Two-dimensional phononic crystals studied using a variational method: Application to lattices of locally resonant materials

Physical Review B - Condensed Matter and Materials Physics

Volumn 67, Issue 14, 2003, Pages

  Goffaux, Cécile ^a   Sánchez Dehesa, José ^a  

^a UNIVERSIDAD AUTÓNOMA DE MADRID   (Spain)

Author keywords

[No Author keywords available]

Indexed keywords

ARTICLE; CRYSTAL; ELASTICITY; MATERIALS; MATHEMATICAL ANALYSIS; MODEL; PHOTON; POLYMERIZATION;

EID: 0037764107     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.67.144301     Document Type: Article

References (35)

1. J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals (Princeton University Press, Princeton, 1995).
2. M M. Sigalas and E N. Economou, J. Sound Vib.158, 377 (1992).
3. M M. Sigalas and E N. Economou, Solid State Commun.86, 141 (1993).
4. E N. Economou and M M. Sigalas, Phys. Rev. B48, 13 434 (1993).
5. M S. Kushwaha, P. Halevi, L. Dobrzynski, and B. Djafari-Rouhani, Phys. Rev. Lett.71, 2022 (1993)
6. M S. Kushwaha, P. Halevi, G. Martínez, L. Dobrzynski, and B. Djafari-Rouhani, Phys. Rev. B49, 2313 (1994)
7. R. Martínez-Sala, J. Sancho, J V. Sánchez, V. Gómez, J. Llinares, and F. Meseguer, Nature (London)378, 241 (1995).
8. J V. Sánchez-Pérez, D. Caballero, R. Mártinez-Sala, C. Rubio, J. Sánchez-Dehesa, F. Meseguer, J. Llinares, and F. Gálvez, Phys. Rev. Lett.80, 5325 (1998).
9. D. Caballero, J. Sánchez-Dehesa, C. Rubio, R. Mártinez-Sala, J V. Sánchez-Pérez, F. Meseguer, and J. Llinares, Phys. Rev. E60, R6316 (1999).
10. M. Kafesaki, R S. Penciu, and E N. Economou, Phys. Rev. Lett.84, 6050 (2000).
11. C. Goffaux and J P. Vigneron, Phys. Rev. B64, 075118 (2001).
12. F. Cervera, L. Sanchis, J V. Sanchez-Pérez, R. Martínez-Sala, C. Rubio, F. Meseguer, C. López, D. Caballero, and J. Sánchez-Dehesa, Phys. Rev. Lett.88, 023902 (2002).
13. F R. Montero de Espinosa, E. Jimenez, and M. Torres, Phys. Rev. Lett.80, 1208 (1998).
14. M. Torres, F R. Montero de Espinosa, and J L. Aragon, Phys. Rev. Lett.86, 4282 (2001).
15. J O. Vasseur, P A. Deymier, G. Frantziskonis, G. Hong, B. Djafari-Rouhani, and L. Dobrzynski, J. Phys.: Condens. Matter10, 6051 (1998).
16. J O. Vasseur, P A. Deymier, B. Chenni, B. Djafari-Rouhani, L. Dobrzynski, and D. Prevost, Phys. Rev. Lett.86, 3012 (2001).
17. a review of this method see M S. Kuswaha, Recent Res. Devel. Appl. Phys.2, 743 (1999).
18. M. Kafesaki and E N. Economou, Phys. Rev. B60, 11 993 (1999).
19. Z. Liu, C T. Chan, P. Sheng, A L. Goertzen, and J H. Page, Phys. Rev. B62, 2446 (2000).
20. Y Y. Chen and Z. Ye, Phys. Rev. E64, 036616 (2001);
21. Y Y. ChenZ. YePhys. Rev. Lett.87, 184301 (2001).
22. M. Kafesaki, E. N. Economou, and M. M. Sigalas, Photonic Band Gap Materials, edited by C. M. Soukoulis (Kluwer Academic Publishers, The Netherlands, 1996), p. 143.
23. M. Sigalas and N. García, J. Appl. Phys.87, 3122 (2000).
24. Y. Tanaka, Y. Tomoyasu, and S I. Tamura, Phys. Rev. B62, 7387 (2000).
25. C. Goffaux, Ph.D. thesis, Presses universitaires de Namur, Namur, 2002.
26. L. Sanchis, A. Hakansson, F. Cervera, and J. Sánchez-Dehesa, Phys. Rev. B67, 035422 (2003).
27. Z. Liu, X. Zhang, Y. Mao, Y Y. Zhu, Z. Yang, C T. Chan, and Ping Sheng, Science289, 1734 (2000).
28. Z. Liu, C T. Chan, and P. Cheng, Phys. Rev. B65, 165116 (2002).
29. J. Pendry, J. Mod. Opt.41, 209 (1994).
30. C. Goffaux, J. Sánchez-Dehesa, A L. Yeyati, Ph. Lambin, A. Khelif, J O. Vasseur, and B. Djafari-Rouhani, Phys. Rev. Lett.88, 225502 (2002).
31. C. de Boor, Practical Guide to Splines (Springer, New York, 1978).
32. E N. Economou and M M. Sigalas, J. Acoust. Soc. Am.95, 1734 (1994).
33. J O. Vasseur and P A. Deymier, J. Mater. Res.12, 2207 (1997).
34. See, for example, the classical book by L. Brillouin, Wave Propagation in Periodic Structures (Dover, New York, 1953).
35. J H. Vincent, Philos. Mag.46, 557 (1898).