Dispersion relations and their symmetry properties of electromagnetic and elastic metamaterials in two dimensions

Physical Review B - Condensed Matter and Materials Physics

Volumn 79, Issue 19, 2009, Pages

  Wu, Ying ^a   Zhang, Zhao Qing ^a  

^a HONG KONG UNIVERSITY OF SCIENCE AND TECHNOLOGY   (Hong Kong)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 67049098970     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.79.195111     Document Type: Article

References (41)

1. E. Yablonovitch and T. J. Gmitter, Phys. Rev. Lett. 63, 1950 (1989) 10.1103/PhysRevLett.63.1950
2. K. M. Ho, C. T. Chan, and C. M. Soukoulis, Phys. Rev. Lett. 65, 3152 (1990) 10.1103/PhysRevLett.65.3152
3. Th. Koschny, P. Markoš, E. N. Economou, D. R. Smith, D. C. Vier, and C. M. Soukoulis, Phys. Rev. B 71, 245105 (2005). 10.1103/PhysRevB.71.245105
4. J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals Molding the Flow of Light (Princeton University Press, Princeton, 1995).
5. M. S. Kushwaha, P. Halevi, L. Dobrzynski, and B. Djafari-Rouhani, Phys. Rev. Lett. 71, 2022 (1993) 10.1103/PhysRevLett.71.2022
6. J. O. Vasseur, P. A. Deymier, B. Chenni, B. Djafari-Rouhani, L. Dobrzynski, and D. Prevost, Phys. Rev. Lett. 86, 3012 (2001). 10.1103/PhysRevLett.86.3012
7. M. Kafesaki and E. N. Economou, Phys. Rev. B 60, 11993 (1999) 10.1103/PhysRevB.60.11993
8. J. Mei, Z. Liu, J. Shi, and D. Tian, Phys. Rev. B 67, 245107 (2003). 10.1103/PhysRevB.67.245107
9. S. Datta, C. T. Chan, K. M. Ho, and C. M. Soukoulis, Phys. Rev. B 48, 14936 (1993). 10.1103/PhysRevB.48.14936
10. O. Ouchetto, C. W. Qiu, S. Zouhdi, L. W. Li, and A. Razek, IEEE Trans. Microwave Theory Tech. 54, 3893 (2006). 10.1109/TMTT.2006.885082
11. L. D. Landau, E. M. Lifshitz, and L. P. Pitaevskii, Electrodynamics of Continuous Media (Butterworth-Heinemann, Oxford, 1984).
12. P. Halevi, A. A. Krokhin, and J. Arriaga, Phys. Rev. Lett. 82, 719 (1999). 10.1103/PhysRevLett.82.719
13. A. A. Krokhin, P. Halevi, and J. Arriaga, Phys. Rev. B 65, 115208 (2002). 10.1103/PhysRevB.65.115208
14. Z. Y. Liu, X. X. Zhang, Y. W. Mao, Y. Y. Zhu, Z. Y. Yang, C. T. Chan, and P. Sheng, Science 289, 1734 (2000) 10.1126/science.289.5485.1734
15. Z. Liu, C. T. Chan, and P. Sheng, Phys. Rev. B 71, 014103 (2005) 10.1103/PhysRevB.71.014103
16. C. Goffaux, J. Sánchez-Dehesa, A. Levy Yeyati, Ph. Lambin, A. Khelif, J. O. Vasseur, and B. Djafari-Rouhani, Phys. Rev. Lett. 88, 225502 (2002). 10.1103/PhysRevLett.88.225502
17. Y. Ding, Z. Liu, C. Qiu, and J. Shi, Phys. Rev. Lett. 99, 093904 (2007). 10.1103/PhysRevLett.99.093904
18. L. D. Landau and E. M. Lifshitz, Theory of Elasticity (Butterworth-Heinemann, Oxford, 1986).
19. D. Royer and E. Dieulesaint, Elastic Waves in Solids I (Springer, New York, 1999).
20. Q. Ni and J. Cheng, J. Appl. Phys. 101, 073515 (2007). 10.1063/1.2715582
21. Q. Ni and J. Cheng, Phys. Rev. B 72, 014305 (2005). 10.1103/PhysRevB.72. 014305
22. 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
23. R. A. Shelby, D. R. Smith, S. C. Nemat-Nasser, and S. Schultz, Appl. Phys. Lett. 78, 489 (2001) 10.1063/1.1343489
24. R. A. Shelby, D. R. Smith, and S. Schultz, Science 292, 77 (2001) 10.1126/science.1058847
25. J. B. Pendry, Phys. Rev. Lett. 85, 3966 (2000) 10.1103/PhysRevLett.85. 3966
26. N. Garcia and M. Nieto-Vesperinas, Phys. Rev. Lett. 88, 207403 (2002). 10.1103/PhysRevLett.88.207403
27. D. R. Smith, J. B. Pendry, and M. C. K. Wiltshire, Science 305, 788 (2004). 10.1126/science.1096796
28. P. T. Rakich, M. S. Dahlem, S. Tandon, M. Ibanescu, M. Soljačić, G. S. Petrich, J. D. Joannopoulos, L. A. Kolodziejski, and E. P. Ippen, Nature Mater. 5, 93 (2006) 10.1038/nmat1568
29. A. F. Matthews, S. K. Morrison, and Y. S. Kivshar, Opt. Commun. 279, 313 (2007). 10.1016/j.optcom.2007.07.053
30. J. Mei, Z. Liu, W. Wen, and P. Sheng, Phys. Rev. Lett. 96, 024301 (2006). 10.1103/PhysRevLett.96.024301
31. Y. Wu, Y. Lai, and Z. Q. Zhang, Phys. Rev. B 76, 205313 (2007). 10.1103/PhysRevB.76.205313
32. Y. Wu, J. Li, Z. Q. Zhang, and C. T. Chan, Phys. Rev. B 74, 085111 (2006). It should be noted that a logarithmic in the denominator of ε s was missing in this paper. The correct expression of ε s should be ε s =2F (ks rs) εs / [1+ ks2 rs2 ln (k0 rs) F (ks rs) μ0 / μs]. 10.1103/PhysRevB.74.085111
33. P. P. Ewald, Ann. Phys. 64, 253 (1921). 10.1002/andp.19213690304
34. S. K. Chin, N. A. Nicorovici, and R. C. McPhedran, Phys. Rev. E 49, 4590 (1994). 10.1103/PhysRevE.49.4590
35. N. A. Nicorovici, R. C. McPhedran, and B. Ke-Da, Phys. Rev. E 51, 690 (1995). 10.1103/PhysRevE.51.690
36. W. Lamb, D. M. Wood, and N. W. Ashcroft, Phys. Rev. B 21, 2248 (1980). 10.1103/PhysRevB.21.2248
37. A. K. Sarychev, R. C. McPhedran, and V. M. Shalaev, Phys. Rev. B 62, 8531 (2000). 10.1103/PhysRevB.62.8531
38. S. T. Chui and Z. F. Lin, Phys. Rev. E 78, 065601 (R) (2008). 10.1103/PhysRevE.78.065601
39. D. Han, Y. Lai, K. H. Fung, Z. Q. Zhang, and C. T. Chan, Phys. Rev. B (to be published).
40. L.-M. Li and Z.-Q. Zhang, Phys. Rev. B 58, 9587 (1998). 10.1103/PhysRevB.58.9587
41. M. S. Kushwaha, P. Halevi, G. Martínez, L. Dobrzynski, and B. Djafari-Rouhani, Phys. Rev. B 49, 2313 (1994). 10.1103/PhysRevB.49.2313