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Copyright (2011) American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics. along with the following message: The following article appeared in Journal of Applied Physics , Volume 110, Issue 1 and may be found at http://scitation.aip.org/content/aip/journal/jap/110/1/10.1063/1.3599886. Authors own version of final article on e-print servers ; The physical properties of a periodic distribution of absorbent resonators is used in this work to design a tunable wideband bandstop acoustic filter. Analytical and numerical simulations as well as experimental validations show that the control of the resonances and the absorption of the scatterers along with their periodic arrangement in air introduce high technological possibilities to control noise. Sound manipulation is perhaps the most obvious application of the structures presented in this work. We apply this methodology to develop a device as an alternative to the conventional acoustic barriers with several properties from the acoustical point of view but also with additional esthetic and constructive characteristics. © 2011 American Institute of Physics. ; This work was supported by MEC (Spanish Government) and FEDER funds, under Grant No. MAT2009-09438. ; Romero García, V.; Sánchez Pérez, JV.; García-Raffi, LM. (2011). Tunable wideband bandstop acoustic filter based on two-dimensional multiphysical phenomena periodic systems. Journal of Applied Physics. 110(1):149041-149049. https://doi.org/10.1063/1.3599886 ; S ; 149041 ; 149049 ; 110 ; 1 ; Yablonovitch, E. (1987). Inhibited Spontaneous Emission in Solid-State Physics and Electronics. Physical Review Letters, 58(20), 2059-2062. doi:10.1103/physrevlett.58.2059 ; John, S. (1987). Strong localization of photons in certain disordered dielectric superlattices. Physical Review Letters, 58(23), 2486-2489. doi:10.1103/physrevlett.58.2486 ; Sigalas, M. M., & Economou, E. N. (1992). Elastic and ...

Complex band structures and multiple scattering theory have been used in this paper to analyze the overlapping of the evanescent waves localized in point defects in sonic crystals (SCs). The extended plane wave expansion (EPWE) with supercell approximation gives the imaginary part of the Bloch vectors that produces the decay of the localized modes inside the periodic system. Double cavities can present a coupling between the evanescent modes localized in the defect, showing a symmetric or antisymmetric mode. When point defects are close, the complex band structures reveal a splitting of the frequencies of the localized modes. Both the real part and the imaginary values of k of the localized modes in the cavities present different values for each localized mode, which gives different properties for each mode. The novel measurements, in very good agreement with analytical data, show experimental evidence of the symmetric and antisymmetric localized modes for a double-point defect in SCs. The investigation of the localization phenomena and the coupling between defects in periodic systems has fundamental importance in both pure and applied physics. ; This work was supported by MEC (the Spanish Government) and FEDER funds through grants MAT2009-09438 and MTM2009-14483-C02-02. ; Romero García, V.; Sánchez Pérez, JV.; García-Raffi, LM. (2010). Propagating and evanescent properties of duble-point defect in sonic crystals. New Journal of Physics. 12:1-14. doi:10.1088/1367-2630/12/8/083024 ; S ; 1 ; 14 ; 12

The complex band structures calculated using the extended plane wave expansion (EPWE) reveal the presence of evanescent modes in periodic systems, never predicted by the classical ω(kE) methods, providing novel interpretations of several phenomena as well as a complete picture of the system. In this work, we theoretically and experimentally observe that in the ranges of frequencies where a deaf band is traditionally predicted, an evanescent mode with excitable symmetry appears, changing drastically the interpretation of the transmission properties. On the other hand, the simplicity of the sonic crystals in which only the longitudinal polarization can be excited is used to interpret, without loss of generality, the level repulsion between symmetric and antisymmetric bands in sonic crystals as the presence of an evanescent mode connecting both repelled bands. These evanescent modes, obtained using EPWE, explain both the attenuation produced in this range of frequencies and the transfer of symmetry from one band to the other in good agreement with both experimental results and multiple scattering predictions. Thus, the evanescent properties of the periodic system have been revealed to be necessary for the design of new acoustic and electromagnetic applications based on periodicity. ; VRG and LMGR are grateful for the hospitality and the facilities provided by the Institut d'Electronique, de Microelectronique et de Nanotechnologie (IEMN UMR CNRS 8520). LMGR thanks the Universidad Politecnica de Valencia for the grant 'Programa de Apoyo a la Investigacion y Desarrollo (PAID-00-11)'. VRG is grateful for the support provided by 'Programa de Contratos Post-Doctorales con Movilidad UPV (CEI-01-11)'. This work was supported by MCI Secretaria de Estado de Investigacion (the Spanish government) and FEDER funds under grant no. MAT2009-09438. ; Romero García, V.; Vasseur, J.; García-Raffi, LM.; Hladky-Hennion, A. (2012). Theoretical and experimental evidence of level repulsion states and evanescent modes in sonic crystal ...

