Wide field-of-hearing metalens for aberration-free sound capture

The study addresses the long-standing limitation of planar acoustic metalenses: degraded performance at oblique incidence due to off-axis (Seidel) aberrations such as coma, field curvature, and astigmatism. Acoustic lenses are central to applications in communication, diagnostics, nondestructive evaluation, energy harvesting, tweezers, and imaging. While metamaterials, superlenses, and hyperlenses have pushed resolution limits, and optical metalenses have shown progress toward wide field-of-view imaging, the acoustic counterpart—wide field-of-hearing (FOH)—has not been introduced or realized. The authors aim to realize a wide-FOH acoustic metalens that maintains high focusing efficiency and predictable focal positions over large angles while remaining thin, planar, and compact.

Prior work spans curvilinear and Fresnel acoustic lenses for ultrasound and compact focusing, as well as metamaterial-based superlenses and hyperlenses that break the diffraction limit in optics and acoustics. Optical metalenses have advanced high-NA performance, broadband achromats, large-scale manufacturing, and wide field-of-view structured light, with efforts toward holography and LiDAR. In acoustics, numerous metasurface-based focusing approaches have been reported (e.g., impedance-matched metasurfaces, asymmetric focusing, broadband focusing, nonlocal metasurfaces, and reconfigurable/active designs). However, planar acoustic metalenses have been fundamentally limited in FOH coverage, suffering from angle-induced third-order aberrations that suppress focusing efficiency as angle increases. Wide-FOV concepts in optics based on symmetry transformation (rotational to translational) motivate an acoustic analog, but a wide-FOH acoustic metalens had not been demonstrated prior to this work.

Theory and design: The authors adopt a quadratic one-dimensional phase profile Φ(y) = −k0 y^2/(2f), derived from symmetry conversion of a spherically symmetric gradient-index lens to a planar lens, achieving a perfect transformation from rotational to translational symmetry. Under an angle of incidence θ, the effective exit-pupil phase becomes Φ_EP(y, θ) = −k0(y + f sinθ)^2/(2f) + f k0 sin^2θ, implying that oblique incidence introduces a predictable transverse focal shift of f sinθ on a planar receiving plane without requiring angle-dispersive meta-atoms. This approach preserves the point spread function across AOIs, akin to a Fourier lens, and supports wide-angle spatial filtering and compressed sensing. The modulation transfer function (MTF) is analyzed to quantify resolution for high NA (≈0.9) with f = 2λ and aperture D = 8.4λ. The effective aperture Deff = 2f defines an evanescent zone acting as a self-adjustable aperture stop that suppresses marginal rays and coma onset. Design of meta-atoms: The metalens comprises a single subwavelength layer combining Helmholtz resonators (HRs) within a straight waveguide and a zigzag channel. HRs provide impedance matching and phase compensation; the zigzag channel provides Fabry–Perot-like resonance and phase delay, while the opened straight waveguide enables efficient energy transfer. By tuning geometric parameters (notably w4 and h1), simultaneous modulation of transmission τ and phase φ is achieved with τ > 0.9 across selected unit cells. The sampling periodicity p = 1/12.5 λ ensures deep-subwavelength discretization to avoid spatial aliasing and follow rapid phase gradients. Representative geometry: w0 = 0.75λ, λ (design) = 75 mm for unit-cell studies; for experiments the operating wavelength is 100 mm (3.43 kHz). Additional parameters include h0 = 8 mm, h1 = 45 mm, w1 = w2 = h2 = 1 mm, w3 = 10 mm. The meta-atoms are angle-invariant in functionality under oblique incidence. Numerical simulation: Full-wave simulations are performed in COMSOL Multiphysics 6.1 (pressure acoustics). Air: density 1.21 kg m−3, sound speed 343 m s−1. Resin: density 1170 kg m−3, sound speed 2700 m s−1; structures treated as acoustically rigid. Experimental setup: A stereolithography (SLA) 3D-printed UV-resin metalens (fabricated in three combined sections) operates at 3.43 kHz (λ = 100 mm), chosen per printer capability and chamber size. Experiments are conducted in a 2D waveguide chamber (200 × 200 × 6 cm^3). A 22-element loudspeaker array (TC5FB00-08; Peerless) with 8 mm spacing generates plane waves. The metalens is placed 100 cm from the source. Four 1/4-inch microphones (Type 4957; Brüel & Kjær) mounted on the top plate scan a 30 × 45 cm^2 region with 1 × 1 cm^2 sampling near the focal plane. AOIs are tested from 0° to 60° in steps (also reported up to 70° for focal tracking), by tilting the metalens. Instrumentation includes a function generator (Keysight 33220A), power amplifier (NF HSA 4052), and multi-channel DAQ (Brüel & Kjær Pulse Type 3676) with Labshop software. Simulated and measured intensity distributions and PSFs are compared to theory.

