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Photonics Research, Volume. 13, Issue 10, 2864(2025)

Electromagnetic and mechanical performance analysis of conformal jigsaw-shaped metasurfaces

Yan Zhang1、*, Haoran Ye1, Xurui Zhang1, Siyuan Liu1, Bingchen Bai1, Yawen Zheng1, Ahmed A. Kishk2, and Shanwei Lü1
Author Affiliations
  • 1School of Electronic and Information Engineering, Beihang University, Beijing 100191, China
  • 2Department of Electrical and Computer Engineering, Concordia University, Montreal, Quebec, Canada
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    Two kinds of self-locking structures. (a) Jigsaw puzzle. (b) Circular-protrusion. (c) Mortise and tenon joint wooden structure. (d) Square-protrusion.

    Fig. 1. Two kinds of self-locking structures. (a) Jigsaw puzzle. (b) Circular-protrusion. (c) Mortise and tenon joint wooden structure. (d) Square-protrusion.

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    CPJS-MS model. (a) 3D view of 3×3 units. (b) Top view of the unit element. (c) Bottom view of the unit element.

    Fig. 2. CPJS-MS model. (a) 3D view of 3×3 units. (b) Top view of the unit element. (c) Bottom view of the unit element.

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    SPJS-MS model. (a) 3D view of 3×3 units. (b) Top view of the unit element. (c) Bottom view of the unit element.

    Fig. 3. SPJS-MS model. (a) 3D view of 3×3 units. (b) Top view of the unit element. (c) Bottom view of the unit element.

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    Equivalent circuit of JS-MS. (a) Model A. (b) Model B. (c) Model C.

    Fig. 4. Equivalent circuit of JS-MS. (a) Model A. (b) Model B. (c) Model C.

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    Comparison of simulated results by HFSS and ADS.

    Fig. 5. Comparison of simulated results by HFSS and ADS.

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    Sketch of normal/oblique incidence to planar MS. (a) TE mode. (b) TM mode.

    Fig. 6. Sketch of normal/oblique incidence to planar MS. (a) TE mode. (b) TM mode.

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    Transmission coefficient of infinite planar CPJS-MS under different incidence angles. (a) TE mode. (b) TM mode.

    Fig. 7. Transmission coefficient of infinite planar CPJS-MS under different incidence angles. (a) TE mode. (b) TM mode.

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    Transmission coefficient of infinite planar SPJS-MS under different incidence angles. (a) TE mode. (b) TM mode.

    Fig. 8. Transmission coefficient of infinite planar SPJS-MS under different incidence angles. (a) TE mode. (b) TM mode.

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    SG-MS model. (a) 3D view of 3×3 units. (b) Top view of the unit element. (c) Bottom view of the unit element.

    Fig. 9. SG-MS model. (a) 3D view of 3×3 units. (b) Top view of the unit element. (c) Bottom view of the unit element.

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    Comparison of the MS unit element. (a) CPJS-MS, (b) SPJS-MS, and (c) SG-MS.

    Fig. 10. Comparison of the MS unit element. (a) CPJS-MS, (b) SPJS-MS, and (c) SG-MS.

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    Reflection and transmission coefficient of three MSs.

    Fig. 11. Reflection and transmission coefficient of three MSs.

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    Comparison of the transmission coefficient of infinite planar SG-MS and JS-MS. (a) CPJS-MS for TE mode. (b) CPJS-MS for TM mode. (c) SPJS-MS for TE mode. (d) SPJS-MS for TM mode.

    Fig. 12. Comparison of the transmission coefficient of infinite planar SG-MS and JS-MS. (a) CPJS-MS for TE mode. (b) CPJS-MS for TM mode. (c) SPJS-MS for TE mode. (d) SPJS-MS for TM mode.

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    Cylindrical conformal CPJS-MS model. (a) r=100 mm. (b) r=150 mm. (c) r=200 mm.

    Fig. 13. Cylindrical conformal CPJS-MS model. (a) r=100  mm. (b) r=150  mm. (c) r=200  mm.

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    Sketch of conformal MS for normal incidence. (a) TE mode. (b) TM mode.

    Fig. 14. Sketch of conformal MS for normal incidence. (a) TE mode. (b) TM mode.

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    Comparison of simulated results of conformal and planar CPJS-MSs. (a) TE mode. (b) TM mode.

    Fig. 15. Comparison of simulated results of conformal and planar CPJS-MSs. (a) TE mode. (b) TM mode.

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    Bending MS structure with a certain curvature radius.

