Dynamic generation and modulation of acoustic bottle-beams by metasurfaces

Scientific Reports, Aug 2018

Acoustic bottle-beams have been realized by acoustic metasurfaces (AMs) composed of space-coiling subunits. By manipulating the transmitted acoustical phase, the special AM can generate two intersecting accelerating beams along the designed convex trajectories, forming the acoustic bottle-beam. The transmitted acoustic bottle-beams are investigated theoretically and demonstrated numerically. We find that the shape and area of the acoustic bottle-beam could be statically controlled by designing the AM as well as dynamically modulated by the incident angles. In addition, the highly efficient acoustic focusing could be obtained at the convergence point of the bottle-beams, which also could be adjusted dynamically by the incident angles. It is further found that this focusing is robust against the obstacle scattering. The realization and manipulation of acoustic bottle-beams may have potential applications in biomedical imaging/therapy and non-destructive evaluation.

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Dynamic generation and modulation of acoustic bottle-beams by metasurfaces

Abstract Acoustic bottle-beams have been realized by acoustic metasurfaces (AMs) composed of space-coiling subunits. By manipulating the transmitted acoustical phase, the special AM can generate two intersecting accelerating beams along the designed convex trajectories, forming the acoustic bottle-beam. The transmitted acoustic bottle-beams are investigated theoretically and demonstrated numerically. We find that the shape and area of the acoustic bottle-beam could be statically controlled by designing the AM as well as dynamically modulated by the incident angles. In addition, the highly efficient acoustic focusing could be obtained at the convergence point of the bottle-beams, which also could be adjusted dynamically by the incident angles. It is further found that this focusing is robust against the obstacle scattering. The realization and manipulation of acoustic bottle-beams may have potential applications in biomedical imaging/therapy and non-destructive evaluation. Introduction Bottle-beam has become a subject of immense interest in the past decade because of their attractive fundamentals and applications1,2,3,4,5,6,7,8. Initially, many efforts have been devoted into optical bottle-beams, which were mainly used in optical tweezers for trapping and manipulating small particles9,10,11,12,13. Inspired by optical bottle-beams, acoustic bottle-beams have also received increasing attention due to their potential applications in micro-particle manipulation, medical ultrasound, and ultrasonic imaging14,15,16. Up to now, the generations of the acoustic bottle-beams depend on the transducer arrays14,15. However, the bulky size and sophisticated configuration of the transducer design hamper their further applications. The emergence of metasurfaces (artificially engineered surfaces comprising phase shifters) provides a new way to manipulate wavefront freely17,18,19. In particular, the metasurface can be fashioned into a compact planar profile with subwavelength thickness, thereby reducing the size of acoustic device. Many novel acoustic phenomena including negative extraordinary reflection/refraction20, diffuse reflection21, focusing22,23,24, and beam steering25,26,27 have been realized based on acoustic metasurfaces (AMs). In this work, we achieve the acoustic bottle-beam using well-designed AMs. A recent proposed three-layer acoustic space-coiling (TAS) structure is used as subunits to build the AM28 and the thickness of acoustic bottle-beam generator can be reduced down to 0.22λ. The acoustic field distributions of the acoustic bottle-beams have been demonstrated numerically using finite element method (FEM). It is found that the shape and area of the bottle-beams can be dynamically controlled by adjusting the geometry of the space-coiling subunit or the incident angle. In addition, we further study the focus performance of the generated acoustic bottle-beams. Results We consider the coordinate system depicted in Fig. 1(a). An acoustic plane wave propagates from the down side into the AM (brown line) placed in the x-axis. x = f(z) denotes an arbitrary designed trajectory (red line), which will be realized by the transmitted acoustic waves with the spatial phase profiles through the AM. The spatial phase profile Φ(x) can be expressed as $${\rm{\Phi }}(x)=\varphi (x)+\varphi ^{\prime} (x,\phi ),$$ (1) where ϕ(x) is the phase shift caused by the AM and \(\varphi ^{\prime} (x,\phi )\) is the phase shift due to the incident angle φ. When an acoustic plane wave normally impinges on the AM, \(\varphi ^{\prime} (x,\phi )=0\). Suppose that (x0, z0) is a point on the trajectory and θ is the angle between the z-axis and the tangent line (blue line) through the point (x0,z0). The cross point of the tangent line and the x-axis is (x, 0). According to the Fermat’s principle29, the derivative of the phase accumulated along the actual trajectory should be zero with respect to infinitesimal variations of the path. The phase relation depicted in the light blue circle in Fig. 1(a) can be described as $${\rm{\Phi }}(x)+d{\rm{\Phi }}(x)+k\cdot dx\cdot \,\sin (\theta )={\rm{\Phi }}(x),$$ (2) where dΦ(x) represents the phase shift, dx is the infinitesimal distance between two cross points along the x direction, and k is the wavenumber. Then, the relation between the spatial phase profile Φ(x) and the angle θ can be deduced as $$\frac{d{\rm{\Phi }}(x)}{dx}=-\,k\,\sin (\theta )\Rightarrow \frac{d\varphi (x)}{dx}+\frac{d\varphi ^{\prime} (x,\phi )}{dx}=-\,k\frac{\tan (\theta )}{\sqrt{1+{\tan }^{2}(\theta )}}.$$ (3) Figure 1 Illustration of an arbitrary convex trajectory x = f(z) (red line), the tangent line (blue lines) and the AM (brown line). \({\rm{\Phi }}(x)=\varphi (x)+\varphi ^{\prime} (x,\phi )\) is the spatial phase profile in the x-axis, where ϕ(x) is the phase shift caused by the AM and \(\varphi ^{\prime} (x,\phi )\) is the phase shift caused by the incident angle φ. x0,z0 is a poi (...truncated)


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Di-Chao Chen, Xing-Feng Zhu, Qi Wei, Da-Jian Wu, Xiao-Jun Liu. Dynamic generation and modulation of acoustic bottle-beams by metasurfaces, Scientific Reports, 2018, Issue: 8, DOI: 10.1038/s41598-018-31066-5