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A novel retrieval method of the effective constitutive parameters of metamaterials based on TE10 rectangular waveguide is proposed, which is adopted to extract effective relative permittivity ε and permeability μ for the composite ferrite and wire array metamaterial in multiple symmetrical unit cell configuration. Much attention has been paid to choose the correct branch of the real part of the propagation constant β for the metamaterial with multiple unit cells, and in terms of the relationship between the measured values and theoretical values in the measurement theory, β values in the case of multiple unit cells are determined by taking the extracted β values for a single unit cell as the measured values for the multiple unit cells case. Owing to the coupling effect between the unit cells of the metamaterial with multiple unit cells, the electromagnetic wave mainly behaves as the periodic Bloch wave, which is usually negligible for a single unit cell, so the extracted effective constitutive parameters for a single unit cell generally can not be assigned as those for the metamaterial with multiple unit cells directly. However, β values for a single unit cell is generally prone to be extracted, which can be the first step to extract the β values in multiple unit cells case. It is pointed out that the extracted effective constitutive parameters can be physically meaningful only if attenuation coefficients of higher Bloch wave modes are larger than that of the fundamental Bloch mode in the periodic metamaterial, and under this condition, higher Bloch wave modes will get further attenuated with increase of the unit cell number, leaving only the fundamental mode propagation, which makes the extracted ε and μ more stable and convergent.
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Keywords:
- TE10 rectangular waveguide /
- metamaterial /
- extraction of effective constitutive parameters /
- ferrite and wire array metamaterial
[1] Shelby R A, Smith D R, Schultz S 2001 Science 292 77
[2] Rev. E 71 036617
[3] Meng F Y, Wu Q, Wu J 2006 Acta Phys. Sin. 55 2200 (in Chinese) [孟繁义、 吴 群、 吴 健 2006 物理学报 55 2200]
[4] Dai X Y, Wen S C, Xiang Y J 2008 Chin. Phys. B 17 186
[5] Wang J F, Qu S B, Xu Z, Zhang J Q, Ma H, Yang Y M, Gu C 2009 Acta Phys. Sin. 58 3224 (in Chinese)[王甲富、 屈绍波、 许 卓、 张介秋、 马 华、 杨一鸣、 顾 超 2009 物理学报 58 3224]
[6] Lu W B, Cui T J, Yin X X, Qian Z G, Hong W 2005 IEEE Trans. Micro. Theo. Tech. 53 1154
[7] Ansoft Inc. High Frequency Structure Simulator (Pittsburgh, PA)
[8] Li D, Sarris C D 2008 IEEE Trans. Micro. Theo. Tech. 56 1928
[9] Cheng Q, Liu R P, Huang D, Cui T J 2007 Appl. Phys. Lett. 91 234105
[10] Smith D R, Vier D C, Koschny Th, Soukoulis C M 2005 Phys.
[11] Smith D R, Pendry J B 2006 J. Opt. Soc. Am. B 23 391
[12] Smith D R, Schultz S, Markos P, Soukoulis C M 2002 Phys. Rev. B 65 195104
[13] Ziolkowski R W 2003 IEEE Trans. Micro. Theo. Tech. 51 1516
[14] Chen X D, Grzegorczyk T M, Wu B-I, Jr. J P, Kong J A 2004 Phys. Rev. E 70 016608
[15] Mao S G,Chen S L, Huang C W 2005 IEEE Trans. Micro. Theo. Tech. 53 1515
[16] Rochstuhl C R, Paul T, Lederer F, Pertsch, T, Zentgraf T, Meyrath T P, Giessen H 2008 Phys. Rev. B 77 035126
[17] Koschny T, Markos P, Smith D R, Soukoulis C M 2003 Phys. Rev. E 68 065602
[18] Markos P, Soukoulis C M 2003 Opt. Express 11 649
[19] Chu Q X, Gong J Q 2008 Acta Phys. Sin. 57 2925 (in Chinese)[褚庆昕、 龚建强 2008 物理学报 57 2925]
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[1] Shelby R A, Smith D R, Schultz S 2001 Science 292 77
[2] Rev. E 71 036617
[3] Meng F Y, Wu Q, Wu J 2006 Acta Phys. Sin. 55 2200 (in Chinese) [孟繁义、 吴 群、 吴 健 2006 物理学报 55 2200]
[4] Dai X Y, Wen S C, Xiang Y J 2008 Chin. Phys. B 17 186
[5] Wang J F, Qu S B, Xu Z, Zhang J Q, Ma H, Yang Y M, Gu C 2009 Acta Phys. Sin. 58 3224 (in Chinese)[王甲富、 屈绍波、 许 卓、 张介秋、 马 华、 杨一鸣、 顾 超 2009 物理学报 58 3224]
[6] Lu W B, Cui T J, Yin X X, Qian Z G, Hong W 2005 IEEE Trans. Micro. Theo. Tech. 53 1154
[7] Ansoft Inc. High Frequency Structure Simulator (Pittsburgh, PA)
[8] Li D, Sarris C D 2008 IEEE Trans. Micro. Theo. Tech. 56 1928
[9] Cheng Q, Liu R P, Huang D, Cui T J 2007 Appl. Phys. Lett. 91 234105
[10] Smith D R, Vier D C, Koschny Th, Soukoulis C M 2005 Phys.
[11] Smith D R, Pendry J B 2006 J. Opt. Soc. Am. B 23 391
[12] Smith D R, Schultz S, Markos P, Soukoulis C M 2002 Phys. Rev. B 65 195104
[13] Ziolkowski R W 2003 IEEE Trans. Micro. Theo. Tech. 51 1516
[14] Chen X D, Grzegorczyk T M, Wu B-I, Jr. J P, Kong J A 2004 Phys. Rev. E 70 016608
[15] Mao S G,Chen S L, Huang C W 2005 IEEE Trans. Micro. Theo. Tech. 53 1515
[16] Rochstuhl C R, Paul T, Lederer F, Pertsch, T, Zentgraf T, Meyrath T P, Giessen H 2008 Phys. Rev. B 77 035126
[17] Koschny T, Markos P, Smith D R, Soukoulis C M 2003 Phys. Rev. E 68 065602
[18] Markos P, Soukoulis C M 2003 Opt. Express 11 649
[19] Chu Q X, Gong J Q 2008 Acta Phys. Sin. 57 2925 (in Chinese)[褚庆昕、 龚建强 2008 物理学报 57 2925]
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