• Wide field-of-hearing: The metalens demonstrates robust focusing across an angular span of approximately 140° (±70°), with focal positions following the predicted transverse shift f sinθ up to 70° AOI. - High NA and compactness: With f = 2λ and D = 8.4λ, the system achieves NA ≈ 0.9, enabling a short aperture-to-hearing plane distance and compact implementation. - Aberration suppression: The quadratic phase profile and symmetry conversion yield angle-invariant, flat-like MTF curves across AOIs and spatial frequencies, preserving PSF quality at large angles, unlike conventional hyperbolic metalenses whose MTF rapidly degrades beyond ~10° AOI. - Measured focusing performance: Simulated and experimental intensity maps at AOIs of 0°, 20°, 40°, and 60° show aberration-free focusing and good agreement with theory. The PSF full-width at half maximum (FWHM) remains near the diffraction limit across angles (representative values in the reported sequences range approximately 0.39–0.43 λ). - Focusing efficiency: The WFOH lens exhibits nearly constant focusing efficiency versus AOI up to 70°, while conventional metalenses show strong AOI-dependent degradation. The moderate absolute efficiency is attributed to the effective aperture Deff = 2f. - Signal quality: The average peak signal-to-noise ratio (PSNR) of the focused spots is 20.32 dB, indicating high-fidelity sound capture. - Additional insight: The evanescent zone outside Deff acts as a self-adjustable aperture stop, suppressing marginal rays and mitigating coma. - Fabrication and operation: A single-layer, highly transmissive metasurface (τ > 0.9 for selected cells) using HRs and zigzag channels, 3D printed in UV resin, validates the design at 3.43 kHz in air.

The work directly addresses the challenge of maintaining focusing performance over wide incident angles in planar acoustic lenses. By converting rotational symmetry (of a spherical gradient-index lens) into translational symmetry in a planar metasurface, the design produces a quadratic phase that yields predictable focal shifts (f sinθ) on a planar receiving plane and preserves PSF quality over large AOIs without requiring angle-dispersive meta-atoms. This approach minimizes off-axis aberrations such as coma and field curvature that plague conventional metalenses, resulting in flat MTFs and near-constant focusing efficiency across angles. The compact, high-NA implementation reduces the aperture-to-hearing plane distance and reception area, offering advantages for space-efficient, wide-angle source-tracking and sensing. The findings suggest broad applicability in remote acoustic collection, SONAR-like sensing, particle manipulation, and medical HIFU/imaging, and the Fourier-lens-like behavior opens opportunities in spatial filtering and compressed sensing with a thin planar platform.

The authors introduce and experimentally validate the concept of a wide field-of-hearing (WFOH) acoustic metalens that achieves aberration-free, wide-angle focusing via perfect acoustic symmetry conversion and a quadratic phase profile. A single-layer, highly transmissive metasurface delivers robust focusing across ~140° angular range with high NA and compact form factor, maintaining PSF quality and focusing efficiency across AOIs. This establishes a practical pathway for wide-angle acoustic sensing and imaging in air, with potential extensions to ultrasonic and underwater domains. Future work includes extending from one-dimensional to fully two- and three-dimensional implementations, exploring bianisotropic and non-local meta-atom designs to further enhance FOH, and addressing wideband and achromatic performance, as well as impedance-matching and boundary-layer challenges at higher frequencies (e.g., medical ultrasound).

• Demonstration is in a one-dimensional audible regime within a 2D waveguide; extension to full 2D/3D operation is future work. - The focusing efficiency, while angle-invariant, is moderated by the effective aperture constraint (Deff = 2f). - The prototype operates at a single frequency (3.43 kHz) chosen for fabrication and chamber constraints; achieving wideband and achromatic behavior remains open. - Scaling to high-frequency ultrasonic regimes will require addressing impedance mismatch, boundary-layer effects, and meta-atom periodicity constraints. - The study focuses on phase modulation (amplitude largely near unity for selected cells); broader amplitude-phase control was not exploited here.