The effect of the geometrical parameters and composing materials type on the bandgap width of two-dimensional phononic crystals

[1] M. M. Sigalas, "Defect states of acoustic waves in a two-dimensional lattice of solid cylinders." Journal of Applied Physics, 84 (1998) 3026.
[2] S. Yang, J. H. Page, Z. Liu, M. L. Cowan, C. T. Chan, P. Sheng "Focusing of sound in a 3D phononic crystal." Physical review letters, 93 (2004) 024301.
[3] E. Yablonovitch, "Inhibited spontaneous emission in solid-state physics and electronics." Physical review letters, 58 (1987) 2059.
[4] C. Luo, S. G. Johnson, J. D. Joannopoulos, and J. B. Pendry, "Subwavelength imaging in photonic crystals." Physical Review B, 68 (2003) 045115.
[5] J. O. Vasseur, P A Deymier, B. Chenni, B. Djafari-Rouhani, L. Dobrzynski, D. Prevost "Experimental and theoretical evidence for the existence of absolute acoustic band gaps in two dimensional solid phononic crystals." Physical
Review Letters, 86 (2001) 3012.
[6] F. Cervera, L. Sanchis, J. V. Sánchez-Pérez, R. Martinez-Sala, C. Rubio, F. Meseguer, C. López, D. Caballero, J. Sánchez-Dehesa "Refractive acoustic devices for airborne sound." physical review letters, 88 (2001) 023902.
[7] N. Garcia, M. Nieto-Vesperinas, E. V. Ponizovskaya, and M. Torres. "Theory for tailoring sonic devices: Diffraction dominates over- refraction." Physical Review E, 67 (2003) 046606.

[8] M. Torres, F. R. Montero de Espinosa, and J. L.Aragon. "Ultrasonic wedges for elastic wave bending and splitting without requiring a full band gap." Physical Review Letters, 86 (2001) 4282.
[9] Y. Suxia, J. H. Page, Z. Liu, M. L. Cowan, C. T. Chan, and P. Sheng. "Focusing of sound in a 3D phononic crystal." Physical review letters, 93 (2004) 024301.
[10] Drumheller, S. Douglas Introduction to wave propagation in nonlinear fluids and solids. Cambridge; University Press, 1998.
[11] Gupta, C. Bikash, and Z. Ye "Theoretical analysis of the focusing of acoustic waves by two-dimensional sonic crystals." Physical Review E, 67 (2003) 03660.
[12] D. Espinosa, F.R. Montero, E. Jimenez, and M. Torres "Ultrasonic band gap in a periodic two dimensional
composite." Physical Review Letters, 80 (1998) 1208.
[13] W. M. Robertson, and J. F. Rudy "Measurement of acoustic stop bands in two-dimensional periodic
scattering arrays." The Journal of the Acoustical Society of America 104 (1998) 694.
[14] M. Toyokatsu. "Sonic crystals and sonic waveguides." Measurement Science andTe chnology, 16 (2005) R47.
[15] Y. Suxia, J. H. Page, Z. Liu, M. L. Cowan, C. T. Chan, and P. Sheng. "Ultrasound tunneling through 3D phononic crystals." Physical review letters, 88 (2002) 104301.
[16] O. Jerome, A-C. Hladky-Hennion, B. Djafari- Rouhani, F. Duval, B. Dubus, Y. Pennec, and P. A. Deymier. "Waveguiding in two-dimensionalpiezoele ctric phononic crystal plates." Journal of applied physics, 101 (2007) 114904.
[17] A. Khelif, A. Choujaa, S. Benchabane, B. Djafari- Rouhaniand, V. Laude, "Guiding and bending of acoustic waves in highly confined phononic crystal waveguides;" Applied physics letters, 84 (2004) 4400.
[18] M. Torres, F. R. Montero de Espinosa, and J. L. Aragon. "Ultrasonic wedges for elastic wave bending and splitting without requiring a full band gap." Physical Review Letters, 86 (2001) 4282.
[19] A. Khelif, A. Choujaa, B. Djafari-Rouhani, M. Wilm, S. Ballandras, and V. Laude " Trapping and guiding of acoustic waves by defect modes in a full-band-gap ultrasonic crystal" Physical Review B, 68 (2003) 214301.
[20] F. Van Der Biest, A. Sukhovich, A. Tourin, J. H. Page, B. A.Van Tiggelen, Z. Liu, and M. Fink,"Resonant tunneling of acoustic waves througha double barrier consisting of two phononic crystals." Europhysics Letters, 71 (2005) 63.
[21] S. Jinjie, S. Chin, S. Lin, and T. Jun Huang; "Wideband acoustic collimating by phononic crystal
composites." Applied Physics Letters, 92 (2008)111901.
[22] J. O. Vasseur, P. A. Deymier, B. Chenni, B. Djafari-Rouhani, L. Dobrzynski, and D. Prevost,
"Experimental and theoretical evidence for the existence of absolute acoustic band gaps in two dimensional
solid phononic crystals." Physical Review Letters, 86 (2001) 3012.
[23] F. L. Hsiao, A. Khelif, H. Moubchir, A. Choujaa, C. C. Chen, and V. Laude, "Complete band gaps
and deaf bands of triangular and honeycomb water-steel phononic crystals." Journal of
applied physics, 101 (2007) 044903.
[24] P. A. Deymier, B. Merheb, J. O. Vasseur, A. Sukhovichand, J. H. Page, "Focusing of acoustic waves by flat lenses made from negatively refracting two-dimensional photonic crystals." Revista mexicana de física, 54 (2008)
74.
[25] M. B. Assouar, B. Vincent, H. Moubchir, O. Elmazria, A. Khelif, and V. Laude, "Domains Inversion in LiNbO3 Using Electron Beam Irradiation for Phononic Crystals." 15th IEEE international symposium on the applications of
ferroelectrics. IEEE, 2006.
[26] Z. Xiao-Zhou, Y. S. Wang, and C. Zhang; "Essentialrole of material parameters on the band gaps of phononic crystals." IEEE; Ultrasonics Symposium. IEEE, 2008

