Conclusions We have demonstrated theoretically by using the TMM and experimentally by acoustic transmission measured directly, the formation of acoustic cavity

modes in GHz frequencies by introduction of defects into periodic structures based on PS. Acoustic resonances can be tuned at different frequencies by changing the porosity of the defect. And we proved that these resonant modes appear due to the localization of the field into the defect. The acoustic mirrors and cavity structures based on PS have a performance which is at least comparable with that devices based on semiconductor superlattices. This study could be useful for the design of acoustic devices, such as highly selective frequency filters with applications in GHz range. Acknowledgements The authors acknowledge CONACyT for support under PF-02341066 solubility dmso project No. 167939. References 1. Kushwaha MS, Halevi P, Dobrzynski L, Djafari-Rouhani B: Acoustic band structure of periodic elastic composites. Phys Rev Lett 1993, 71:2022. 10.1103/PhysRevLett.71.2022CrossRef 2. Kushwaha MS, Halevi P, Martínez G: Theory of acoustic band structure of periodic VRT752271 supplier elastic composites. Phys Rev B 1994, 49:2313. 10.1103/PhysRevB.49.2313CrossRef 3. Sigalas MM, Economou EN: Attenuation of multiple-scattered sound. Europhys Lett 1996, 36:241. 10.1209/epl/i1996-00216-4CrossRef 4. Kushwaha

MS, Halevi P: Giant acoustic stop bands in two-dimensional periodic arrays of liquid cylinders. Appl Phys Lett 1996, 69:31. 10.1063/1.118108CrossRef 5. Sánchez-Pérez JV, Caballero D, Martínez-Sala R, Rubio C, Sánchez-Dehesa J, Meseguer F, Llinares

J, Gálvez F: Sound attenuation by a two-dimensional array of rigid cylinders. Phys Rev Lett 1998, 80:5325. 10.1103/PhysRevLett.80.5325CrossRef 6. Sigalas MM: Elastic wave band gaps and defect states in two-dimensional composites. J Acoust Soc Am 1997, 101:1256. 10.1121/1.418156CrossRef 7. Sigalas MM: Defect states of acoustic waves in a two-dimensional lattice of Immune system solid cylinders. J Appl Phys 1998, 84:3026. 10.1063/1.368456CrossRef 8. Kafesaki M, Sigalas MM, Garca N: Frequency modulation in the transmittivity of wave guides in elastic-wave band-gap materials. Phys Rev Lett 2000, 85:4044. 10.1103/PhysRevLett.85.4044CrossRef 9. Khelif A, Djafari-Rouhani B, Vasseur JO, Deymier PA: Transmission and dispersion relations of perfect and defect-containing waveguide structures in phononic band gap materials. Phys Rev B 2003, 68:024302.CrossRef 10. Lacharmoise P, Fainstein A, Jusserand B, Thierry-Mieg V: Optical cavity enhancement of light–sound interaction in acoustic phonon cavities. Appl Phys Lett 2004, 84:3274. 10.1063/1.1734686CrossRef 11. Fokker PA, Dijkhuis JI, de Wijn HW: Stimulated emission of phonons in an acoustical cavity. Phys Rev B 1997, 55:2925.CrossRef 12. Camps I, Makler SS, Pastawski HM, Foa Torres LEF: GaAs-Al x Ga 1− x As double-barrier heterostructure phonon laser: a full quantum treatment. Phys Rev B 2011, 64:125311.CrossRef 13.