Analysis of Scattering Behavior in the Cavity of Phononic Crystals with Archimedean Tilings
The defect mode of two-dimensional phononic crystals with Archimedean tilings was explored in the present study. Finite element method and supercell method were used to obtain dispersion relation of phononic crystals. The simulations of the acoustic wave propagation within phononic crystals are demonstrated. Around the cavity which is created by removing several cylinders in the perfect Archimedean tilings, whispering-gallery mode (WGM) can be observed. The effects of the cavity geometry on the WGM modes are investigated. The WGM modes with high Q-factor and high cavity pressure can be obtained by phononic crystals with Archimedean tilings.
[1] M. Torres, F. R. Montero de Espinosa, D. Garcia-Pablos, and N. Garcia, “Sonic band gaps in finite elastic media: surface states and localization phenomena in linear and point defects,” Phys. Rev. Lett., vol. 83, pp. 3054-3057, 1999.
[2] M. Kafesaki, M. M. Sigalas, and N. Garcia, “Wave guides in two-dimensional elastic wave band-gap materials,” Physica B, vol. 296, pp. 190-194, 2001.
[3] M. S. Kushwaha and P. Halevi, “Giant acoustic stop bands in two-dimensional periodic arrays of liquid cylinders,” Appl. Phys. Lett., vol. 69(1), pp. 31-33, 1996.
[4] M. M. Sigalas, “Elastic wave band gaps and defect states in two-dimensional composites,” J. Acoust. Soc. Am., vol. 101(3), pp. 1256-1261, 1997.
[5] M. M. Sigalas, “Defect states of acoustic waves in a two-dimensional lattice of solid cylinders,” J. Appl. Phys., vol. 84(6), pp. 3026-3030, 1998.
[6] F. Wu, Z. Hou, Z. Liu, and Y. Liu, “Point defect states in two-dimensional phononic crystals,” Phys. Lett. A, vol. 292(3), pp.198-202, 2001.
[7] F. Wu, Z. Liu, and Y. Liu, “Splitting and tuning characteristics of the point defect modes in two-dimensional phononic crystals,” Phys. Rev. E , vol. 69(6), 066609, 2004.
[8] M. Kafesaki, M. M. Sigalas, and N. Garcia, “Frequency Modulation in the transmittivity of wave guides in elastic-wave band-gap materials,” Phys. Rev. Lett., vol. 85(19), pp. 4044-4047, 2000.
[9] M. Kafesaki, M. M. Sigalas, and N. Garcia, “Wave guides in two-dimensional elastic wave band-gap materials,” Physica B, vol. 296(1-3), pp. 190-194, 2001.
[10] T. Miyashita and C. Inoue, “Numerical investigations of transmission and waveguide properties of sonic crystals by finite-difference time-domain method,” Jpn. J. Appl. Phys., vol. 40(5B), pp. 3488-3492, 2001.
[11] T. Miyashita, “Sonic crystals and sonic wave-guides,” Meas. Sci. Technol., vol. 16(5), pp. R47-R63, 2005.
[12] T. Miyashita, “Experimental study of a sharp bending wave-guide constructed in a sonic-crystal slab of an array of short aluminum rods in air,” IEEE Ultransonics Symposium, pp. 946-949, 2004.
[13] F. Wu, H. Zhong, S. Zhong, Z. Liu, and Y. Liu, “Localized states of acoustic waves in three-dimensional periodic composites with point defects,” Eur. Phys. J. B, vol. 34(3), pp. 265-268, 2003.
[14] L. Rayleigh, “The problem of the whispering gallery,” Philos. Mag. Series 6, vol. 20(120), pp. 1001-1004, 2009.
[15] M. Xing, W. Zheng, Y. Zhang, G. Ren, X. Du, K. Wang, and L. Chen, “The whispering gallery mode in photonic crystal ring cavity,” SPIE, 6984, pp. 698438-1-4.
[16] K. Nagahara, M. Morifuji, and M. Kondow, “Optical coupling between a cavity mode and a waveguide in a two-dimensional photonic crystal,” Photon. Nanostr. Fundam. Appl., vol. 9(3), pp. 261-268, 2011.
[17] Y. Q. Wang, “Coupled-resonator optical waveguides in photonic crystals with Archimedean-like tilings,” Europhys Lett., vol. 74(2), pp. 261-267, 2006.
[18] J. Li, Y. S. Wang, and C. Zhang, “Finite element method for analysis of band structures of phononic crystal slabs with Archimedean-like tilings,” IEEE IUS, pp.1548-1551, 2009.
[19] Y. L. Xu, C. Q. Chen, and X. G. Tian, “Tunable band structures of 2D multi-atom Archmedean-like phononic crystals,” Int. J. Comp. Mat. Sci. Eng., vol. 1(2), 1250016, 2012.
[20] COMSOL 3.5a. The COMSOL Group, Stockholm, Sweden, 2009.
[21] Y. J. Cao and Y. Z. Li, “Symmetry and coupling efficiency of the defect modes in two-dimensional phononic crystals,” Mod. Phys. Lett. B, vol. 21 (22), pp. 1479-1488, 2007.
[1] M. Torres, F. R. Montero de Espinosa, D. Garcia-Pablos, and N. Garcia, “Sonic band gaps in finite elastic media: surface states and localization phenomena in linear and point defects,” Phys. Rev. Lett., vol. 83, pp. 3054-3057, 1999.
