## 2 Numerical Simulations
### Simulation of a Unidirectional Probe
According to the above values, the dependence of the real (Figure 3a) and imaginary (Figure 3b) parts of the relative permittivity was plotted at frequencies of 2-10 GHz. \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & **Skin** & **Fat** & **Muscle** & **Bone** \\ \hline \(\varepsilon_{\infty}\) & 4 & 2.5 & 4 & 2.5 \\ \(\sigma\) & 0.0002 & 0.035 & 0.2 & 0.02 \\ \(\alpha_{1}\) & 0 & 0.2 & 0.1 & 0.2 \\ \(\alpha_{2}\) & 0.2 & 0.1 & 0.1 & 0.2 \\ \(\alpha_{3}\) & — & 0.05 & 0.1 & 0.2 \\ \(\alpha_{4}\) & — & 0.1 & 0 & 0 \\ \(\Delta\varepsilon_{1}\) & 32 & 9 & 50 & 10 \\ \(\Delta\varepsilon_{2}\) & 1100 & 35 & \(7\times 10^{3}\) & 180 \\ \(\Delta\varepsilon_{3}\) & — & \(33\times 10^{3}\) & \(12\times 10^{5}\) & \(5\times 10^{3}\) \\ \(\Delta\varepsilon_{4}\) & — & \(1\times 10^{7}\) & \(2.5\times 10^{7}\) & \(1\times 10^{5}\) \\ \(\tau_{1}\) & \(7.234\times 10^{-12}\) & \(7.958\times 10^{-12}\) & \(7.234\times 10^{-12}\) & \(13.263\times 10^{-12}\) \\ \(\tau_{2}\) & \(0.324\times 10^{-7}\) & \(0.159\times 10^{-7}\) & \(3.537\times 10^{-7}\) & \(0.795\times 10^{-7}\) \\ \(\tau_{3}\) & — & \(15.915\times 10^{-6}\) & \(31.831\times 10^{-6}\) & \(15.915\times 10^{-6}\) \\ \(\tau_{4}\) & — & \(1.595\times 10^{-3}\) & \(0.274\times 10^{-3}\) & \(1.591\times 10^{-3}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Values of parameters for formula (1). Figure 3: Frequency dependence of the real (**a**) and imaginary (**b**) parts of the relative permittivity on the frequency. The glucose concentration values were taken as follows: 0, 4, 5.3, 7.5 mmol/L. As in the previous study, to calculate the relative permittivity, we use the data obtained by [PERSON] and [PERSON] from Department of Electrical and Microelectronic Engineering Rochester Institute of Technology [20], which is based on a modified Cole-Cole equation:  
\[\epsilon(\omega)=Re\Bigg{[}\epsilon_{\infty}+\sum_{m-1}^{2}\frac{ \Delta\varepsilon_{m}}{1+(j\omega\tau_{m})^{1-\alpha_{m}}}\Bigg{]}\] \[(-0.001445)g+1.145882+Im\Bigg{[}\epsilon_{\infty}+\sum_{m-1}^{2 }\frac{\Delta\varepsilon_{m}}{1+(j\omega\tau_{m})^{1-\alpha_{m}}}+\frac{ \sigma_{i}}{j\omega\epsilon_{0}}\Bigg{]} \tag{2}\]  
where, \(\varepsilon_{\infty}\), \(\varepsilon\) - are the \"static\" and \"infinite frequency\" of the dielectric permittivity, \(\omega\) is the angular frequency, \(\tau\) is the time constant, \(\alpha\) is the exponent parameter takes values from 0 to 1, \(\epsilon(\omega)\) is the complex dielectric permittivity, \(g\)--blood glucose concentration in mg/dL. The data obtained are presented in the form of graphs of the dependences of the real and imaginary parts of glucose permittivity on the frequency in Figure 4.  
The general scheme of the numerical simulation is shown in Figure 5. The figure shows a flat-layered multilayer structure consisting of the biological tissues described above, as well as a unidirectional probe. The probe is located at a distance of 1 mm from the flat layered medium as in the previous study [18]. Figure 4: Frequency dependence of the real (**a**) and imaginary (**b**) parts of the relative permittivity on the frequency for blood with different glucose concentrations. Detailed studies have been carried out on the optimal distance to place the metal plate. The main task in the selection of the distance was to obtain resonant sections of the reflected signal at low frequencies. This approach will allow to accurately determine changes in the concentration of glucose in the blood. The distance between the probe and the metal plate was changed by the fitting method by 1 mm from the probe in the range of 0-5 mm. The best results are shown in Figure 6. Simulations were performed in the frequency range 2-10 GHz. In numerical simulation, the probe was fed by a discrete port representing an impedance element (50 Ohm). Figure 6 shows the values of the reflected signal of an unidirectional probe and a bidirectional probe (red line) for clarity. As can be seen from the graphs, the reflected signals change significantly.