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Chojnacki B, Schynol K, Halek M, Muniak A. Sustainable Perforated Acoustic Wooden Panels Designed Using Third-Degree-of-Freedom Bezier Curves with Broadband Sound Absorption Coefficients. MATERIALS (BASEL, SWITZERLAND) 2023; 16:6089. [PMID: 37763367 PMCID: PMC10532742 DOI: 10.3390/ma16186089] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/31/2023] [Revised: 08/29/2023] [Accepted: 08/31/2023] [Indexed: 09/29/2023]
Abstract
The current interior design scope places high demands on acoustic treatment manufacturers. The state of the art does not provide satisfactory material proposals for architects to satisfy design needs. There is a need for a novel approach concerning decorative, recognized materials that adapts them to the acoustic surface properties. The final design proposed in this study presents a modern functional solution with high acoustic properties, which can be produced with sustainable materials such as FSC wood and has a low environmental impact because of its low waste production. This research presents the complete design process of a novel type of wooden acoustic panel. A comprehensive explanation of the scientific development is covered, including basic material testing in an impedance tube, FEM simulations of the initial designs, and final measurements in a reverberation chamber. The solution's novelty is based on the optimized placement of the perforation holes on the surface of a wooden overlay using a ship deck optimization algorithm. The methods used cover the original solution of mixing FEM modeling of the surface impedance with the application of the Jeong-Thomasson correction for random incidence sound absorption coefficient simulation. The contribution of this research is the development of wooden perforated panels with Class A sound absorption and an overall depth of 90 mm, including the 50 mm depth of the backing material. The discussion will explain the difficulties of working with this material and the need for a combination of the aesthetic and acoustic sides of the project.
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Affiliation(s)
- Bartlomiej Chojnacki
- Department of Mechanics and Vibroacoustics, AGH University of Science and Technology, Mickiewicza Av. 30, 30-059 Cracow, Poland
| | - Kamil Schynol
- Form At Wood sp. z o.o., Technologiczna 2, 45-839 Opole, Poland; (K.S.); (M.H.)
| | - Mateusz Halek
- Form At Wood sp. z o.o., Technologiczna 2, 45-839 Opole, Poland; (K.S.); (M.H.)
| | - Alicja Muniak
- Department of Mechanics and Vibroacoustics, AGH University of Science and Technology, Mickiewicza Av. 30, 30-059 Cracow, Poland
- Soundway Acoustics, Owocowa 17, 26-600 Radom, Poland
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2
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Wang YT, Shen Z, Neil TR, Holderied MW, Skelton EA, Craster RV. Models for resonant acoustic metasurfaces with application to moth wing ultrasound absorption. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2022; 380:20220005. [PMID: 36209814 PMCID: PMC9548399 DOI: 10.1098/rsta.2022.0005] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 01/21/2022] [Accepted: 05/04/2022] [Indexed: 06/16/2023]
Abstract
Taking as bioinspiration the remarkable acoustic absorption properties of moth wings, we develop a simple analytical model that describes the interaction between acoustic pressure fields, and thin elastic plates incorporating resonant sub-structures. The moth wing is an exemplar of a natural acoustic metamaterial; the wings are deeply subwavelength in thickness at the frequencies of interest, the absorption is broadband and the tiny scales resonate on the moth wing acting in concert. The simplified model incorporates only the essential physics and the scales are idealized to flat rigid rectangular plates coupled via a spring to an elastic plate that forms the wing; all the components are deep-subwavelength at desired frequencies. Based on Fourier analysis, complemented by phenomenological modelling, our theory shows excellent agreement with simulation mimicking the moth-wing structure. Moth wings operate as broadband sound absorbers employing a range of scale sizes. We demonstrate that a random distribution of scale sizes generates a broadband absorption spectrum. To further illustrate the potential of the model, we design a deeply sub-wavelength acoustic counterpart of electromagnetically induced reflectance. This article is part of the theme issue 'Wave generation and transmission in multi-scale complex media and structured metamaterials (part 2)'.
