Programmable Acoustic Wave Control

• Programmable acoustic wave control is the dynamic manipulation of wave amplitude, phase, and frequency through reconfigurable hardware and materials.
• It spans from classical GHz-range filters to quantum phononic state engineering, enhancing applications in signal processing, imaging, and haptics.
• Techniques include electromechanical modulation, ML-driven control, and integrated circuitry, offering high precision and scalable reprogrammability.

Programmable acoustic wave control refers to the precise, real-time manipulation of acoustic wave amplitude, phase, frequency, dispersion, topology, and even quantum state through hardware, materials, and algorithms that can be reconfigured or dynamically tuned. Implementations span classical GHz-range filters, quantum phononic state engineering, electronically modulated metasurfaces, nonlinear self-assembled lattices, and machine learning–driven control over metamaterial wave dynamics. Key progress has enabled device architectures that allow for full programmability both at the circuit level and at the meta-material scale, with implications for signal processing, quantum information, imaging, haptics, and energy management.

1. Quantum Programmable Control of Phonons

Programmable quantum acoustic wave control has been demonstrated by coupling a superconducting transmon qubit to a single-mode surface acoustic wave (SAW) resonator via an rf-SQUID–based inductor on a flip-chip assembly, forming a macroscopic hybrid quantum system (Satzinger et al., 2018). The Jaynes–Cummings Hamiltonian describes the qubit–phonon interaction:

$$H = \hbar\omega_q\,\frac{\sigma_z}{2} + \hbar\omega_m\,a^\dagger a + \hbar g\,(a\,\sigma_+ + a^\dagger\,\sigma_-)$$

Here, $g$ (tunable up to $7.3$ MHz) yields programmable phonon “gates” via precise flux-pulses and microwave drives to swap, prepare, and map Fock and superposed phononic states. Wigner tomography reconstructs the resonator state via coherent displacement and parity measurements; fidelities for $|0\rangle$, $|1\rangle$, and $(|0\rangle + |1\rangle)/\sqrt{2}$ reach 0.985, 0.858, and 0.945 respectively. The platform enables on-demand generation, storage, and readout of arbitrary mechanical quantum states as well as phonon-mediated coupling between disparate quantum subsystems.

2. Metamaterials and Acoustic Metasurfaces: Static and Spatiotemporal Programmability

Programmable metasurfaces leverage spatial, temporal, and topological controls to manipulate wavefronts, harmonics, and scattering. Designs include:

• Hyperuniform phononic nanostructures: Bandgap-like suppression is achieved by distributing gold nanopillars in stealthy hyperuniform patterns on LiNbO₃ (Diego et al., 8 Jan 2025). Waveguides “carved” into this pattern transmit acoustic energy in otherwise opaque spectral ranges; freeform routing, including S-shaped channels, is possible. Dynamic reconfiguration is feasible via electrostatic, piezoelectric, phase-change, or micro-fluidic actuation, paving the way for arbitrary programmable GHz-range devices.
• Electromechanical space–time-coding metasurfaces: Meta-atoms with fast-actuated Helmholtz cavities can encode arbitrary space–time binary phase patterns for spectral and spatial shaping (Rajabalipanah et al., 2020). Programmable coding sequences engineer harmonic generation and beam steering; conversion efficiency for harmonics exceeds 80% for optimized codes. Real-time adaptive beam patterns and multi-frequency imaging modes are possible.
• Two-sided acoustic metascreens: Broadband control over both reflection and transmission phase/amplitude is enabled by tuning the cross-sectional geometry of subwavelength air channels within each unit cell (Chen et al., 12 Mar 2024). Three geometric degrees of freedom map independently onto reflected and transmitted wave parameters across 4–8 kHz, supporting fully programmable diffusers, 3D holography, and sound-field engineering.
• Phase and amplitude geometric controls: Continuous-amplitude modulation (grayscale acoustic masking) is realized passively via geometric-phase interference between two mode-conversion paths in deep-subwavelength meta-atoms arranged with a programmable orientation θ; the output amplitude is $A_{\text{out}}(\theta) = 2|t_0|P_0|\cos(q\theta)|$ (Liu et al., 10 Oct 2024).

3. Active, Electronically and Thermally Tunable Architectures

Active manipulation is enabled via direct electro-acoustic, thermal, or magnetic control:

• Electronically modulated SAW circuits: On-chip phase, amplitude, and frequency shifting of gigahertz-range SAWs is implemented via programmable electrodes on LiNbO₃, supporting serrodyne phase modulation, Mach–Zehnder amplitude modulation (>15 dB extinction), and nonreciprocal (isolation >40 dB) signal routing (Shao et al., 2021). The phase shift obeys $\phi(t) = \pi V(t)/V_\pi$, with $\sim 1$ kHz bandwidth, sub-phonon noise, and compatibility with quantum processors.
• Thermo-acoustic modulation: Resistive heating of integrated microheaters adjacent to SAW waveguides and cavities provides continuous phase and amplitude tuning (Shao et al., 2022, Bilobran et al., 2020). Phase changes up to $>720^\circ$, responsivities 2.6°/mW (bulk LN), switching speeds 18–120 Hz, and robust amplitude modulation via MZI architectures are practical; transient response times are $\sim$200–1000 ms.
• Magnetically programmable filters: The center frequency and attenuation depth of SAW notch filters can be toggled by programming the magnetization state (parallel/antiparallel) of dense arrays of Co/Ni islets exhibiting perpendicular magnetic anisotropy on LiTaO₃ substrates (Steinbauer et al., 31 Jul 2025). Magnetostatic stray-field interactions shift spin-wave dispersion by up to 1.25 GHz in 2D arrays, yielding on/off transmission changes of nearly 29 dB/mm at 3.8 GHz.

