Effective-medium properties of metamaterials: A quasimode theory

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

Volumn 79, Issue 6, 2009, Pages

  Sun, Shulin ^a   Chui, S T ^b   Zhou, Lei ^a  

^a FUDAN UNIVERSITY   (China)

^b UNIVERSITY OF DELAWARE   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

COHERENT POTENTIAL APPROXIMATION; DENSITY OF STATE; EFFECTIVE PERMITTIVITY; MEAN-FREE PATH; METALLIC WIRE; OPTICAL MODES; QUASI-MODE THEORY; SELF ENERGY; SPLIT RING RESONATOR;

ELECTRONIC EQUIPMENT;

METAMATERIALS;

EID: 67650151031     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.79.066604     Document Type: Article

References (37)

1. D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, Phys. Rev. Lett. 84, 4184 (2000). 10.1103/PhysRevLett.84.4184
2. R. A. Shelby, D. R. Smith, and S. Schultz, Science 292, 77 (2001). 10.1126/science.1058847
3. J. B. Pendry, Phys. Rev. Lett. 85, 3966 (2000). 10.1103/PhysRevLett.85. 3966
4. J. B. Pendry, D. Schurig, and D. R. Smith, Science 312, 1780 (2006). 10.1126/science.1125907
5. D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, Science 314, 977 (2006). 10.1126/science.1133628
6. L. D. Landau, E. M. Lifschitz, and L. P. Pitaevskii, Electrodynamics of Continuous Media, 2nd ed. (Pergamon, Oxford, 1984).
7. J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, IEEE Trans. Microwave Theory Tech. 47, 2075 (1999). 10.1109/22.798002
8. J. Baker-Jarvis, E. J. Vanzura, and W. A. Kissick, IEEE Trans. Microwave Theory Tech. 38, 1096 (1990). 10.1109/22.57336
9. D. R. Smith, S. Schultz, P. Markos, and C. M. Soukoulis, Phys. Rev. B 65, 195104 (2002). 10.1103/PhysRevB.65.195104
10. P. Markos and C. M. Soukoulis, Opt. Express 11, 649 (2003).
11. D. R. Smith, D. C. Vier, T. Koschny, and C. M. Soukoulis, Phys. Rev. E 71, 036617 (2005). 10.1103/PhysRevE.71.036617
12. X. Chen, B.-I. Wu, J. Au Kong, and T. M. Grzegorczyk, Phys. Rev. E 71, 046610 (2005). 10.1103/PhysRevE.71.046610
13. O. Ouchetto, C. Qiu, S. Zouhdi, L. Li, and A. Razek, IEEE Trans. Microwave Theory Tech. 54, 3893 (2006). 10.1109/TMTT.2006.885082
14. L. Hou, J. Y. Chin, X. M. Yang, X. Q. Lin, R. Liu, F. Y. Xu, and T. J. Cui, J. Appl. Phys. 103, 064904 (2008). 10.1063/1.2885351
15. D. R. Smith, D. C. Vier, N. Kroll, and S. Schultz, Appl. Phys. Lett. 77, 2246 (2000). 10.1063/1.1314884
16. S. A. Cummer and B. I. Popa, Appl. Phys. Lett. 85, 4564 (2004). 10.1063/1.1823595
17. B. Popa and S. A. Cummer, Phys. Rev. B 72, 165102 (2005). 10.1103/PhysRevB.72.165102
18. D. R. Smith and J. B. Pendry, J. Opt. Soc. Am. B 23, 391 (2006). 10.1364/JOSAB.23.000391
19. M. Silveirinha, Phys. Rev. B 75, 115104 (2007). 10.1103/PhysRevB.75. 115104
20. Y. Wu, J. Li, Z. Q. Zhang, and C. T. Chan, Phys. Rev. B 74, 085111 (2006). 10.1103/PhysRevB.74.085111
21. V. Fokin, M. Ambati, C. Sun, and X. Zhang, Phys. Rev. B 76, 144302 (2007). 10.1103/PhysRevB.76.144302
22. S. T. Chui and Z. F. Lin, Phys. Rev. E 78, 065601 (2008). 10.1103/PhysRevE.78.065601
23. See footnote [12] of J. Li, L. Zhou, C. T. Chan, and P. Sheng, Phys. Rev. Lett. 90, 083901 (2003). 10.1103/PhysRevLett.90.083901
24. C. Rockstuhl, T. Paul, F. Lederer, T. Pertsch, T. Zentgraf, T. P. Meyrath, and H. Giessen, Phys. Rev. B 77, 035126 (2008). 10.1103/PhysRevB.77. 035126
25. J. Zhou, T. Koschny, M. Kafesaki, and C. M. Soukoulis, Photonics Nanostruct. Fundam. Appl. 6, 96 (2008). 10.1016/j.photonics.2007.10.003
26. P. Sheng, Introduction to Wave Scattering, Localization, and Mesoscopic Phenomena (Academic Press, San Diego, 1995).
27. T. Decoopman, G. Tayeb, S. Enoch, D. Maystre, and B. Gralak, Phys. Rev. Lett. 97, 073905 (2006). 10.1103/PhysRevLett.97.073905
28. One should redefine the metamaterial slab when calculating the effect parameters for another propagation direction.
29. The configuration average is still meaningful even for a periodic metamaterial, since there are many different ways to realize the same configuration as shown in Fig. 1.
30. G. D. Manhan, Many Particle Physics (Plenum, New York, 1990).
31. J. M. Ziman, Principles of the Theory of Solids, 2nd ed. (Cambridge University Press, Cambridge, England, 1972).
32. Comsol Multiphysics by COMSOL ©, ver. 3.5, network license (2008).
33. Since the computations were rather time consuming, we only chose several typical values of μref to calculate the DOS and MFP vs εref in the regions far away from the highest peak of DOS. However, when approaching it, we have added much more μref points to carefully identify the peak positions.
34. Here, we set μref = μeff for each spectrum calculated at different frequencies.
35. D. W. Shen, Y. Zhang, L. X. Yang, J. Wei, H. W. Ou, J. K. Dong, C. He, B. P. Xie, J. F. Zhao, B. Zhou, M. Arita, K. Shimada, H. Namatame, M. Taniguchi, J. Shi, and D. L. Feng, Phys. Rev. Lett. 101, 226406 (2008). 10.1103/PhysRevLett.101.226406
36. We note that typically only transmission spectrum is taken into account when one calculates the effective parameters in the standard retrieval method.
37. Here, we set εref = εeff for each spectrum calculated at different frequencies.