[EN] We report the experimental design of a one-dimensional stealth acoustic material, namely a material that suppresses the acoustic scattering for a given set of incident wave vectors. The material consists of multiple scatterers, rigid diaphragms, located in an air-filled acoustic waveguide. The position of the scatterers has been chosen such that in the Born approximation a suppression of the scattering for a broad range of frequencies is achieved and thus a broadband transparency. Experimental results are found in excellent agreement with the theory despite the presence of losses and the finite size of the material, features that are not captured in the theory. This robustness as well as the generality of the results motivates realistic potential applications for the design of transparent materials in acoustics and other fields of wave physics. ; This work has been funded by RFI Le Mans Acoustique (Region Pays de la Loire) in the framework of the APA-MAS project, by the project HYPERMETA funded under the program Etoiles Montantes of the Region Pays de la Loire as well as by the Ministerio de Economia y Competitividad (Spain) and European Union FEDER through project FIS2015-65998-C2-2-P. V. Romero-Garcia and L. M. Garcia-Raffi acknowledge the short-term scientific mission (STSM) funded by the COST (European Cooperation in Science and Technology) Action DENORMS - CA15125. ; Romero-García, V.; Lamothe, N.; Theocharis, G.; Richoux, O.; García-Raffi, LM. (2019). Stealth Acoustic Materials. Physical Review Applied. 11(5):1-9. https://doi.org/10.1103/PhysRevApplied.11.054076 ; S ; 1 ; 9 ; 11 ; 5 ; Shen, C., Xu, J., Fang, N. X., & Jing, Y. (2014). Anisotropic Complementary Acoustic Metamaterial for Canceling out Aberrating Layers. Physical Review X, 4(4). doi:10.1103/physrevx.4.041033 ; Jiménez, N., Cox, T. J., Romero-García, V., & Groby, J.-P. (2017). Metadiffusers: Deep-subwavelength sound diffusers. Scientific Reports, 7(1). doi:10.1038/s41598-017-05710-5 ; Shen, H., Lu, D., VanSaders, B., Kan, J. J., ...

[EN] We report the optimal focusing of acoustic vortex beams by using flat lenses based on a Fresnelspiral diffraction grating. The flat lenses are designed by spiral-shaped Fresnel zone plates composed of one or several arms. The constructive and destructive interferences of the diffracted waves by the spiral grating result in sharp acoustic vortex beams, following the focal laws obtained in analogy with the Fresnel zone plate lenses. In addition, we show that the number of arms determines the topological charge of the vortex, allowing the precise manipulation of the acoustic wave field by flat lenses. The experimental results in the ultrasonic regime show excellent agreement with the theory and full-wave numerical simulations. A comparison with beam focusing by Archimedean spirals also showing vortex focusing is given. The results of this work may have potential applications for particle trapping, ultrasound therapy, imaging, or underwater acoustic transmitters. ; This work was supported by the Spanish Ministry of Economy and Innovation (MINECO) and European Union FEDER through Project Nos. FIS2015-65998-C2-1 and FIS2015-65998-C2-2. N.J. acknowledges financial support from Generalitat Valenciana through Grant No. APOSTD-2017-042. ; Jimenez, N.; Romero García, V.; García-Raffi, LM.; Camarena Femenia, F.; Staliunas, K. (2018). Sharp acoustic vortex focusing by Fresnel-spiral zone plates. Applied Physics Letters. 112(20):204101-1-204101-5. https://doi.org/10.1063/1.5029424 ; S ; 204101-1 ; 204101-5 ; 112 ; 20 ; J. Nye and M. Berry ,Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences(The Royal Society, 1974), Vol.336, pp. 165–190. ; Grier, D. G. (2003). A revolution in optical manipulation. Nature, 424(6950), 810-816. doi:10.1038/nature01935 ; Volke-Sepúlveda, K., Santillán, A. O., & Boullosa, R. R. (2008). Transfer of Angular Momentum to Matter from Acoustical Vortices in Free Space. Physical Review Letters, 100(2). doi:10.1103/physrevlett.100.024302 ; Anhäuser, A., ...

