Transparent Gradient-Index Lens for Underwater Sound Based on Phase Advance

Spatial gradients in a refractive index are used extensively in acoustic metamaterial applications to control wave propagation through phase delay. This study reports the design and experimental realization of an acoustic gradient-index lens using a sonic crystal lattice that is impedance matched to water over a broad bandwidth. In contrast to previous designs, the underlying lattice features refractive indices that are lower than the water background, which facilitates propagation control based on a phase advance as opposed to a delay. The index gradient is achieved by varying the filling fraction of hollow, air-filled aluminum tubes that individually exhibit a higher sound speed than water and matched impedance. Acoustic focusing is observed over a broad bandwidth of frequencies in the homogenization limit of the lattice, with intensity magnifications in excess of 7 dB. An anisotropic lattice design facilitates a flat-faceted geometry with low backscattering at 18 dB below the incident sound-pressure level. A three-dimensional Rayleigh-Sommerfeld integration that accounts for the anisotropic refraction is used to accurately predict the experimentally measured focal patterns.This work is supported by the Office of Naval Research.Martin, TP.; Naify, C.; Skerritt, E.; Layman, C.; Nicholas, M.; Calvo, D.; Orris, GJ.... (2015). Transparent Gradient-Index Lens for Underwater Sound Based on Phase Advance. Physical Review Applied. 4(3):034003-1-034003-8. doi:10.1103/PhysRevApplied.4.034003S034003-1034003-843Naify, C. J., Martin, T. P., Layman, C. N., Nicholas, M., Thangawng, A. L., Calvo, D. C., & Orris, G. J. (2014). Underwater acoustic omnidirectional absorber. Applied Physics Letters, 104(7), 073505. doi:10.1063/1.4865480Li, R.-Q., Zhu, X.-F., Liang, B., Li, Y., Zou, X.-Y., & Cheng, J.-C. (2011). A broadband acoustic omnidirectional absorber comprising positive-index materials. Applied Physics Letters, 99(19), 193507. doi:10.1063/1.3659690Climente, A., Torrent, D., & Sánchez-Dehesa, J. (2012). Omnidirectional broadband acoustic absorber based on metamaterials. Applied Physics Letters, 100(14), 144103. doi:10.1063/1.3701611Martin, T. P., Layman, C. N., Moore, K. M., & Orris, G. J. (2012). Elastic shells with high-contrast material properties as acoustic metamaterial components. Physical Review B, 85(16). doi:10.1103/physrevb.85.161103Titovich, A. S., & Norris, A. N. (2014). Tunable cylindrical shell as an element in acoustic metamaterial. The Journal of the Acoustical Society of America, 136(4), 1601-1609. doi:10.1121/1.4894723Zhang, B., Chan, T., & Wu, B.-I. (2010). Lateral Shift Makes a Ground-Plane Cloak Detectable. Physical Review Letters, 104(23). doi:10.1103/physrevlett.104.233903Yin, M., Yong Tian, X., Xue Han, H., & Chen Li, D. (2012). Free-space carpet-cloak based on gradient index photonic crystals in metamaterial regime. Applied Physics Letters, 100(12), 124101. doi:10.1063/1.3696040Torrent, D., & Sánchez-Dehesa, J. (2007). Acoustic metamaterials for new two-dimensional sonic devices. New Journal of Physics, 9(9), 323-323. doi:10.1088/1367-2630/9/9/323Climente, A., Torrent, D., & Sánchez-Dehesa, J. (2010). Sound focusing by gradient index sonic lenses. Applied Physics Letters, 97(10), 104103. doi:10.1063/1.3488349Martin, T. P., Nicholas, M., Orris, G. J., Cai, L.