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Affiliation(s)
- Yao-Ting Wang
- Department of Mathematics, Imperial College London, London SW7 2AZ, UK
| | - Zhiyuan Shen
- School of Biological Sciences, University of Bristol, Bristol BS8 1TQ, UK
| | - Thomas R. Neil
- School of Biological Sciences, University of Bristol, Bristol BS8 1TQ, UK
| | - Marc W. Holderied
- School of Biological Sciences, University of Bristol, Bristol BS8 1TQ, UK
| | | | - Richard V. Craster
- Department of Mathematics, Imperial College London, London SW7 2AZ, UK
- Department of Mechanical Engineering, Imperial College London, London SW7 2AZ, UK
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Meng Y, Romero-García V, Gabard G, Groby JP, Bricault C, Goudé S, Sheng P. Fundamental constraints on broadband passive acoustic treatments in unidimensional scattering problems. Proc Math Phys Eng Sci 2022. [DOI: 10.1098/rspa.2022.0287] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022] Open
Abstract
In a passive lossy acoustical system, sum rules derived from passivity explicitly relate the broadband response to the spatial dimension of the system, which provide important design criteria as well. In this work, the theory of Herglotz function is applied systematically to derive sum rules for unidimensional scattering problems relying on passive acoustic treatments which are generally made of rigid, motionless and subwavelength structures saturated by air. The rigid-boundary reflection, soft-boundary reflection and transmission problems are analysed. The derived sum rules are applied for guiding the designs of passive absorbers and mufflers: the required minimum space is directly predicted from the target (i.e. the desired absorption or transmission-loss spectra) without any specific design. Besides, it is possible to break this type of sum rules and fundamental constraints in particular cases. This property, if well used, could result in ultra-compact absorbers working at long wavelength up to infinity.
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Affiliation(s)
- Yang Meng
- Laboratoire d’Acoustique de l’Université du Mans, UMR CNRS 6613, Institut d’Acoustique—Graduate School, CNRS, Le Mans Université, Le Mans, France
| | - Vicente Romero-García
- Laboratoire d’Acoustique de l’Université du Mans, UMR CNRS 6613, Institut d’Acoustique—Graduate School, CNRS, Le Mans Université, Le Mans, France
- Departamento de Matemática Aplicada, Instituto Universitario de Matemática Pura y Aplicada, Universitat Politècnica de València, Camino de Vera, s/n, València 46022, Spain
| | - Gwénaël Gabard
- Laboratoire d’Acoustique de l’Université du Mans, UMR CNRS 6613, Institut d’Acoustique—Graduate School, CNRS, Le Mans Université, Le Mans, France
| | - Jean-Philippe Groby
- Laboratoire d’Acoustique de l’Université du Mans, UMR CNRS 6613, Institut d’Acoustique—Graduate School, CNRS, Le Mans Université, Le Mans, France
| | - Charlie Bricault
- Vibrations and Acoustics Laboratory, Valeo Thermal Systems, Paris, France
| | - Sébastien Goudé
- Vibrations and Acoustics Laboratory, Valeo Thermal Systems, Paris, France
| | - Ping Sheng
- Department of Physics, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong, People’s Republic of China
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Design of ultra-thin underwater acoustic metasurface for broadband low-frequency diffuse reflection by deep neural networks. Sci Rep 2022; 12:12037. [PMID: 35835947 PMCID: PMC9283483 DOI: 10.1038/s41598-022-16312-1] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/26/2022] [Accepted: 07/07/2022] [Indexed: 11/30/2022] Open
Abstract
Underwater acoustic metasurfaces have broad application prospects for the stealth of underwater objects. However, problems such as a narrow operating frequency band, poor operating performance, and considerable thickness at low frequencies remain. In this study a reverse design method for ultra-thin underwater acoustic metasurfaces for low-frequency broadband is proposed using a tandem fully connected deep neural network. The tandem neural network consists of a pre-trained forward neural network and a reverse neural network, based on which a set of elements with flat phase variation and an almost equal phase shift interval in the range of 700–1150 Hz is designed. A diffuse underwater acoustic metasurface with 60 elements was designed, showing that the energy loss of the metasurface in the echo direction was greater than 10 dB. Our work opens a novel pathway for realising low-frequency wideband underwater acoustic devices, which will enable various applications in the future.
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Spiral sound-diffusing metasurfaces based on holographic vortices. Sci Rep 2021; 11:10217. [PMID: 33986336 PMCID: PMC8119454 DOI: 10.1038/s41598-021-89487-8] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/04/2020] [Accepted: 04/23/2021] [Indexed: 02/03/2023] Open
Abstract
In this work, we show that scattered acoustic vortices generated by metasurfaces with chiral symmetry present broadband unusual properties in the far-field. These metasurfaces are designed to encode the holographic field of an acoustical vortex, resulting in structures with spiral geometry. In the near field, phase dislocations with tuned topological charge emerge when the scattered waves interference destructively along the axis of the spiral metasurface. In the far field, metasurfaces based on holographic vortices inhibit specular reflections because all scattered waves also interfere destructively in the normal direction. In addition, the scattering function in the far field is unusually uniform because the reflected waves diverge spherically from the holographic focal point. In this way, by triggering vorticity, energy can be evenly reflected in all directions except to the normal. As a consequence, the designed metasurface presents a mean correlation-scattering coefficient of 0.99 (0.98 in experiments) and a mean normalized diffusion coefficient of 0.73 (0.76 in experiments) over a 4 octave frequency band. The singular features of the resulting metasurfaces with chiral geometry allow the simultaneous generation of broadband, diffuse and non-specular scattering. These three exceptional features make spiral metasurfaces extraordinary candidates for controlling acoustic scattering and generating diffuse sound reflections in several applications and branches of wave physics as underwater acoustics, biomedical ultrasound, particle manipulation devices or room acoustics.