This article may be downloaded for personal use only. Any other use requires prior permission of the author and AIP Publishing. The following article appeared in Applied Physics Letters 107, 204103 (2015); doi:10.1063/1.4935917 and may be found at http://dx.doi.org/10.1063/1.4935917. ; We report the nonlinear focusing of ultrasonic waves by an axisymmetric diffraction grating immersed in water. In the linear regime, the system presents high focal gain (32 dB), with a narrow beam-width and intense side lobes as it is common in focusing by Fresnel-like lenses. Activating the nonlinearity of the host medium by using high amplitude incident waves, the focusing properties of the lens dramatically change. Theoretical predictions show that the focal gain of the system extraordinary increases in the strongly nonlinear regime (Mach number of 6.1 x 10(-4)). Particularly, the harmonic generation is locally activated at the focal spot, and the second harmonic beam is characterized by strongly reduced side-lobes and an excellent beam profile as experiments show in agreement with theory. The results can motivate applications in medical therapy or second harmonic imaging. (c) 2015 AIP Publishing LLC. ; The work was supported by Spanish Ministry of Science and Innovation and European Union FEDER through Projects FIS2011-29734-C02-01 and -02, MTM2012-36740c02-02, and PAID 2012/253. ; Jimenez, N.; Romero García, V.; Picó Vila, R.; García-Raffi, LM.; Staliünas, K. (2015). Nonlinear focusing of ultrasonic waves by an axisymmetric diffraction grating embedded in water. Applied Physics Letters. 107(20). doi:10.1063/1.4935917 ; S ; 204103 ; 107 ; 20 ; Farnow, S. A., & Auld, B. A. (1974). Acoustic Fresnel zone plate transducers. Applied Physics Letters, 25(12), 681-682. doi:10.1063/1.1655359 ; Sleva, M. Z., Hunt, W. D., & Briggs, R. D. (1994). Focusing performance of epoxy‐ and air‐backed polyvinylidene fluoride Fresnel zone plates. The Journal of the Acoustical Society of America, 96(3), 1627-1633. doi:10.1121/1.410242 ; Wang, ...

An acoustic metamaterial made of a two-dimensional (2D) periodic array of multi-resonant acoustic scatterers is analyzed both experimentally and theoretically. The building blocks consist of a combination of elastic beams of low-density polyethylene foam (LDPF) with cavities of known area. Elastic resonances of the beams and acoustic resonances of the cavities can be excited by sound producing several attenuation peaks in the low frequency range. Due to this behavior the periodic array with long wavelength multi-resonant structural units can be classified as a locally multi-resonant acoustic metamaterial (LMRAM) with strong dispersion of its effective properties. The results presented in this paper could be used to design effective tunable acoustic filters for the low frequency range. (C) 2012 Elsevier Ltd. All rights reserved. ; This work was supported by MCI Secretaria de Estado de Investigacion (Spanish government) and FEDER funds, under Grants MAT2009-09438 and MTM2009-14483-C02-02. V.R.G. is grateful for the support of "Programa de Contratos Post-Doctorales con Movilidad UPV (CEI-01-11)". A.K. and O.U. are grateful for the support of EPSRC (UK) through research Grant EP/E063136/1. ; Romero García, V.; Krynkin, A.; García-Raffi, LM.; Umnova, O.; Sánchez Pérez, JV. (2013). Multi-resonant scatterers in sonic crystals: Locally multi-resonant acoustic metamaterial. Journal of Sound and Vibration. 332(1):184-198. doi:10.1016/j.jsv.2012.08.003 ; S ; 184 ; 198 ; 332 ; 1

