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The relations between the scattering matrix and relative Bloch permeability of periodic symmetric magnetic resonance metamaterial are investigated in detail by means of network theory and Floquet's theorem, and we retrieve the Bloch constitutive parameters for four split ring resonators using the relations. Full wave simulations in conjunction with numerical retrieval algorithms show that when we load the interdigital capacitance at the gap of split ring resonator, the magnetic resonance frequency drastically lowers. Our work provides not only theoretical foundation for the Bloch permeability parameter retrieval from periodic metamaterials, but also a novel design way of miniaturizing magnetic resonance metamaterial configurations.
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Keywords:
- periodic structure /
- interdigital capacitance /
- magnetic resonance /
- miniaturization
[1] Veselago V G 1968 Soviet. Physics---Uspekh1 10 509
[2] Smith D R, Padilla W J 2000 Physical Review Letters 84 4184
[3] Eleftheriades G V, Iyer A K, Kremer P C 2002 IEEE Trans. Microwave Theroy Tech. 50 2702
[4] Pendry J B 2000 Physical Review Letters 85 3966
[5] Yu G X, Cui T J 2008 Chin. Phys. B 17 0164
[6] Zhang S, Qu S B, Ma H, Xie F, Xu Z 2009 Acta Phys. Sin. 58 3961 (in Chinese) [张松, 屈绍波, 马华, 谢峰, 徐卓 2009 58 3961]
[7] Meng F Y, Wu Q, Wu J 2006 Acta Phys. Sin. 55 2200 (in Chinese) [孟繁义, 吴群, 吴健 2006 55 2200]
[8] Dai X Y, Wen S C, Xiang Y J 2008 Chin. Phys. B 17 186
[9] Li D, Sarris C D 2008 IEEE Trans. Micro. Theo. Tech. 56 1928
[10] Dai X Y, Wen S C, Xiang Y J 2008 Chin. Phys. B 17 186
[11] Smith D R, Schultz S 2002 Phys. Rev. B 65 195104
[12] Smith D R, Vier D C, Koschny Th, Soukoulis C M 2005 Phys. Rev. E 71 036617
[13] Liu R, Cui T J, Huang D, Zhao B, Smith D R 2007 Phys. Rev. E 76 026606
[14] Gong J Q, Liang C H, Wu J 2011 Acta Phys. Sin. 60 059204 (in Chinese) ［龚建强, 梁昌洪 2011 60 059204］
[15] Smith D R 2010 Phys. Rev. E 81 036605
[16] Pendry J B, Holden A J, Robbins D J, Stewart W J 1999 IEEE Trans. Microwave Theroy Tech. 47 11
[17] Tang M C, Xiao S Q Deng T W, Wang D, Bai Y Y, Jin D P Wang B Z 2010 Acta Phys. Sin. 59 4715 (in Chinese) [唐明春, 肖绍球, 邓天伟, 王多, 柏艳英, 金大鹏, 王秉中 2010 59 4715]
[18] Pozar D M, Microwave Engineering, 2nd ed. (John Wiley & Sons, New York, 1998d, p. 211)
[19] 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 Soviet. Physics---Uspekh1 10 509
[2] Smith D R, Padilla W J 2000 Physical Review Letters 84 4184
[3] Eleftheriades G V, Iyer A K, Kremer P C 2002 IEEE Trans. Microwave Theroy Tech. 50 2702
[4] Pendry J B 2000 Physical Review Letters 85 3966
[5] Yu G X, Cui T J 2008 Chin. Phys. B 17 0164
[6] Zhang S, Qu S B, Ma H, Xie F, Xu Z 2009 Acta Phys. Sin. 58 3961 (in Chinese) [张松, 屈绍波, 马华, 谢峰, 徐卓 2009 58 3961]
[7] Meng F Y, Wu Q, Wu J 2006 Acta Phys. Sin. 55 2200 (in Chinese) [孟繁义, 吴群, 吴健 2006 55 2200]
[8] Dai X Y, Wen S C, Xiang Y J 2008 Chin. Phys. B 17 186
[9] Li D, Sarris C D 2008 IEEE Trans. Micro. Theo. Tech. 56 1928
[10] Dai X Y, Wen S C, Xiang Y J 2008 Chin. Phys. B 17 186
[11] Smith D R, Schultz S 2002 Phys. Rev. B 65 195104
[12] Smith D R, Vier D C, Koschny Th, Soukoulis C M 2005 Phys. Rev. E 71 036617
[13] Liu R, Cui T J, Huang D, Zhao B, Smith D R 2007 Phys. Rev. E 76 026606
[14] Gong J Q, Liang C H, Wu J 2011 Acta Phys. Sin. 60 059204 (in Chinese) ［龚建强, 梁昌洪 2011 60 059204］
[15] Smith D R 2010 Phys. Rev. E 81 036605
[16] Pendry J B, Holden A J, Robbins D J, Stewart W J 1999 IEEE Trans. Microwave Theroy Tech. 47 11
[17] Tang M C, Xiao S Q Deng T W, Wang D, Bai Y Y, Jin D P Wang B Z 2010 Acta Phys. Sin. 59 4715 (in Chinese) [唐明春, 肖绍球, 邓天伟, 王多, 柏艳英, 金大鹏, 王秉中 2010 59 4715]
[18] Pozar D M, Microwave Engineering, 2nd ed. (John Wiley & Sons, New York, 1998d, p. 211)
[19] 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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