[2] M. Kafesaki, M. M. Sigalas, and N. Garcia, “Wave guides in two-dimensional elastic wave band-gap materials,” Physica B, vol. 296, pp. 190-194, 2001.
[3] M. S. Kushwaha and P. Halevi, “Giant acoustic stop bands in two-dimensional periodic arrays of liquid cylinders,” Appl. Phys. Lett., vol. 69(1), pp. 31-33, 1996.
[4] M. M. Sigalas, “Elastic wave band gaps and defect states in two-dimensional composites,” J. Acoust. Soc. Am., vol. 101(3), pp. 1256-1261, 1997.
[5] M. M. Sigalas, “Defect states of acoustic waves in a two-dimensional lattice of solid cylinders,” J. Appl. Phys., vol. 84(6), pp. 3026-3030, 1998.
[6] F. Wu, Z. Hou, Z. Liu, and Y. Liu, “Point defect states in two-dimensional phononic crystals,” Phys. Lett. A, vol. 292(3), pp.198-202, 2001.
[7] F. Wu, Z. Liu, and Y. Liu, “Splitting and tuning characteristics of the point defect modes in two-dimensional phononic crystals,” Phys. Rev. E , vol. 69(6), 066609, 2004.
[8] M. Kafesaki, M. M. Sigalas, and N. Garcia, “Frequency Modulation in the transmittivity of wave guides in elastic-wave band-gap materials,” Phys. Rev. Lett., vol. 85(19), pp. 4044-4047, 2000.
[9] M. Kafesaki, M. M. Sigalas, and N. Garcia, “Wave guides in two-dimensional elastic wave band-gap materials,” Physica B, vol. 296(1-3), pp. 190-194, 2001.
[10] T. Miyashita and C. Inoue, “Numerical investigations of transmission and waveguide properties of sonic crystals by finite-difference time-domain method,” Jpn. J. Appl. Phys., vol. 40(5B), pp. 3488-3492, 2001.
[11] T. Miyashita, “Sonic crystals and sonic wave-guides,” Meas. Sci. Technol., vol. 16(5), pp. R47-R63, 2005.
[12] T. Miyashita, “Experimental study of a sharp bending wave-guide constructed in a sonic-crystal slab of an array of short aluminum rods in air,” IEEE Ultransonics Symposium, pp. 946-949, 2004.
[13] F. Wu, H. Zhong, S. Zhong, Z. Liu, and Y. Liu, “Localized states of acoustic waves in three-dimensional periodic composites with point defects,” Eur. Phys. J. B, vol. 34(3), pp. 265-268, 2003.
[14] L. Rayleigh, “The problem of the whispering gallery,” Philos. Mag. Series 6, vol. 20(120), pp. 1001-1004, 2009.
[15] M. Xing, W. Zheng, Y. Zhang, G. Ren, X. Du, K. Wang, and L. Chen, “The whispering gallery mode in photonic crystal ring cavity,” SPIE, 6984, pp. 698438-1-4.
[16] K. Nagahara, M. Morifuji, and M. Kondow, “Optical coupling between a cavity mode and a waveguide in a two-dimensional photonic crystal,” Photon. Nanostr. Fundam. Appl., vol. 9(3), pp. 261-268, 2011.
[17] Y. Q. Wang, “Coupled-resonator optical waveguides in photonic crystals with Archimedean-like tilings,” Europhys Lett., vol. 74(2), pp. 261-267, 2006.
[18] J. Li, Y. S. Wang, and C. Zhang, “Finite element method for analysis of band structures of phononic crystal slabs with Archimedean-like tilings,” IEEE IUS, pp.1548-1551, 2009.
[19] Y. L. Xu, C. Q. Chen, and X. G. Tian, “Tunable band structures of 2D multi-atom Archmedean-like phononic crystals,” Int. J. Comp. Mat. Sci. Eng., vol. 1(2), 1250016, 2012.
[20] COMSOL 3.5a. The COMSOL Group, Stockholm, Sweden, 2009.
[21] Y. J. Cao and Y. Z. Li, “Symmetry and coupling efficiency of the defect modes in two-dimensional phononic crystals,” Mod. Phys. Lett. B, vol. 21 (22), pp. 1479-1488, 2007.
@article{"International Journal of Mechanical, Industrial and Aerospace Sciences:73265", author = "Yi-Hua Chen and Hsiang-Wen Tang and I-Ling Chang and Lien-Wen Chen", title = "Analysis of Scattering Behavior in the Cavity of Phononic Crystals with Archimedean Tilings", abstract = "The defect mode of two-dimensional phononic crystals with Archimedean tilings was explored in the present study. Finite element method and supercell method were used to obtain dispersion relation of phononic crystals. The simulations of the acoustic wave propagation within phononic crystals are demonstrated. Around the cavity which is created by removing several cylinders in the perfect Archimedean tilings, whispering-gallery mode (WGM) can be observed. The effects of the cavity geometry on the WGM modes are investigated. The WGM modes with high Q-factor and high cavity pressure can be obtained by phononic crystals with Archimedean tilings.
", keywords = "Defect mode, Archimedean tilings, phononic crystals, whispering- gallery modes.", volume = "10", number = "7", pages = "1204-6", }
