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By using the transfer-matrix method,we study the Anderson localization behavior in one-dimensional periodic-on-average disordered system composed of two different single-negative(SNG) metamaterials. Non-dispersive and dipersive models have been studied respectively. It was found that the disorder has great effect on waves with frequency in the pass band of the corresponding periodic structure. However,inside the gap,the effect can be almost ignored. These features are different from those we ever found in the random single-negative system. The main reason of the difference should be the number of the interfaces between two kinds of single negative metamateirals,which should be the basic mechanism of the wave propagation in systems made of single negative metamaterials. In periodic-on-average disordered systems,the number of the interface is the same as that in periodic one. However,there is an obvious decrease in random systems,which will have a great effect on the ability of wave transport,leading to small localization length. In the case of a dispersive model,it has been proved that the randomness has no effect on the wave propagation with frequency at the center of the gap. Especially,this special point becomes a delocalization point when the ratio of effective optical thickness of two single negative materials equals one. The results facilitates further understanding of the wave transport mechanism in systems composed of metamaterials.
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Keywords:
- single-negative metamaterial /
- localization length /
- transfer-matrix method /
- delocalization
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[1] Pendry J B, Holden A J, Robbins D J, Stewart W J 1999 IEEE T. Microw. Theory 47 2075
[2] Smith D R, Padilla W J, Vier D C, Nemat-Nasser S C, Schultz S 2000 Phys. Rev. Lett. 84 4184
[3] Express 16 6860
[4] Shelby R A, Smith D R, Schultz S 2001 Science 292 77
[5] Pendry J B 2000 Phys. Rev. Lett. 85 3966
[6] Pendry J B 2006 Science 312 1780
[7] Chen H, Wu B I, Zhang B, Kong J A 2007 Phys. Rev. Lett. 99 063903
[8] Yablonovitch E 1987 Phys. Rev. Lett. 58 2059
[9] John S 1987 Phys. Rev. Lett. 58 2486
[10] Li J, Zhou L, Chan C T, Sheng P 2003 Phys. Rev. Lett. 90 083901
[11] Wang Z D, Liu N H 2009 Acta Phys. Sin. 58 0559 (in Chinese) [王振德、 刘念华 2009 58 0559]
[12] Shadrivov I V, Sukhorukov A A, Kivshar Y S 2005 Phys. Rev. Lett. 95 193903
[13] Jiang H, Chen H, Li H, Zhang Y, Zi J 2004 Phys. Rev. E 69 066607
[14] Chen Y H, Dong J W, Wang H Z 2006 Appl. Phys. Lett. 89 141101
[15] Anderson P W 1958 Phys. Rev. 109 1492
[16] Wiersma D S 1997 Nature 390 671
[17] Storzer M, Gross P, Aegerter C M, Maret G 2006 Phys. Rev. Lett. 96 063904
[18] Foret M, Courtens E, Vacher R, Suck J B 1996 Phys. Rev. Lett. 77 3831
[19] Billy J 2008 Nature 453 891
[20] Roati G 2008 Nature 453 895
[21] Jahnke L, Kantelhardt J W, Berkovits R 2008 Phys. Rev. Lett. 101 175702
[22] Sheng P 1990 Scattering and Localization of Classical Waves in Random Media (Singapore: World Scientific)
[23] Ghulinyan M 2007 Phys. Rev. Lett. 99 063905
[24] Sebbah P, Hu B, Klosner J M, Genack A Z 2006 Phys. Rev. Lett. 96 183902
[25] Han P, Zheng C J 2008 Phys. Rev. E 77 041111
[26] Han P, Wang H Z 2005 Acta Phys. Sin. 54 338 (in Chinese) [韩 鹏、 汪河洲 2005 54 338]
[27] Han P, Wang H Z 2003 Chin. Phys. Lett. 20 1520
[28] Hu D S, Lu X J, Zhang Y M, Zhu C P 2009 Chin. Phys. B 18 2498
[29] Dong Y, Zhang X 2006 Phys. Lett. A 359 542
[30] Asatryan IIA A, Botten L C, Byrne M A, Freilikher V D, Gredeskul S A 2007 Phys. Rev. Lett. 99 193902
[31] Nascimento E M, Moura F A B F de, Lyra M L 2008 Opt.
[32] Han P, Chan C T, Zhang Z Q 2008 Phys. Rev. B 77 115332
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