Photonics Research, Volume. 12, Issue 6, 1115(2024)

Interdigitated terahertz metamaterial sensors: design with the dielectric perturbation theory

Lei Cao1,2, Fanqi Meng2、*, Esra Özdemir2, Yannik Loth3, Merle Richter3, Anna Katharina Wigger3, Maira Beatriz Pérez Sosa4, Alaa Jabbar Jumaah4, Shihab Al-Daffaie4, Peter Haring Bolívar3, and Hartmut G. Roskos2,5
Author Affiliations
  • 1State Key Laboratory of Advanced Electromagnetic Technology, Huazhong University of Science and Technology, Wuhan 430074, China
  • 2Physikalisches Institut, Johann Wolfgang Goethe-Universität, Frankfurt am Main, Germany
  • 3University of Siegen, Institute for High Frequency and Quantum Electronics, Siegen, Germany
  • 4Department of Electrical Engineering, Eindhoven University of Technology, 5612 AE Eindhoven, The Netherlands
  • 5e-mail: roskos@physik.uni-frankfurt.de
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    Figures & Tables(16)
    Schematics of two gap structures used in SRRs: (a) 1D slot-like gap; (b) 2D interdigitated gap structure. The areas plotted in pink color represent the regions with high electric field. If G=g and if the same voltages are applied, the electric fields in the gap regions in (a) and (b) are of similar magnitude.
    Proposed interdigitated electric split-ring-resonator (ID-eSRR) MMs for THz sensing applications. In the unit cell structure, n is the size of the square ID-eSRR, h the width of the metal stripes, G the gap width, l the finger length, w the finger width, and g the width of the minigap between adjacent fingers.
    (a) Transmittance spectra of the bare ID-eSRR and eSRR MMs. (b) Refractive index sensing: frequency shift as a function of analyte thickness (d). Inset shows the location of the analyte in all simulations. The analyte material is SiO2 (ϵr=3.75+j·0.0004).
    Two top rows of panels: Electric field distribution in the plane of the metal surface at the respective resonance frequency for the three structures: (a) ID-eSRR; (b) eSRR (G=0.6 μm); and (c) eSRR (G=12 μm). Bottom row of panels: Cuts through the 3D electric field distribution along the red dashed lines shown in the middle row of panels. The amplitude of the incident electric field is 8.09×104 V/m for all structures.
    (a) SEM image of an ID-eSRR structure fabricated by electron beam lithography. (b) Simulated transmittance spectra of the ID-eSRR MM (G=12 μm; w=g=0.6 μm) and the eSRR MM (G=12 μm) without analyte. (c) Measured transmittance spectra of the ID-eSRR and eSRR MMs without analyte.
    (a) Measured transmittance spectra of the ID-eSRR structure loaded with a SiO2 layer of varying thickness (from 23 to 150 nm). (b) Likewise, but for the eSRR structure (SiO2 layer thickness varying from 20 to 155 nm). (c) Simulated and measured resonance frequency shift in dependence of the SiO2 layer thickness.
    Radiation power flow on a sphere with a radius of 1 m for a single resonator in air: (a) ID-eSRR; (b) eSRR (G=0.6 μm); and (c) eSRR (G=12 μm).
    2D projection of the radiation power flow of a single resonator in air: (a) x-y plane; (b) y-z plane; and (c) x-z plane.
    Electric field enhancement factor (Emax/Ein) along the z axis around the metal corner where the electric field is maximal at resonance frequencies for the three structures: z<0 represents the substrate side; and z>0 represents the air side.
    Influences of minigap width (g) on the transmittance spectra and resonance frequencies. (a) Transmittance spectra with the variation of g from 0.2 to 1.2 μm, while the finger width kept constant (w=0.6 μm). (b) Resonance frequency and frequency shift when 100 nm SiO2 is deposited on the unit cell structure.
    Transmittance spectra for the ID-eSRR MMs sensor at different incident angle of THz radiation.
    Transmittance spectra for the ID-eSRR MMs sensor with the variation of analyte (SiO2) thickness from 0 (no analyte) to 20 μm.
    • Table 1. Structural Parameters (in μm) of the ID-eSRR and eSRR MM Sensors Working at 300 GHz

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      Table 1. Structural Parameters (in μm) of the ID-eSRR and eSRR MM Sensors Working at 300 GHz

      ID-eSRReSRR (G=0.6  μm)eSRR (G=12  μm)
      Period (p)240240240
      Metal stripe length (n)107150168
      Metal stripe width (h)13.813.813.8
      Gap width (G)120.612
      Finger length (l)11
      Finger width (w)0.6
      Minigap width (g)0.6
    • Table 2. Resonance Frequency, Q-factor, Resonance Depth, and Mode Volume for the ID-eSRR and eSRR MMs

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      Table 2. Resonance Frequency, Q-factor, Resonance Depth, and Mode Volume for the ID-eSRR and eSRR MMs

      ID-eSRReSRR (G=0.6  μm)eSRR (G=12  μm)
      f0 (GHz)296.3297.5296.9
      Q43.111.05.8
      QR113.712.56.2
      QC71.089.999.6
      QD3380.33122.51909.6
      Tr0.420.560.49
      Veff (μm3)2610420
    • Table 3. Sensing Performances of the ID-eSRR and eSRR MMs

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      Table 3. Sensing Performances of the ID-eSRR and eSRR MMs

      StructureAnalyte Thickness (nm)S (GHz/RIU)FOM (RIU1)TN-FOM (μm1RIU1)
      ID-eSRR10022.63.2932.87
      50063.09.1618.33
      100070.110.2010.20
      eSRR (G=0.6μm)1005.90.222.18
      50020.50.761.52
      100027.71.021.02
      eSRR (G=12  μm)1001.60.030.31
      5006.30.120.25
      100010.50.210.21
    • Table 4. Performance Comparison with Other THz Metamaterial Sensors Described in the Literaturea

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      Table 4. Performance Comparison with Other THz Metamaterial Sensors Described in the Literaturea

      Analyte Thicknessf0 (GHz)QS (GHz/RIU)FOM (RIU1)TN-FOM (μm1RIU1)Unit Cell StructureReference
      2.17 μm40748.10.080.04SRR[14]
      1 μm51528b16.70.91b0.91baDSRR[10]
      345 nm136.511.87.50.651.88Labyrinth[47]
      250 nm422.69.6b6.00.14b0.54bToroidal aDSRR[48]
      240 nm60010b18.00.30b1.25bI-shaped structure[17]
      40 nm9902010.80.225.45aDSRR[39]
      47 nm27617.712.10.7816.51ID-eSRRThis work
      150 nm27617.733.52.1514.32ID-eSRRThis work
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    Lei Cao, Fanqi Meng, Esra Özdemir, Yannik Loth, Merle Richter, Anna Katharina Wigger, Maira Beatriz Pérez Sosa, Alaa Jabbar Jumaah, Shihab Al-Daffaie, Peter Haring Bolívar, Hartmut G. Roskos, "Interdigitated terahertz metamaterial sensors: design with the dielectric perturbation theory," Photonics Res. 12, 1115 (2024)

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    Paper Information

    Category: Optical Devices

    Received: Dec. 15, 2023

    Accepted: Mar. 4, 2024

    Published Online: May. 17, 2024

    The Author Email: Fanqi Meng (fmeng@physik.uni-frankfurt.de)

    DOI:10.1364/PRJ.516228

    CSTR:32188.14.PRJ.516228

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