A kirigami-based reconfigurable metasurface for selective electromagnetic transmission modulation

Electromagnetic metasurfaces, defined by subwavelength unit cells rather than chemical composition, can manipulate amplitude, polarization, direction, and phase of electromagnetic waves and underpin applications such as negative refractive index materials, advanced antennas, cloaking, superlenses, and electromagnetic black holes. Conventional 2D metasurfaces are functionally fixed after fabrication, limiting in-use adjustability. To enable dynamic control, tunable metasurfaces have been explored using magnetic fields, temperature, pressure, optical excitation, and voltage. Prior approaches include thermally repositioned SRRs via rapid thermal annealing (allowing one-time tuning), strain-tuned 3D flexible frequency selective surfaces, origami-based metasurfaces exhibiting tunable chirality, and wrinkling-based reconfigurable metasurfaces for polarization control and holography. However, these methods often require complex designs and smart materials. Kirigami provides a simpler route to complex, out-of-plane deformations and manufacturing, offering a promising strategy for reconfigurable EM metasurfaces. This work presents a kirigami-based metasurface that transitions from 2D to 3D via uniaxial stretch, selectively modulating TE/TM linear polarizations and LCP/RCP circular polarizations while maintaining near-constant resonance, by ensuring SRRs undergo rigid rotation rather than deformation.

The paper surveys tuning strategies for EM metasurfaces: magnetic-field control, thermal tuning (including semiconductor SRRs and thermally tunable silicon metasurfaces), barometric/pressure control, optical pumping, and electrical biasing. Examples include rapid thermal annealing to reposition SRRs for transmission tuning (limited to one-time adjustment), a 3D flexible FSS with strain-stable transmission, origami-based Miura-ori structures enabling tunable chirality, and wrinkling-based metasurfaces that switch between planar and wrinkled states for polarization control and near-field holography. These methods typically modify material properties or unit-cell arrangement, but often rely on complex designs and intelligent materials. Kirigami-based designs have emerged as a simpler alternative enabling intricate deformation and easier fabrication for reconfigurable EM metasurfaces.

Design and geometry: The metasurface comprises a kirigami-cut polyimide (PI) thin-film substrate and periodically arranged copper (Cu) SRRs. Unit cell dimensions: length l = 18 mm, width w = 14 mm; SRR geometry parameters a = 2 mm, b = 1 mm, c = 1 mm; slit width ≈ 0.1 mm; Cu thickness t1 = 0.01 mm; PI substrate thickness t2 = 0.1 mm; an additional PI layer behind each SRR (t3 = 0.3 mm) mitigates bending and strain in SRRs. Under uniaxial stretch along y, the kirigami deforms out of plane and SRRs rigidly rotate by angle θ relative to the xOy plane. An analytical relation between θ and applied strain ε_app is derived (details in Supplementary Note 1). Equivalent-circuit guidance uses a rectangular SRR with side length d and split gap k, targeting X-band (8–12 GHz). Optimization selected SRR side length 4 mm and split gap 1 mm, corresponding to f ≈ 10.37 GHz. Fabrication: Standard flexible printed circuit (FPC) process. A 10 μm Cu film is deposited onto a 0.1 mm PI film; SRRs are patterned by photolithography and wet etching; kirigami slits are laser-cut. A 0.3 mm PI rectangle is laminated behind each SRR. The sample comprises a 10 × 10 array of unit cells (20 × 20 SRRs), total active area 180 × 140 mm, with 20 × 140 mm holders on both ends for clamping (overall 220 × 140 mm). Mechanics simulation: ABAQUS finite element analysis (C3D8R elements) with five elements through thickness, linear elastic PI (E = 2.914 GPa, ν = 0.34) and Cu (E = 120 GPa, ν = 0.3). Geometric nonlinearity is included; a small perturbation force triggers out-of-plane buckling. Unit-cell simulations use symmetric boundaries to eliminate edge effects. Outputs include rotation angle vs. ε_app, out-of-plane displacement, and principal strain distributions. Electromagnetic simulation: Deformed unit-cell geometries from ABAQUS are converted via Hypermesh and imported into CST Microwave Studio. Hexahedral mesh; unit-cell boundary conditions in x and y; open (add space) in z; PI relative permittivity 3.5; Cu conductivity 5.8×10^7 S/m. Frequency-domain analysis yields S21 spectra for TE, TM, and circular polarizations under various strains. Measurements: Experiments conducted in an anechoic chamber using two broadband horn antennas (8.2–12.4 GHz) and a vector network analyzer (Rohde & Schwarz). Antenna separation >2 m (far-field). The sample is mounted on a custom plastic stretcher; conical absorbing material surrounds the sample boundary to minimize diffraction, leaving a test window. Alignment ensured by laser. Reference measured without sample; transmission coefficients (S21) are recorded for strains from 0% to 30%. Additional tests evaluate bending (30°–60°) and twisting (15°–45°) effects on S21. Analysis: Equivalent-circuit model with L = μ0 d and C = ε0 2π d ln(2d/k), resonant frequency f = 1/(2π√(LC)), and quality factor Q ∝ 1/R √(C), where R inversely relates to surface current density. Simulated surface current distributions at resonance explain transmission changes with SRR rotation for TE and TM.