    Fig. 16. Bending MS structure with a certain curvature radius.

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    Three types of MS samples under free-space measurement. (a) CPJS-MS sample. (b) SPJS-MS sample. (c) SG-MS sample. (d) Free-space measurement.

    Fig. 17. Three types of MS samples under free-space measurement. (a) CPJS-MS sample. (b) SPJS-MS sample. (c) SG-MS sample. (d) Free-space measurement.

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    Strain measurement for three MS samples. (a) SG-MS. (b) SPJS-MS. (c) CPJS-MS.

    Fig. 18. Strain measurement for three MS samples. (a) SG-MS. (b) SPJS-MS. (c) CPJS-MS.

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    Comparison of simulated results of conformal and planar SPJS-MSs. (a) TE mode. (b) TM mode.

    Fig. 19. Comparison of simulated results of conformal and planar SPJS-MSs. (a) TE mode. (b) TM mode.

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    Comparison of the simulated results of conformal and planar SG-MSs. (a) TE mode. (b) TM mode.

    Fig. 20. Comparison of the simulated results of conformal and planar SG-MSs. (a) TE mode. (b) TM mode.

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    Simulation results of mono-static RCS of CPJS-MS under different incident angles. (a) 0°, TE mode. (b) 0°, TM mode. (c) 20°, TE mode. (d) 20°, TM mode. (e) 40°, TE mode. (f) 40°, TM mode.

    Fig. 21. Simulation results of mono-static RCS of CPJS-MS under different incident angles. (a) 0°, TE mode. (b) 0°, TM mode. (c) 20°, TE mode. (d) 20°, TM mode. (e) 40°, TE mode. (f) 40°, TM mode.

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    Strain distribution of conformal CPJS-MS. (a) r=100 mm. (b) r=150 mm. (c) r=200 mm.

    Fig. 22. Strain distribution of conformal CPJS-MS. (a) r=100  mm. (b) r=150  mm. (c) r=200  mm.

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    Strain distribution of conformal SPJS-MS. (a) r=100 mm. (b) r=150 mm. (c) r=200 mm.

    Fig. 23. Strain distribution of conformal SPJS-MS. (a) r=100  mm. (b) r=150  mm. (c) r=200  mm.

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    Strain distribution of conformal SG-MS. (a) r=100 mm. (b) r=150 mm. (c) r=200 mm.

    Fig. 24. Strain distribution of conformal SG-MS. (a) r=100  mm. (b) r=150  mm. (c) r=200  mm.

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    Comparison of the simulated and measured results of MSs. (a) CPJS-MS sample in TE mode. (b) SPJS-MS sample in TE mode. (c) SG-MS sample in TE mode. (d) CPJS-MS sample in TM mode. (e) SPJS-MS sample in TM mode. (f) SG-MS sample in TE mode.

    Fig. 25. Comparison of the simulated and measured results of MSs. (a) CPJS-MS sample in TE mode. (b) SPJS-MS sample in TE mode. (c) SG-MS sample in TE mode. (d) CPJS-MS sample in TM mode. (e) SPJS-MS sample in TM mode. (f) SG-MS sample in TE mode.

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    • Table 1. Parameters of Equivalent Circuit

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      Table 1. Parameters of Equivalent Circuit

      ParameterValueParameterValue
      C10.58 pFL1102 nH
      C25.2 pFL29.0 nH
      Cs4.6 pFLT7.2 nH

    • Table 2. Comparison of Transmission Coefficient of Infinite Planar MS

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      Table 2. Comparison of Transmission Coefficient of Infinite Planar MS

      Incidence AngleModef0 (GHz)BW (GHz)Relative BW
      CPJS-MS0°TE2.351.51 (1.59–3.10)64.4%
      TM2.331.47 (1.59–3.06)63.2%
      20°TE2.361.43 (1.64–3.07)60.7%
      TM2.371.57 (1.58–3.15)66.4%
      40°TE2.381.15 (1.80–2.95)48.4%
      TM2.391.88 (1.45–3.33)78.7%
      SPJS-MS0°TE2.331.51 (1.57–3.08)64.9%
      TM2.321.50 (1.57–3.07)64.7%
      20°TE2.331.40 (1.63–3.03)60.1%
      TM2.331.58 (1.54–3.12)67.8%
      40°TE2.371.19 (1.77–2.96)50.3%
      TM2.361.90 (1.41–3.31)80.5%
      SG-MS0°TE2.311.39 (1.61–3.00)60.3%
      TM2.291.34 (1.62–2.96)58.5%
      20°TE2.321.35 (1.64–2.99)58.3%
      TM2.351.60 (1.55–3.15)68.1%
      40°TE2.331.09 (1.78–2.87)46.9%
      TM2.341.71 (1.48–3.19)73.2%

