 物理学报62 184203] [4] Taflove A, Hagness S C 2005 Computational Electrodynamics: The Finite-Difference Time-Domain Method, third ed. (Boston: Artech House) [5] Sullivan D M, Hagness S C 2005 Electromagnetic Simulation Using the FDTD Method (New York: IEEE Press) [6] Prokopidis K P, Tsiboukis T D 2007 Appl. Comput. Eletron. 22 287 [7] Deinega A, John S 2012 Opt. Lett. 37 112 [8] Vial A, Grimault A-S, Macías D, Barchiesi D, Chapelle M L 2005 Phys. Rev. B 71 085416 [9] Sha W, Huang Z X, Chen M S, Wu X L 2008 IEEE Trans. Antennas Propag. 56 493 [10] Hirono T, Lui W, Seki S, Yoshikuni Y 2001 IEEE Trans. Microw. Thory Tech. 49 1640 [11] Wang H, Huang Z X, Wu X L, Ren X G 2011 Chin. Phys. B 20 114701 [12] Ren X G, Huang Z X, Wu X L, Lu S L, Wang H, Wu L, Li S 2012 Comput. Phys. Commun. 183 1192
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##### 出版历程
• 收稿日期:  2013-11-11
• 修回日期:  2013-12-31
• 刊出日期:  2014-04-05

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