Acoustic Geometric-Phase Meta-Array

Metasurfaces based on geometric phase acquired from the conversion of the optical spin states provide a robust control over the wavefront of light, and have been widely employed for construction of various types of functional metasurface devices. However, this powerful approach cannot be readily transferred to the manipulation of acoustic waves because acoustic waves do not possess the spin degree of freedom. Here, we propose the concept of acoustic geometric-phase meta-array by leveraging the conversion of orbital angular momentum of acoustic waves, where well-defined geometric-phases can be attained through versatile topological charge conversion processes. This work extends the concept of geometric-phase metasurface from optics to acoustics, and provides a new route for acoustic wave control.

Geometric-phase metasurfaces (GPMs) have been widely employed as an efficient and robust means to control the scattering of electromagnetic waves with the controllable geometric phase acquired via a spin conversion process [1][2][3]. Due to the simple relationship between the geometric-phase and the orientation of anisotropic nanostructures for generating the spin conversion, GPMs can be used for flexible wavefront manipulation, such as imaging [4,5], holography [6,7], harmonic generations [8,9], trapping [10,11], quantum technology [12,13], etc. However, this concept cannot be directly extended to acoustics due to the lack of such spin conversion process in acoustics. Therefore, the common strategies involved in the design of acoustic metasurfaces or metamaterials mainly focus on acoustic surface impedance engineering and effective acoustic refractive index modulation, such as Helmholtz resonators [14][15][16][17], grooves [18][19][20], coiling-space structures [21][22][23][24][25], pentamode metamaterials [26], mass-membrane system [27], just to name a few. In addition, most of the reported acoustic meta-devices can only support a given acoustic wave modulation, i.e., the functionality of acoustic meta-device is fixed once the geometry of the structures is determined. Hence, acoustic metasurfaces usually require precise spatial arrangement of the meta-atoms by following a rigorous meta-device design procedure [28]. As a result, recent works on tunable acoustic meta-atoms suffer from the resonance-based phase delay, which unavoidably couples with the transmission amplitude and requires delicate control over some critical geometry parameters [29][30][31].
In this work, we propose an acoustic meta-array based on acoustic geometric phases which are obtained through versatile acoustic vortex topological charge (TC) conversion occurring within each pixel of the meta-array-a cylindrical acoustic waveguide with judiciously engineered interior structures. Each meta-pixel waveguide, containing a number of acoustic geometric meta-plates (AGM), is designed to implement sequential manipulations on the incident acoustic wave including generation and conversion of vortex beams of various TCs. A geometric phase arises from the conversion between two different orbital angular momenta, which can be continuously controlled by varying the orientation of the conversion element, i.e., the AGM for the designated TC conversion process. As a proof of principle, flexible acoustic field manipulations including acoustic beam steering and focusing can be realized with the proposed geometric-phase meta-array. Our design opens a new avenue for flexible acoustic field generation and the controllable phase manipulation.
We start by a brief description of the geometric phase with optical metasurfaces. When a circularly polarized light is incident onto a geometric-phase metasurface, the transmitted light carries a geometric phase term of exp$% '( − *+, -/ 0, where '( and *+, refer to the spin of input and output circularly polarized light, / is the orientation angle of the nanoantenna, as illustrated by Fig. 1(a). Therefore, only the cross-polarized component of the In order to understand the mechanism of the presence of the acoustic geometric phase obtained through TC conversions, we consider a general TC conversion case which involves the orbital angular momentum transfer from TC '( to TC *+, . By defining the complex transmission of an AGM of TC and orientation angle 5 as 8 ( 5 ), then we have: The numerical calculation is conducted with the finite element method (FEM). Fig. 2 show the geometric-phase modulation obtained through the TC conversion processes.
To showcase the potential of acoustic geometric phase in wavefront manipulation, we theoretically study the beam steering and beam focusing by using the ideal geometric-phase meta-arrays described above. Fig. 3(a) shows the full-wave simulation of the beam steering via |1⟩ → |0⟩. The geometric-phase meta-array consists of 12 pixels of TC = 1. The operating wavelength is selected as 12 cm, the pixel size LV,W is 9 cm, which is slightly larger than the outer diameter of waveguide (8 cm Next, we utilize realistic acoustic meta-structures to achieve wave manipulation based on the acoustic geometric phase. Here, the acoustic meta-atoms designed for different sections are classical Helmholtz resonator-straight pipe hybrid structures [33], as shown in of the Helmholtz resonators of each layer, a high transmission can be achieved. Fig. 4(a) shows the design of two meta-plates of TC = 1 and = 2, with the detailed geometry parameters of the constituent units given in Section IV of Supplementary Material [32]. Here, AGMs of TC = 1 and = 2 are numerically investigated, and the optimized working frequency in our design is 2.88 kHz. Fig. 4 (b) shows the TC generation, conversion and detection with the above two types of AGMs, where the acoustic vortex sources are obtained by illuminating plane acoustic waves onto the meta-plate of TC = 1. Fig. 4(c) and (d) show the acoustic geometric phase (red solid triangle) and the corresponding transmitted amplitude (blue solid circle) for two systems with cascaded AGMs for realizing geometric phase based on |1⟩ → |0⟩ and |1⟩ → |−1⟩ TC conversion processes, respectively. It is obvious that the geometric-phase modulation obtained with the realistic acoustic meta-plates agrees well with theoretical predictions. However, due to the multiple scattering induced by the realistic AGMs, the transmitted field uniformity and transmission efficiency would be deteriorated when more AGMs are cascaded. In our simulation, the distance between two meta-plates in |1⟩ → |0⟩ process shown in Fig. 4(c) and the interval among three metaplates in |1⟩ → |−1⟩ process shown in Fig. 4 (d) are optimized as 30 cm and 10 cm, respectively. It should be noted that the influence of thermal viscosity on the acoustic geometric-phase modulation is negligible (see Section V of Supplementary Material [32]). In Section VI of Supplementary Material [32], we provide the full-wave simulation of broadband beam bending (from 1.9 kHz to 3.1 kHz) realized by a geometric-phase metaarray made up of the realistic acoustic meta-plates. It is found that our geometric-phase acoustic meta-array could operate in a broadband frequency range, benefitting from the dispersionless character of geometric phase.
In summary, we have proposed the concept of acoustic geometric phase generated in the process of TC conversions, which is a generalization of optical geometric phase for spin conversion. Different from the conventional resonance-type phase modulation, which relies on the geometry and usually tangled with transmission amplitude, acoustic geometric phase is highly robust, and it enables arbitrary phase manipulation by simply rotating the meta-plates.
Our work transfers the concept of optical geometric phase to acoustics, and shows its potential in constructing broadband and reconfigurable acoustic meta-devices for arbitrary field generations and manipulations.