    • Table 3. Simulated Results of Planar and Conformal CPJS-MSs

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      Table 3. Simulated Results of Planar and Conformal CPJS-MSs

      Curvature Radius (mm)ModeCenter Frequency (GHz)3 dB Bandwidth (GHz)Relative Bandwidth
      100TE2.261.26 (1.63–2.89)55.8%
      TM2.431.45 (1.71–3.16)59.5%
      150TE2.411.35 (1.73–3.08)56.1%
      TM2.441.32 (1.78–3.10)54.1%
      200TE2.381.36 (1.70–3.06)57.1%
      TM2.451.29 (1.80–3.09)52.8%
      Finite planarTE2.341.40 (1.64–3.04)59.8%
      TM2.421.27 (1.78–3.05)52.6%
      Infinite planarTE2.351.51 (1.59–3.10)64.4%
      TM2.331.47 (1.59–3.06)63.2%

    • Table 4. Simulated Results of Conformal MS

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      Table 4. Simulated Results of Conformal MS

      Curvature Radius (mm)FSS TypeMaximum Principal Strain ValueCenter Frequency (GHz)Bandwidth (GHz)a
      TETMTETM
      100CPJS1.209×10−42.262.431.26(55.80%)1.45(59.70%)
      SPJS9.917×10−52.282.381.21(53.20%)1.46(61.30%)
      SG3.110×10−42.362.440.90(38.00%)1.32(54.10%)
      150CPJS8.066×10−52.412.441.35(56.00%)1.32(54.10%)
      SPJS6.606×10−52.422.431.29(53.30%)1.34(55.10%)
      SG8.794×10−52.492.361.11(44.60%)1.38(58.50%)
      200CPJS6.047×10−52.382.451.36(57.10%)1.29(52.70%)
      SPJS4.949×10−52.422.451.31(54.10%)1.32(53.90%)
      SG6.360×10−52.372.501.28(54.20%)1.21(48.40%)
      Finite planarCPJS–2.342.421.40(59.80%)1.27(52.50%)
      SPJS–2.392.411.32(55.20%)1.31(54.40%)
      SG–2.442.301.10(45.10%)1.22(53.00%)

    • Table 5. Mechanically Simulated Maximum Principal Strain of CPJS-MS with Different Radii and Substrates

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      Table 5. Mechanically Simulated Maximum Principal Strain of CPJS-MS with Different Radii and Substrates

      Radius (mm)100150200
      Rogers 58801.209×10−48.066×10−56.047×10−5
      Rogers 43502.483×10−41.625×10−41.127×10−4
      FR43.318×10−42.504×10−42.120×10−4
      Polyimide1.175×10−46.953×10−55.589×10−5

    • Table 6. Measurement Results of Principal Strain

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      Table 6. Measurement Results of Principal Strain

      Curvature Radius (mm)MS TypeMaximum Principal Strain Value
      SimulationMeasurement
      100CPJS1.209×10−41.570×10−4
      SPJS9.917×10−58.192×10−5
      SG3.110×10−42.769×10−4
      150CPJS8.066×10−57.745×10−5
      SPJS6.606×10−56.340×10−5
      SG8.794×10−58.570×10−5
      200CPJS6.047×10−55.810×10−5
      SPJS4.949×10−55.150×10−5
      SG6.360×10−57.300×10−5
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    Yan Zhang, Haoran Ye, Xurui Zhang, Siyuan Liu, Bingchen Bai, Yawen Zheng, Ahmed A. Kishk, Shanwei Lü, "Electromagnetic and mechanical performance analysis of conformal jigsaw-shaped metasurfaces," Photonics Res. 13, 2864 (2025)

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    Paper Information

    Category: Optical and Photonic Materials

    Received: Mar. 3, 2025

    Accepted: Jul. 10, 2025

    Published Online: Sep. 23, 2025

    The Author Email: Yan Zhang (yanzhang@buaa.edu.cn)

    DOI:10.1364/PRJ.560862

    CSTR:32188.14.PRJ.560862

    Topics

    laser devices and laser physics
    Lasers and Laser Optics
    Laser physics
    laser manufacturing
    Instrumentation, Measurement and Metrology