Designing transparent piezoelectric metasurfaces for adaptive optics

Piezoelectric devices are widely used in robotics, precision optics, healthcare, consumer electronics, and MEMS due to compactness, lack of electromagnetic interference, low noise and fast response. Under an electric field, piezoelectric materials produce stress/strain via the inverse effect, enabling diverse vibration modes. To implement multi-functional interaction in a single device, the classic solution bonds several multilayer stacks to realize multiple degrees of freedom, e.g., combining longitudinal (33-mode) and orthogonal shear (15-mode) stacks for 3-DOF manipulators. Such systems become cumbersome and complex. Recent ordered-structure designs have enabled artificial modes (stretching, shear, bending, torsion) and up to 5-DOF actuation, but typically depend on different boundary conditions for different modes, precluding simultaneous access to multiple coupled modes under a uniform boundary. Other metamaterial approaches with nonzero piezoelectric coefficients under stress-free conditions require different unit arrangements/electric-field directions for each mode and often excitation at resonance to suppress parasitics. There is thus a practical need to achieve various vibration/motion modes from piezoelectric units under uniform boundary conditions and across a wide frequency range. To address this, the authors propose a transparent piezoelectric metasurface (PM) that, through topological design, unit dimensions, and boundary structures, simultaneously provides linear motions along X, Y, Z; rotary motions about X, Y, Z; and coupled modes with high strains over a broad frequency band. They implement the PM using transparent [001]-poled PIN-PMN-PT (PIMNT) single crystals and demonstrate an adaptive lens (ALENS) that uses only one PM to achieve focus adjustment (AF) and optical image stabilization (OIS).

Prior multi-DOF piezoelectric systems typically assemble multiple multilayer stacks to combine distinct modes (e.g., 33 and 15), yielding bulky, complex devices. Li et al. introduced a 3D ordered piezoceramic structure exploiting synergic strain to realize artificial modes (stretching, shear, bending, torsion) and 5-DOF actuation, but different modes required different boundary conditions, preventing simultaneous coupled modes. Liu et al. designed electromechanical metamaterials with all non-zero piezoelectric coefficients using uniform-strain units under stress-free conditions; yet, different unit arrangements and field directions were needed for target modes and often required operation at characteristic resonances to suppress parasitics. Traditional ALENS implementations usually need multiple actuators to combine AF and OIS. These limitations motivate an integrated, uniform-boundary approach enabling multiple linear/rotary and coupled modes over a wide frequency range with a compact structure and fewer actuators.

Design of the piezo metasurface (PM): A two-dimensional array of piezoelectric units arranged in the X–Y plane using a center-outward expansion method. Units are labeled Aij; layer index i = 1 (first layer, polarized along −Z) or 2 (second layer, polarized along +Z); j denotes the central unit (0) and surrounding units (1–4). All units share a common ground electrode. By grouping units and applying AC voltages with defined phase offsets, the PM produces transverse-extension or axial-bending deformations that synthesize: linear X (artificial 31-mode), linear Y (artificial 32-mode), linear Z (artificial 33- or 33*-mode), and rotary α (about X), β (about Y), γ (about Z). Example: For linear X, units {A11, A14, A21, A24} receive V1 and {A12, A13, A22, A23} receive V2 with phase shift π to create opposite transverse-extension strains and a net translation. For linear Z, layer-1 units receive V1 and layer-2 units receive V2 (phase π) to yield opposite axial deformations and a net bending along Z. Rotary modes are generated via spatially alternating groups excited with phase differences (π or π/2 for γ) to create bending/torsion patterns. Arrays of 5×2 (ten-unit), 9×2, and 21×2 are possible; this work fabricates a 5×2 PM. Simulation and optimization: Finite element method (COMSOL Multiphysics piezoelectric module) modeled motion modes and output displacements. Material sets included soft PZT-5 ceramics and transparent [001]-poled PIMNT crystals. Three key factors were optimized: (1) boundary properties (Young’s modulus; selected ~750 kPa; too low leads to support deformation), (2) boundary topology (PM0–PM3 variants; PM2 selected for more uniform, higher stress and largest ε3), (3) geometric dimensions (boundary and unit sizes). For PM2, boundary dimensions were optimized (HHS = 4.8 mm, LHS = 13 mm, WHS = 0.5 mm). The length-to-thickness ratio (LTR) was swept; ε1 and rotation angles (α, γ) increased approximately linearly with LTR; ε3 showed nonlinear increase. At LTR = 100 (simulated, 400 V/mm), ε3 for PIMNT PM2 reached 1.97% vs 0.76% for PZT PM2, and 0.21% (PIMNT PM1), 0.15% (PZT PM1). Fabrication: PIMNT single crystals grown by modified Bridgman, oriented ([100], [010], [001]) via X-ray diffraction, diced and polished to 10 mm × 10 mm × 0.25 mm (LTR = 40). 200 nm ITO transparent electrodes were sputtered. Poling used a bipolar triangular wave (1 Hz, 10 cycles, peak 1 kV/mm). Boundary structure and frame were 3D-printed; boundary Young’s modulus measured ~742 kPa. Experimental setup: Drive signals (1–400 Hz, up to 1600 V/mm) from a waveform generator and amplifier; displacements measured with a laser rangefinder; optical path included neutral density filters, pinhole, PM-based ALENS, and CCD. ALENS integration: The PM (ten transparent PIMNT units) mounted within a boundary/frame, glass film, and silicone oil to form an adaptive lens. Euler angles describe rotations: pitch (X), yaw (Y), roll (Z). Frequency response, actuation vs field, hysteresis, impedance, durability, and creep were characterized. Calculations of strains (ε1–ε3), rotation angles (α, β, γ), and focal length used provided supplementary equations; thin lens approximation f = R/(n − 1) with silicone oil refractive index n = 1.55.

