Design Method of Acoustic Metamaterials for Negative Refractive Index Acoustic Lenses Based on the Transmission-Line Theory

The design theory for electromagnetic metamaterials with negative refractive indices by using a distributed transmission-line model is introduced to the design of acoustic metamaterials, and a negative refractive index (NRI) acoustic lens is designed theoretically. Adjustments to the negative refractive indices of metamaterials have been carried out by calculations with numerical simulators in conventional design methods. As the results show, many calculations are needed to determine the shape of the unit structures and there are issues in that it is difficult to design those rigorously, meaning that limitations regarding the degree of freedom in the designs are many. On the other hand, the transmission-line model can rigorously design the unit cell structures of both the negative refractive index metamaterials and the background media with the positive refractive indices by calculations with the design formulas and modifying the error from the theory with a small calculation. In this paper, a meander acoustic waveguide unit cell structure is proposed in order to realize a structure with characteristics equivalent to the model, and the waveguide width and length for realizing an NRI acoustic lens are determined from the design formula of the model. The frequency dispersion characteristics of the proposed structure are also computed by eigenvalue analysis and the error in the waveguide length from the theoretical value is modified by a minor adjustment of the waveguide length. In addition, the NRI acoustic lens is constituted by periodically arranging the proposed unit cell structure with the calculated parameters, and the full-wave simulations are carried out to show the validity of the design theory. The results show that the designed lens operates at 2.5 kHz.

[1]  Jiuhui Wu,et al.  Acoustic focusing and imaging via phononic crystal and acoustic metamaterials , 2022, Journal of Applied Physics.

[2]  A. Sanada,et al.  Broadband transmission-line illusions based on transformation electromagnetic , 2019, EPJ Applied Metamaterials.

[3]  Yuren Wang,et al.  Design of an acoustic superlens using single-phase metamaterials with a star-shaped lattice structure , 2018, Scientific Reports.

[4]  Kang I L Lee,et al.  Experimental verification of zeroth-order resonance phenomenon in an acoustic composite right/left-handed metamaterial resonator , 2017, The Journal of the Acoustical Society of America.

[5]  Peifeng Ji,et al.  Design and demonstration of an underwater acoustic carpet cloak , 2017, Scientific Reports.

[6]  Y. Wang,et al.  Observation of acoustic Dirac-like cone and double zero refractive index , 2017, Nature Communications.

[7]  Bin Liang,et al.  Three-dimensional broadband acoustic illusion cloak for sound-hard boundaries of curved geometry , 2016, Scientific Reports.

[8]  Gaokun Yu,et al.  Acoustic superlens using Helmholtz-resonator-based metamaterials , 2015 .

[9]  Atsushi Sanada,et al.  Planar Distributed Full-Tensor Anisotropic Metamaterials for Transformation Electromagnetics , 2015, IEEE Transactions on Microwave Theory and Techniques.

[10]  G. Lerosey,et al.  Negative refractive index and acoustic superlens from multiple scattering in single negative metamaterials , 2015, Nature.

[11]  Jong Jin Park,et al.  Acoustic superlens using membrane-based metamaterials , 2015 .

[12]  M. Badreddine Assouar,et al.  Acoustic superfocusing by solid phononic crystals , 2014 .

[13]  Gengkai Hu,et al.  Experimental study on acoustic subwavelength imaging of holey-structured metamaterials by resonant tunneling. , 2014, The Journal of the Acoustical Society of America.

[14]  S. Cummer,et al.  Three-dimensional broadband omnidirectional acoustic ground cloak. , 2014, Nature materials.

[15]  Q. Wei,et al.  Acoustic subwavelength imaging of subsurface objects with acoustic resonant metalens , 2013 .

[16]  Christina J. Naify,et al.  Experimental realization of a variable index transmission line metamaterial as an acoustic leaky-wave antenna , 2013 .

[17]  Anne-Christine Hladky-Hennion,et al.  Negative refraction of acoustic waves using a foam-like metallic structure , 2013 .

[18]  Bin Liang,et al.  Acoustic Illusion near Boundaries of Arbitrary Curved Geometry , 2013, Scientific Reports.

[19]  S. Cummer,et al.  Measurement of a broadband negative index with space-coiling acoustic metamaterials. , 2012, Physical review letters.

[20]  P. Burgholzer,et al.  Focusing and subwavelength imaging of surface acoustic waves in a solid-air phononic crystal , 2012 .

[21]  Jensen Li,et al.  Extreme acoustic metamaterial by coiling up space. , 2012, Physical review letters.

[22]  Xueqin Huang,et al.  Dirac cones at k→=0 in acoustic crystals and zero refractive index acoustic materials , 2012 .

[23]  Bin Liang,et al.  Acoustic cloaking by a superlens with single-negative materials. , 2011, Physical review letters.

[24]  Chunguang Xia,et al.  Broadband acoustic cloak for ultrasound waves. , 2010, Physical review letters.

[25]  Xiaobo Yin,et al.  A holey-structured metamaterial for acoustic deep-subwavelength imaging , 2011 .

[26]  Hervé Lissek,et al.  Acoustic transmission line metamaterial with negative/zero/positive refractive index , 2010 .

[27]  Sam-Hyeon Lee,et al.  Composite acoustic medium with simultaneously negative density and modulus. , 2010, Physical review letters.

[28]  N. Fang,et al.  Focusing ultrasound with an acoustic metamaterial network. , 2009, Physical review letters.

[29]  Daniel Torrent,et al.  Acoustic cloaking in two dimensions: a feasible approach , 2008 .

[30]  A. Norris.  Acoustic cloaking theory , 2008, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[31]  Huanyang Chen,et al.  Acoustic cloaking in three dimensions using acoustic metamaterials , 2007 .

[32]  Chunyin Qiu,et al.  Metamaterial with simultaneously negative bulk modulus and mass density. , 2007, Physical review letters.

[33]  S. Cummer,et al.  One path to acoustic cloaking , 2007 .

[34]  N. Fang,et al.  Ultrasonic metamaterials with negative modulus , 2006, Nature materials.

[35]  T. Itoh,et al.  Planar distributed structures with negative refractive index , 2004, IEEE Transactions on Microwave Theory and Techniques.

[36]  T. Itoh,et al.  Characteristics of the composite right/left-handed transmission lines , 2004, IEEE Microwave and Wireless Components Letters.

[37]  Steven G. Johnson,et al.  Subwavelength imaging in photonic crystals , 2003 .

[38]  T. Itoh,et al.  Surface plasmons at the interface between right-handed and left-handed 2D metamaterials , 2003, IEEE Antennas and Propagation Society International Symposium. Digest. Held in conjunction with: USNC/CNC/URSI North American Radio Sci. Meeting (Cat. No.03CH37450).

[39]  M. Rosenbluth,et al.  Limitations on subdiffraction imaging with a negative refractive index slab , 2002, cond-mat/0206568.

[40]  G. Eleftheriades,et al.  Planar negative refractive index media using periodically L-C loaded transmission lines , 2002 .

[41]  T. Itoh,et al.  Application of the transmission line theory of left-handed (LH) materials to the realization of a microstrip "LH line" , 2002, IEEE Antennas and Propagation Society International Symposium (IEEE Cat. No.02CH37313).

[42]  A. Oliner.  A periodic-structure negative-refractive-index medium without resonant elements , 2002 .

[43]  J. Pendry,et al.  Negative refraction makes a perfect lens , 2000, Physical review letters.