The idea of Babinet inversion and the complementary structure of a metasurface. Applying Babinet inversion is not clear for a homogeneous metal plate with finite negative permittivity. In all cases, we assume that the thicknesses of the structures are at a deep sub-wavelength scale.|@|~(^,^)~|@|Metasurfaces for spoof electric and magnetic surface plasmons. (a) A metasurface of negative effective permittivity, made of PEC ring resonators. The red dot contour denotes the unit lattice of the metasurface. Here, we set a = 3 mm, b = 42 mm, P_x = 6 mm, P_y = 45 mm. The thickness of the metasurface is set to be 1 mm. For the resonators, the width of the rim is 1 mm. The distance between neighboring unit resonators in both x and y directions is given as 1 mm. (b) The complementary structure of (a). PEC, perfect electric conductor.|@|~(^,^)~|@|Finite-difference time-domain (FDTD)-calculated spectra of near-field enhancement of H_x (black solid curve), and far-field transmission (blue dashed line). The near field is taken at the center of the core perfect electric conductor (PEC) plate of the unit resonator [Fig. 2(b)], with the measuring height 0.2 mm from the Babinet-inverted metasurface. The enhancement factor is defined as |H_x|_loc / |H_x|_inc, where |H_x|_loc and |H_x|_inc are amplitudes of the local magnetic field and the incident, respectively. For transmission, 1.0 means a 100% transmission.|@|~(^,^)~|@|Local enhancement of H_x by the excitation of spoof magnetic surface plasmons. (a) Schematic of the system of metasurface with diffractive perfect electric conductor (PEC) rods. The structural parameters for the metasurface are the same as those in Fig. 3. The width and thickness of the PEC rods are 2.5 mm and 1 mm, respectively, and the rods are located 1 mm from the metasurface. The yellow dot in the top view indicates the origin of the x-y plane. p₁ and p₂ are 0.2 mm from the metasurface. The periodic boundary condition (PBC) is applied to the system, resulting in an infinitely periodic system in both x- and y-directions. (b) Finite-difference time-domain (FDTD)-calculated spectra of H_x taken at p₁ (black solid curve) and p₂ (red dashed curve). All spectra are normalized by the amplitude of the incident.|@|~(^,^)~|@|Higher order resonance of spoof magnetic surface plasmons. (a) Schematic of the system of metasurface and PEC rods with increased periodicity of the rods. All structural parameters, except for the periodicity of the PEC rods are exactly the same as those used in Fig. 4. In the side-view, p₁ and p₂ are 0.2 mm from the metasurface. (b) FDTD-calculated spectra of H_x taken at p. PEC, perfect electric conductor; FDTD, finite-difference time-domain.|@|~(^,^)~|@|FDTD-calculated near-field x-y maps of |H_x| for the rods/metasurface system where the periodicity of the rods is 3p_x (Fig. 4). The maps are taken at three different distances from the metasurface as denoted by m₁, m₂, and m₃ in (a). (a) Maps for 2.907 GHz and (b) 3.079 GHz incident frequencies. FDTD, finite-difference time-domain.|@|~(^,^)~|@|FDTD-calculated near-field x-y maps of |H_x| for the rods/metasurface system where the periodicity of the rods is 5p_x (Fig. 5). The maps are taken at two different distances from the metasurface as denoted by m₁, and m₃ in (a). (a) Maps for 3.044 GHz and (b) 3.090 GHz incident frequencies. FDTD, finite-difference time-domain.

Curr. Opt. Photon. 2023;7:97~103 https://doi.org/10.3807/COPP.2023.7.1.97