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单负(仅介电常数或仅磁导率小于零)超材料以及由导线-开口谐振环组成的双负超材料本构参数的提取通常采用传统的S参数方法. 由于磁电耦合超材料存在交叉极化现象, 仅用介电常数和磁导率两个本构参数无法准确描述其电磁特性. 传统的S参数提取方法一开始就假定超材料仅具有介电常数和磁导率两个本构参数, 所以采用该方法提取磁电耦合超材料本构参数存在明显局限性. 将磁电耦合超材料中的电元件和磁元件分别等效为面电流和面磁流, 通过推导平均电通密度和磁通密度与外加电磁场的相互关系, 从理论上获取了磁电耦合超材料2×2 的本构参数矩阵, 确定了磁电耦合超材料这四个本构参数与磁元件的磁导率、电元件的介电常数、空间色散项和耦合系数之间的关系解析公式, 进而获得了折射率理论计算公式. 利用该折射率公式对折射率提取值进行了非线性拟合, 发现提取值和理论值之间的误差很小, 这个结果很好地验证了所给出的本构矩阵解析式和折射率公式的正确性. 根据拟合结果, 获得了磁电耦合超材料本构矩阵中四个电磁参数的频率响应曲线. 所提出的磁电耦合超材料本构矩阵参数获取方法将为研究磁电超材料中电元件和磁元件的耦合现象提供重要的理论参考.The constitutive parameters of single negative (only electric permittivity or only permeability less than zero) metamaterials and wires-split ring resonator metamaterials can usually be retrieved by the S parameter method. Due to the cross polarization phenomenon in magnetoelectric coupling metamaterial, only two constitutive parameters of permittivity and permeability cannot accurately describe the electromagnetic characteristics of the magnetoelectric coupling metamaterial. The traditional S parameter retrieval method starts with the assumption that the metamaterial has only two constitutive parameters of permittivity and permeability, so the method to retrieve the constitutive parameters of magnetoelectric coupling metamaterials is obviously restricted. In this paper, the electric component and magnetic component in a magnetoelectric coupling metamaterial cell are treated as being equivalent to the surface current and surface magnetic flow, respectively. By deriving the relationship of the average electric flux density and the average magnetic flux density to the external electromagnetic field, we obtain a constitutive parameters matrix (2×2) of the magnetoelectric coupling metamaterial, and find analytical formulas for the relationship between these four constitutive parameters of the magnetoelectric coupling metamaterial and the parameters such as the permittivity of the electric component, permeability of magnetic element, spatial dispersion, and coupling coefficient, and then deduce the refractive index formula. We use the refractive index formula to nonlinearly fit retrieval refractive index curves, and find very good agreement between the refractive index values theoretically predicted by analytical formulas and those obtained from numerical retrievals based on full-wave simulations, thereby verifying the proposed constitutive matrix analytic formula and the refractive index expression. According to the fitting results, we obtain the frequency response curves of the four electromagnetic parameters in constitutive matrix. The proposed method of retrieving the constitutive matrix parameters will provide an important theoretical reference for the researchers engaged in analyzing and studying the coupling phenomenon between electric component and magnetic component in a magnetoelectric metamaterial cell.
