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Extracting the equivalent parameters of the weak-coupling and strong-coupling fishnet structure metamaterial based on the traditional retrieval algorithm and the improved algorithm of Kramers-Kronig relations are proposed, respectively. A comparative analysis of the effectiveness and applicability of the two algorithms are also included. The theoretical analysis and numerical results show that the traditional retrieval algorithm can retrieve the equivalent parameters of the weak-coupling and strong-coupling cases of electromagnetic metamaterials accurately, but with high computational complexity. While the improved algorithm based on the Kramers-Kronig relations can reduce the computational complexity and extract the equivalent parameters only for the weak-coupling case of electromagnetic metamaterials. However, it is not suitable for the strong-coupling case which may disobey the continuity requirement of the Kramers-Kronig relations. The presented results may extend the equivalent medium theory and provide a theoretical reference for the design of new metamaterials.
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Keywords:
- metamaterials /
- retrieval algorithm /
- Kramers-Kronig relation /
- equivalent parameter
[1] Veselago V G 1968 Sov. Hys. Usp. 10 509
[2] Houck A A, Brock J B, Chuang I L 2003 Phys. Rev. Lett. 90 137401
[3] Seddon N, Bearpark T 2003 Science 302 1537
[4] Parazzoli C G, Greegor R B, Li K, Koltenbah B E C, Tanielian M 2003 Phys. Rev. Lett. 90 107401
[5] Pendry J B 2000 Phys. Rev. Lett. 85 3966
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[9] Smith D R 2010 Phys. Rev. E 81 036605
[10] Minowa Y, Nagai M, Tao H, Fan K, Strikwerda A C, Zhang X, Averitt R D, Tananka K 2011 IEEE Trans. Terahertz Sci. Tech. 1 441
[11] Koschny T, Markos P, Economou E N, Smith D R, Vier D C, Soukoulis C M 2005 Phys. Rev. B 71 245105
[12] Smith D R, Vier D C, Koschny T, Soukoulis C M 2005 Phys. Rev. E 71 036617
[13] Lucarini V, Saarinen J J, Peiponen K E, Vartiainen E M 2005 \linebreak Kramers-Kronig Relations in Optical Materials Research (Berlin: Springer-Verlag) p28
[14] Peiponen K E, Saarinen J J 2009 Rep. Prog. Phys. 72 056401
[15] Akyurtlu A, Kussow A G 2010 Phys. Rev. A 82 055802
[16] Tatartschuk E, Radkovskaya A, Shamonina E, Solymar L 2010 Phys. Rev. B 81 115110
[17] Powell D A, Lapine M, Gorkunov M V, Shadrivov I V, Kivshar Y S 2010 Phys. Rev. B 82 155128
[18] Valentine J, Zhang S, Zentgraf T, Ulin-Avila E, Genov D A, Bartal G, Zhang X 2008 Nature 455 376
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[1] Veselago V G 1968 Sov. Hys. Usp. 10 509
[2] Houck A A, Brock J B, Chuang I L 2003 Phys. Rev. Lett. 90 137401
[3] Seddon N, Bearpark T 2003 Science 302 1537
[4] Parazzoli C G, Greegor R B, Li K, Koltenbah B E C, Tanielian M 2003 Phys. Rev. Lett. 90 107401
[5] Pendry J B 2000 Phys. Rev. Lett. 85 3966
[6] Wang J F, Zhang J Q, Ma H, Yang Y M, Gu C, Qu S B, Xu Z 2009 Acta Phys. Sin. 58 3224 (in Chinese) [王甲富, 张介秋, 马华, 杨一鸣, 顾超, 屈绍波, 徐卓 2009 58 3224]
[7] 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]
[8] Dolling G, Enkrich C, Wegener M, Soukoulis C M, Linden S 2006 Opt. Lett. 31 1800
[9] Smith D R 2010 Phys. Rev. E 81 036605
[10] Minowa Y, Nagai M, Tao H, Fan K, Strikwerda A C, Zhang X, Averitt R D, Tananka K 2011 IEEE Trans. Terahertz Sci. Tech. 1 441
[11] Koschny T, Markos P, Economou E N, Smith D R, Vier D C, Soukoulis C M 2005 Phys. Rev. B 71 245105
[12] Smith D R, Vier D C, Koschny T, Soukoulis C M 2005 Phys. Rev. E 71 036617
[13] Lucarini V, Saarinen J J, Peiponen K E, Vartiainen E M 2005 \linebreak Kramers-Kronig Relations in Optical Materials Research (Berlin: Springer-Verlag) p28
[14] Peiponen K E, Saarinen J J 2009 Rep. Prog. Phys. 72 056401
[15] Akyurtlu A, Kussow A G 2010 Phys. Rev. A 82 055802
[16] Tatartschuk E, Radkovskaya A, Shamonina E, Solymar L 2010 Phys. Rev. B 81 115110
[17] Powell D A, Lapine M, Gorkunov M V, Shadrivov I V, Kivshar Y S 2010 Phys. Rev. B 82 155128
[18] Valentine J, Zhang S, Zentgraf T, Ulin-Avila E, Genov D A, Bartal G, Zhang X 2008 Nature 455 376
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