Schematic diagrams of (a) wire-grid structure and (b) cut-wire-grid structure. Equivalent circuits are also shown.
Electromagnetic wave propagation in a two-layer system. , , , and (, 1, 2, and 3) are amplitudes of the electric fields, refractive index, and wavenumber in each layer. The superscripts and – denote the positive and negative directions. and are the Fresnel transmission and reflection coefficients. The subscript denotes the interfaces between the layers and . Equation (6) is derived from the boundary conditions at , , and (Ref. 19).
Real parts of the relative permittivity and conductivity of the metallic ink on the paper. Open circles are obtained by the terahertz-TDS measurements. Solid lines are fitted to the Drude model whose plasma frequency is and the relaxation time is .
Transmittance and phase shift of the cut-wire-gird structures printed on the substrate papers. Their characteristic dimensions are the wire period , wire width , cut period , and cut with , 0.1, 0.2, and 0.3 mm. The substrate papers have the thickness of 0.07 mm and the refractive index of . The ink thickness is about . The inset photograph shows a typical picture of the sample with the cut width of 0.1 mm
Effective conductivity and relative permittivity deduced from the transmittance and phase shift in Fig. 4. Open circles are the experimental data. Solid curves in the permittivity spectra are the fitted curves to Eqs. (1) and (4). The fitting parameters are listed in Table I.
Effective conductivity and relative permittivity of the random cut-wire-grid metamaterials. The inset photo is the case of .
(a) Unit cell of the FDTD simulation model. We used the periodic boundary conditions in the and directions. The incident waves are linearly polarized along the direction and have the amplitude of unity. The period of the cuts is 1 mm, wire period is 0.4 mm, and wire width is 0.2 mm. The substrate paper has the refractive index of and thickness of 0.07 mm. The metallic ink is defined as a Drude metal whose plasma frequency and collision time are obtained from Fig. 3. The thickness of the ink is 0.01 mm. (b) Change of the transmission spectrum of the cut-wire-grid structures when the cut width is changed from 0 to 0.3 mm.
Electric field distributions in the cut wire-grid-structures. The observation areas are placed on the plane in the paper and away from the metallic ink.
Fitting parameters in Fig. 5(b).
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