4. Algorithmic and Machine Learning–Driven Programmable Control

Algorithmic frameworks now enable direct mapping of hardware and metamaterial states to acoustical objectives via interpretable ML and control pipelines:

• Physics-informed ML control: Trainable neural networks with embedded physics (PDE and PML layers) generalize wave control to arbitrary metamaterial configurations, fully capturing dissipative and scattering effects (Shah et al., 2023). Model-predictive control (MPC) adapts scatterer geometry in real time to minimize or focus scattered energy. Only low-resolution wave snapshots are required as input, supporting partial observability.
• Sparse robotic actuation: Explicit 1D latent physics models connected to sparse actuator–sensor networks allow robust MPC of scattered energy using robotic manipulation of scatterer locations and dimensions, with interpretable physical guarantees and competitive performance to semi-analytical classical methods (Shah et al., 12 Feb 2025). Fast (<10×) inference and sample-efficiency compared to NODE-based black-box networks are achieved.

5. Programmable Integrated Circuits and Large-Scale Systems

Scaling programmable acoustics to circuit and chip-level architectures is now feasible:

• Phononic ICs: High-density integration (3,000 elements/cm²) of gigahertz-frequency GaN-on-sapphire building blocks—waveguides, Y-splitters, MMIs, microring resonators, polarisation converters, and thermo-elastic phase shifters—enables 128-way splitting, 21-channel frequency demultiplexing (3.8 MHz resolution), and four-channel frequency synthesizers with switching times near 0.1–1 ms (Xu et al., 30 Oct 2025).
• Programmable vibrotactile metamaterials: Dual-state unit cells harness commodity LRAs to switch in real time between active (displacement source) and passive (resonator) states, sculpting subwavelength bandgaps for millisecond-speed spatial encoding of haptic stimuli (Daunizeau et al., 19 Aug 2024). Reconfigurable tactile pixels and paths are demonstrated on $<$25 ms timescales, with resilience to boundary condition drift.

6. Nonlinear, Topological, and Phase-Transition–Enabled Control

Nonlinear and topological regimes extend programmability beyond static bandstructure:

• Feedback-based topological metamaterials: Arrays of transducers/sensors in a slab waveguide with programmable impedance feedback engineer valley Hall/topologically protected channels for robust, real-time steerable beams along arbitrarily shaped software-defined paths (Sirota et al., 2020). 100% transmission along zig-zag interfaces and chiral one-way beams through corners are achieved; nonlocal/time-varying feedback supports arbitrary dispersion engineering.
• Phase-transitioning lattices: Self-assembled magnetic disk lattices feature two programmable geometric phases (plus, square), each with a distinct acoustic dispersion; real-time sliding of the boundary toggles stop-band and pass-band filtering for sub-Hz to several Hz signals (Watkins et al., 2021). >40 dB insertion loss in stop-band and reversible, tunable bandstructure modulation is achievable within seconds.
• Temporal effective media: Time-domain modulation of resonant strength $a_i(t)$ or frequency $\omega_{0,i}(t)$ in multi-resonator metamaterials yields explicit averaging rules for the effective susceptibility $\chi_{i,\text{eff}}$ (Zhu et al., 9 May 2025). For low-frequency (dispersive) modes, modulating $a_i$ leads to direct temporal averages $\chi_{i,\text{eff}}=\langle\chi_i\rangle$, while modulating $\omega_{0,i}$ leads to reciprocal averages $1/\chi_{i,\text{eff}}=\langle1/\chi_i\rangle$. High-frequency modes are renormalized as nondispersive backgrounds. These principles underpin the design of programmable non-Hermitian amplifiers, topologically robust waveguides, and filters.

7. Design Rules, Comparative Metrics, and Outlook

Programmable acoustic wave control architecture is dictated by desired control dimension (quantum/classical, amplitude/phase/frequency/topology), operating frequency range (Hz-GHz), reconfiguration method (electrical, thermal, magnetic, mechanical), and scale (unit cell, integrated circuit, spatial array). Tables below summarize main device classes and capabilities:

Method	Control Knob	Bandwidth
Quantum qubit–SAW (Satzinger et al., 2018)	Flux, microwave pulse	GHz, Fock/superposed states
Metasurface (Rajabalipanah et al., 2020)	Phase, time coding	kHz–MHz, harmonics
Electro-acoustic (Shao et al., 2021)	Voltage waveform	100 kHz–10 GHz
Thermo-acoustic (Shao et al., 2022)	Microheater power	MHz, ms switching
Magnetostrictive (Steinbauer et al., 31 Jul 2025)	Magnetization	GHz, static to ms
ML/robotic ((Shah et al., 2023)/(Shah et al., 12 Feb 2025))	Metamaterial geometry, actuator signal	Hz–kHz, s–ms

Performance is fundamentally limited by loss, switching speed, spatial resolution, and fabrication constraints. Full reprogrammability is achieved through stacking spatial, temporal, and physical control layers, and future directions include integration with CMOS, quantum processors, broadband haptics, opto-acoustic hybrids, and algorithmic platforms for dynamic design and adaptation.