Electromagnetic response of closely spaced metal meshes

The electromagnetic transmittance of a double layer of identical square arrays of square holes (mesh) in a perfectly conducting sheet is analytically modeled using a modal matching technique. The structure supports families of standing-wave modes together with surface modes that, close to the onset of diffraction, interact with each other. For frequencies below the onset of diffraction, it is the strength of this interaction mediated by evanescent diffraction in the near fields that dictates the electromagnetic response, which is studied as a function of mesh separation and the lateral misalignment between the meshes.

Figure 1

Schematic of the investigated geometry; 2D square array of square holes (unshaded) in a PEC sheet (shaded).

Figure 2

Transmission for $d$ = 10 mm, $a$ = 4.5 mm for (a) $g$ = 0.1 mm, (b) $g$ = 4 mm, and (c) $g$ = 14 mm. Each graph shows the results for both the aligned system and when the meshes are misaligned by 5 mm with respect to each other.

Figure 3

Gray-scale plot of normal incidence transmission as a function of frequency and mesh separation with pitch 10 mm and hole sides 4.5 mm for (a) $b$ = 0 mm and (b) $b$ = 5 mm. The ideal Fabry-Pérot modes refer to the half-wavelength condition (i.e., λ = 2$d$/$n$ for $n$ = 1,2,3…).

Figure 4

Gray-scale plot of normal incidence transmission as a function of frequency and misalignment with pitch 10 mm and hole sides 4.5 mm for (a) mesh separation 14 mm and (b) mesh separation 0.1 mm.

Figure 5

Complex magnitude E field plots in the $XZ$ plane for a double-mesh-layer system of pitch $d$ = 10 mm, hole side length $a$ = 4.5 mm, and mesh separation $g$ = 0.1 mm at (a) 27.7 GHz with misalignment $b$ = 0 mm; (b) 20.4 GHz with misalignment $b$ = 5 mm; (c) 25.5 GHz with misalignment $b$ = 0 mm; and (d) 29.9 GHz with misalignment $b$ = 5 mm. The metal meshes are represented by thick black lines.

Figure 6

Schematic of possible charge distributions for a double layer of identical metal slit arrays (one-dimensional grids) when the layers are (a) aligned with respect to each other; (b) slightly misaligned with respect to each other, and (c) at maximum misalignment with respect to each other.

Figure 7

Directional E field plots in the $XZ$ plane in the region between the two meshes for a double-mesh-layer system of pitch $d$ = 10 mm, hole side length $a$ = 4.5 mm, and mesh separation $g$ = 1 mm at (a) 26.7 GHz with misalignment $b$ = 0 mm; (b) 28.0 GHz with misalignment $b$ = 0 mm; (c) 23.3 GHz with misalignment $b$ = 5 mm; and (d) 29.9 GHz with misalignment $b$ = 5 mm. The metal meshes are represented by thick black lines.