Binary Acoustic Metasurfaces (BAMs)

• Binary acoustic metasurfaces are engineered interfaces composed of discrete pixels imparting either 0 or π phase shifts, enabling beam steering and focal manipulation.
• They utilize design strategies such as passive delay structures, 3D-printed origami, and active piezoelectric coding to achieve efficient and reconfigurable sound control.
• Experimental demonstrations reveal 30–35% diffraction efficiency, precise vortex generation, and promising applications in acoustic imaging, therapy, and manipulation.

A binary acoustic metasurface (BAM) is an engineered, subwavelength interface composed of discrete acoustic elements or “pixels,” each imparting precisely one of two possible phase shifts (0 or π) to an incident wavefront. This quantized phase control enables rapid, low-complexity synthesis of diffractive acoustic devices capable of tasks including focusing, steering, vortex generation, and programmable manipulation of sound fields. Binary quantization is realized through mechanisms such as spatial delay lines (“bricks”), bistable origami cells, piezoelectric domain inversion, or optimized material topologies. BAMs are notable for their fabrication simplicity, ease of reconfiguration, and competitive efficiency in a variety of practical and biomedical applications (Memoli et al., 2016, Hu, 18 Jan 2026, Le et al., 2024, Noguchi et al., 2020, Li et al., 2022).

1. Principles of Binary Phase Quantization

The operational basis for BAMs is the mapping of a desired continuous phase profile $\phi(x,y)$ onto a discrete, binary phase mask $\phi_q(x,y)$ with values in $\{0, \pi\}$. Formally, this is realized by quantizing $\phi(x,y)$ to the nearest multiple of $\pi$: $$\phi_q(x,y) = Q[\phi(x,y)] = \text{round}(\phi(x,y)/\pi) \cdot \pi$$ where $Q$ denotes the quantizer. In practice, phase prescriptions for focusing, steering, or vortex beams are computed from the propagation Green’s function or via time-reversal procedures when dealing with inhomogeneous media (e.g., the human skull) (Memoli et al., 2016, Hu, 18 Jan 2026).

Each pixel (or “meta-brick”) imparts this phase delay by virtue of its physical or controllable property—path length, resonance, bistable geometry, or domain polarization. The simplicity of only two phase states yields low hardware complexity and robust tolerance to fabrication errors, but at the cost of reduced diffraction efficiency compared to multi-bit designs—the theoretical limit for a binary phase grating is $\eta_\text{ideal} \approx (2/\pi)^2 \approx 0.405$ (Memoli et al., 2016, Hu, 18 Jan 2026).

2. Metasurface Architectures and Coding Strategies

2.1 Passive Delay Structures

Classic BAMs utilize subwavelength rigid “bricks,” each either providing a straight channel (state 0, delay 0) or a labyrinthine path $\Delta L = \lambda/2$ (state 1, delay $\pi$), where $\lambda = c/f$ is the wavelength at operating frequency $f$ (Memoli et al., 2016). Modular bricks enable assembly in any phase pattern, as prescribed by the quantized target wavefront.

2.2 3D-Printed Layered and Origami Metasurfaces

Additive manufacturing allows fine control over pixel geometry and bistability. One approach stacks binary-thickness PLA pixels on a thin plate, with each pixel’s height $d$ tuned to induce a phase shift $$\Delta \phi = k_1 d - k_2 d = 2\pi f d (1/c_1 - 1/c_2)$$, where $c_1$ and $c_2$ are host and pixel sound speeds, respectively. This yields near-unity amplitude transmission at the design frequency (Hu, 18 Jan 2026).

Kresling origami BAMs exploit two mechanically bistable origami cell states differing in axial height and twist: switching between “collapsed” and “deployed” states modulates the local reflection phase by $\pi$ (Le et al., 2024). This affords rapid, reversible, and electronics-free reconfigurability by applying modest force or torque to individual cells.

2.3 Active Piezoelectric Coding

Active BAMs comprise arrays of piezoelectric meta-atoms, with phase state set by the polarization orientation $p_i=\pm1$ in PZT slabs. An AC voltage $V(t)$ generates normal displacement $u_i(t)\propto d_{33}p_iV_0\cos\omega t$, leading to radiated pressure with phase $0$ (up-polled) or $\pi$ (down-polled). This binary phase is frequency independent, since it is set by permanent domain orientation rather than path-length or resonance (Li et al., 2022).

3. Computational and Optimization Frameworks

BAM design is driven by computational synthesis of the required binary phase mask for a given field objective. Key workflows include:

• Analogue-to-Digital Conversion and Wavelet Decomposition: The continuous phase profile is expanded in a localized, multi-scale basis (wavelets), coefficients quantized, and the binary mask mapped to the metasurface (Memoli et al., 2016).
• Time-Reversal and Vortex Synthesis: For complex media (e.g., skull), virtual sources are used in time-domain simulations to back-propagate the desired field; the measured incident phase is combined with synthetic vortex terms, then binarized per pixel (Hu, 18 Jan 2026).
• Topology Optimization: Binary material layouts in the unit cell are optimized using two-scale homogenization and level-set evolution to achieve target steering or modulation performance. The process iteratively solves for effective parameters $(A^*, B^*, K^{*-1}, F^*)$ and updates the domain via topological derivatives (Noguchi et al., 2020).

