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将薄的磁谐振介质板等效为面磁流, 利用周期性边界条件, 给出了面磁流的指数形式. 通过计算无穷个面磁流在不同空间位置上产生的总电场和总磁场, 推导出了周期性磁谐振人工材料的色散关系和布洛赫阻抗, 进而获取了布洛赫本构参数的理论计算公式. 由于考虑了磁谐振人工材料中的电反谐振对布洛赫介电常数和磁导率的影响, 所以基于仿真实验的布洛赫本构参数的提取值和布洛赫本构参数理论预测值之间的误差很小, 这说明本文推导的布洛赫本构参数的理论计算公式在描述周期性磁谐振材料的电磁特性方面是十分有效的. 这些理论公式将在解释磁谐振现象、设计和优化周期性磁谐振材料等方面提供重要的理论依据.The thin magnetic resonance dielectric plate is equivalent to a surface magnetic current. Using periodic boundary conditions, the exponential form of the surface magnetic current density is given. The dispersion relation and Bloch impedance of a periodic magnetic resonator metamaterial are derived by calculating the total electric and magnetic fields at the different positions excited by the infinite number of surface magnetic currents, and thus the theoretical formulas for Bloch constitutive parameters are obtained. Since the electric anti-resonance influence on the Bloch permittivity and permeability of magnetic resonator metamaterial is considered, thus the Bloch constitutive parameter difference between theoretical values and retrieval results based on simulations is very small, which shows that the Bloch constitutive parameter formula derived in the paper is very effective to describe the electromagnetic properties of the periodic magnetic resonant material. These theoretical formulas will provide important theoretical basis for the interpretation of the magnetic resonance phenomenon, the design and optimization of the periodic magnetic resonant material.
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Keywords:
- periodic structure /
- magnetic resonance /
- Bloch constitutive parameters /
- surface magnetic current
[1] Veselago V G 1968 Sov. Phys. Usp. 10 509
[2] Shelby R A, Smith D R, Schultz S 2001 Science 292 77
[3] Pendry J B 2000 Phys. Rev. Lett. 85 3966
[4] Schurig D R, Mock J J, Smith D R 2006 Appl. Phys. Lett. 88 041109
[5] Pendry J B, Holden A J, Robbins D J 1999 IEEE Trans. Microwave Theory Tech. 47 2075
[6] Li J C, Guo L X, Liu S H 2012 Acta Phys. Sin. 61 124102 (in Chinese) [李俊成, 郭立新, 刘松华 2012 61 124102]
[7] Yang C, Zhang H X, Wang H X, Xu N, Xu Y Y, Huang L Y, Zhang K X 2012 Acta Phys. Sin. 61 164101 (in Chinese) [杨晨, 张洪欣, 王海侠, 徐楠, 许媛媛, 黄丽玉, 张可欣 2012 61 164101]
[8] Xu X H, Xiao S Q, Gan Y H, Fu C F, Wang B Z 2012 Acta Phys. Sin. 61 124103 (in Chinese) [徐新河, 肖绍球, 甘月红, 付崇芳, 王秉中 2012 61 124103]
[9] Dai X Y, Wen S C, Xiang Y J 2008 Chin. Phys. B 17 186
[10] Liu R, Cui T J, Huang D, Zhao B, Smith D R 2007 Phys. Rev. E 76 026606
[11] Smith D R 2010 Phys. Rev. E 81 03660
[12] Smith D R, Schultz S 2002 Phys. Rev. B 65 195104
[13] Smith D R, Pendry J B 2006 J. Opt. Soc. Am. B 23 391
[14] Smith D R, Vier D C, Koschny T, Soukoulis C M 2005 Phys. Rev. E 71 036617
[15] Chen X, Grzegorczyk T M, Wu B I, Pacheco Jr J, Kong J A 2004 Phys. Rev. E 70 016608
[16] Gong J Q, Liang C H 2011 Acta Phys. Sin. 60 059204 (in Chinese) [龚建强, 梁昌洪 2011 60 059204]
[17] Varadan V, Sheng Z, Penumarthy S, Puligalla S 2006 Microwave Opt. Technol. Lett. 48 1549
[18] Chen H S 2005 Ph. D. Dissertation (Hangzhou: Zhejiang University) (in Chinese) [陈红胜2005 博士学位论文(杭州: 浙江大学)]
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[1] Veselago V G 1968 Sov. Phys. Usp. 10 509
[2] Shelby R A, Smith D R, Schultz S 2001 Science 292 77
[3] Pendry J B 2000 Phys. Rev. Lett. 85 3966
[4] Schurig D R, Mock J J, Smith D R 2006 Appl. Phys. Lett. 88 041109
[5] Pendry J B, Holden A J, Robbins D J 1999 IEEE Trans. Microwave Theory Tech. 47 2075
[6] Li J C, Guo L X, Liu S H 2012 Acta Phys. Sin. 61 124102 (in Chinese) [李俊成, 郭立新, 刘松华 2012 61 124102]
[7] Yang C, Zhang H X, Wang H X, Xu N, Xu Y Y, Huang L Y, Zhang K X 2012 Acta Phys. Sin. 61 164101 (in Chinese) [杨晨, 张洪欣, 王海侠, 徐楠, 许媛媛, 黄丽玉, 张可欣 2012 61 164101]
[8] Xu X H, Xiao S Q, Gan Y H, Fu C F, Wang B Z 2012 Acta Phys. Sin. 61 124103 (in Chinese) [徐新河, 肖绍球, 甘月红, 付崇芳, 王秉中 2012 61 124103]
[9] Dai X Y, Wen S C, Xiang Y J 2008 Chin. Phys. B 17 186
[10] Liu R, Cui T J, Huang D, Zhao B, Smith D R 2007 Phys. Rev. E 76 026606
[11] Smith D R 2010 Phys. Rev. E 81 03660
[12] Smith D R, Schultz S 2002 Phys. Rev. B 65 195104
[13] Smith D R, Pendry J B 2006 J. Opt. Soc. Am. B 23 391
[14] Smith D R, Vier D C, Koschny T, Soukoulis C M 2005 Phys. Rev. E 71 036617
[15] Chen X, Grzegorczyk T M, Wu B I, Pacheco Jr J, Kong J A 2004 Phys. Rev. E 70 016608
[16] Gong J Q, Liang C H 2011 Acta Phys. Sin. 60 059204 (in Chinese) [龚建强, 梁昌洪 2011 60 059204]
[17] Varadan V, Sheng Z, Penumarthy S, Puligalla S 2006 Microwave Opt. Technol. Lett. 48 1549
[18] Chen H S 2005 Ph. D. Dissertation (Hangzhou: Zhejiang University) (in Chinese) [陈红胜2005 博士学位论文(杭州: 浙江大学)]
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