Copyright (2010) American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics along with the following message: The following article appeared in "Romero García, V.; Sánchez Pérez, JV.; Castiñeira Ibáñez, S.; García-Raffi, LM. (2010). Evidences of evanescent Bloch waves in phononic crystals. Applied Physics Letters. 96:1241021-1241021. doi:10.1063/1.3367739" and may be found at http://dx.doi.org/10.1063/1.3367739. Authors own version of final article on e-print servers ; We show both experimentally and theoretically the evanescent behavior of modes in the band gap of finite phononic crystal (PC). Based on experimental and numerical data we obtain the imaginary part of the wave vector in good agreement with the complex band structures obtained by the extended plane wave expansion. The calculated and measured acoustic field of a localized mode out of the point defect inside the PC presents also evanescent behavior. The correct understanding of evanescent modes is fundamental for designing narrow filters and waveguides based on PCs with defects. ; This work was supported by MEC (Spanish Government) and FEDER funds, under Grant Nos. MAT2009-09438 and MTM2009-14483-C02-02. The authors would like to thank J. M. Herrero, S. Garcia-Nieto, and X. Blasco for their work in the control and acquisition system of 3DReAMS. ; Romero García, V.; Sánchez Pérez, JV.; Castiñeira Ibáñez, S.; García-Raffi, LM. (2010). Evidences of evanescent Bloch waves in phononic crystals. Applied Physics Letters. 96(12):1241021-1241021. doi:10.1063/1.3367739 ; S ; 1241021 ; 1241021 ; 96 ; 12 ; Sigalas, M., & Economou, E. N. (1993). Band structure of elastic waves in two dimensional systems. Solid State Communications, 86(3), 141-143. doi:10.1016/0038-1098(93)90888-t ; Kushwaha, M. S., Halevi, P., Martínez, G., Dobrzynski, L., & Djafari-Rouhani, B. (1994). Theory of acoustic band structure of periodic elastic composites. ...

The transmission of acoustic waves in a fractal distribution of rigid scatterers embedded in air is reported in this work. The Sierpinsky fractal is used to produce a compact small device containing several periodicities, therefore the fractal distribution contains several finite sonic crystals. The attenuation band produced by the fractal distribution results from the sum of the Bragg peaks of each periodicity. On the other hand, bandgaps of sonic crystal depend on the well-known filling fraction, thus the radii of the scatterers in the fractal distribution has been optimized using genetic algorithm in order to overlap the bandgaps of each periodicity obtaining a wide and full attenuation band. ; This work was supported by MCI (Spanish Government) and FEDER funds, under Grant Nos. MAT2009-09438 and MTM2009-14483-C02-02. The authors would like to thank Prof. K. ATTENBOROUGH and Dr. E. A. SANCHEZ-PEREZ for their suggestions and for the revision of the manuscript. ; Castiñeira Ibáñez, S.; Romero García, V.; Sánchez Pérez, JV.; García-Raffi, LM. (2010). Overlapping of acoustic bandgaps using fractal geometries. EPL. 92(2):240071-240073. doi:10.1209/0295-5075/92/24007 ; S ; 240071 ; 240073 ; 92 ; 2

543 554 17 5 ; Senia ; The propagation of intense acoustic waves in a one-dimensional phononic crystal is studied. The medium consists in a structured fluid, formed by a periodic array of fluid layers with alternating linear acoustic properties and quadratic nonlinearity coefficient. The spacing between layers is of the order of the wavelength, therefore Bragg effects such as band gaps appear. We show that the interplay between strong dispersion and nonlinearity leads to new scenarios of wave propagation. The classical waveform distortion process typical of intense acoustic waves in homogeneous media can be strongly altered when nonlinearly generated harmonics lie inside or close to band gaps. This allows the possibility of engineer a medium in order to get a particular waveform. Examples of this include the design of media with effective (e.g., cubic) nonlinearities, or extremely linear media (where distortion can be canceled). The presented ideas open a way towards the control of acoustic wave propagation in nonlinear regime. Work supported by Spanish Ministry of Economy and Innovation and European Union FEDER through projects FIS2011-29731-C02-02 and MTM2012-36740-C02-02. AM and LMGR acknowledge Generalitat Valenciana under grants Santiago Grisolia program (grant 2012/029) and BEST2015/279 respectively. RP and VJSM acknowledge the Spanish Ministry of Economy and Innovation under grants CAS14/00232 and PRX14/00705 respectively. Jimenez, N.; Mehrem, A.; Picó Vila, R.; García-Raffi, LM.; Sánchez Morcillo, VJ. (2016). Nonlinear propagation and control of acoustic waves in phononic superlattices. Comptes Rendus Physique. 17(5):543-554. doi:10.1016/j.crhy.2016.02.004