[27] I. A. Veres, D. M. Profunser, O. B. Wright, O. Matsuda, and U. Lang, "Real-time simulations and experiments on ultrahigh frequency surface waves in micro-structured phononic crystals." IEEE International Ultrasonics
Symposium. IEEE, 2009
[28] S. Mohammadi, A. A. Eftekhar, and A. Adibi. "Support loss-free micro/nano-mechanical resonators using phononic crystal slab waveguides;" IEEE International Frequency Control Symposium. IEEE, 2010
[29] H. Y. Zhao, C. F. He, B. Wu, and Y. S. Wang, "Experimental realization of lower-frequency complete band gaps in 2D phononic crystals." Symposium on Piezoelectricity, Acoustic Waves and Device Applications (SPADA). IEEE, 2011.
[30] D. W. Branch, P. J. Clews, J. Nguyen, B. Kim, and P. T. Rakich, "Dispersion engineering in aluminum nitride phononic crystal plates." IEEE International Ultrasonics Symposium (IUS) IEEE, 2013.
[31] Y. Y. Chen, Y. R. Lin, T. T. Wu, and S. Y. Pao, "Anchor loss reduction of quartz resonators utilizing phononic crystals." IEEE International Ultrasonics Symposium (IUS). IEEE, 2015.
[32] Y. Deng, and Y. Jing. "Zone folding induced topological insulators in phononic crystals." IEEE International Ultrasonics Symposium (IUS). IEEE, 2017.
[33] M. Wajih Ullah Siddiqi, J. E-Y. Lee; "AlN-on-Si MEMS resonator bounded by wide acoustic bandgap two-dimensional phononic crystal anchors." IEEE Micro Electro Mechanical Systems (MEMS). IEEE, 2018.
[34] F. Bao, J. Bao, X. Li, X. Zhou, Y. Song, and X. Zhang, "Reflective strategy based on tetherintegrated phononic crystals for 10 MHz MEMS resonator." Joint Conference of the IEEE International Frequency Control Symposium and European Frequency and Time Forum (EFTF/IFC). IEEE, 2019.
[35] J. Gao, X. Y. Zou, J. C. Cheng, and B. Li, "Band gaps of lower-order Lamb wave in a thin plate with one-dimensional phononic crystal layer: Effect of the substrate" Applied Physics Letters, 92 (2008) 023510.
[36] Y. Yao, F. Wu, X. Zhang, and Z. Hou, "Lamb wave band gaps in locally resonant phononic crystal strip waveguides." Physics Letters A, 376 (2012) 579.
[37] J. J. Chen, K. W. Zhang, J. Gao, and J. C. Cheng, "Stopbands for lower-order Lamb waves in onedimensional
composite thin plates." Physical Review B, 73(2006) 094307.
[38] V. Zega, C. Gazzola, A. Buffoli, M. Conti, L. G. Falorni, G. Langfelder, A. Frangi "A defectbased MEMS phononic crystal slab waveguide." 35th IEEE International Conference on Micro Electro Mechanical Systems Conference (MEMS) 2022 Jan 9 (pp. 176-179).
[39] K. Nishimiya, T. Ohbuchi, N. Wakatsuki, K. Mizutani, and K. Yamamoto. "Visualization of negative refraction in phononic crystal using pulsed light source." IEEE International Ultrasonics Symposium, pp. 1545-1547. IEEE, 2009.
[40] F. Lucklum, and M. J. Vellekoop "Realization of complex 3-D phononic crystals with wide complete acoustic band gaps." IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control, 63 (2016) 796.
[41] M. Pyung Sik, K. Kim, and Y. Young Kim. "Remote beam steering with phononic crystalbased elastic waveguides;" IEEE International Ultrasonics Symposium (IUS). IEEE, 2016 [42] L. Astolfi, R. L. Watson, D. A. Hutchins, P. J. Thomas, M. Askari, A. T. Clare, L.,Nie, S. Freear, S. Laureti, and M. Ricci, "Negative refraction in conventional and additively manufactured phononic crystals." IEEE International Ultrasonics Symposium (IUS). IEEE, 2019.
[43] T. Vasileiadis, J. Varghese, V. Babacic, J. Gomis- Bresco, D. Navarro Urrios, and B. Graczykowski, "Progress and perspectives on phononic crystals." Journal of Applied Physics, 129 (2021) 160901.