• Multifunctional actuation: A single ten-unit transparent PM generates linear motions (X, Y, Z), rotary motions (α about X, β about Y, γ about Z), and coupled modes under uniform boundaries over a wide 1–400 Hz frequency band.
• High strain: Experimental artificial 33-mode strain ε3 = 0.756% at 800 V/mm (LTR = 40) with [001]-poled PIMNT, exceeding the material’s natural strain (~0.054%) by over an order of magnitude. Simulations (400 V/mm, LTR = 100) predict ε3 up to 1.97% for PIMNT PM2 vs 0.76% for PZT PM2.
• Boundary optimization: PM2 boundary structure yields the highest output strain (simulated ε3 up to 0.405% at 400 V/mm for certain configurations) due to more uniform stress distribution; lower boundary Young’s modulus increases ε3 but must remain stiff enough to support units (~750 kPa used).
• Geometry scaling: Increasing LTR increases ε1 and rotation angles (α, γ) roughly linearly; ε3 increases nonlinearly. Optimized boundary geometry: HHS = 4.8 mm, LHS = 13 mm, WHS = 0.5 mm.
• Experimental validation (2 Hz, up to 800 V/mm): Displacements scale linearly with field. For PIMNT PM, experimental vs simulated strains at 800 V/mm: ε1 = 0.022% vs 0.030%, ε2 = 0.023% vs 0.030%, ε3 = 0.756% vs 0.666%; PZT PM: ε1 = 0.006% vs 0.008%, ε2 = 0.006% vs 0.008%, ε3 = 0.182% vs 0.240%.
• ALENS performance (1600 V/mm): AF and AF′ focal lengths reduced to 35.82 cm and 28.67 cm. Displacements: X = 4.88 µm, Y = 5.05 µm, Z (AF) = 69.8 µm, AF′ = 31.4 µm. Rotation angles: pitch (X) = 43.41′, yaw (Y) = 44.02′, roll (Z) = 17.90′.
• Dynamic characteristics: Hysteresis low at 2–50 Hz (max ~3.9%, 3.8%, 4.2%). Impedance shows resonances at 2.9 kHz and 13.8 kHz; below 2 kHz AF output remains stable. Estimated minimum response time ~0.5 ms. Durable over 14,400 cycles with negligible degradation; displacement variation ~0.8% over 500 s; minimal creep.
• Optical functionality: Ray tracing and spot diagrams confirm AF, pitch, roll, and coupled AF+pitch and AF+roll modes; RMS spot radius reduced markedly (e.g., from ~1520 µm to ~137 µm in AF), and coupled modes maintain focusing while inducing controlled angular motion.

The PM architecture addresses the key challenge of realizing multiple, reconfigurable actuation modes under a uniform boundary and over a broad frequency range. By spatially organizing polarized units and tailoring phase relationships of drive voltages, the PM synthesizes transverse and axial-bending deformations into targeted linear and rotary motions, as well as coupled modes, with substantially amplified strains compared to the intrinsic material response. Boundary and geometric optimization (PM2 and LTR scaling) are central to maximizing strain and rotation output while maintaining structural support. Compared to traditional multi-actuator systems for adaptive optics, the PM-based ALENS achieves both AF and OIS using a single compact actuator, reducing complexity and enabling integration. Experimental results corroborate simulations, with close agreement in most modes and a notably higher measured ε3, attributed to boundary and surface deformation effects. The device exhibits low hysteresis, fast response, stability, and durability, making it suitable for practical optical systems where rapid, precise focusing and stabilization are required. The transparent PIMNT units further facilitate direct optical integration without obstructing light paths.

This work introduces a transparent piezoelectric metasurface that, through topological unit arrangement, boundary engineering, and phase-programmed excitation, enables linear, rotary, and coupled motions with high strain across a wide frequency range. A ten-unit PIMNT-based PM achieves ε33 ≈ 0.76% experimentally and supports multifunctional adaptive optics in a compact ALENS, delivering wide-range focusing (down to ~35.82 cm focal length), effective image stabilization (micrometer-scale lateral displacements), and controlled tilts (tens of arcminutes). The approach simplifies system architecture by replacing multiple actuators with a single metasurface, while maintaining low hysteresis, fast response, and robustness. Future work may explore scaling to larger arrays for finer control, further optimization of boundary stiffness and geometry, reduction of required electric fields, integration with additional optical elements, and extension to other high-performance piezoelectric materials to broaden application scope in MEMS and advanced imaging systems.

Performance depends critically on boundary design; too low boundary stiffness leads to support deformation and degraded mode generation, while fabrication imperfections in boundaries contribute to discrepancies between simulated and measured outputs. The system requires relatively high electric fields (up to 1600 V/mm in ALENS demonstrations), which may challenge low-power operation and driver design. Stable actuation is demonstrated up to 400 Hz (and below ~2 kHz for AF stability due to resonances); beyond this, resonant behavior (peaks at ~2.9 kHz and ~13.8 kHz) can affect response. Precise voltage phasing and unit-to-unit uniformity are necessary to suppress parasitic modes. The measured enhancement in ε3 over simulations, attributed to inhomogeneous surface deformation and boundary effects, indicates sensitivity to manufacturing tolerances. The prototype focal length range, while wide, is limited to tens of centimeters and may require further scaling for some applications.