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An Experimental Study of the Performance of a Crossed Rib Diffuser in Room Acoustic Control. APPLIED SCIENCES-BASEL 2021. [DOI: 10.3390/app11093781] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
Abstract
This paper presents a crossed rib diffuser (CRD) as an effective tool for room acoustic control. We performed an experimental investigation of its effectiveness using a specimen manufactured for this trial. The CRD is constructed by overlapping two one-dimensional (1D) periodic rib diffusers with different specifications so that they are crossed at non-right angles. The CRD achieves a higher scattering coefficient than 1D periodic rib diffusers in a wide band while maintaining the simple and friendly design of 1D periodic rib diffusers applicable to various architectural spaces. Moreover, inserting an absorbing layer between upper and lower ribs of the CRD, (CRD-A) yields a high broadband absorption coefficient. We first evaluated the random-incidence scattering coefficient of CRD using a 1/5 scaled model in comparison with those of 1D periodic diffusers assessed with a numerical method. Then, absorption coefficients for the CRD and the CRD-A were measured using a reverberation room. Subsequently, an experiment on a small meeting room with a 1D periodic rib diffuser, the CRD and the CRD-A was conducted to present performance of the CRD in room acoustic control. Impulse response measurements and evaluations of reverberation parameters (T20 and EDT) and speech clarity (D50) were conducted. Additionally, we present differences in structure of reflected sounds found for the flat wall, the CRD and the CRD-A visually using a four-channel sound field microphone.
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Abstract
Metamaterials assemble multiple subwavelength elements to create structures with extraordinary physical properties (1-4). Optical metamaterials are rare in nature and no natural acoustic metamaterials are known. Here, we reveal that the intricate scale layer on moth wings forms a metamaterial ultrasound absorber (peak absorption = 72% of sound intensity at 78 kHz) that is 111 times thinner than the longest absorbed wavelength. Individual scales act as resonant (5) unit cells that are linked via a shared wing membrane to form this metamaterial, and collectively they generate hard-to-attain broadband deep-subwavelength absorption. Their collective absorption exceeds the sum of their individual contributions. This sound absorber provides moth wings with acoustic camouflage (6) against echolocating bats. It combines broadband absorption of all frequencies used by bats with light and ultrathin structures that meet aerodynamic constraints on wing weight and thickness. The morphological implementation seen in this evolved acoustic metamaterial reveals enticing ways to design high-performance noise mitigation devices.
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Sound Absorption and Diffusion by 2D Arrays of Helmholtz Resonators. APPLIED SCIENCES-BASEL 2020. [DOI: 10.3390/app10051690] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
Abstract
We report a theoretical and experimental study of an array of Helmholtz resonators optimized to achieve both efficient sound absorption and diffusion. The analysis starts with a simplified 1D model where the plane wave approximation is used to design an array of resonators showing perfect absorption for a targeted range of frequencies. The absorption is optimized by tuning the geometry of the resonators, i.e., by tuning the viscothermal losses of each element. Experiments with the 1D array were performed in an impedance tube. The designed system is extended to 2D by periodically replicating the 1D array. The 2D system has been numerically modeled and experimentally tested in an anechoic chamber. It preserves the absorption properties of the 1D system and introduces efficient diffusion at higher frequencies due to the joint effect of resonances and multiple scattering inside the discrete 2D structure. The combined effect of sound absorption at low frequencies and sound diffusion at higher frequencies, may play a relevant role in the design of noise reduction systems for different applications.
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The Present and Future Role of Acoustic Metamaterials for Architectural and Urban Noise Mitigations. ACOUSTICS 2019. [DOI: 10.3390/acoustics1030035] [Citation(s) in RCA: 25] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 01/08/2023]
Abstract
Owing to a steep rise in urban population, there has been a continuous growth in construction of buildings, public or private transport like cars, motorbikes, trains, and planes at a global level. Hence, urban noise has become a major issue affecting the health and quality of human life. In the current environmental scenario, architectural acoustics has been directed towards controlling and manipulating sound waves at a desired level. Structural engineers and designers are moving towards green technologies, which may help improve the overall comfort level of residents. A variety of conventional sound absorbing materials are being used to reduce noise, but attenuation of low-frequency noise still remains a challenge. Recently, acoustic metamaterials that enable low-frequency sound manipulation, mitigation, and control have been widely used for architectural acoustics and traffic noise mitigation. This review article provides an overview of the role of acoustic metamaterials for architectural acoustics and road noise mitigation applications. The current challenges and prominent future directions in the field are also highlighted.
