Metascreen-Based Acoustic Passive Phased Array

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Metascreen-Based Acoustic Passive Phased Array

Yong Li, Xue Jiang, Bin Liang, Jian-chun Cheng, and Likun Zhang

Phys. Rev. Applied 4, 024003 – Published 6 August 2015

Abstract

Conventional phased arrays require a large number of sources in forming a complex wave front, resulting in complexity and a high cost to operate the individual sources. We present a passive phased array using an acoustic metascreen that transmits sound energy from a single source and steers the transmitted wave front to form the desired fields. The metascreen is composed of elements that have a discrete resolution along the screen at an order smaller than the wavelength, allowing for fine wave-front shaping beyond the paraxial approximation. The performance is verified in experiment by forming a self-bending beam. Our metascreen-based passive array with its simplicity and capability has applications in places where conventional active arrays are complex and have limitations.

Received 11 January 2015

DOI:https://doi.org/10.1103/PhysRevApplied.4.024003

Authors & Affiliations

Yong Li^1,2,*, Xue Jiang³, Bin Liang^3,†, Jian-chun Cheng^3,‡, and Likun Zhang^4,§

¹CNRS, Institut Jean Lamour, Vandœuvre-lès-Nancy F-54500, France
²Université de Lorraine, Institut Jean Lamour, Boulevard des Aiguillettes, BP: 70239, Vandœuvre-lès-Nancy 54506, France
³Key Laboratory of Modern Acoustics, MOE, Department of Physics, Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing 210093, People’s Republic of China
⁴Department of Physics and Center for Nonlinear Dynamics, University of Texas at Austin, Austin, Texas 78712, USA

^*yong.li@univ-lorraine.fr
^†liangbin@nju.edu.cn
^‡jccheng@nju.edu.cn
^§lzhang@chaos.utexas.edu

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Vol. 4, Iss. 2 — August 2015

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Images

Figure 1
Illustration of penetrating sound energy from a primary source through a passive screen at $x = 0$ (the thin black box) that adds a phase shift $ϕ (y)$ on transmitted fields to shape wave-front propagation along a desired path $y = f (x)$ . The illustrated sound field (pressure level in units of decibels and referenced to the maximum value) is a self-bending beam whose path is the white arc line of radius $r = 3.5 λ$ ( $λ$ is the sound wavelength) shaped from $ϕ (y) = - k (y - 2 k r \sqrt{y / r})$ .
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Figure 2
The passive screen is stacked up by an array of passive elements. (a) Each element is designed to have a hybrid structure consisting of a straight pipe of height $h_{1}$ and four Helmholtz resonators (HRs) of height $h_{3}$ ; the element dimensions are $w = λ / 2$ and $h = λ / 10$ . (b) Phase shift (red, solid) and transmission rate (blue, solid) of the hybrid structure as a function of height ratio $h_{1} / h$ (or, correspondingly, $h_{3} / h$ ), and a comparison with that of Helmholtz resonators (red and blue dashed). Other parameters are fixed as $(w_{1}, w_{2}, w_{3}) = (0.22, 0.03, 0.225) w$ and $h_{2} = 0.1 h$ that are not too small to minimize the viscous effect. (c) Simulated sound transmission through individual elements for an equally increased phase shift with a step of $π / 4$ , corresponding to the eight dots in (b) with $h_{1} / h = 0.28$ , 0.33, 0.41, 0.55, 0.16, 0.18, 0.20, and 0.24. Plotted snapshot of the sound field is referenced to the amplitude of incident plane waves.
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Figure 3
(a) Transmission coefficient and (b) phase shift as a function of frequency $f$ for the eight elements presented in Fig. 2, showing that the elements work effectively within a finite band of frequency $f$ around the Fabry-Perot resonant frequency $f_{0}$ (corresponding to $w = λ / 2$ ) shown by the gray area for $f / f_{0} \in [0.937, 1.053]$ (see text for details). The phase shift in (b) is shown as the difference of the phase shift from that provided by the element with $h_{1} / h = 0.28$ .
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Figure 4
Redirection of acoustic beams by a 150-element screen that provides a stair-step phase profile along the screen. (a) Sound fields simulated for the screen that redirects a normally incident acoustic beam of $f = f_{0}$ at an angle of 38° (denoted by green arrow) away from its incident direction (denoted by black arrow). (b) Polar directivity graph of the redirected beams measured at ten wavelengths away from the center of the screen, at $f = f_{0}$ (solid curve), and at the two cutoff frequencies in Fig. 3 (dot-dashed curves).
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Figure 5
Experimental samples and setup. (a) Fabricated samples of the eight elementary units for varying the phase from 0 to $2 π$ with a step of $π / 4$ ; the sample’s dimension is for sound waves of resonant wavelength $λ = 10 cm$ (viz., frequency $f_{0} = 3430 Hz$ in air). (b) Experimental setup for shaping monochromatic sound of frequency $f_{0}$ from a loudspeaker to form a wave front as in Fig. 1 by using an 80-unit screen sandwiched between two plexiglass plates ( $300 \times 120 \times 0.5 {cm}^{3}$ of a 2.1−cm gap. Wedge−shaped sound−absorbing foam is installed at the boundaries of the plates to mimic an anechoic environment. The speaker dimension is $3 \times 3 {cm}^{2}$ , and sound fields are measured in the scanning region using a $1 / 4$ -in. microphone (Brüel & Kjær type 4961); both magnitude and phase are recorded by referring to a signal recorded by a second microphone at a fixed point.
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Figure 6
Experimental realization of a nonparaxial self-bending beam using a screen of 80 units. (a) Distribution of the 80 elements along the screen as indicated by their discrete phase shift (the 80 red hollow circles) resembling the desired phase profile $ϕ (y)$ (black curves; see text for detail). (b) Self-bending beam measured in the scanning region of Fig. 5, where the white circle denotes the desired sound path. (c) Sound field simulated for the 80 elements and loudspeaker, where the field at $x > 0$ is sound pressure level [(SPL) normalized by the maximum value] and at $x < 0$ is a snapshot of normalized sound pressure. The white dotted rectangular region refers to the area where experimental measurements are taken. (d) Comparison of the experimental measurements with numerical simulation for the beam along the white-colored trajectory in (b) and (c).
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