Band Gaps and Single Scattering of Phononic Crystal
Xiaoyi Huang, Jingcui Peng, Huanyou Wang, Gui Jin
DOI: 10.4236/ampc.2011.13014   PDF    HTML     4,529 Downloads   8,588 Views  

Abstract

A method is introduced to study the transmission and scattering properties of acoustic waves in two–dimen- sional phononic band gap (PBG) materials. First, it is used to calculate the transmission coefficients of PBG samples. Second, the transmitted power is calculated based on the far field approach. We have also calcu- lated the scattering cross section, the results indicate that phononic band gap appear in frequency regions between two well separated resonance states.

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Huang, X. , Peng, J. , Wang, H. and Jin, G. (2011) Band Gaps and Single Scattering of Phononic Crystal. Advances in Materials Physics and Chemistry, 1, 86-90. doi: 10.4236/ampc.2011.13014.

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1] M. S. Kushwaha, “Stop-Bands for Periodic Metallic Rods: Sculptures That Can Filter the Noise,” Applied Physics Letters, Vol. 70, No. 24, 1997, pp. 3218-3220. doi:10.1063/1.119130
[2] H. Sanchis Alepuz, Y. A. Kosevich and J. Sanchez Dehesa, “Acoustic Analogue of Electronic Bloch Oscillations and Resonant Zener Tunneling in Ultrasonic Superlattices,” Physical Review Letters, Vol. 98, No. 13, 2007, pp. (134301-1)-(134301-4). doi:10.1103/PhysRevLett.98.134301
[3] M. Torres, F. R. Montero de Espinosa, D. García-Pablos and N. García, “Sonic Band Gaps in Finite Elastic Media: Surface States and Local-ization Phenomena in Linear and Point Defects,” Physical Re-view Letters, Vol. 82, No. 15, 1999, pp. 3054-3057. doi:10.1103/PhysRevLett.82.3054
[4] D. Sutter Widmer, S. Deloudi and W. Steurer, “Prediction of Bragg-Scattering-Induced Band Gaps in Phononic Quasicrys-tals,” Physical Review Letters, Vol. 75, No. 9, 2007, pp. (094304-1)-(094304-11). doi:10.1103/PhysRevB.75.094304
[5] M. Torres, F. R. Mon-tero de Espinosa and J. L. Aragón, “Ultrasonic Wedges for Elastic Wave Bending and Splitting without Requiring a Full Band Gap,” Physical Review Letters, Vol. 86, No. 19, 2001, pp. 4282-4285. doi:10.1103/PhysRevLett.86.4282
[6] D. Garcia-Pablos, F. R. Montero de Espinosa, M. Torres, M. Kafesaki and N. García, “Theory and Experiments on Elastic Band Gaps,” Physical Review Letters, Vol. 84, No. 19, 2000, pp. 4349-4352. doi:10.1103/PhysRevLett.84.4349
[7] J. O. Vasseur, P. A. Deymier, B. Djafari-Rouhani, L. Dobrzynski and D. Prevost, “Experimental and Theoretical Evidence for the Existence of Absolute Acoustic Band Gaps in Two-Dimensional Solid Pho-nonic Crystals,” Physical Review Letters, Vol. 86, No. 14, 2001, pp. 3012-3015. doi:10.1103/PhysRevLett.86.3012
[8] S. X. Yang, J. H. Page, Z. Y. Liu, M. L. Cowan, C. T. Chan and P. Sheng, Physical Review Letters, Vol. 88, No. 10, 2001, pp. (104301-1)-(104301-4).
[9] S. X. Yang, J. H. Page, Z. Y. Liu, M. L. Cowan, C. T. Chan and P. Sheng, Physical Review Let-ters, Vol. 93, No. 2, 2004, pp. (024301-1)-(024301-4).
[10] Z. Y. Liu, X. X. Zhang, Y. W. Mao, Y. Y. Zhu, Z. Y. Yang, C. T. Chan and P. Sheng, “Locally Resonant Sonic Materials,” Sci-ence, Vol. 289, No. 8, 2000, pp. 1734- 1736. doi:10.1126/science.289.5485.1734
[11] F. Cervera, L. San-chis, J. V. Sánchez-Pérez, R. Martínez- Sala, C. Rubio, F. Me-seguer, C. López, D. Caballero and J. Sánchez-Dehesa, Physi-cal Review Letters, Vol. 88, No. 2, 2002, pp. (023902-1)-(023902-4).
[12] M. S. Kuswaha, Applied Physics Letters, Vol. 2, 1999, pp. 743-755.
[13] C. Goffaux and J. Sanchez-Dehesa, “Two-Dimensional Phononic Crystals Stud-ied Using a Variational Method: Application to Lattices of Locally Resonant Materials,” Physical Review B, Vol. 67, No. 14, 2003, pp. (144301- 1)-(144301-10). doi:10.1103/PhysRevB.67.144301
[14] Y. Y. Chen and Z. Ye, “Theoretical Analysis of Acoustic Stop Bands in Two-Dimensional Periodic Scattering Arrays,” Physical Re-view E, Vol. 64, No. 3, 2001, pp. (036616-1)-(036616-6). doi:10.1103/PhysRevE.64.036616
[15] Y. Tanaka, Y. Tomo-yasu and S. I. Tamura, Physical Review B, Vol. 62, 2000, pp. 7383-7395.
[16] R. M. White, Journal of the Acoustical Soci-ety of America, Vol. 30, No. 8, 1958, pp. 771-785.
[17] J. D. Jackson, “Classica Electrodynamics,” Wiley, New York, 1975.
[18] M. M. Sigalas and E. N. Economou, Journal of Sound and Vibration, Vol. 158, No. 2, 1992, pp. 377-382.
[19] E. N. Economou and M. M. Sigalas, “Classical Wave Propagation in Periodic Structures: Cermet versus Network Topology,” Physical Review B, Vol. 48, No. 18, 1993, pp. 13434-13438. doi:10.1103/PhysRevB.48.13434
[20] M. M. Sigalas and E. N. Economou, “Attenuation of Multiple-Scattered Sound,” Euro-physics Letters, Vol. 36, No. 4, 1996, pp. 241-246. doi:10.1209/epl/i1996-00216-4
[21] C. Kittel, “Introduction to Solid State Physics,” Wiley, New York, 1971.
[22] R. D. Meade, K. D. Brommer, A. M. Rappe and J. D. Joannopoulos, “Electromagnetic Bloch Waves at the Surface of a Photonic Crystal,” Physical Review B, Vol. 44, No. 19, 1991, pp. 10961-10964. doi:10.1103/PhysRevB.44.10961
[23] M. Kafesaki and E. N. Economou, “Interpretation of the Band-Structure Results for Elastic and Acoustic Waves by Analogy with the LCAO Ap-proach,” Physical Review B, Vol. 52, No. 18, 1995, pp. 13317-13331. doi:10.1103/PhysRevB.52.13317

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