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10
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Cao WK, Wu LT, Zhang C, Ke JC, Cheng Q, Cui TJ, Jing Y. Asymmetric transmission of acoustic waves in a waveguide via gradient index metamaterials. Sci Bull (Beijing) 2019; 64:808-813. [PMID: 36659670 DOI: 10.1016/j.scib.2019.01.002] [Citation(s) in RCA: 24] [Impact Index Per Article: 4.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/30/2018] [Revised: 12/12/2018] [Accepted: 12/25/2018] [Indexed: 01/21/2023]
Abstract
We demonstrate that asymmetric acoustic wave transmission in a waveguide can be achieved via gradient index metamaterials (GIMs). We theoretically prove that the acoustic wave can be efficiently converted to surface waves (SWs) via GIMs. The GIMs in a waveguide can allow the transmission of acoustic waves in one direction but block them in the other direction. This theory is validated by experiments. Our findings may provide new applications in various scenarios such as high-efficiency acoustic couplers and noise control.
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Affiliation(s)
- Wen-Kang Cao
- State Key Laboratory of Millimeter Waves, Department of Radio Engineering, Southeast University, Nanjing 210096, China
| | - Li-Ting Wu
- State Key Laboratory of Millimeter Waves, Department of Radio Engineering, Southeast University, Nanjing 210096, China
| | - Cheng Zhang
- State Key Laboratory of Millimeter Waves, Department of Radio Engineering, Southeast University, Nanjing 210096, China
| | - Jun-Chen Ke
- State Key Laboratory of Millimeter Waves, Department of Radio Engineering, Southeast University, Nanjing 210096, China
| | - Qiang Cheng
- State Key Laboratory of Millimeter Waves, Department of Radio Engineering, Southeast University, Nanjing 210096, China.
| | - Tie-Jun Cui
- State Key Laboratory of Millimeter Waves, Department of Radio Engineering, Southeast University, Nanjing 210096, China.
| | - Yun Jing
- Department of Mechanical and Aerospace Engineering, North Carolina State University, Raleigh, NC 27695, USA.
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Cotterill PA, Nigro D, Abrahams ID, Garcia-Neefjes E, Parnell WJ. Thermo-viscous damping of acoustic waves in narrow channels: A comparison of effects in air and water. THE JOURNAL OF THE ACOUSTICAL SOCIETY OF AMERICA 2018; 144:3421. [PMID: 30599677 DOI: 10.1121/1.5078528] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/08/2018] [Accepted: 10/21/2018] [Indexed: 06/09/2023]
Abstract
Recent work in the acoustic metamaterial literature has focused on the design of metasurfaces that are capable of absorbing sound almost perfectly in narrow frequency ranges by coupling resonant effects to visco-thermal damping within their microstructure. Understanding acoustic attenuation mechanisms in narrow, viscous-fluid-filled channels is of fundamental importance in such applications. Motivated by recent work on acoustic propagation in narrow, air-filled channels, a theoretical framework is presented that demonstrates the controlling mechanisms of acoustic propagation in arbitrary Newtonian fluids, focusing on attenuation in air and water. For rigid-walled channels, whose widths are on the order of Stokes's boundary layer thickness, attenuation in air at 10 kHz can be over 200 dB m-1; in water it is less than 37 dB m-1. However, in water, fluid-structure-interaction effects can increase attenuation dramatically to over 77 dB m-1 for a steel-walled channel, with a reduction in phase-speed approaching 70%. For rigid-walled channels, approximate analytical expressions for dispersion relations are presented that are in close agreement with exact solutions over a broad range of frequencies, revealing explicitly the relationship between complex phase-speed, frequency and channel width.
