Analysis of Wave Propagation in Two-dimensional Phononic Crystals with Hollow Cylinders

Authors: Zi-Gui Huang, Tsung-Tsong Wu

Abstract:

Large full frequency band gaps of surface and bulk acoustic waves in two-dimensional phononic band structures with hollow cylinders are addressed in this paper. It is well-known that absolute frequency band gaps are difficultly obtained in a band structure consisted of low-acoustic-impedance cylinders in high-acoustic-impedance host materials such as PMMA/Ni band structures. Phononic band structures with hollow cylinders are analyzed and discussed to obtain large full frequency band gaps not only for bulk modes but also for surface modes. The tendency of absolute frequency band gaps of surface and bulk acoustic waves is also addressed by changing the inner radius of hollow cylinders in this paper. The technique and this kind of band structure are useful for tuning the frequency band gaps and the design of acoustic waveguides.

Keywords: Phononic crystals, Band gap, SAW, BAW.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1075571

References:

[1] S. G. Johnson and J. D. Joannopoulos, PHOTONIC CRYSTALS: The road from theory to practice, Kluwer academic publishers, Boston, 2003.
[2] J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals: Molding the flow of light, Princeton University Press, Princeton, NJ, 1995.
[3] M. S. Kushwaha, P. Halevi, L. Dobrzynski, and B. Djafari-Rouhani, "Acoustic Band Structure of Periodic Elastic Composites," Phys. Rev. Lett. 71, 2022, 1993.
[4] J. O. Vasseur, P. A. Deymier, G. Frantziskonis, G. Hong, B. Djafari-Rouhani, and L. J. Dobrzynski, "Experimental evidence for the existence of absolute acoustic band gaps in two-dimensional periodic composite media," J. Phys.: Condens. Matter 10, 6051, 1998.
[5] C. Goffaux and J. P. Vigneron, "Theoretical study of a tunable phononic band gap system," Phys. Rev. B 64, 075118, 2001.
[6] M. Kafesaki and E. N. Economou, "Multiple-scattering theory for three-dimensional periodic acoustic composites," Phys. Rev. B 60, 11993, 1999.
[7] I. E. Psarobas and N. Stefanou, "Scattering of elastic waves by periodic arrays of spherical bodies," Phys. Rev. B 62, 278, 2000.
[8] Z. Liu, C. T. Chan, and P. Sheng, "Elastic wave scattering by periodic structures of spherical objects: Theory and experiment," Phys. Rev. B 62, 2446, 2000.
[9] D. Garica-Pablos, M. Sigalas, F. R. Montero de Espinosa, M. Torres, M. Kafesaki, and N. Garcia, "Theory and Experiments on Elastic Band gaps," Phys. Rev. Lett. 84, 4349, 2000.
[10] J. H. Sun and T.-T. Wu, "Analyses of mode coupling in joined parallel phononic crystal waveguides," Phys. Rev. B 71, 174303, 2005.
[11] Y. Tanaka and S. Tamura, "Surface acoustic waves in two-dimensional periodic elastic structures," Phys. Rev. B 58, 7958, 1998.
[12] T.-T. Wu, Z. G. Huang, and S. Lin, "Surface and bulk acoustic waves in two-dimensional phononic crystals consisting of materials with general anisotropy," Phys. Rev. B 69, 094301, 2004.
[13] Z. G. Huang and T.-T. Wu, "Temperature effects on bandgaps of surface and bulk acoustic waves in two-dimensional phononic crystals," IEEE Trans. Ultrason. Ferroelectr. Freq. Control 52, 365, 2005.
[14] T.-T. Wu and Z. G. Huang, "Level repulsion of bulk acoustic waves in composite materials," Phys. Rev. B 70, 214304, 2004.
[15] T.-T. Wu, Z. C. Hsu, and Z. G. Huang, "Band gaps and the Electromechanical coupling coefficient of a surface acoustic wave in a two-dimensional piezoelectric phononic crystal," Phys. Rev. B 71, 064303, 2005.
[16] V. Laude, M. Wilm, S. Benchabane, A. Khelif, "Full band gap for surface acoustic waves in a piezoelectric phononic crystal," Phys. Rev. E 71, 036607, 2005.