An efficient finite difference time domain algorithm for band structure calculations of Phononic crystal

[1[ M. S. Kushwaha, P. Halevi, L. Dobrzynski, and B. Djafari-Rouhani, “Acoustic band structure of periodic elastic composites”, Phys. Rev. Lett., Vol. 71, No. 13, pp. 2022-2025, (1993).

[2[ R. Martinez-Sala, J. Sancho, J. V. Sanchez, V. Gomez, J. Llinares, and F. Meseguer, “Sound attenuation by sculpture”, Nature., Vol. 378, No. 6554, pp. 241-241, (1995).

[3[ F. R. Montero de Espinosa, E. Jime´nez, and M. Torres, “Ultrasonic Band Gap in a Periodic Two-Dimensional Composite”, Phys. Rev. Lett., Vol. 80, No. 6, pp. 1208-1211, (1998).

[4] A. Khelif, A. Choujaa, R. laihem, M. Wilm, S. Ballandras, and V. Laude, “Experimental study of band gaps and defect modes in a two-dimensional ultrasonic crystal”, IEEE Ultrasonics Symposium, pp. 377-380, (2003).

[5] Y. Pennec, B. Djafari-Rouhani, J. O. Vasseur, A. Khelif, and P. A. Deymier, “Tunable filtering and demultiplexing in phononic crystals with hollow cylinders”, Phys. Rev. E., Vol. 69, 046608, (2004).

[6[ W. Liu, J. W. Chen, and X. Y. Su, “Local resonance phononic band gaps in modified two-dimensional lattice materials”, Acta Mech. Sin., Vol. 28, pp. 659-669, (2012).

[7[ M. Kafesaki, M. M. Sigalas, and N. García, “Frequency Modulation in the Transmittivity of Wave Guides in Elastic-Wave Band-Gap Materials”, Phys. Rev. Lett., Vol. 85, No. 19, pp. 4044-4047, (2000).

[8] A. Khelif, B. Djafari-Rouhani, J. O. Vasseur, and P. A. Deymier, “Transmission and dispersion relations of perfect and defect-containing waveguide structures in phononic band gap materials”, Phys. Rev. B., Vol. 68, No. 2, 024302, (2003).

[9[ Y. Yao, Z. Hou, and Y. Liu, “The two-dimensional phononic band gaps tuned by the position of the additional rod”, Phys Let. A., Vol. 362, No. 5-6, pp. 494-499, (2007).

[10[ B. Wu, R. Wei, H. Zhao, and C. He, “Phononic Band Gaps in Two-Dimensional Hybrid Triangular Lattice”, Acta Mech. Solida Sin., Vol. 23, No. 3, pp. 255-259, (2010).

[11[ Y. Tanaka, Y. Tomoyasu, and S. Tamura, “Band structure of acoustic waves in phononic lattices: Two-dimensional composites with large acoustic mismatch”, Phys. Rev. B., Vol. 62, No. 11, pp. 7387-7392, (2000).

[12[ P. Hsieh, T. Wu, and J. Sun, “Three-Dimensional Phononic Band Gap Calculations Using the FDTD Method and a PC Cluster System”, Ieee T. Ultrason. Ferr., Vol. 53, No. 1, pp. 148-158, (2006).

[13] D. García-Pablos, M. Sigalas, F. R. Montero de Espinosa, M. Torres, M. Kafesaki, and N. García, “Theory and Experiments on Elastic Band Gaps”, Phys. Rev. Lett., Vol. 84, No. 19, pp. 4349 -4352, (2000).

[14] A. Khelif, P. A. Deymier, B. Djafari-Rouhani, J. O. Vasseur, and L. Dobrzynski, “Two-dimensional phononic crystal with tunable narrow pass band: Application to a waveguide with selective frequency”, J. Appl. Phys., Vol. 94, No. 3, pp. 1308-1311, (2003).

[15] J. H. Sun, and T. T. Wu, “Analyses of mode coupling in joined parallel phononic crystal waveguides”, Phys. Rev. B., Vol. 71, 174303, (2005).

[16] Y. Pennec, B. Djafari-Rouhani, H. Larabi, J. Vasseur, and A. C. Hladky-Hennion, “Phononic crystals and manipulation of sound”, Phys. Status Solidi C., Vol. 6, No. 9, pp. 2080-2085, (2009).

[17] H. F. Gao, T. Matsumoto, T. Takahashi, and H. Isakari, “Analysis of Band Structure for 2D Acoustic Phononic Structure by BEM and the Block SS Method”, CMES-Comp. Model. Eng., Vol. 90, No. 4, pp. 283-301, (2013).

[18] M. Kafesaki, and E. N. Economou, “Multiple-scattering theory for three dimensional periodic acoustic composites”, Phy. Rev. B., Vol. 60, No.17, 11993, (1999).

[19] Z. Z. Yan, and Y. S. Wang, “Wavelet-based method for calculating elastic band gaps of two-dimensional phononic crystals”, J. Comput. Phys., Vol. 74, 224303, (2006).

[20] B. Djafari-Rouhani, J. O. Vasseur, A. C. Hladky-Hennion, P. Deymier, F. Duval, B. Dubus, and Y. Pennec, “Absolute band gaps and waveguiding in free standing and supported phononic crystal slabs”, Photonic Nanostruct., Vol. 6, No. 1, pp. 32-37, (2008).

[21] M. Liu, J. Xiang, Y. Zhong, “The band gap and transmission characteristics investigation of local resonant quaternary phononic crystals with periodic coating”, Appl. Acoust., Vol. 100, pp. 10-17, (2015).

[22] M. Liu, P. Li, Y. Zhong, and J. Xiang, “Research on the band gap characteristics of two-dimensional phononic crystals micro-cavity with local resonant structure”, Shock. Vib., Vol. 2015, 239832, (2015).

[23] Y. Cao, Z. Hou, and Y. Liu, “Finite difference time domain method for band-structure calculations of two-dimensional phononic crystals”, Solid State Commun., Vol. 132, No. 8, pp. 539-543, (2004).

[24] A. Taflove, Advances in Computational Electrodynamics, Artech House, London, (1999).

[25] T. T. Wu, J. H. Sun, “4G-3 Guided Surface Acoustic Waves in Phononic Crystal Waveguides”, IEEE Ultrasonics Symposium, pp. 673-676, (2006).