-W., Torrent, D., & Sánchez-Dehesa, J. (2010). Sonic gradient index lens for aqueous applications. Applied Physics Letters, 97(11), 113503. doi:10.1063/1.3489373Peng, S., He, Z., Jia, H., Zhang, A., Qiu, C., Ke, M., & Liu, Z. (2010). Acoustic far-field focusing effect for two-dimensional graded negative refractive-index sonic crystals. Applied Physics Letters, 96(26), 263502. doi:10.1063/1.3457447Sanchis, L., Yánez, A., Galindo, P. L., Pizarro, J., & Pastor, J. M. (2010). Three-dimensional acoustic lenses with axial symmetry. Applied Physics Letters, 97(5), 054103. doi:10.1063/1.3474616Zigoneanu, L., Popa, B.-I., & Cummer, S. A. (2011). Design and measurements of a broadband two-dimensional acoustic lens. Physical Review B, 84(2). doi:10.1103/physrevb.84.024305Lin, S.-C. S., Tittmann, B. R., & Huang, T. J. (2012). Design of acoustic beam aperture modifier using gradient-index phononic crystals. Journal of Applied Physics, 111(12), 123510. doi:10.1063/1.4729803Chang, T. M., Dupont, G., Enoch, S., & Guenneau, S. (2012). Enhanced control of light and sound trajectories with three-dimensional gradient index lenses. New Journal of Physics, 14(3), 035011. doi:10.1088/1367-2630/14/3/035011Hladky-Hennion, A.-C., Vasseur, J. O., Haw, G., Croënne, C., Haumesser, L., & Norris, A. N. (2013). Negative refraction of acoustic waves using a foam-like metallic structure. Applied Physics Letters, 102(14), 144103. doi:10.1063/1.4801642Ren, C., Xiang, Z., & Cen, Z. (2010). Design of acoustic devices with isotropic material via conformal transformation. Applied Physics Letters, 97(4), 044101. doi:10.1063/1.3467852Layman, C. N., Martin, T. P., Moore, K. M., Calvo, D. C., & Orris, G. J. (2011). Designing acoustic transformation devices using fluid homogenization of an elastic substructure. Applied Physics Letters, 99(16), 163503. doi:10.1063/1.3652914Maldovan, M. (2013). Sound and heat revolutions in phononics. Nature, 503(7475), 209-217. doi:10.1038/nature12608Kadic, M., Bückmann, T., Schittny, R., & Wegener, M. (2013). Metamaterials beyond electromagnetism. Reports on Progress in Physics, 76(12), 126501. doi:10.1088/0034-4885/76/12/126501Torrent, D., & Sánchez-Dehesa, J. (2008). Anisotropic mass density by two-dimensional acoustic metamaterials. New Journal of Physics, 10(2), 023004. doi:10.1088/1367-2630/10/2/023004Parazzoli, C. G., Koltenbah, B. E. C., Greegor, R. B., Lam, T. A., & Tanielian, M. H. (2006). Eikonal equation for a general anisotropic or chiral medium: application to a negative-graded index-of-refraction lens with an anisotropic material. Journal of the Optical Society of America B, 23(3), 439. doi:10.1364/josab.23.000439Ward, G. P., Lovelock, R. K., Murray, A. R. J., Hibbins, A. P., Sambles, J. R., & Smith, J. D. (2015). Boundary-Layer Effects on Acoustic Transmission Through Narrow Slit Cavities. Physical Review Letters, 115(4). doi:10.1103/physrevlett.115.044302Guild, M. D., García-Chocano, V. M., Kan, W., & Sánchez-Dehesa, J. (2015). Acoustic metamaterial absorbers based on multilayered sonic crystals. Journal of Applied Physics, 117(11), 114902. doi:10.1063/1.4915346Reyes-Ayona, E., Torrent, D., & Sánchez-Dehesa, J. (2012). Homogenization theory for periodic