The propagation of intense acoustic waves in a one-dimensional phononic crystal is studied. The medium consists in a structured fluid, formed by a periodic array of fluid layers with alternating linear acoustic properties and quadratic nonlinearity coefficient. The spacing between layers is of the order of the wavelength, therefore Bragg effects such as band gaps appear. We show that the interplay between strong dispersion and nonlinearity leads to new scenarios of wave propagation. The classical waveform distortion process typical of intense acoustic waves in homogeneous media can be strongly altered when nonlinearly generated harmonics lie inside or close to band gaps. This allows the possibility of engineer a medium in order to get a particular waveform. Examples of this include the design of media with effective (e.g., cubic) nonlinearities, or extremely linear media (where distortion can be canceled). The presented ideas open a way towards the control of acoustic wave propagation in nonlinear regime. ; Work supported by Spanish Ministry of Economy and Innovation and European Union FEDER through projects FIS2011-29731-C02-02 and MTM2012-36740-C02-02. AM and LMGR acknowledge Generalitat Valenciana under grants Santiago Grisolia program (grant 2012/029) and BEST2015/279 respectively. RP and VJSM acknowledge the Spanish Ministry of Economy and Innovation under grants CAS14/00232 and PRX14/00705 respectively. ; Jimenez, N.; Mehrem, A.; Picó Vila, R.; García-Raffi, LM.; Sánchez Morcillo, VJ. (2016). Nonlinear propagation and control of acoustic waves in phononic superlattices. Comptes Rendus Physique. 17(5):543-554. https://doi.org/10.1016/j.crhy.2016.02.004 ; S ; 543 ; 554 ; 17 ; 5

[EN] The acoustic pressure levels experienced by the spacecraft and launchers during the lift-off is due among other factor by the reflection of the sound waves on the launch pad. The acoustic load distribution in the area of the launcher depends on the geometric, mechanical and acoustic characteristics of the ground facilities. This work is intended to study the acoustic environment of the launch pad. A numerical and experimental investigation is developed in order to study in the linear regime the acoustic behaviour of a subscale model of the VEGA's launch pad. The acoustic measurements are performed in an anechoic chamber using an electroacoustic source that emits incoherent noise, mimicking the real acoustic source. The acoustic pressure field is measured at different positions in front of the launch pad mock-up, in the area where the acoustic waves are reflected. Among the future perspectives of this work is to study and develop new methods for the mitigation of the sound pressure levels. ; Authors acknowledge the support of the European Space Agency under contract ¿Sonic Crystals For Noise Reduction At The Launch Pad¿ ESA ITT 1-7094 (ITI) and the 441-2015 Co-Sponsered PhD ¿Acoustic Reduction Methods for the Launch Pad¿. The work was supported by Spanish Ministry of Economy and Innovation (MINECO) and European Union FEDER through project FIS2015-65998-C2-2. Authors aknowledge Dhéric Mutel, Cyril Bernard and Clément Jost for their contribution to this work ; Picó Vila, R.; Herrero-Durá, I.; Sánchez Morcillo, VJ.; Salmerón-Contreras, LJ.; García-Raffi, LM. (2016). Acoustic behavior of the VEGA launch pad environment. Universidade do Porto. 1-6. http://hdl.handle.net/10251/181097 ; S ; 1 ; 6

