Phononic Integrated Circuitry

• Phononic integrated circuitry is an engineered micro- and nanoscale platform that manipulates GHz acoustic phonons via guided modes in piezoelectric or high-index-contrast substrates.
• Its architecture features precisely designed waveguides, couplers, splitters, resonators, and modulators using materials such as GaN, LiNbO₃, and diamond for high-density signal routing.
• These circuits support versatile applications including RF signal processing, quantum state manipulation, and robust nonreciprocal phononic transport with topologically protected features.

Phononic integrated circuitry (PnIC) is an engineered micro- and nanoscale platform for manipulating gigahertz (GHz) elastic waves—acoustic phonons—by analogy with electronic and photonic integrated circuits. PnICs realize programmable, high-density signal routing, filtering, splitting, phase control, and multi-channel signal processing using guided acoustic modes in piezoelectric or high-index-contrast substrates. Enabled by advances in materials (e.g., GaN, LiNbO₃, diamond, silicon), scalable fabrication, and gigahertz-frequency design methodologies, PnICs provide a distinct physical layer in information processing, complementary to electrons and photons, for applications in RF signal processing, quantum transduction, sensing, and inertial measurement (Xu et al., 30 Oct 2025, Duan et al., 20 Nov 2025).

1. Materials Platforms, Guiding Mechanisms, and Waveguide Design

PnICs exploit materials with strong acoustic index contrast and, usually, moderate to strong piezoelectricity. Prominent platforms include:

• GaN on Sapphire or SiC: GaN (density ρ ≈ 6150 kg/m³, vₜ ≈ 5.3–4.5 km/s), on high-velocity substrates (sapphire v ≈ 11 km/s, SiC v ≈ 7.6 km/s), yields strong index contrast without suspension (Bicer et al., 2023, Bicer et al., 2021, Wang et al., 2020). Waveguide cores are typically 0.5–1.5 μm thick, widths 1–3 μm, supporting Rayleigh-like and Love-like surface acoustic modes.
• Lithium Niobate on Sapphire (LNOI/LNOS): Thin-film LiNbO₃ (t ≈ 500–700 nm) on sapphire provides both high piezoelectric coefficients (d₂₄ ≈ 70 pC/N), k² ≈ 0.15, and large index contrast, supporting GHz bandguiding and efficient interdigital transducer (IDT) coupling (Mayor et al., 2020, Duan et al., 20 Nov 2025).
• Silicon, Diamond, and AlN Platforms: Silicon-on-insulator and diamond support structures for quantum applications and high-coherence; diamond with integrated AlN IDTs supports GHz surface acoustic wave (SAW) routing, crucial for coupling to strain-sensitive color centers (Ding et al., 2023, Patel et al., 2017).
• Modal Engineering: Both quasi-Rayleigh (out-of-plane) and quasi-Love (in-plane) modes are routinely engineered. Dispersion near 1–5 GHz is approximately linear, ω(k) ≈ v_p·k + αk³, with v_p ≈ 3–5 km/s (Xu et al., 30 Oct 2025). Adiabatic tapers realize mode conversion between R and L modes with >98% efficiency (Wang et al., 2022).

Waveguide cross-sections are lithographically defined, typically ∼1 μm × ∼1 μm, supporting one or a few acoustic modes in the GHz range. Mode index contrast is set by the total internal reflection of the slow (core) layer atop a fast (substrate) layer; effective modal confinement is quantified by energy fraction in the core (often >80%).

2. Phononic Building Blocks: Couplers, Splitters, Resonators, and Modulators

Programmable PnICs leverage a suite of functional elements:

• Directional Couplers and Beam Splitters: Two parallel waveguides evanescently coupled realize beam splitters with tunable ratios determined by coupling length L_c = π/(2κ), with κ the coupling coefficient. Measured 50:50 Y-splitters exhibit broadband operation with insertion loss <0.5 dB (Xu et al., 30 Oct 2025, Zivari et al., 2023).
• Multimode Interferometers (MMI): Wide waveguides (∼8 μm) support self-imaging; interferometer lengths follow L_mmi = (3λ_g W_eff)/(4n_eff), allowing N-way splitting or combining (Xu et al., 30 Oct 2025).
• Resonators: Microring or racetrack resonators (R ≈ 50–200 μm) achieve loaded Q ≈ 10³–10⁴ at room temperature, up to several ×10⁴ at cryogenic temperatures (f·Q ≈ 10¹⁴–10¹⁵), bandwidths set by group velocity and circumference (Bicer et al., 2023, Xu et al., 2022).
• Bandgap Engineering: Periodic gratings in waveguides open stopbands (Δf ≈ 33 MHz for N=200 periods), enabling filtering and isolation (Xu et al., 30 Oct 2025).
• Phase and Amplitude Modulators: Thermoacoustic Mach–Zehnder Interferometers (MZIs) achieve Δφ(P) ≈ 4.03 rad/W for L=100 μm, with switching ratios 15–29 dB. Piezo-acoustomechanical shifters achieve ±π phase shifts over 10–50 μm using 10–50 V (Taylor et al., 2021, Xu et al., 30 Oct 2025). Direct electro-acoustic tuning is possible with lithium niobate/SiN (Shao et al., 2021).

3. Integration Architectures and Density Scaling

Large-scale PnICs use design principles analogous to photonic integration:

• Tree and Mesh Topologies: Binary-tree Y-splitter layouts enable N × M power routing; a 1×128 splitter with depth l=7 achieves integration density 3.3×10³/cm² (∼100× denser than BAW/SAW filters) (Xu et al., 30 Oct 2025).
• Minimal Footprint vs. Loss Trade-offs: The product of total splitters N_layers, insertion loss per splitter IL_split, and propagation loss α_wg sets total IL_total = N_layers·IL_split + L_tot·α_wg. Reducing α_wg shrinks the required length L, increasing available bandwidth Δf ≈ v_g/(L_eff n_eff) but may enlarge the footprint (Xu et al., 30 Oct 2025).
• Hybrid and Stacked Architectures: "Zhengfu" co-integration combines phononic, photonic, and electronic domains on GaN/LiNbO₃, exploiting piezoelectric and photoelastic couplings (Duan et al., 20 Nov 2025).

Scalable optical/phononic routing employs separate waveguide bands with independent thermal or electro-optic tuning for N×M channel mapping (Zhang et al., 2 Mar 2025).

4. System-Level Demonstrations: Signal Processing, Quantum Devices, and Nonreciprocity

Robust system-level circuits are realized:

• High-Channel-Count Splitters and Demultiplexers: Demonstrated 1×128 splitter (gross area 0.0039 cm², density 3.3×10³ cm⁻²) and 21-port acoustic arrayed waveguide grating demultiplexer with channel spacings Δf ≈ 3.8 MHz, passband isolation >10 dB (Xu et al., 30 Oct 2025).
• Frequency Synthesizer and Reconfigurable Processing: Four-channel, MZI-controlled frequency synthesizer achieves on/off ratios of 15–29 dB and thermal phase noise <−80 dBc/Hz at 10 kHz offset (Xu et al., 30 Oct 2025).
• Active Gyroscopes and Saser-based Sensing: Brillouin saser gyroscopes on LNOI reach angle random walk (ARW) sensitivity of ∼0.1 deg/√h using saser (phonon) readout, outperforming all-optical designs at moderate power and Q (Duan et al., 20 Nov 2025).
• Quantum Regime and Fock-State Manipulation: Single-phonon directional couplers demonstrate quantum-superposition splitting and second-order cross-correlation g^{(2)}_{om,ij} = 3–4, well above the classical threshold (Zivari et al., 2023). On-chip memories enable >90% quantum-state-transfer fidelity via programmable couplings (Taylor et al., 2021).
• Nonreciprocal Acoustic Modulation: Voltage-programmable nonreciprocal phononic circuits on LiNbO₃/SiN achieve >40 dB direction contrast at GHz, using required three-phase modulator segments for traveling-wave E-field synchronization (Shao et al., 2021).