distributions of elastic cylinders embedded in a viscous fluid. The Journal of the Acoustical Society of America, 132(4), 2896-2908. doi:10.1121/1.4744933Molerón, M., Serra-Garcia, M., & Daraio, C. (2014). Acoustic Fresnel lenses with extraordinary transmission. Applied Physics Letters, 105(11), 114109. doi:10.1063/1.4896276Li, Y., Yu, G., Liang, B., Zou, X., Li, G., Cheng, S., & Cheng, J. (2014). Three-dimensional Ultrathin Planar Lenses by Acoustic Metamaterials. Scientific Reports, 4(1). doi:10.1038/srep06830Gao, Y., Liu, J., Zhang, X., Wang, Y., Song, Y., Liu, S., & Zhang, Y. (2012). Analysis of focal-shift effect in planar metallic nanoslit lenses. Optics Express, 20(2), 1320. doi:10.1364/oe.20.001320Born, M., Wolf, E., Bhatia, A. B., Clemmow, P. C., Gabor, D., Stokes, A. R., … Wilcock, W. L. (1999). Principles of Optics. doi:10.1017/cbo9781139644181Shen, 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.4.041033Dubois, M., Farhat, M., Bossy, E., Enoch, S., Guenneau, S., & Sebbah, P. (2013). Flat lens for pulse focusing of elastic waves in thin plates. Applied Physics Letters, 103(7), 071915. doi:10.1063/1.4818716Dubois, M., Bossy, E., Enoch, S., Guenneau, S., Lerosey, G., & Sebbah, P. (2015). Time-Driven Superoscillations with Negative Refraction. Physical Review Letters, 114(1). doi:10.1103/physrevlett.114.013902Kock, W. E., & Harvey, F. K. (1949). Refracting Sound Waves. The Journal of the Acoustical Society of America, 21(5), 471-481. doi:10.1121/1.1906536Liang, Z., & Li, J. (2012). Extreme Acoustic Metamaterial by Coiling Up Space. Physical Review Letters, 108(11). doi:10.1103/physrevlett.108.114301Xie, Y., Konneker, A., Popa, B.-I., & Cummer, S. A. (2013). Tapered labyrinthine acoustic metamaterials for broadband impedance matching. Applied Physics Letters, 103(20), 201906. doi:10.1063/1.4831770Frenzel, T., David Brehm, J., Bückmann, T., Schittny, R., Kadic, M., & Wegener, M. (2013). Three-dimensional labyrinthine acoustic metamaterials. Applied Physics Letters, 103(6), 061907. doi:10.1063/1.4817934Bozhko, A., García-Chocano, V. M., Sánchez-Dehesa, J., & Krokhin, A. (2015). Redirection of sound in straight fluid channel with elastic boundaries. Physical Review B, 91(9). doi:10.1103/physrevb.91.094303García-Meca, C., Carloni, S., Barceló, C., Jannes, G., Sánchez-Dehesa, J., & Martínez, A. (2014). Transformational acoustic metamaterials based on pressure gradients. Physical Review B, 90(2). doi:10.1103/physrevb.90.024310Cummer, S. A., & Schurig, D. (2007). One path to acoustic cloaking. New Journal of Physics, 9(3), 45-45. doi:10.1088/1367-2630/9/3/045Chen, H., & Chan, C. T. (2007). Acoustic cloaking in three dimensions using acoustic metamaterials. Applied Physics Letters, 91(18), 183518. doi:10.1063/1.2803315Cummer, S. A., Popa, B.-I., Schurig, D., Smith, D. R., Pendry, J., Rahm, M., & Starr, A. (2008). Scattering Theory Derivation of a 3D Acoustic Cloaking Shell. Physical Review Letters, 100(2). doi:10.1103/physrevlett.100.024301Guild, M. D., Haberman, M. R., & Alù, A. (2012). Plasmonic-type acoustic cloak made of a bilaminate shell. Physical Review B, 86(10). doi:10.1103/physrevb.86.104302Martin, T. P., & Orris, G. J. (2012). Hybrid inertial method for broadband scattering reduction. Applied Physics Letters, 100(3), 033506. doi:10.1063/1.367863