The formation of high-order Bessel beams by a passive acoustic device consisting of an Archimedes' spiral diffraction grating is theoretically, numerically, and experimentally reported in this paper. These beams are propagation-invariant solutions of the Helmholtz equation and are characterized by an azimuthal variation of the phase along its annular spectrum producing an acoustic vortex in the near field. In our system, the scattering of plane acoustic waves by the spiral grating leads to the formation of the acoustic vortex with zero pressure on axis and the angular phase dislocations characterized by the spiral geometry. The order of the generated Bessel beam and, as a consequence, the size of the generated vortex can be fixed by the number of arms in the spiral diffraction grating. The obtained results allow for obtaining Bessel beams with controllable vorticity by a passive device, which has potential applications in low-cost acoustic tweezers and acoustic radiation force devices. ; We acknowledge financial support from MINECO of the Spanish Government under Grants No. MTM2012-36740-C02-02, No. FIS2015-65998-C2-1-P, and No. FIS2015-65998-C2-2-P. N.J. acknowledges financial support from PAID-2011 Universitat Politecnica de Valencia. ; Jimenez, N.; Picó Vila, R.; Sánchez Morcillo, VJ.; Romero García, V.; García-Raffi, LM.; Staliünas, K. (2016). Formation of high-order acoustic Bessel beams by spiral diffraction gratings. Physical Review E. 94(5). doi:10.1103/PhysRevE.94.053004 ; S ; 053004 ; 94 ; 5

6 12 ; S ; This work theoretically analyzes the sound absorption properties of a chirped multi-layer porous material including transmission, in particular showing the broadband unidirectional absorption properties of the system. Using the combination of the impedance matching condition and the balance between the leakage and the intrinsic losses, the system is designed to have broadband unidirectional and quasi perfect absorption. The transfer and scattering matrix formalism, together with numerical simulations based on the finite element method are used to demonstrate the results showing excellent agreement between them. The proposed system allows to construct broadband sound absorbers with improved absorption in the low frequency regime using less amount of material than the complete bulk porous layer. (C) 2016 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/). This work has been funded by the Metaudible project ANR-13-BS09-0003, co-funded by ANR and FRAE, and also by Ministerio de Economia y Competitividad (Spain) and European Union FEDER through project FIS2015-65998-C2-2-P. We acknowledge project AICO/2016/060 by Consellera de Educacion, Investigacion, Cultura y Deporte de la Generalitat Valenciana. Jimenez, N.; Romero García, V.; Cebrecos, A.; Picó Vila, R.; Sánchez Morcillo, VJ.; García-Raffi, LM. (2016). Broadband quasi perfect absorption using chirped multi-layer porous materials. AIP Advances. 6(12). https://doi.org/10.1063/1.4971274 Ma, G., Yang, M., Xiao, S., Yang, Z., & Sheng, P. (2014). Acoustic metasurface with hybrid resonances. Nature Materials, 13(9), 873-878. doi:10.1038/nmat3994 Ma, G., & Sheng, P. (2016). Acoustic metamaterials: From local resonances to broad horizons. Science Advances, 2(2), e1501595. doi:10.1126/sciadv.1501595 Merkel, A., Theocharis, G., Richoux, O., Romero-García, V., & Pagneux, V. (2015). Control of acoustic absorption in one-dimensional ...

Asymmetric propagation of acoustic waves is theoretically reported in a chirped phononic crystal made of the combination of two different nonlinear solids. The dispersion of the system is spatially dependent and allows the rainbow trapping inside the structure. Nonlinearity is used to activate the self-demodulation effect, which is enhanced due to the particular dispersion characteristics of the system. The performed numerical study reveals an efficient generation of the demodulated wave, up to 15% in terms of the pressure amplitude, as well as strong attenuation for undesired frequency components above the cut-off frequency. The obtained energy rectification ratio is in the order of 104 for the whole range of amplitudes employed in this work, indicating the robustness of the asymmetry and non-reciprocity of the proposed device for a wide operational range. (C) 2016 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/). ; This work was supported by Ministerio de Economa y Competitividad (Spain) and European Union FEDER through project FIS2015-65998-C2-2-P, and by PROPASYM project funded by the Region Pays-dela-Loire and by project AICO/2016/060 by Conselleria de Educacion, Investigacion, Cultura y Deporte de la Generalitat Valenciana. NJ acknowledges financial support from PAID-2011 of the Universitat Politcnica de Valncia. ; Cebrecos, A.; Jimenez, N.; Romero García, V.; Picó Vila, R.; Sánchez Morcillo, VJ.; García-Raffi, LM. (2016). Asymmetric propagation using enhanced self-demodulation in a chirped phononic crystal. AIP Advances. 6(12). https://doi.org/10.1063/1.4968612 ; S ; 6 ; 12