• Kirigami-enabled 2D-to-3D transformation by uniaxial stretch rotates SRRs out of plane without deforming them, yielding selective transmission modulation while keeping resonance nearly constant.
• Mechanics: Analytical model and FEA agree on rotation angle vs. strain; SRRs reach ~70° rotation at ε_app = 30%. Out-of-plane altitude difference ≈ −6.6 mm at 30% strain. Maximum principal strain localizes at kirigami tips; Cu SRR strain remains below ~1% yield even at 30% stretch.
• Linear polarization (X-band 8.2–12.4 GHz): At 0% strain (planar), TE shows strong stopband with resonant frequency ~9.886 GHz and transmission ~−40 dB. With increasing strain to 30%, TE transmission increases substantially (e.g., S21 from ~−40 dB to ~−5 dB), with only minor resonance shift. TM exhibits opposite behavior: from near-pass (e.g., −3 dB) at 0% to suppressed (−10 dB) at 30% strain, again with small resonance shift.
• Simulations (CST with imported deformed meshes) reproduce experimental TE/TM trends; simulated bandwidths are narrower and transmissions stronger, attributed to fabrication-induced nonuniform deformation. Resonant frequencies vs. strain match closely between experiment and simulation.
• Mechanism: For TE excitation (E along x), SRR rotation increases induced surface current density, reducing effective impedance R, increasing Q, and thereby enhancing transmission. For TM excitation (H along x), rotation decreases surface current density and Q, reducing transmission.
• Geometrical dependence: At 0% strain, x-direction spacing influences TE resonant frequency; y-direction spacing has minimal effect on TE and TM (TM largely transmissive). At 20% strain, both x- and y-direction spacings reduce TE transmission and resonant frequency; TM transmission also decreases with spacing changes, with resonant frequencies varying across spacings.
• Circular polarization: In the planar (0% strain) symmetric state, LCP and RCP transmissions are nearly identical (achiral). At 20% strain (3D state), chiral response emerges: the metasurface blocks ~90% of LCP while nearly fully transmitting RCP at resonance. Circular dichroism increases with strain from 0% to 20%.
• Robustness: Under bending (30°–60°) and twisting (15°–45°), TE and TM transmissions change only slightly, indicating insensitivity to these deformations.
• Practical advantages: No additional elastomeric substrate; thin, lightweight construction via standard FPC; SRRs undergo rigid rotation, minimizing resonant frequency drift compared with designs where SRRs deform.

The study addresses the challenge of continuously tunable metasurfaces that selectively modulate polarization without large resonance drift or complex smart materials. The kirigami architecture translates in-plane tensile strain into uniform out-of-plane rotation of rigid SRR arrays, enabling selective control over TE/TM transmissions and the emergence of chirality for circular polarizations. Equivalent-circuit and surface-current analyses link SRR rotation to changes in effective impedance and quality factor: rotation enhances TE surface currents (higher Q, stronger transmission) while suppressing TM currents (lower Q, weaker transmission). The near-constant resonance arises because the SRRs rotate rigidly rather than deform, preserving inductance–capacitance characteristics. Parametric studies show that unit-cell spacing mainly tunes resonant frequencies under both zero and finite strain, offering a design handle for frequency targeting while strain serves as an in situ transmission control. The metasurface maintains performance under moderate bending and twisting, suggesting robustness for real-world deployment. Together, these results validate kirigami as a practical, manufacturable route to reconfigurable EM metasurfaces with selective, strain-controlled transmission.

This work introduces a kirigami-based reconfigurable metasurface that achieves selective, strain-controlled transmission for both linear (TE/TM) and circular (LCP/RCP) polarizations while keeping the resonant frequency largely stable. The design leverages rigid SRR rotation on a thin PI kirigami substrate, enabling efficient fabrication via standard FPC processes and eliminating the need for additional elastomeric layers. Experiments and simulations confirm substantial TE/TM transmission modulation up to 30% strain and switchable achiral-to-chiral behavior with strong circular dichroism under strain. Geometrical parameter studies provide guidance for frequency tuning and device optimization. The approach is promising for deformable frequency selective surfaces, negative-index metasurfaces, perfect absorbers, and stretchable RF devices, including space-constrained applications such as deployable satellite components and solar panels. Future work could integrate dielectric elastic composites for further resonance stability, explore more complex SRR orientations and coupling, and expand operation across broader frequency bands and deformation modes.

• Manufacturing inconsistencies lead to locally nonuniform deformation, narrowing simulated bandwidths and altering transmission strength relative to experiments.
• Simulations cannot fully replicate the practical test environment, contributing to slight resonance discrepancies.
• Demonstrations focus on X-band (8–12 GHz) and uniaxial tensile strains up to 30%; broader frequency ranges and larger or different loading modes (e.g., complex multiaxial strains) were not explored.
• Bending and twisting robustness was assessed over limited angle ranges (bending 30°–60°, twisting 15°–45°); performance under harsher mechanical conditions remains to be characterized.
• The approach relies on precise kirigami cuts and assembly; scalability and long-term durability under cyclic loading were not reported.