Systematic design and experimental demonstration of bianisotropic metasurfaces for scattering-free manipulation of acoustic wavefronts

ARTICLE DOI: 10.1038/s41467-018-03778-9 OPEN Systematic design and experimental demonstration of bianisotropic metasurfaces for scattering-free manipulation of acoustic wavefronts 1234567890():,; Junfei Li1, Chen Shen 1, Ana Díaz-Rubio2, Sergei A. Tretyakov2 & Steven A. Cummer1 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. 1 Department of Electrical and Computer Engineering, Duke University, Durham, North Carolina 27708, USA. 2 Department of Electronics and Nanoengineering, Aalto University, P. O. Box 15500, FI-00076 Aalto, Finland. These authors contributed equally: Junfei Li, Chen Shen. Correspondence and requests for materials should be addressed to S.A.T. (email: sergei.tretyakov@aalto.fi) or to S.A.C. (email: ) NATURE COMMUNICATIONS | (2018)9:1342 | DOI: 10.1038/s41467-018-03778-9 | www.nature.com/naturecommunications 1 ARTICLE NATURE COMMUNICATIONS | DOI: 10.1038/s41467-018-03778-9 T he ability to fully control the behavior of classical waves (e.g., electromagnetic and acoustic waves) has long been desired and is at present a highly active research area. Among numerous routes, metamaterials have served as a primary approach in recent years1,2. The possibilities are enabled by engineering subwavelength structures with local resonance to achieve arbitrary effective parameters not found in nature. In contrast to the volumetric modulation using metamaterials, twodimensional arrangements of subwavelength cells offer an alternative solution of molding wave propagation within a planar or nearly flat geometry. These two-dimensional patterned surfaces, termed metasurfaces, have facilitated unprecedented possibilities for controlling waves at will3,4. One of the most attractive aspects of metasurfaces is the ability to engineer the scattered wavefronts by packing phase shifts along the gradient metasurface, which have awakened interest as an approach for the design of lenses, beam splitters, and more5,6. In both electromagnetic7–9 and acoustic10–16 metamaterials, the conventional gradient metasurface design approach is based on the implementation of local phase modulation which dictates the behavior of outgoing waves according to the generalized Snell’s law (GSL)12. In acoustics, various unit cell topologies have been proposed to achieve a homogenized effective index to control the local transmitted or reflected phase10–12,14–19. They have been applied to acoustic devices for different functionalities, such as wavefront manipulation10–16, sound absorption16,19,20, asymmetric transmission21, and cloaking22,23. However, the efficiency of phase-shift devices is fundamentally restricted by the reflection and scattering into unwanted directions. To enable better performance, many approaches have been applied to improve the transmission of the unit cells through impedance matching17,24–28. However, recent work has shown that the local phase gradient alone cannot provide full control over the scattered wave29–35. Consider anomalous refraction as an example, which is the simplest functionality offered by gradient metasurfaces in transmission. For an optimal performance, the metasurface must transmit all the illuminating energy into another arbitrary direction. As was pointed out for electromagnetic and acoustic waves, the fundamental limitation associated with all conventional GSL designs originates in the impedance mismatch between incident and refracted waves. To overcome the problem, one has to control not only the phase gradient along the metasurfaces but also the impedance matching between the incident and the desired scattered waves. Rigorous analysis of the problem has shown that the macroscopic impedance matching required for theoretically perfect anomalous refraction of plane waves can be realized if the metasurface exhibits bianisotropy: magneto-electric coupling for electromagnetic metasurfaces30–32 and Willis coupling for the acoustic counterpart29,36,37. The bianisotropic response can be implemented by asymmetric unit cells, where the scattered fields are different depending on the direction of illumination. For electromagnetic metasurfaces, typical solutions are based on three cascaded impedance layers. By independently controlling the impedance of each layer, the asymmetric response can be fully controlled38,39. These structures have been numerically and experimentally verified. In acoustics, however, practical design or experimental realization of perfect anomalous refractive metasufaces has remained scarce. Interest in bianisotropy in acoustics begun recently37,40,41. Bianisotropy provide two new possibilities for acoustic metasurfaces: independently control the reflection and transmission phases40, or the difference in the reflection phases41. A deep analysis of the physics behind this phenomenon and clear analogy between electromagnetic and acoustic bianisotropy has been 2 NATURE COMMUNICATIONS | (2018)9:1342 reported37. These results indicate that acoustic bianisotropy could bring new directions for designing efficient metasurfaces, as in the electromagnetic counterpart. The next step is designing acoustic metasurfaces, which benefit from bianisotropy. Bianisotropic meta-atoms in macroscopic acoustic metasurfaces for wavefront modulation have been recently proposed by Koo et al.40 where different gradients were applied in reflection and transmission to control the reflected and transmitted wavefronts simultaneously. However, part of the energy will be scattered without control. Scattering-free manipulation of the wavefronts requires strict control over the metaatom properties depending on the desired transformation29. An approach for perfect anomalous refraction was theoretically proposed using three membranes29. However, the surface tension, uniformity, and durability, etc. of the membranes are extremely difficult to control and it is questionable whether this design can be practically realized. To design bianisotropic metasurfaces, one has to deal with three important issues. First, the tangential dimension of the meta- (...truncated)