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Keywords:
- magnetoelectric coupling /
- metamaterials /
- constitutive matrix /
- nonlinearly fitting
[1] Veselago V G 1968 Soviet Physics Uspekhi 10 509
[2] Smith D R, Schultz S 2002 Phys. Rev. B 65 195104
[3] Smith D R, Pendry J B 2006 J. Opt. Soc. Am. B 23 391
[4] Smith D R, Vier D C, Koschny T, Soukoulis C M 2005 Phys. Rev. E 71 036617
[5] Gong J Q, Liang C H 2011 Acta Phys. Sin. 60 059204 (in Chinese) [龚建强, 梁昌洪 2011 物理学报 60 059204]
[6] Chen X, Grzegorczyk T M, Wu B I, Pacheco Jr J, Kong J A 2004 Phys. Rev. E 70 016608
[7] Xu H X, Wang G M, Wang J F, Yang Z M 2012 Chin. Phys. B 21 124101
[8] He X J, Wang Y, Mei J S, Gui T L, Yin J H 2012 Chin. Phys. B 21 044101
[9] Xiong H, Hong J S, Jin D L 2013 Chin. Phys. B 22 014101
[10] Smith D R 2010 Phys. Rev. E 81 036605
[11] Xu X H, Wu X, Xiao S Q, Gan Y H, Wang B Z 2013 Acta Phys. Sin. 62 084101 (in Chinese) [徐新河, 吴夏, 肖绍球, 甘月红, 王秉中 2013 物理学报 62 084101]
[12] Liu R P, Cui T J, Huang D, Zhao B, Smith D R 2007 Phys. Rev. E 76 026606
[13] Xu X H, Xiao S Q, Gan Y H, Wang B Z 2013 Acta Phys. Sin. 62 104101 (in Chinese) [徐新河, 肖绍球, 甘月红, 王秉中 2013 物理学报 62 104101]
[14] Marque's R, Medina F, Rafii-El-Idrissi R 2002 Phys. Rev. E 65 144440
[15] Zhang K Q, Li D J 2007 Electromagnetic Theory for Microwave and Optoelectronics (2nd Ed.) (New York: Berlin Heidelberg) p11
[16] Schurig D, Mock J J, Smith D R 2006 Appl. Phys. Lett. 88 041109
[17] Pendry J B, Holden A J, Robbins D J, Stewart W J 1999 IEEE Trans. Microwave Theory Tech. 47 2075
[18] Sihvola A H 1992 IEEE Trans. Antennas Propag. 40 188
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[1] Veselago V G 1968 Soviet Physics Uspekhi 10 509
[2] Smith D R, Schultz S 2002 Phys. Rev. B 65 195104
[3] Smith D R, Pendry J B 2006 J. Opt. Soc. Am. B 23 391
[4] Smith D R, Vier D C, Koschny T, Soukoulis C M 2005 Phys. Rev. E 71 036617
[5] Gong J Q, Liang C H 2011 Acta Phys. Sin. 60 059204 (in Chinese) [龚建强, 梁昌洪 2011 物理学报 60 059204]
[6] Chen X, Grzegorczyk T M, Wu B I, Pacheco Jr J, Kong J A 2004 Phys. Rev. E 70 016608
[7] Xu H X, Wang G M, Wang J F, Yang Z M 2012 Chin. Phys. B 21 124101
[8] He X J, Wang Y, Mei J S, Gui T L, Yin J H 2012 Chin. Phys. B 21 044101
[9] Xiong H, Hong J S, Jin D L 2013 Chin. Phys. B 22 014101
[10] Smith D R 2010 Phys. Rev. E 81 036605
[11] Xu X H, Wu X, Xiao S Q, Gan Y H, Wang B Z 2013 Acta Phys. Sin. 62 084101 (in Chinese) [徐新河, 吴夏, 肖绍球, 甘月红, 王秉中 2013 物理学报 62 084101]
[12] Liu R P, Cui T J, Huang D, Zhao B, Smith D R 2007 Phys. Rev. E 76 026606
[13] Xu X H, Xiao S Q, Gan Y H, Wang B Z 2013 Acta Phys. Sin. 62 104101 (in Chinese) [徐新河, 肖绍球, 甘月红, 王秉中 2013 物理学报 62 104101]
[14] Marque's R, Medina F, Rafii-El-Idrissi R 2002 Phys. Rev. E 65 144440
[15] Zhang K Q, Li D J 2007 Electromagnetic Theory for Microwave and Optoelectronics (2nd Ed.) (New York: Berlin Heidelberg) p11
[16] Schurig D, Mock J J, Smith D R 2006 Appl. Phys. Lett. 88 041109
[17] Pendry J B, Holden A J, Robbins D J, Stewart W J 1999 IEEE Trans. Microwave Theory Tech. 47 2075
[18] Sihvola A H 1992 IEEE Trans. Antennas Propag. 40 188
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