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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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