5. Topological, Chiral, and Bulk-Immune Architectures

PnICs leverage elasticity-based topological protection and chiral states for low-loss, backscatter-immune transport:

• Topological Phononic Circuits: 2D phononic crystals implementing quantum spin Hall analogues for Lamb-like waves (Yu et al., 2017), and anomalous chiral bulk states (CABS) through finite Dirac-mass boundary engineering on thin-film LiNbO₃ achieve unidirectional, defect-immune transmission over 180–195 MHz (15 MHz bandwidth), and group velocities v_g ≈ 600–1100 m/s (Li et al., 25 Feb 2025). Transmission remains flat (<0.5 dB variation) in the presence of engineered defects, with slow-wave dispersion providing nanosecond-scale delays in sub-mm footprints.
• Programmatic Circuit Elements: Bends, splitters, spin-selective couplers, and resonators are demonstrated with negligible loss and strong robustness to disorder, given the gap-protected edge states or chiral bulk character (Yu et al., 2017, Li et al., 25 Feb 2025).

6. Performance Metrics, Practical Considerations, and Outlook

Quantitative system-level figures of merit are:

Metric	Phononic (GaN/Sapphire)	Photonic PICs	Electronic (RF)
Integration density [cm⁻²]	~3×10³	~10⁵	~10⁹ (transistors)
Bandwidth (Δf)	GHz-scale	100 GHz–THz	up to tens of GHz
Propagation loss	α ≈ 1–3 dB/mm	~0.1 dB/cm	≪1 dB/mm
Loaded Q (room T, 3–5 GHz)	≈10³–10⁴	≫10⁵ (optical)	≲10³ (BAW/SAW)
f·Q product	10¹³–10¹⁵ Hz	—	10¹⁰–10¹² Hz
Delay per mm	300 ns/mm	≲10 ps/mm	<1 ns/mm

Key challenges include thermal crosstalk in heaters, surface/interface losses, lithographic phase-matching variability, and bandwidth-lifetime trade-offs. Integration with photonics/electronics (for full hybrid chips) is progressing via shared substrates and multi-level architectures. Quantum information applications are advancing, with on-chip memories, entanglement distribution, and quantum transduction feasible through strong phonon-photon and piezo-electric couplings (Xu et al., 30 Oct 2025, Duan et al., 20 Nov 2025, Taylor et al., 2021).

Prospective directions include 3D phononic layer stacking, higher k² piezoelectrics (e.g., LiNbO₃), dynamic nonreciprocity, programmable SU(N) phononic interferometry, and large-scale hybrid quantum/cryogenic networks.

• Large-scale programmable phononic integrated circuits (Xu et al., 30 Oct 2025)
• Chip-integrated Brillouin Saser Gyroscope (Duan et al., 20 Nov 2025)
• Low-loss GHz frequency phononic integrated circuits in Gallium Nitride for compact radio-frequency acoustic wave devices (Bicer et al., 2023)
• Scalable photonic-phononic integrated circuitry for reconfigurable signal processing (Zhang et al., 2 Mar 2025)
• Reconfigurable quantum phononic circuits via piezo-acoustomechanical interactions (Taylor et al., 2021)
• A single-phonon directional coupler (Zivari et al., 2023)
• Adiabatic conversion between gigahertz quasi-Rayleigh and quasi-Love modes for phononic integrated circuits (Wang et al., 2022)
• High-frequency traveling-wave phononic cavity with sub-micron wavelength (Xu et al., 2022)
• High-acoustic-index-contrast phononic circuits: numerical modeling (Wang et al., 2020)
• Monolithic On-Chip Phononic Chiral Anomalous Bulk States on LiNbO3 Thin-films (Li et al., 25 Feb 2025)
• A Monolithic Topologically Protected Phononic Circuit (Yu et al., 2017)
• Gallium nitride phononic integrated circuits for future RF front-ends (Bicer et al., 2021)
• Integrated Phononic Waveguides in Diamond (Ding et al., 2023)
• A single-mode phononic wire (Patel et al., 2017)
• Electrical Control of Surface Acoustic Waves (Shao et al., 2021)