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Affiliation(s)
- Philip A Cotterill
- School of Mathematics, University of Manchester, Oxford Road, Manchester, M13 9PL, United Kingdom
| | - David Nigro
- Thales United Kingdom, 350 Longwater Avenue Green Park, Reading, RG2 6GF, United Kingdom
| | - I David Abrahams
- Isaac Newton Institute, University of Cambridge, Clarkson Road, Cambridge, CB3 0EH, United Kingdom
| | - Erik Garcia-Neefjes
- School of Mathematics, University of Manchester, Oxford Road, Manchester, M13 9PL, United Kingdom
| | - William J Parnell
- School of Mathematics, University of Manchester, Oxford Road, Manchester, M13 9PL, United Kingdom
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12
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Long H, Cheng Y, Liu X. Reconfigurable sound anomalous absorptions in transparent waveguide with modularized multi-order Helmholtz resonator. Sci Rep 2018; 8:15678. [PMID: 30356082 PMCID: PMC6200729 DOI: 10.1038/s41598-018-34117-z] [Citation(s) in RCA: 23] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/11/2018] [Accepted: 10/11/2018] [Indexed: 11/18/2022] Open
Abstract
Helmholtz resonators offer an ideal platform for advanced sound absorbers, but their utility has been impeded by inherent frequency range limitations and the lack of function reconfiguration. Here, we introduce a multi-order Helmholtz resonator (MHR) that allows multiple monopolar resonant modes theoretically and experimentally. The combination of these modularized MHRs further creates reconfigurable multi-band anomalous absorbers in a two-port transparent waveguide while maintaining undisturbed air ventilation. In asymmetric absorption state through coupling of artificial sound soft boundary with preposed MHR, sound energy is almost totally absorbed in multiple frequency ranges when sound waves are incident from one side while it is largely reflected back from the opposite side. Interestingly, the original asymmetric absorber would turn into symmetric bidirectional absorber if one post MHR concatenates after the soft boundary. Using combination of identical MHRs, we demonstrate function selective asymmetric/symmetric absorber in multi-bands, highlighting the potential to use MHRs in the design of diverse devices for more versatile applications.
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Affiliation(s)
- Houyou Long
- Key Laboratory of Modern Acoustics, Department of Physics and Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing, 210093, China
| | - Ying Cheng
- Key Laboratory of Modern Acoustics, Department of Physics and Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing, 210093, China. .,State Key Laboratory of Acoustics, Institute of Acoustics, Chinese Academy of Sciences, Beijing, 100190, China.
| | - Xiaojun Liu
- Key Laboratory of Modern Acoustics, Department of Physics and Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing, 210093, China. .,State Key Laboratory of Acoustics, Institute of Acoustics, Chinese Academy of Sciences, Beijing, 100190, China.
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Li J, Shen C, Díaz-Rubio A, Tretyakov SA, Cummer SA. Systematic design and experimental demonstration of bianisotropic metasurfaces for scattering-free manipulation of acoustic wavefronts. Nat Commun 2018; 9:1342. [PMID: 29632385 PMCID: PMC5890261 DOI: 10.1038/s41467-018-03778-9] [Citation(s) in RCA: 152] [Impact Index Per Article: 25.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/28/2017] [Accepted: 03/12/2018] [Indexed: 12/03/2022] Open
Abstract
Recent advances in gradient metasurfaces have shown that by locally controlling the bianisotropic response of the cells one can ensure full control of refraction, that is, arbitrarily redirect the waves without scattering into unwanted directions. In this work, we propose and experimentally verify the use of an acoustic cell architecture that provides enough degrees of freedom to fully control the bianisotropic response and minimizes the losses. The versatility of the approach is shown through the design of three refractive metasurfaces capable of redirecting a normally incident plane wave to 60°, 70°, and 80° on transmission. The efficiency of the bianisotropic designs is over 90%, much higher than the corresponding generalized Snell’s law based designs (81%, 58%, and 35%). The proposed strategy opens a new way of designing practical and highly efficient bianisotropic metasurfaces for different functionalities, enabling nearly ideal control over the energy flow through thin metasurfaces. Acoustic bianisotropy does not exist in natural materials but can be designed with acoustic metamaterials. Here, Li et al. utilized acoustic bianisotropy and develop a practical metamaterial with improved transmission efficiency which outperforms the Generalized Snell’s Law.
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Affiliation(s)
- Junfei Li
- Department of Electrical and Computer Engineering, Duke University, Durham, North Carolina, 27708, USA
| | - Chen Shen
- Department of Electrical and Computer Engineering, Duke University, Durham, North Carolina, 27708, USA
| | - Ana Díaz-Rubio
- Department of Electronics and Nanoengineering, Aalto University, P. O. Box 15500,, FI-00076, Aalto, Finland
| | - Sergei A Tretyakov
- Department of Electronics and Nanoengineering, Aalto University, P. O. Box 15500,, FI-00076, Aalto, Finland.
| | - Steven A Cummer
- Department of Electrical and Computer Engineering, Duke University, Durham, North Carolina, 27708, USA.
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