Table 1 summarizes representative BAM design frameworks:

Approach	Phase Control Mechanism	Design Protocol
Modular bricks	Path-length $\Delta L=0,\lambda/2$	Quantized mapping, assembly (Memoli et al., 2016)
Origami unit cells	Snap-through bistability	Mechanical state selection (Le et al., 2024)
Piezoelectric slabs	Domain orientation (up/down)	Local poling pattern (Li et al., 2022)
Topology optimization	Binary air/solid distribution	Level-set homogenization (Noguchi et al., 2020)

4. Experimental Demonstrations and Performance Metrics

BAMs have been experimentally validated across a range of functionalities:

• Focusing/Steering: Binary metasurface lenses focus or steer beams, with measured efficiencies $\eta = 30\text{–}35\%$ (diffraction), side-lobe level $<$ –10 dB, and focal spot widths within ±5% of theoretical predictions (Memoli et al., 2016, Hu, 18 Jan 2026).
• Vortex Generation: BAMs can synthesize focused ultrasound vortices of arbitrary topological charge $\ell$ inside complex media; measured phase errors are $<0.3$ rad even after aberration correction through bone (Hu, 18 Jan 2026, Li et al., 2022).
• Mechanical Reconfigurability: Multi-material origami BAMs achieve programmable reflectance profiles, with π-phase contrast bandwidths of ~±100 Hz and beam-steering tunable up to $±40^\circ$ via direct actuation (Le et al., 2024).
• Active Functionality: Piezoelectric BAMs achieve beam steering, sub-diffraction focusing (FWHM $D \approx 0.63\lambda$), acoustic vortex trapping, and broadband acoustic tweezing, using only a single electrical feed (Li et al., 2022).

Performance parameters typically measured include:

• Diffraction/transmission efficiency ($\eta$)
• Focal spot size (FWHM)
• Side-lobe level (SLL)
• Phase and amplitude fidelity (phase error $\sigma_\phi$)
• Bandwidth (stable operation over ±10–20% frequency span)
• Reconfiguration speed (mechanical or electrical)

5. Applications in Acoustic Manipulation, Imaging, and Biomedicine

BAMs’ binary coding enables diverse applications:

• Acoustic Levitation and Tweezing: Stable trapping of microparticles and droplets via rapidly reconfigurable phase gradients. BAMs with vortex coding achieve 3D trapping, manipulation, and orbital angular momentum transfer (Memoli et al., 2016, Hu, 18 Jan 2026, Li et al., 2022).
• Ultrasound Imaging: Subwavelength resolution in pulse-echo imaging, B-mode and C-mode ultrasonic imaging, and transcranially focused fields within brain-mimicking phantoms (Hu, 18 Jan 2026, Li et al., 2022).
• Therapy and Neuromodulation: Focused vortex BAMs used to steer acoustic fields through bone to induce pressure, torque, or mechanotransduction deep within tissue—enabling clot manipulation and potential neural stimulation (Hu, 18 Jan 2026).
• Programmable Acoustic Devices: Multi-material origami BAMs allow electronics-free, on-demand switching of acoustic functionalities (lensing, splitting, steering); enabling deployable and reconfigurable ultrasonic hardware (Le et al., 2024).

6. Fabrication, Scalability, and Reconfigurability

BAMs are inherently fabrication-friendly:

• Material Systems: Bricks and pixels produced in rigid plastics (ABS, epoxy, PLA), multi-material composites (e.g., VeroMagentaV+Agilus30 in origami), or PZT ceramics for active BAMs.
• Manufacturing: 3D printing, stereolithography, and CNC machining deliver high geometrical precision ($\pm$0.1 mm).
• Assembly: Modular/plug-and-play; brick or origami units slotted or glued into frames; origami and active BAMs offer in situ mechanical or electrical reconfiguration (Memoli et al., 2016, Le et al., 2024, Li et al., 2022).
• Scalability: BAMs scale from sub-cm lab prototypes (100s of pixels) to extended arrays (kilo-pixel and up) for large-aperture or high-resolution applications.

Reconfigurable BAMs (origami, piezoelectric) can switch functionalities without hardware exchange: origami units by manual actuation, piezoelectric units potentially via in situ re-poling or frequency tuning (Le et al., 2024, Li et al., 2022).

7. Limitations, Efficiency Tradeoffs, and Future Directions

Binary quantization ($B=1$ bit) limits maximum theoretical diffraction/transmission efficiency, and introduces quantization-dependent side lobes. Passive BAMs are constrained to static functionality once assembled, unless actuated (origami) or re-polable (piezoelectric). Advanced optimization (topology or adjoint-based) has shown potential in tailoring binary pixel arrangements for focused functionalities, potentially mitigating efficiency loss or customizing steering (Noguchi et al., 2020).

Recent advances extend BAM concepts to:

• Transmission through highly inhomogeneous media (e.g., correction of skull-induced aberrations by time-reversed phase coding) (Hu, 18 Jan 2026)
• Programmable, electrically or mechanically reconfigurable metasurfaces for dynamic tasks
• Integration into compact, low-cost biomedical devices (acoustic tweezers, combined imaging/manipulation platforms) (Li et al., 2022)

A plausible implication is that further increase in device versatility will depend on hybridizing active (electrical, piezoelectric) reconfiguration with mechanical bistability or topological optimization to maximize efficiency while retaining the simplicity and robustness of binary coding.

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References:

(Memoli et al., 2016): Metamaterial bricks and quantization of meta-surfaces (Hu, 18 Jan 2026): Wavefront Shaping of Ultrasound Vortex through the Human Skull Enabled by Binary Acoustic Metasurfaces (Le et al., 2024): Reconfigurable Manipulation of Sound with a Multi-material 3D-Printed Origami Metasurface (Noguchi et al., 2020): Topology optimization of acoustic metasurfaces by using a two-scale homogenization method (Li et al., 2022): Active Coding Piezoelectric Metasurfaces