# The Electromagnetic Shielding of Optoelectronic Devices by Mesh Structures
## 4 Results and Discussion  
The attenuation in these samples was measured at frequencies of 99 GHz, 12 GHz, 11 GHz, 10 GHz, 9 GHz, 8 GHz, 4 GHz, 3.5 GHz, 3 GHz, and 2.5 GHz to check the shielding properties. A full transmission spectrum was obtained in the wavelength range of 0.185-3000 \(\upmu\)m (100 GHz-1620 THz). In addition to the one-mode calculation, the Kontorovich calculation of the transmission coefficient was performed in a frequency range of 1-300 GHz (Equation (2)). The experimental transmission coefficient of the mesh structures on the K108 glass (blue points), the numerical calculation of the transmission coefficient of the free-standing mesh structures and on the OHARA S-BSL7 (Ohara Inc., Sagamihara, Japan) and Schott N-BK7 glass (red and pink lines, respectively), and the model calculations of transmission coefficient of the free-standing mesh structures (the black line is the one-mode calculation, and the green line is the Kontorovich calculation) are shown in Figure 4.  
Figure 3: Experimental setups: a Photon RT spectrophotometer (**a**); a Bruker Vertex 70 Fourier-spectrometer (**b**); a Tera K8 Menlo Systems THz time-domain spectrometer (**c**); and setups to measure attenuation at frequencies of 99 GHz (**d**), 8–12 GHz (**e**), and 2.2–4 GHz (**f**). The Kontorovich calculation of the free-standing mesh structure transmission coefficient fits sufficiently well with the numerical calculation at low frequencies. The Kontorovich calculation mismatches the numerical one by 7% at a frequency of 38 GHz, at which the attenuation in sample 1 is 18 dB. The mismatch between transmission coefficients obtained by the numerical calculation and the Kontorovich calculation for sample 2 is 5% even at a frequency of 150 GHz with the same attenuation level of 18 dB. With an increase in a frequency the mismatch between the transmission coefficient obtained by Kontorovich calculation, the numerical calculation increases. Oscillations in the transmission coefficient spectrum are shown in Figures 4 and 5 for the mesh structures on the substrate. The transmission maxima and minima are explained by an interference in the glass (constructive and destructive interferences). The interference occurs between waves reflected from an air-glass interface and transmitted through the structure. The numerical calculation shows that the interference of waves should be observed in the experiment as well, but a frequency resolution and a small number of frequency points in the frequency range from 2.5 GHz to 150 GHz do not allow us to detect the interference in the experiment. Figure 4: Comparison of the experimental transmission of a mesh structure on K108 glass with a numerical calculation of the transmission of the mesh structure on OHARA S-BSL7/Schott N-BK7 glass, and the model and numerical calculations of free-standing mesh structure transmission for sample 1 (**a**) and sample 2 (**b**). Figure 5: Numerical calculation of the transmission of sample 1 (**a**) and sample 2 (**b**): numerical calculation of the transmission of a free-standing mesh structure and a mesh structure on OHARA S-BSL7/Schott N-BK7 glass. One-mode calculation of free-standing mesh structure transmission. The mismatch between the experimental data and the numerical calculation of the transmission coefficient may be associated with a measurement error because the transmission coefficient in this frequency range is less than a percent. The attenuation estimated by the one-mode calculation in the frequency range of 1-150 GHz differs from that of the numerical calculation. The transmission coefficient was calculated using the one-mode calculation to evaluate the standard deviation from the numerical calculation of the free-standing filter transmission. For sample 1, the standard deviation equals to 7%, and for sample, it equals 2-0.5%.